diff --git "a/3yqpirzxudw.txt" "b/3yqpirzxudw.txt"
new file mode 100644--- /dev/null
+++ "b/3yqpirzxudw.txt"
@@ -0,0 +1,8523 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT OpenCourseWare continue to
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+ 
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+offer high quality educational resources
+
+ align:start position:0%
+offer high quality educational resources
+ 
+
+ align:start position:0%
+offer high quality educational resources
+for free
+
+ align:start position:0%
+for free
+ 
+
+ align:start position:0%
+for free
+to make a donation or to view additional
+
+ align:start position:0%
+to make a donation or to view additional
+ 
+
+ align:start position:0%
+to make a donation or to view additional
+materials from hundreds of MIT courses
+
+ align:start position:0%
+materials from hundreds of MIT courses
+ 
+
+ align:start position:0%
+materials from hundreds of MIT courses
+visit MIT opencourseware at ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ok guys hope you enjoyed the the brief
+
+ align:start position:0%
+ok guys hope you enjoyed the the brief
+ 
+
+ align:start position:0%
+ok guys hope you enjoyed the the brief
+break from the heavy technical stuff cuz
+
+ align:start position:0%
+break from the heavy technical stuff cuz
+ 
+
+ align:start position:0%
+break from the heavy technical stuff cuz
+we're gonna get right back into it and
+
+ align:start position:0%
+we're gonna get right back into it and
+ 
+
+ align:start position:0%
+we're gonna get right back into it and
+developed the neutron transport equation
+
+ align:start position:0%
+developed the neutron transport equation
+ 
+
+ align:start position:0%
+developed the neutron transport equation
+today the one that you see on
+
+ align:start position:0%
+today the one that you see on
+ 
+
+ align:start position:0%
+today the one that you see on
+everybody's t-shirts here in the
+
+ align:start position:0%
+everybody's t-shirts here in the
+ 
+
+ align:start position:0%
+everybody's t-shirts here in the
+department so I think multiple years
+
+ align:start position:0%
+department so I think multiple years
+ 
+
+ align:start position:0%
+department so I think multiple years
+folks have used this equation on the
+
+ align:start position:0%
+folks have used this equation on the
+ 
+
+ align:start position:0%
+folks have used this equation on the
+back of t-shirts to just be like we're
+
+ align:start position:0%
+back of t-shirts to just be like we're
+ 
+
+ align:start position:0%
+back of t-shirts to just be like we're
+awesome and we do difficult math well
+
+ align:start position:0%
+awesome and we do difficult math well
+ 
+
+ align:start position:0%
+awesome and we do difficult math well
+this is when you're gonna start to do it
+
+ align:start position:0%
+this is when you're gonna start to do it
+ 
+
+ align:start position:0%
+this is when you're gonna start to do it
+in fact it's big enough and hard enough
+
+ align:start position:0%
+in fact it's big enough and hard enough
+ 
+
+ align:start position:0%
+in fact it's big enough and hard enough
+that we're gonna spend all day today
+
+ align:start position:0%
+that we're gonna spend all day today
+ 
+
+ align:start position:0%
+that we're gonna spend all day today
+developing it like actually writing out
+
+ align:start position:0%
+developing it like actually writing out
+ 
+
+ align:start position:0%
+developing it like actually writing out
+the terms of the equation and
+
+ align:start position:0%
+the terms of the equation and
+ 
+
+ align:start position:0%
+the terms of the equation and
+understanding what it actually means
+
+ align:start position:0%
+understanding what it actually means
+ 
+
+ align:start position:0%
+understanding what it actually means
+before on Thursday and Friday we're
+
+ align:start position:0%
+before on Thursday and Friday we're
+ 
+
+ align:start position:0%
+before on Thursday and Friday we're
+going to reduce it down to a much
+
+ align:start position:0%
+going to reduce it down to a much
+ 
+
+ align:start position:0%
+going to reduce it down to a much
+simpler equation something that you can
+
+ align:start position:0%
+simpler equation something that you can
+ 
+
+ align:start position:0%
+simpler equation something that you can
+actually solve and do some simple
+
+ align:start position:0%
+actually solve and do some simple
+ 
+
+ align:start position:0%
+actually solve and do some simple
+reactor calculations with we started off
+
+ align:start position:0%
+reactor calculations with we started off
+ 
+
+ align:start position:0%
+reactor calculations with we started off
+the whole idea of the neutron transport
+
+ align:start position:0%
+the whole idea of the neutron transport
+ 
+
+ align:start position:0%
+the whole idea of the neutron transport
+equation as a way to track some
+
+ align:start position:0%
+equation as a way to track some
+ 
+
+ align:start position:0%
+equation as a way to track some
+population of neutrons see I'm gonna
+
+ align:start position:0%
+population of neutrons see I'm gonna
+ 
+
+ align:start position:0%
+population of neutrons see I'm gonna
+have our variable list up here what I'll
+
+ align:start position:0%
+have our variable list up here what I'll
+ 
+
+ align:start position:0%
+have our variable list up here what I'll
+probably do is on Thursday and Friday
+
+ align:start position:0%
+probably do is on Thursday and Friday
+ 
+
+ align:start position:0%
+probably do is on Thursday and Friday
+I'll just have it back up on the screen
+
+ align:start position:0%
+I'll just have it back up on the screen
+ 
+
+ align:start position:0%
+I'll just have it back up on the screen
+so that we don't have to write it twice
+
+ align:start position:0%
+so that we don't have to write it twice
+ 
+
+ align:start position:0%
+so that we don't have to write it twice
+but there's gonna be a lot of variables
+
+ align:start position:0%
+but there's gonna be a lot of variables
+ 
+
+ align:start position:0%
+but there's gonna be a lot of variables
+in this equation I'm gonna do my best
+
+ align:start position:0%
+in this equation I'm gonna do my best
+ 
+
+ align:start position:0%
+in this equation I'm gonna do my best
+again to make the difference between V
+
+ align:start position:0%
+again to make the difference between V
+ 
+
+ align:start position:0%
+again to make the difference between V
+and nu very obvious and anything else
+
+ align:start position:0%
+and nu very obvious and anything else
+ 
+
+ align:start position:0%
+and nu very obvious and anything else
+like that but the goal is to track some
+
+ align:start position:0%
+like that but the goal is to track some
+ 
+
+ align:start position:0%
+like that but the goal is to track some
+population of neutrons at some position
+
+ align:start position:0%
+population of neutrons at some position
+ 
+
+ align:start position:0%
+population of neutrons at some position
+at some energy traveling in some
+
+ align:start position:0%
+at some energy traveling in some
+ 
+
+ align:start position:0%
+at some energy traveling in some
+direction Omega as a function of time
+
+ align:start position:0%
+direction Omega as a function of time
+ 
+
+ align:start position:0%
+direction Omega as a function of time
+and the 3d representation of what we're
+
+ align:start position:0%
+and the 3d representation of what we're
+ 
+
+ align:start position:0%
+and the 3d representation of what we're
+looking at here is let's say we had some
+
+ align:start position:0%
+looking at here is let's say we had some
+ 
+
+ align:start position:0%
+looking at here is let's say we had some
+small volume element which we'll call
+
+ align:start position:0%
+small volume element which we'll call
+ 
+
+ align:start position:0%
+small volume element which we'll call
+that R DV that's got normal vectors
+
+ align:start position:0%
+that R DV that's got normal vectors
+ 
+
+ align:start position:0%
+that R DV that's got normal vectors
+sticking out of it we'll call those n
+
+ align:start position:0%
+sticking out of it we'll call those n
+ 
+
+ align:start position:0%
+sticking out of it we'll call those n
+hats in all directions and inside there
+
+ align:start position:0%
+hats in all directions and inside there
+ 
+
+ align:start position:0%
+hats in all directions and inside there
+let's say if this is our energy scale
+
+ align:start position:0%
+let's say if this is our energy scale
+ 
+
+ align:start position:0%
+let's say if this is our energy scale
+we're tracking the population of
+
+ align:start position:0%
+we're tracking the population of
+ 
+
+ align:start position:0%
+we're tracking the population of
+neutrons that occupy some small energy
+
+ align:start position:0%
+neutrons that occupy some small energy
+ 
+
+ align:start position:0%
+neutrons that occupy some small energy
+group de and is also traveling in some
+
+ align:start position:0%
+group de and is also traveling in some
+ 
+
+ align:start position:0%
+group de and is also traveling in some
+small direction that we designate as D
+
+ align:start position:0%
+small direction that we designate as D
+ 
+
+ align:start position:0%
+small direction that we designate as D
+Omega so that's the goal of this whole
+
+ align:start position:0%
+Omega so that's the goal of this whole
+ 
+
+ align:start position:0%
+Omega so that's the goal of this whole
+equation is to track the number of
+
+ align:start position:0%
+equation is to track the number of
+ 
+
+ align:start position:0%
+equation is to track the number of
+neutrons at any given position so let's
+
+ align:start position:0%
+neutrons at any given position so let's
+ 
+
+ align:start position:0%
+neutrons at any given position so let's
+call this distance
+
+ align:start position:0%
+call this distance
+ 
+
+ align:start position:0%
+call this distance
+or the vector are in this little volume
+
+ align:start position:0%
+or the vector are in this little volume
+ 
+
+ align:start position:0%
+or the vector are in this little volume
+traveling in some direction Omega with
+
+ align:start position:0%
+traveling in some direction Omega with
+ 
+
+ align:start position:0%
+traveling in some direction Omega with
+some infinitesimally small energy group
+
+ align:start position:0%
+some infinitesimally small energy group
+ 
+
+ align:start position:0%
+some infinitesimally small energy group
+D that's gonna be the goal of the whole
+
+ align:start position:0%
+D that's gonna be the goal of the whole
+ 
+
+ align:start position:0%
+D that's gonna be the goal of the whole
+thing and what we'll do is write this to
+
+ align:start position:0%
+thing and what we'll do is write this to
+ 
+
+ align:start position:0%
+thing and what we'll do is write this to
+say the change in the population of
+
+ align:start position:0%
+say the change in the population of
+ 
+
+ align:start position:0%
+say the change in the population of
+neutrons at a given distance energy
+
+ align:start position:0%
+neutrons at a given distance energy
+ 
+
+ align:start position:0%
+neutrons at a given distance energy
+angle and time over time is just gonna
+
+ align:start position:0%
+angle and time over time is just gonna
+ 
+
+ align:start position:0%
+angle and time over time is just gonna
+be a sum of gain and loss terms and what
+
+ align:start position:0%
+be a sum of gain and loss terms and what
+ 
+
+ align:start position:0%
+be a sum of gain and loss terms and what
+I think will take all day today to do is
+
+ align:start position:0%
+I think will take all day today to do is
+ 
+
+ align:start position:0%
+I think will take all day today to do is
+to figure out what are the actual
+
+ align:start position:0%
+to figure out what are the actual
+ 
+
+ align:start position:0%
+to figure out what are the actual
+physical things that neutrons can do in
+
+ align:start position:0%
+physical things that neutrons can do in
+ 
+
+ align:start position:0%
+physical things that neutrons can do in
+and out of this volume and how do we
+
+ align:start position:0%
+and out of this volume and how do we
+ 
+
+ align:start position:0%
+and out of this volume and how do we
+turn those into math something that we
+
+ align:start position:0%
+turn those into math something that we
+ 
+
+ align:start position:0%
+turn those into math something that we
+can abstract and solve there's a couple
+
+ align:start position:0%
+can abstract and solve there's a couple
+ 
+
+ align:start position:0%
+can abstract and solve there's a couple
+other terms that we're going to put up
+
+ align:start position:0%
+other terms that we're going to put up
+ 
+
+ align:start position:0%
+other terms that we're going to put up
+here we'll say that the flux of neutrons
+
+ align:start position:0%
+here we'll say that the flux of neutrons
+ 
+
+ align:start position:0%
+here we'll say that the flux of neutrons
+which is usually the variable that we
+
+ align:start position:0%
+which is usually the variable that we
+ 
+
+ align:start position:0%
+which is usually the variable that we
+actually track is just the velocity
+
+ align:start position:0%
+actually track is just the velocity
+ 
+
+ align:start position:0%
+actually track is just the velocity
+times the neutron population and also
+
+ align:start position:0%
+times the neutron population and also
+ 
+
+ align:start position:0%
+times the neutron population and also
+let's define some angular ly independent
+
+ align:start position:0%
+let's define some angular ly independent
+ 
+
+ align:start position:0%
+let's define some angular ly independent
+terms because in the end we've been
+
+ align:start position:0%
+terms because in the end we've been
+ 
+
+ align:start position:0%
+terms because in the end we've been
+talking about what's the probability of
+
+ align:start position:0%
+talking about what's the probability of
+ 
+
+ align:start position:0%
+talking about what's the probability of
+some neutron or particle interacting
+
+ align:start position:0%
+some neutron or particle interacting
+ 
+
+ align:start position:0%
+some neutron or particle interacting
+with some electron going out at some
+
+ align:start position:0%
+with some electron going out at some
+ 
+
+ align:start position:0%
+with some electron going out at some
+angle but as we're interested in how
+
+ align:start position:0%
+angle but as we're interested in how
+ 
+
+ align:start position:0%
+angle but as we're interested in how
+many neutrons are there in the reactor
+
+ align:start position:0%
+many neutrons are there in the reactor
+ 
+
+ align:start position:0%
+many neutrons are there in the reactor
+we usually don't care in which direction
+
+ align:start position:0%
+we usually don't care in which direction
+ 
+
+ align:start position:0%
+we usually don't care in which direction
+they're traveling so the first
+
+ align:start position:0%
+they're traveling so the first
+ 
+
+ align:start position:0%
+they're traveling so the first
+simplification that we will do is get
+
+ align:start position:0%
+simplification that we will do is get
+ 
+
+ align:start position:0%
+simplification that we will do is get
+rid of any sort of angular dependence
+
+ align:start position:0%
+rid of any sort of angular dependence
+ 
+
+ align:start position:0%
+rid of any sort of angular dependence
+getting rid of two of the seven
+
+ align:start position:0%
+getting rid of two of the seven
+ 
+
+ align:start position:0%
+getting rid of two of the seven
+variables that we're dealing with here
+
+ align:start position:0%
+variables that we're dealing with here
+ 
+
+ align:start position:0%
+variables that we're dealing with here
+so all these variables right here will
+
+ align:start position:0%
+so all these variables right here will
+ 
+
+ align:start position:0%
+so all these variables right here will
+be dependent on angle and all these
+
+ align:start position:0%
+be dependent on angle and all these
+ 
+
+ align:start position:0%
+be dependent on angle and all these
+variables right here will be angular ly
+
+ align:start position:0%
+variables right here will be angular ly
+ 
+
+ align:start position:0%
+variables right here will be angular ly
+and you literally independence
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so there'll be some corresponding
+
+ align:start position:0%
+so there'll be some corresponding
+ 
+
+ align:start position:0%
+so there'll be some corresponding
+capital N or number of neutrons as a
+
+ align:start position:0%
+capital N or number of neutrons as a
+ 
+
+ align:start position:0%
+capital N or number of neutrons as a
+function of re and T will call this flux
+
+ align:start position:0%
+function of re and T will call this flux
+ 
+
+ align:start position:0%
+function of re and T will call this flux
+we'll call this number
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there's going to be a number of
+
+ align:start position:0%
+there's going to be a number of
+ 
+
+ align:start position:0%
+there's going to be a number of
+cross-sections that we need to worry
+
+ align:start position:0%
+cross-sections that we need to worry
+ 
+
+ align:start position:0%
+cross-sections that we need to worry
+about so we'll refer to little Sigma as
+
+ align:start position:0%
+about so we'll refer to little Sigma as
+ 
+
+ align:start position:0%
+about so we'll refer to little Sigma as
+a function of energy as our micro cross
+
+ align:start position:0%
+a function of energy as our micro cross
+ 
+
+ align:start position:0%
+a function of energy as our micro cross
+section and big Sigma of e as a
+
+ align:start position:0%
+section and big Sigma of e as a
+ 
+
+ align:start position:0%
+section and big Sigma of e as a
+macroscopic cross section then you want
+
+ align:start position:0%
+macroscopic cross section then you want
+ 
+
+ align:start position:0%
+macroscopic cross section then you want
+to remember the relation between these
+
+ align:start position:0%
+to remember the relation between these
+ 
+
+ align:start position:0%
+to remember the relation between these
+two the solid angle not quite that's
+
+ align:start position:0%
+two the solid angle not quite that's
+ 
+
+ align:start position:0%
+two the solid angle not quite that's
+let's see there's a difference between
+
+ align:start position:0%
+let's see there's a difference between
+ 
+
+ align:start position:0%
+let's see there's a difference between
+and so what these physically mean as
+
+ align:start position:0%
+and so what these physically mean as
+ 
+
+ align:start position:0%
+and so what these physically mean as
+little Sigma means the probability of
+
+ align:start position:0%
+little Sigma means the probability of
+ 
+
+ align:start position:0%
+little Sigma means the probability of
+interaction with one particle and this
+
+ align:start position:0%
+interaction with one particle and this
+ 
+
+ align:start position:0%
+interaction with one particle and this
+is just a total probability of
+
+ align:start position:0%
+is just a total probability of
+ 
+
+ align:start position:0%
+is just a total probability of
+interaction with all the particles that
+
+ align:start position:0%
+interaction with all the particles that
+ 
+
+ align:start position:0%
+interaction with all the particles that
+may be there so yeah Chris there's
+
+ align:start position:0%
+may be there so yeah Chris there's
+ 
+
+ align:start position:0%
+may be there so yeah Chris there's
+number density already we have another
+
+ align:start position:0%
+number density already we have another
+ 
+
+ align:start position:0%
+number density already we have another
+variable conflict how do we want to
+
+ align:start position:0%
+variable conflict how do we want to
+ 
+
+ align:start position:0%
+variable conflict how do we want to
+resolve this let's see I'll have to
+
+ align:start position:0%
+resolve this let's see I'll have to
+ 
+
+ align:start position:0%
+resolve this let's see I'll have to
+change the symbol somehow let's make it
+
+ align:start position:0%
+change the symbol somehow let's make it
+ 
+
+ align:start position:0%
+change the symbol somehow let's make it
+cursive don't know what else to do I
+
+ align:start position:0%
+cursive don't know what else to do I
+ 
+
+ align:start position:0%
+cursive don't know what else to do I
+don't want to give it a number other
+
+ align:start position:0%
+don't want to give it a number other
+ 
+
+ align:start position:0%
+don't want to give it a number other
+than n since we're talking about
+
+ align:start position:0%
+than n since we're talking about
+ 
+
+ align:start position:0%
+than n since we're talking about
+neutrons where that right here is going
+
+ align:start position:0%
+neutrons where that right here is going
+ 
+
+ align:start position:0%
+neutrons where that right here is going
+to be number density and in the end
+
+ align:start position:0%
+to be number density and in the end
+ 
+
+ align:start position:0%
+to be number density and in the end
+we're worried about some sort of
+
+ align:start position:0%
+we're worried about some sort of
+ 
+
+ align:start position:0%
+we're worried about some sort of
+reaction rate which is always going to
+
+ align:start position:0%
+reaction rate which is always going to
+ 
+
+ align:start position:0%
+reaction rate which is always going to
+equal some flux or let's just stick with
+
+ align:start position:0%
+equal some flux or let's just stick with
+ 
+
+ align:start position:0%
+equal some flux or let's just stick with
+some angular ly dependent flux at re
+
+ align:start position:0%
+some angular ly dependent flux at re
+ 
+
+ align:start position:0%
+some angular ly dependent flux at re
+Omega T times some cross-section as a
+
+ align:start position:0%
+Omega T times some cross-section as a
+ 
+
+ align:start position:0%
+Omega T times some cross-section as a
+function of energy and it's these
+
+ align:start position:0%
+function of energy and it's these
+ 
+
+ align:start position:0%
+function of energy and it's these
+reaction rates that are the rates of
+
+ align:start position:0%
+reaction rates that are the rates of
+ 
+
+ align:start position:0%
+reaction rates that are the rates of
+gains and losses of neutrons out of this
+
+ align:start position:0%
+gains and losses of neutrons out of this
+ 
+
+ align:start position:0%
+gains and losses of neutrons out of this
+volume out of this little angle out of
+
+ align:start position:0%
+volume out of this little angle out of
+ 
+
+ align:start position:0%
+volume out of this little angle out of
+this energy group and out of that space
+
+ align:start position:0%
+this energy group and out of that space
+ 
+
+ align:start position:0%
+this energy group and out of that space
+or into that volume energy group in
+
+ align:start position:0%
+or into that volume energy group in
+ 
+
+ align:start position:0%
+or into that volume energy group in
+space so let's see other terms that
+
+ align:start position:0%
+space so let's see other terms that
+ 
+
+ align:start position:0%
+space so let's see other terms that
+we'll want to define
+
+ align:start position:0%
+we'll want to define
+ 
+
+ align:start position:0%
+we'll want to define
+include new like last time we'll call
+
+ align:start position:0%
+include new like last time we'll call
+ 
+
+ align:start position:0%
+include new like last time we'll call
+this Neutron multiplication in other
+
+ align:start position:0%
+this Neutron multiplication in other
+ 
+
+ align:start position:0%
+this Neutron multiplication in other
+words this is the number of neutrons
+
+ align:start position:0%
+words this is the number of neutrons
+ 
+
+ align:start position:0%
+words this is the number of neutrons
+made on average during each fission
+
+ align:start position:0%
+made on average during each fission
+ 
+
+ align:start position:0%
+made on average during each fission
+event and we give it energy dependence
+
+ align:start position:0%
+event and we give it energy dependence
+ 
+
+ align:start position:0%
+event and we give it energy dependence
+because as we saw on the Janus libraries
+
+ align:start position:0%
+because as we saw on the Janus libraries
+ 
+
+ align:start position:0%
+because as we saw on the Janus libraries
+on Friday I think it was what's today
+
+ align:start position:0%
+on Friday I think it was what's today
+ 
+
+ align:start position:0%
+on Friday I think it was what's today
+Tuesday I don't even know anymore I
+
+ align:start position:0%
+Tuesday I don't even know anymore I
+ 
+
+ align:start position:0%
+Tuesday I don't even know anymore I
+think as we saw on Friday that depends
+
+ align:start position:0%
+think as we saw on Friday that depends
+ 
+
+ align:start position:0%
+think as we saw on Friday that depends
+on energy for the higher energy levels
+
+ align:start position:0%
+on energy for the higher energy levels
+ 
+
+ align:start position:0%
+on energy for the higher energy levels
+and there's also going to be some kaiser
+
+ align:start position:0%
+and there's also going to be some kaiser
+ 
+
+ align:start position:0%
+and there's also going to be some kaiser
+or some neutron birth spectrum which
+
+ align:start position:0%
+or some neutron birth spectrum which
+ 
+
+ align:start position:0%
+or some neutron birth spectrum which
+tells you the average energy at which
+
+ align:start position:0%
+tells you the average energy at which
+ 
+
+ align:start position:0%
+tells you the average energy at which
+neutrons are born from fission so
+
+ align:start position:0%
+neutrons are born from fission so
+ 
+
+ align:start position:0%
+neutrons are born from fission so
+regardless of what energy goes in to
+
+ align:start position:0%
+regardless of what energy goes in to
+ 
+
+ align:start position:0%
+regardless of what energy goes in to
+cause the fission there's some
+
+ align:start position:0%
+cause the fission there's some
+ 
+
+ align:start position:0%
+cause the fission there's some
+probability distribution of a neutron
+
+ align:start position:0%
+probability distribution of a neutron
+ 
+
+ align:start position:0%
+probability distribution of a neutron
+being born at a certain energy and it
+
+ align:start position:0%
+being born at a certain energy and it
+ 
+
+ align:start position:0%
+being born at a certain energy and it
+looks something like this where that's
+
+ align:start position:0%
+looks something like this where that's
+ 
+
+ align:start position:0%
+looks something like this where that's
+about one MeV that's about ten MeV and
+
+ align:start position:0%
+about one MeV that's about ten MeV and
+ 
+
+ align:start position:0%
+about one MeV that's about ten MeV and
+that average right there is around two
+
+ align:start position:0%
+that average right there is around two
+ 
+
+ align:start position:0%
+that average right there is around two
+MeV and so it's important to note that
+
+ align:start position:0%
+MeV and so it's important to note that
+ 
+
+ align:start position:0%
+MeV and so it's important to note that
+neutrons are born at different energies
+
+ align:start position:0%
+neutrons are born at different energies
+ 
+
+ align:start position:0%
+neutrons are born at different energies
+because we want to track every single
+
+ align:start position:0%
+because we want to track every single
+ 
+
+ align:start position:0%
+because we want to track every single
+possible de throughout this control
+
+ align:start position:0%
+possible de throughout this control
+ 
+
+ align:start position:0%
+possible de throughout this control
+volume which we'll also call a reactor
+
+ align:start position:0%
+volume which we'll also call a reactor
+ 
+
+ align:start position:0%
+volume which we'll also call a reactor
+let's say what other terms will we need
+
+ align:start position:0%
+let's say what other terms will we need
+ 
+
+ align:start position:0%
+let's say what other terms will we need
+to know the different types of
+
+ align:start position:0%
+to know the different types of
+ 
+
+ align:start position:0%
+to know the different types of
+cross-sections are the different
+
+ align:start position:0%
+cross-sections are the different
+ 
+
+ align:start position:0%
+cross-sections are the different
+interactions that neutrons can have with
+
+ align:start position:0%
+interactions that neutrons can have with
+ 
+
+ align:start position:0%
+interactions that neutrons can have with
+matter what are some of the ones that we
+
+ align:start position:0%
+matter what are some of the ones that we
+ 
+
+ align:start position:0%
+matter what are some of the ones that we
+had talked about well what can neutrons
+
+ align:start position:0%
+had talked about well what can neutrons
+ 
+
+ align:start position:0%
+had talked about well what can neutrons
+do when they run into stuff they can
+
+ align:start position:0%
+do when they run into stuff they can
+ 
+
+ align:start position:0%
+do when they run into stuff they can
+scatter so there's going to be some
+
+ align:start position:0%
+scatter so there's going to be some
+ 
+
+ align:start position:0%
+scatter so there's going to be some
+scattering cross-section and when they
+
+ align:start position:0%
+scattering cross-section and when they
+ 
+
+ align:start position:0%
+scattering cross-section and when they
+scatter the important part here is
+
+ align:start position:0%
+scatter the important part here is
+ 
+
+ align:start position:0%
+scatter the important part here is
+they're going to change in energy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what else can they do
+
+ align:start position:0%
+what else can they do
+ 
+
+ align:start position:0%
+what else can they do
+yep they can be absorbed so we'll have
+
+ align:start position:0%
+yep they can be absorbed so we'll have
+ 
+
+ align:start position:0%
+yep they can be absorbed so we'll have
+some Sigma absorption what are some of
+
+ align:start position:0%
+some Sigma absorption what are some of
+ 
+
+ align:start position:0%
+some Sigma absorption what are some of
+the various things that can happen when
+
+ align:start position:0%
+the various things that can happen when
+ 
+
+ align:start position:0%
+the various things that can happen when
+a neutron is absorbed yep so one of them
+
+ align:start position:0%
+a neutron is absorbed yep so one of them
+ 
+
+ align:start position:0%
+a neutron is absorbed yep so one of them
+is fission what are some of the other
+
+ align:start position:0%
+is fission what are some of the other
+ 
+
+ align:start position:0%
+is fission what are some of the other
+ones yep
+
+ align:start position:0%
+ones yep
+ 
+
+ align:start position:0%
+ones yep
+capture over some of the ones that we
+
+ align:start position:0%
+capture over some of the ones that we
+ 
+
+ align:start position:0%
+capture over some of the ones that we
+talked about during the Chadwick paper
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yep so there can be some we'll call it n
+
+ align:start position:0%
+yep so there can be some we'll call it n
+ 
+
+ align:start position:0%
+yep so there can be some we'll call it n
+I n
+
+ align:start position:0%
+I n
+ 
+
+ align:start position:0%
+I n
+one Neutron goes in i neutrons come out
+
+ align:start position:0%
+one Neutron goes in i neutrons come out
+ 
+
+ align:start position:0%
+one Neutron goes in i neutrons come out
+so one two i neutrons sure anything else
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+encompassed and absorption
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well when we refer to scatter here what
+
+ align:start position:0%
+well when we refer to scatter here what
+ 
+
+ align:start position:0%
+well when we refer to scatter here what
+type of scattering are we talking about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Compton's for photons it's okay
+
+ align:start position:0%
+Compton's for photons it's okay
+ 
+
+ align:start position:0%
+Compton's for photons it's okay
+was it elastic or inelastic scattering
+
+ align:start position:0%
+was it elastic or inelastic scattering
+ 
+
+ align:start position:0%
+was it elastic or inelastic scattering
+elastic scattering so another thing you
+
+ align:start position:0%
+elastic scattering so another thing you
+ 
+
+ align:start position:0%
+elastic scattering so another thing you
+could call an absorption event depending
+
+ align:start position:0%
+could call an absorption event depending
+ 
+
+ align:start position:0%
+could call an absorption event depending
+on what bin you put things in is
+
+ align:start position:0%
+on what bin you put things in is
+ 
+
+ align:start position:0%
+on what bin you put things in is
+inelastic scattering which is that kind
+
+ align:start position:0%
+inelastic scattering which is that kind
+ 
+
+ align:start position:0%
+inelastic scattering which is that kind
+of skites we call it scattering because
+
+ align:start position:0%
+of skites we call it scattering because
+ 
+
+ align:start position:0%
+of skites we call it scattering because
+one Neutron goes in one neutron comes
+
+ align:start position:0%
+one Neutron goes in one neutron comes
+ 
+
+ align:start position:0%
+one Neutron goes in one neutron comes
+out but in reality you have a compound
+
+ align:start position:0%
+out but in reality you have a compound
+ 
+
+ align:start position:0%
+out but in reality you have a compound
+nucleus forming and a neutron emitted
+
+ align:start position:0%
+nucleus forming and a neutron emitted
+ 
+
+ align:start position:0%
+nucleus forming and a neutron emitted
+from a different energy level so it
+
+ align:start position:0%
+from a different energy level so it
+ 
+
+ align:start position:0%
+from a different energy level so it
+doesn't follow the simple ballistic laws
+
+ align:start position:0%
+doesn't follow the simple ballistic laws
+ 
+
+ align:start position:0%
+doesn't follow the simple ballistic laws
+of an kinematic laws of inelastic
+
+ align:start position:0%
+of an kinematic laws of inelastic
+ 
+
+ align:start position:0%
+of an kinematic laws of inelastic
+scattering what else can neutrons do now
+
+ align:start position:0%
+scattering what else can neutrons do now
+ 
+
+ align:start position:0%
+scattering what else can neutrons do now
+we're getting into the real esoteric
+
+ align:start position:0%
+we're getting into the real esoteric
+ 
+
+ align:start position:0%
+we're getting into the real esoteric
+stuff but I want to see if you guys have
+
+ align:start position:0%
+stuff but I want to see if you guys have
+ 
+
+ align:start position:0%
+stuff but I want to see if you guys have
+any idea did you know that neutrons can
+
+ align:start position:0%
+any idea did you know that neutrons can
+ 
+
+ align:start position:0%
+any idea did you know that neutrons can
+decay a lone Neutron is actually not a
+
+ align:start position:0%
+decay a lone Neutron is actually not a
+ 
+
+ align:start position:0%
+decay a lone Neutron is actually not a
+stable particle if you look up on the
+
+ align:start position:0%
+stable particle if you look up on the
+ 
+
+ align:start position:0%
+stable particle if you look up on the
+Kairi table of nuclides it's got a
+
+ align:start position:0%
+Kairi table of nuclides it's got a
+ 
+
+ align:start position:0%
+Kairi table of nuclides it's got a
+half-life of 12 minutes so if you happen
+
+ align:start position:0%
+half-life of 12 minutes so if you happen
+ 
+
+ align:start position:0%
+half-life of 12 minutes so if you happen
+to be able to have neutrons in a bottle
+
+ align:start position:0%
+to be able to have neutrons in a bottle
+ 
+
+ align:start position:0%
+to be able to have neutrons in a bottle
+or something which we actually can do
+
+ align:start position:0%
+or something which we actually can do
+ 
+
+ align:start position:0%
+or something which we actually can do
+there's Centers for ultracold neutrons
+
+ align:start position:0%
+there's Centers for ultracold neutrons
+ 
+
+ align:start position:0%
+there's Centers for ultracold neutrons
+and atoms there's there's one at North
+
+ align:start position:0%
+and atoms there's there's one at North
+ 
+
+ align:start position:0%
+and atoms there's there's one at North
+Carolina State or they actually cool
+
+ align:start position:0%
+Carolina State or they actually cool
+ 
+
+ align:start position:0%
+Carolina State or they actually cool
+down neutrons to cryogenic temperatures
+
+ align:start position:0%
+down neutrons to cryogenic temperatures
+ 
+
+ align:start position:0%
+down neutrons to cryogenic temperatures
+to the point where they can actually
+
+ align:start position:0%
+to the point where they can actually
+ 
+
+ align:start position:0%
+to the point where they can actually
+confine them they only live on average
+
+ align:start position:0%
+confine them they only live on average
+ 
+
+ align:start position:0%
+confine them they only live on average
+12 minutes and then there would also be
+
+ align:start position:0%
+12 minutes and then there would also be
+ 
+
+ align:start position:0%
+12 minutes and then there would also be
+what we call Neutron Neutron
+
+ align:start position:0%
+what we call Neutron Neutron
+ 
+
+ align:start position:0%
+what we call Neutron Neutron
+interactions there is a finite non zero
+
+ align:start position:0%
+interactions there is a finite non zero
+ 
+
+ align:start position:0%
+interactions there is a finite non zero
+but very small probability that neutrons
+
+ align:start position:0%
+but very small probability that neutrons
+ 
+
+ align:start position:0%
+but very small probability that neutrons
+can hit other neutrons but the mean free
+
+ align:start position:0%
+can hit other neutrons but the mean free
+ 
+
+ align:start position:0%
+can hit other neutrons but the mean free
+path for these is on the order of 10 to
+
+ align:start position:0%
+path for these is on the order of 10 to
+ 
+
+ align:start position:0%
+path for these is on the order of 10 to
+the 8th centimeters so this is not
+
+ align:start position:0%
+the 8th centimeters so this is not
+ 
+
+ align:start position:0%
+the 8th centimeters so this is not
+something we have to consider but it's
+
+ align:start position:0%
+something we have to consider but it's
+ 
+
+ align:start position:0%
+something we have to consider but it's
+interesting to know that yes neutrons
+
+ align:start position:0%
+interesting to know that yes neutrons
+ 
+
+ align:start position:0%
+interesting to know that yes neutrons
+can run into other neutrons and these
+
+ align:start position:0%
+can run into other neutrons and these
+ 
+
+ align:start position:0%
+can run into other neutrons and these
+sorts of things have been measured we
+
+ align:start position:0%
+sorts of things have been measured we
+ 
+
+ align:start position:0%
+sorts of things have been measured we
+won't have to worry about this we won't
+
+ align:start position:0%
+won't have to worry about this we won't
+ 
+
+ align:start position:0%
+won't have to worry about this we won't
+have to worry about neutron decay but it
+
+ align:start position:0%
+have to worry about neutron decay but it
+ 
+
+ align:start position:0%
+have to worry about neutron decay but it
+interesting to note that a lone Neutron
+
+ align:start position:0%
+interesting to note that a lone Neutron
+ 
+
+ align:start position:0%
+interesting to note that a lone Neutron
+is not a stable particle it'll
+
+ align:start position:0%
+is not a stable particle it'll
+ 
+
+ align:start position:0%
+is not a stable particle it'll
+spontaneously undergo beta decay and do
+
+ align:start position:0%
+spontaneously undergo beta decay and do
+ 
+
+ align:start position:0%
+spontaneously undergo beta decay and do
+it a proton and an electron pretty neat
+
+ align:start position:0%
+it a proton and an electron pretty neat
+ 
+
+ align:start position:0%
+it a proton and an electron pretty neat
+huh anyway if we sum up all these
+
+ align:start position:0%
+huh anyway if we sum up all these
+ 
+
+ align:start position:0%
+huh anyway if we sum up all these
+possible interactions we have one other
+
+ align:start position:0%
+possible interactions we have one other
+ 
+
+ align:start position:0%
+possible interactions we have one other
+cross-section which we're going to call
+
+ align:start position:0%
+cross-section which we're going to call
+ 
+
+ align:start position:0%
+cross-section which we're going to call
+this the total cross-section the
+
+ align:start position:0%
+this the total cross-section the
+ 
+
+ align:start position:0%
+this the total cross-section the
+probability of absolutely any
+
+ align:start position:0%
+probability of absolutely any
+ 
+
+ align:start position:0%
+probability of absolutely any
+interaction occurring at all because any
+
+ align:start position:0%
+interaction occurring at all because any
+ 
+
+ align:start position:0%
+interaction occurring at all because any
+sort of interaction of that Neutron is
+
+ align:start position:0%
+sort of interaction of that Neutron is
+ 
+
+ align:start position:0%
+sort of interaction of that Neutron is
+going to cause removal from this group
+
+ align:start position:0%
+going to cause removal from this group
+ 
+
+ align:start position:0%
+going to cause removal from this group
+of energy position angle location
+
+ align:start position:0%
+of energy position angle location
+ 
+
+ align:start position:0%
+of energy position angle location
+whatever whether it's absorption or
+
+ align:start position:0%
+whatever whether it's absorption or
+ 
+
+ align:start position:0%
+whatever whether it's absorption or
+fission or elastic scattering or
+
+ align:start position:0%
+fission or elastic scattering or
+ 
+
+ align:start position:0%
+fission or elastic scattering or
+inelastic scattering any sort of event
+
+ align:start position:0%
+inelastic scattering any sort of event
+ 
+
+ align:start position:0%
+inelastic scattering any sort of event
+except for forward scattering which
+
+ align:start position:0%
+except for forward scattering which
+ 
+
+ align:start position:0%
+except for forward scattering which
+means nothing happens is going to result
+
+ align:start position:0%
+means nothing happens is going to result
+ 
+
+ align:start position:0%
+means nothing happens is going to result
+in this neutron either leaving the
+
+ align:start position:0%
+in this neutron either leaving the
+ 
+
+ align:start position:0%
+in this neutron either leaving the
+volume so it might scatter out of our
+
+ align:start position:0%
+volume so it might scatter out of our
+ 
+
+ align:start position:0%
+volume so it might scatter out of our
+little volume or it might change
+
+ align:start position:0%
+little volume or it might change
+ 
+
+ align:start position:0%
+little volume or it might change
+direction scatter out of our D Omega or
+
+ align:start position:0%
+direction scatter out of our D Omega or
+ 
+
+ align:start position:0%
+direction scatter out of our D Omega or
+it will lose some energy or gain some
+
+ align:start position:0%
+it will lose some energy or gain some
+ 
+
+ align:start position:0%
+it will lose some energy or gain some
+energy in some cases leaving our little
+
+ align:start position:0%
+energy in some cases leaving our little
+ 
+
+ align:start position:0%
+energy in some cases leaving our little
+d e which is what we're trying to track
+
+ align:start position:0%
+d e which is what we're trying to track
+ 
+
+ align:start position:0%
+d e which is what we're trying to track
+because we're actually tracking what's
+
+ align:start position:0%
+because we're actually tracking what's
+ 
+
+ align:start position:0%
+because we're actually tracking what's
+the population of neutrons in this
+
+ align:start position:0%
+the population of neutrons in this
+ 
+
+ align:start position:0%
+the population of neutrons in this
+little de in this direction in this
+
+ align:start position:0%
+little de in this direction in this
+ 
+
+ align:start position:0%
+little de in this direction in this
+position at this time and supposedly if
+
+ align:start position:0%
+position at this time and supposedly if
+ 
+
+ align:start position:0%
+position at this time and supposedly if
+we know this term fully we can solve for
+
+ align:start position:0%
+we know this term fully we can solve for
+ 
+
+ align:start position:0%
+we know this term fully we can solve for
+all the neutrons everywhere anywhere in
+
+ align:start position:0%
+all the neutrons everywhere anywhere in
+ 
+
+ align:start position:0%
+all the neutrons everywhere anywhere in
+the reactor with full information so
+
+ align:start position:0%
+the reactor with full information so
+ 
+
+ align:start position:0%
+the reactor with full information so
+we'll spend the rest of today doing is
+
+ align:start position:0%
+we'll spend the rest of today doing is
+ 
+
+ align:start position:0%
+we'll spend the rest of today doing is
+figuring out what are all the possible
+
+ align:start position:0%
+figuring out what are all the possible
+ 
+
+ align:start position:0%
+figuring out what are all the possible
+gain and loss terms so let's start just
+
+ align:start position:0%
+gain and loss terms so let's start just
+ 
+
+ align:start position:0%
+gain and loss terms so let's start just
+putting them out physically or in words
+
+ align:start position:0%
+putting them out physically or in words
+ 
+
+ align:start position:0%
+putting them out physically or in words
+and then we'll put them to math so what
+
+ align:start position:0%
+and then we'll put them to math so what
+ 
+
+ align:start position:0%
+and then we'll put them to math so what
+are some of the ways in which neutrons
+
+ align:start position:0%
+are some of the ways in which neutrons
+ 
+
+ align:start position:0%
+are some of the ways in which neutrons
+can enter our little group of volume
+
+ align:start position:0%
+can enter our little group of volume
+ 
+
+ align:start position:0%
+can enter our little group of volume
+angle and energy our neutrons created
+
+ align:start position:0%
+angle and energy our neutrons created
+ 
+
+ align:start position:0%
+angle and energy our neutrons created
+yeah Luke
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+some vision yep so that's one big source
+
+ align:start position:0%
+some vision yep so that's one big source
+ 
+
+ align:start position:0%
+some vision yep so that's one big source
+so we'll call this a games this is the
+
+ align:start position:0%
+so we'll call this a games this is the
+ 
+
+ align:start position:0%
+so we'll call this a games this is the
+losses and you said a neutron source can
+
+ align:start position:0%
+losses and you said a neutron source can
+ 
+
+ align:start position:0%
+losses and you said a neutron source can
+you be more specific
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so we'll say n I end reactions
+
+ align:start position:0%
+okay so we'll say n I end reactions
+ 
+
+ align:start position:0%
+okay so we'll say n I end reactions
+right okay cool
+
+ align:start position:0%
+right okay cool
+ 
+
+ align:start position:0%
+right okay cool
+how else can we gain neutrons fusion
+
+ align:start position:0%
+how else can we gain neutrons fusion
+ 
+
+ align:start position:0%
+how else can we gain neutrons fusion
+okay ah that is true although fusion
+
+ align:start position:0%
+okay ah that is true although fusion
+ 
+
+ align:start position:0%
+okay ah that is true although fusion
+reactors don't really operate on the
+
+ align:start position:0%
+reactors don't really operate on the
+ 
+
+ align:start position:0%
+reactors don't really operate on the
+principle of neutron criticality or
+
+ align:start position:0%
+principle of neutron criticality or
+ 
+
+ align:start position:0%
+principle of neutron criticality or
+Neutron balance so this discussion for
+
+ align:start position:0%
+Neutron balance so this discussion for
+ 
+
+ align:start position:0%
+Neutron balance so this discussion for
+now is gonna be limited to fission
+
+ align:start position:0%
+now is gonna be limited to fission
+ 
+
+ align:start position:0%
+now is gonna be limited to fission
+reactors but yeah good point
+
+ align:start position:0%
+reactors but yeah good point
+ 
+
+ align:start position:0%
+reactors but yeah good point
+fusion does make neutrons what else yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah they could come from somewhere else
+
+ align:start position:0%
+yeah they could come from somewhere else
+ 
+
+ align:start position:0%
+yeah they could come from somewhere else
+right let's just call that an external
+
+ align:start position:0%
+right let's just call that an external
+ 
+
+ align:start position:0%
+right let's just call that an external
+source in the books and in your reading
+
+ align:start position:0%
+source in the books and in your reading
+ 
+
+ align:start position:0%
+source in the books and in your reading
+you'll just see them treat this external
+
+ align:start position:0%
+you'll just see them treat this external
+ 
+
+ align:start position:0%
+you'll just see them treat this external
+source as some variable s of our e Omega
+
+ align:start position:0%
+source as some variable s of our e Omega
+ 
+
+ align:start position:0%
+source as some variable s of our e Omega
+T so you'll just see this treated as s a
+
+ align:start position:0%
+T so you'll just see this treated as s a
+ 
+
+ align:start position:0%
+T so you'll just see this treated as s a
+source with no further explanation it's
+
+ align:start position:0%
+source with no further explanation it's
+ 
+
+ align:start position:0%
+source with no further explanation it's
+like oh math says that there could be
+
+ align:start position:0%
+like oh math says that there could be
+ 
+
+ align:start position:0%
+like oh math says that there could be
+external sources but I want to tell you
+
+ align:start position:0%
+external sources but I want to tell you
+ 
+
+ align:start position:0%
+external sources but I want to tell you
+where they really come from most
+
+ align:start position:0%
+where they really come from most
+ 
+
+ align:start position:0%
+where they really come from most
+reactors nowadays don't just start up
+
+ align:start position:0%
+reactors nowadays don't just start up
+ 
+
+ align:start position:0%
+reactors nowadays don't just start up
+when you throw a bunch of uranium into a
+
+ align:start position:0%
+when you throw a bunch of uranium into a
+ 
+
+ align:start position:0%
+when you throw a bunch of uranium into a
+pool and pull out the control rods you
+
+ align:start position:0%
+pool and pull out the control rods you
+ 
+
+ align:start position:0%
+pool and pull out the control rods you
+actually have to stick in if this is
+
+ align:start position:0%
+actually have to stick in if this is
+ 
+
+ align:start position:0%
+actually have to stick in if this is
+your little reactor right here you
+
+ align:start position:0%
+your little reactor right here you
+ 
+
+ align:start position:0%
+your little reactor right here you
+actually have to stick in a little piece
+
+ align:start position:0%
+actually have to stick in a little piece
+ 
+
+ align:start position:0%
+actually have to stick in a little piece
+of californium I think the isotope is
+
+ align:start position:0%
+of californium I think the isotope is
+ 
+
+ align:start position:0%
+of californium I think the isotope is
+252 as what we call a kick starter
+
+ align:start position:0%
+252 as what we call a kick starter
+ 
+
+ align:start position:0%
+252 as what we call a kick starter
+source so californium is made mostly in
+
+ align:start position:0%
+source so californium is made mostly in
+ 
+
+ align:start position:0%
+source so californium is made mostly in
+the high fer or the high flux isotope
+
+ align:start position:0%
+the high fer or the high flux isotope
+ 
+
+ align:start position:0%
+the high fer or the high flux isotope
+reactor at the Oak Ridge National Lab in
+
+ align:start position:0%
+reactor at the Oak Ridge National Lab in
+ 
+
+ align:start position:0%
+reactor at the Oak Ridge National Lab in
+Tennessee where they have a really
+
+ align:start position:0%
+Tennessee where they have a really
+ 
+
+ align:start position:0%
+Tennessee where they have a really
+really high power reactor it's 85
+
+ align:start position:0%
+really high power reactor it's 85
+ 
+
+ align:start position:0%
+really high power reactor it's 85
+megawatts it's about that big around and
+
+ align:start position:0%
+megawatts it's about that big around and
+ 
+
+ align:start position:0%
+megawatts it's about that big around and
+this tall it's really really small for a
+
+ align:start position:0%
+this tall it's really really small for a
+ 
+
+ align:start position:0%
+this tall it's really really small for a
+reference that's about the size of the
+
+ align:start position:0%
+reference that's about the size of the
+ 
+
+ align:start position:0%
+reference that's about the size of the
+MIT reactor except our reactor six
+
+ align:start position:0%
+MIT reactor except our reactor six
+ 
+
+ align:start position:0%
+MIT reactor except our reactor six
+megawatts there's as 85 megawatts and
+
+ align:start position:0%
+megawatts there's as 85 megawatts and
+ 
+
+ align:start position:0%
+megawatts there's as 85 megawatts and
+it's designed to be an incredibly high
+
+ align:start position:0%
+it's designed to be an incredibly high
+ 
+
+ align:start position:0%
+it's designed to be an incredibly high
+flux to go by Neutron capture and
+
+ align:start position:0%
+flux to go by Neutron capture and
+ 
+
+ align:start position:0%
+flux to go by Neutron capture and
+neutron capture reactions to build up
+
+ align:start position:0%
+neutron capture reactions to build up
+ 
+
+ align:start position:0%
+neutron capture reactions to build up
+californium to 52 which is spontaneously
+
+ align:start position:0%
+californium to 52 which is spontaneously
+ 
+
+ align:start position:0%
+californium to 52 which is spontaneously
+giving off neutrons like crazy and this
+
+ align:start position:0%
+giving off neutrons like crazy and this
+ 
+
+ align:start position:0%
+giving off neutrons like crazy and this
+right here that's your external source
+
+ align:start position:0%
+right here that's your external source
+ 
+
+ align:start position:0%
+right here that's your external source
+and this helps get reactors going
+
+ align:start position:0%
+and this helps get reactors going
+ 
+
+ align:start position:0%
+and this helps get reactors going
+because you can either very slowly wait
+
+ align:start position:0%
+because you can either very slowly wait
+ 
+
+ align:start position:0%
+because you can either very slowly wait
+for the fission reaction to build up in
+
+ align:start position:0%
+for the fission reaction to build up in
+ 
+
+ align:start position:0%
+for the fission reaction to build up in
+a controlled manner or you can give it a
+
+ align:start position:0%
+a controlled manner or you can give it a
+ 
+
+ align:start position:0%
+a controlled manner or you can give it a
+kick in the pants and get it going this
+
+ align:start position:0%
+kick in the pants and get it going this
+ 
+
+ align:start position:0%
+kick in the pants and get it going this
+hyper reactor is pretty cool like I said
+
+ align:start position:0%
+hyper reactor is pretty cool like I said
+ 
+
+ align:start position:0%
+hyper reactor is pretty cool like I said
+it's 85 megawatts and it's about as
+
+ align:start position:0%
+it's 85 megawatts and it's about as
+ 
+
+ align:start position:0%
+it's 85 megawatts and it's about as
+dense as it can get the fuels actually
+
+ align:start position:0%
+dense as it can get the fuels actually
+ 
+
+ align:start position:0%
+dense as it can get the fuels actually
+made by explosively bonding sheets of
+
+ align:start position:0%
+made by explosively bonding sheets of
+ 
+
+ align:start position:0%
+made by explosively bonding sheets of
+uranium in a certain sort of semi
+
+ align:start position:0%
+uranium in a certain sort of semi
+ 
+
+ align:start position:0%
+uranium in a certain sort of semi
+cylindrical configuration and it
+
+ align:start position:0%
+cylindrical configuration and it
+ 
+
+ align:start position:0%
+cylindrical configuration and it
+produces so much decay heat in so little
+
+ align:start position:0%
+produces so much decay heat in so little
+ 
+
+ align:start position:0%
+produces so much decay heat in so little
+space that if it were to lose cooling
+
+ align:start position:0%
+space that if it were to lose cooling
+ 
+
+ align:start position:0%
+space that if it were to lose cooling
+reactor would melt in eight seconds
+
+ align:start position:0%
+reactor would melt in eight seconds
+ 
+
+ align:start position:0%
+reactor would melt in eight seconds
+usually have days or so before that
+
+ align:start position:0%
+usually have days or so before that
+ 
+
+ align:start position:0%
+usually have days or so before that
+happens in a conventional reactor
+
+ align:start position:0%
+happens in a conventional reactor
+ 
+
+ align:start position:0%
+happens in a conventional reactor
+because the power density just isn't
+
+ align:start position:0%
+because the power density just isn't
+ 
+
+ align:start position:0%
+because the power density just isn't
+that high
+
+ align:start position:0%
+that high
+ 
+
+ align:start position:0%
+that high
+so you can actually see down to the tank
+
+ align:start position:0%
+so you can actually see down to the tank
+ 
+
+ align:start position:0%
+so you can actually see down to the tank
+that contains - if you go for a tour at
+
+ align:start position:0%
+that contains - if you go for a tour at
+ 
+
+ align:start position:0%
+that contains - if you go for a tour at
+Oakridge National Lab and it's way down
+
+ align:start position:0%
+Oakridge National Lab and it's way down
+ 
+
+ align:start position:0%
+Oakridge National Lab and it's way down
+below this gigantic like not quite
+
+ align:start position:0%
+below this gigantic like not quite
+ 
+
+ align:start position:0%
+below this gigantic like not quite
+Olympic but get in there sized pool of
+
+ align:start position:0%
+Olympic but get in there sized pool of
+ 
+
+ align:start position:0%
+Olympic but get in there sized pool of
+water just to make sure that there is
+
+ align:start position:0%
+water just to make sure that there is
+ 
+
+ align:start position:0%
+water just to make sure that there is
+adequate cooling for this thing it's
+
+ align:start position:0%
+adequate cooling for this thing it's
+ 
+
+ align:start position:0%
+adequate cooling for this thing it's
+intense but yeah that's just to notice
+
+ align:start position:0%
+intense but yeah that's just to notice
+ 
+
+ align:start position:0%
+intense but yeah that's just to notice
+that these external sources these are
+
+ align:start position:0%
+that these external sources these are
+ 
+
+ align:start position:0%
+that these external sources these are
+real things that we use in power
+
+ align:start position:0%
+real things that we use in power
+ 
+
+ align:start position:0%
+real things that we use in power
+reactors to get them going what are some
+
+ align:start position:0%
+reactors to get them going what are some
+ 
+
+ align:start position:0%
+reactors to get them going what are some
+other ways that one could make neutrons
+
+ align:start position:0%
+other ways that one could make neutrons
+ 
+
+ align:start position:0%
+other ways that one could make neutrons
+or that neutrons could enter into our
+
+ align:start position:0%
+or that neutrons could enter into our
+ 
+
+ align:start position:0%
+or that neutrons could enter into our
+energy group and the silence is expected
+
+ align:start position:0%
+energy group and the silence is expected
+ 
+
+ align:start position:0%
+energy group and the silence is expected
+because this is usually the hardest part
+
+ align:start position:0%
+because this is usually the hardest part
+ 
+
+ align:start position:0%
+because this is usually the hardest part
+of developing this equation and I want
+
+ align:start position:0%
+of developing this equation and I want
+ 
+
+ align:start position:0%
+of developing this equation and I want
+to introduce it yeah Luke that's exactly
+
+ align:start position:0%
+to introduce it yeah Luke that's exactly
+ 
+
+ align:start position:0%
+to introduce it yeah Luke that's exactly
+it they can scatter in so when we
+
+ align:start position:0%
+it they can scatter in so when we
+ 
+
+ align:start position:0%
+it they can scatter in so when we
+develop this Neutron transport equation
+
+ align:start position:0%
+develop this Neutron transport equation
+ 
+
+ align:start position:0%
+develop this Neutron transport equation
+we're not just tracking the neutrons in
+
+ align:start position:0%
+we're not just tracking the neutrons in
+ 
+
+ align:start position:0%
+we're not just tracking the neutrons in
+this little energy group de Direction D
+
+ align:start position:0%
+this little energy group de Direction D
+ 
+
+ align:start position:0%
+this little energy group de Direction D
+Omega and volume DV you actually have to
+
+ align:start position:0%
+Omega and volume DV you actually have to
+ 
+
+ align:start position:0%
+Omega and volume DV you actually have to
+know what's the population of neutrons
+
+ align:start position:0%
+know what's the population of neutrons
+ 
+
+ align:start position:0%
+know what's the population of neutrons
+at every single group because you might
+
+ align:start position:0%
+at every single group because you might
+ 
+
+ align:start position:0%
+at every single group because you might
+have a neutron at a higher energy level
+
+ align:start position:0%
+have a neutron at a higher energy level
+ 
+
+ align:start position:0%
+have a neutron at a higher energy level
+that undergoes scattering from some
+
+ align:start position:0%
+that undergoes scattering from some
+ 
+
+ align:start position:0%
+that undergoes scattering from some
+different energy E Prime into our energy
+
+ align:start position:0%
+different energy E Prime into our energy
+ 
+
+ align:start position:0%
+different energy E Prime into our energy
+group so continuing with our gigantic
+
+ align:start position:0%
+group so continuing with our gigantic
+ 
+
+ align:start position:0%
+group so continuing with our gigantic
+list of variables we're going to call e
+
+ align:start position:0%
+list of variables we're going to call e
+ 
+
+ align:start position:0%
+list of variables we're going to call e
+is I'll say our energy and this vector
+
+ align:start position:0%
+is I'll say our energy and this vector
+ 
+
+ align:start position:0%
+is I'll say our energy and this vector
+Omega is our direction the one that
+
+ align:start position:0%
+Omega is our direction the one that
+ 
+
+ align:start position:0%
+Omega is our direction the one that
+we're tracking and a prime is going to
+
+ align:start position:0%
+we're tracking and a prime is going to
+ 
+
+ align:start position:0%
+we're tracking and a prime is going to
+be some other energy and Omega vector
+
+ align:start position:0%
+be some other energy and Omega vector
+ 
+
+ align:start position:0%
+be some other energy and Omega vector
+prime is going to be some coming from
+
+ align:start position:0%
+prime is going to be some coming from
+ 
+
+ align:start position:0%
+prime is going to be some coming from
+some other direction and like Luke said
+
+ align:start position:0%
+some other direction and like Luke said
+ 
+
+ align:start position:0%
+some other direction and like Luke said
+this this is what we would refer to as
+
+ align:start position:0%
+this this is what we would refer to as
+ 
+
+ align:start position:0%
+this this is what we would refer to as
+in scattering
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which means some neutron comes that was
+
+ align:start position:0%
+which means some neutron comes that was
+ 
+
+ align:start position:0%
+which means some neutron comes that was
+going in a different direction that did
+
+ align:start position:0%
+going in a different direction that did
+ 
+
+ align:start position:0%
+going in a different direction that did
+have a different energy and has now
+
+ align:start position:0%
+have a different energy and has now
+ 
+
+ align:start position:0%
+have a different energy and has now
+entered into the single group that we're
+
+ align:start position:0%
+entered into the single group that we're
+ 
+
+ align:start position:0%
+entered into the single group that we're
+tracking eventually we're going to
+
+ align:start position:0%
+tracking eventually we're going to
+ 
+
+ align:start position:0%
+tracking eventually we're going to
+integrate over all energies to track all
+
+ align:start position:0%
+integrate over all energies to track all
+ 
+
+ align:start position:0%
+integrate over all energies to track all
+energy groups so that's where we're
+
+ align:start position:0%
+energy groups so that's where we're
+ 
+
+ align:start position:0%
+energy groups so that's where we're
+going and there's one more term that I
+
+ align:start position:0%
+going and there's one more term that I
+ 
+
+ align:start position:0%
+going and there's one more term that I
+want to introduce right now it's what's
+
+ align:start position:0%
+want to introduce right now it's what's
+ 
+
+ align:start position:0%
+want to introduce right now it's what's
+called the scattering kernel don't ask
+
+ align:start position:0%
+called the scattering kernel don't ask
+ 
+
+ align:start position:0%
+called the scattering kernel don't ask
+me why it's called kernel but this is
+
+ align:start position:0%
+me why it's called kernel but this is
+ 
+
+ align:start position:0%
+me why it's called kernel but this is
+just the terminology I want you guys to
+
+ align:start position:0%
+just the terminology I want you guys to
+ 
+
+ align:start position:0%
+just the terminology I want you guys to
+get used to and it's going to be some
+
+ align:start position:0%
+get used to and it's going to be some
+ 
+
+ align:start position:0%
+get used to and it's going to be some
+sort of probability function where a
+
+ align:start position:0%
+sort of probability function where a
+ 
+
+ align:start position:0%
+sort of probability function where a
+neutron starts off at a different energy
+
+ align:start position:0%
+neutron starts off at a different energy
+ 
+
+ align:start position:0%
+neutron starts off at a different energy
+e Prime and in a different direction
+
+ align:start position:0%
+e Prime and in a different direction
+ 
+
+ align:start position:0%
+e Prime and in a different direction
+Omega Prime and it enters into our group
+
+ align:start position:0%
+Omega Prime and it enters into our group
+ 
+
+ align:start position:0%
+Omega Prime and it enters into our group
+energy E and Direction Omega right now
+
+ align:start position:0%
+energy E and Direction Omega right now
+ 
+
+ align:start position:0%
+energy E and Direction Omega right now
+we'll leave it as a highly general
+
+ align:start position:0%
+we'll leave it as a highly general
+ 
+
+ align:start position:0%
+we'll leave it as a highly general
+function what we're gonna find later is
+
+ align:start position:0%
+function what we're gonna find later is
+ 
+
+ align:start position:0%
+function what we're gonna find later is
+there's just some sort of simple line to
+
+ align:start position:0%
+there's just some sort of simple line to
+ 
+
+ align:start position:0%
+there's just some sort of simple line to
+it if you guys remember if some neutron
+
+ align:start position:0%
+it if you guys remember if some neutron
+ 
+
+ align:start position:0%
+it if you guys remember if some neutron
+starts off let's say probability of
+
+ align:start position:0%
+starts off let's say probability of
+ 
+
+ align:start position:0%
+starts off let's say probability of
+entering it to some energy group if you
+
+ align:start position:0%
+entering it to some energy group if you
+ 
+
+ align:start position:0%
+entering it to some energy group if you
+notice if you remember from last time
+
+ align:start position:0%
+notice if you remember from last time
+ 
+
+ align:start position:0%
+notice if you remember from last time
+the neutron when it undergoes any sort
+
+ align:start position:0%
+the neutron when it undergoes any sort
+ 
+
+ align:start position:0%
+the neutron when it undergoes any sort
+of scattering reaction can end up with
+
+ align:start position:0%
+of scattering reaction can end up with
+ 
+
+ align:start position:0%
+of scattering reaction can end up with
+any energy between its original energy
+
+ align:start position:0%
+any energy between its original energy
+ 
+
+ align:start position:0%
+any energy between its original energy
+for the case of theta equals zero and
+
+ align:start position:0%
+for the case of theta equals zero and
+ 
+
+ align:start position:0%
+for the case of theta equals zero and
+this parameter alpha energy for the case
+
+ align:start position:0%
+this parameter alpha energy for the case
+ 
+
+ align:start position:0%
+this parameter alpha energy for the case
+theta equals PI where alpha is a minus 1
+
+ align:start position:0%
+theta equals PI where alpha is a minus 1
+ 
+
+ align:start position:0%
+theta equals PI where alpha is a minus 1
+over a plus 1 squared where a is the
+
+ align:start position:0%
+over a plus 1 squared where a is the
+ 
+
+ align:start position:0%
+over a plus 1 squared where a is the
+atomic mass you guys remember this from
+
+ align:start position:0%
+atomic mass you guys remember this from
+ 
+
+ align:start position:0%
+atomic mass you guys remember this from
+back in the Q equation days when we were
+
+ align:start position:0%
+back in the Q equation days when we were
+ 
+
+ align:start position:0%
+back in the Q equation days when we were
+finding out what's the probability that
+
+ align:start position:0%
+finding out what's the probability that
+ 
+
+ align:start position:0%
+finding out what's the probability that
+a neutron coming in with energy e
+
+ align:start position:0%
+a neutron coming in with energy e
+ 
+
+ align:start position:0%
+a neutron coming in with energy e
+ends up at any energy e prime what this
+
+ align:start position:0%
+ends up at any energy e prime what this
+ 
+
+ align:start position:0%
+ends up at any energy e prime what this
+actually I'll just write this as the
+
+ align:start position:0%
+actually I'll just write this as the
+ 
+
+ align:start position:0%
+actually I'll just write this as the
+scattering kernel what it ends up
+
+ align:start position:0%
+scattering kernel what it ends up
+ 
+
+ align:start position:0%
+scattering kernel what it ends up
+looking like in most cases is just a
+
+ align:start position:0%
+looking like in most cases is just a
+ 
+
+ align:start position:0%
+looking like in most cases is just a
+flat line there's an equal probability
+
+ align:start position:0%
+flat line there's an equal probability
+ 
+
+ align:start position:0%
+flat line there's an equal probability
+of the neutron ending up anywhere
+
+ align:start position:0%
+of the neutron ending up anywhere
+ 
+
+ align:start position:0%
+of the neutron ending up anywhere
+between energy E and anywhere between
+
+ align:start position:0%
+between energy E and anywhere between
+ 
+
+ align:start position:0%
+between energy E and anywhere between
+energy alpha e it's actually a pretty
+
+ align:start position:0%
+energy alpha e it's actually a pretty
+ 
+
+ align:start position:0%
+energy alpha e it's actually a pretty
+simple function it's just a constant
+
+ align:start position:0%
+simple function it's just a constant
+ 
+
+ align:start position:0%
+simple function it's just a constant
+value here and zero everywhere else what
+
+ align:start position:0%
+value here and zero everywhere else what
+ 
+
+ align:start position:0%
+value here and zero everywhere else what
+that means is that if let's say a
+
+ align:start position:0%
+that means is that if let's say a
+ 
+
+ align:start position:0%
+that means is that if let's say a
+neutron hits a uranium atom there's no
+
+ align:start position:0%
+neutron hits a uranium atom there's no
+ 
+
+ align:start position:0%
+neutron hits a uranium atom there's no
+way in hell that it can transfer all of
+
+ align:start position:0%
+way in hell that it can transfer all of
+ 
+
+ align:start position:0%
+way in hell that it can transfer all of
+its energy to a uranium atom because of
+
+ align:start position:0%
+its energy to a uranium atom because of
+ 
+
+ align:start position:0%
+its energy to a uranium atom because of
+conservation and energy and conservation
+
+ align:start position:0%
+conservation and energy and conservation
+ 
+
+ align:start position:0%
+conservation and energy and conservation
+of energy and momentum like we've been
+
+ align:start position:0%
+of energy and momentum like we've been
+ 
+
+ align:start position:0%
+of energy and momentum like we've been
+harping on for kind of this whole class
+
+ align:start position:0%
+harping on for kind of this whole class
+ 
+
+ align:start position:0%
+harping on for kind of this whole class
+what's the only time that this alpha e
+
+ align:start position:0%
+what's the only time that this alpha e
+ 
+
+ align:start position:0%
+what's the only time that this alpha e
+could actually extend all the way to
+
+ align:start position:0%
+could actually extend all the way to
+ 
+
+ align:start position:0%
+could actually extend all the way to
+zero what case would that be you're
+
+ align:start position:0%
+zero what case would that be you're
+ 
+
+ align:start position:0%
+zero what case would that be you're
+hitting another neutron which as we said
+
+ align:start position:0%
+hitting another neutron which as we said
+ 
+
+ align:start position:0%
+hitting another neutron which as we said
+is a very rare event that is true or
+
+ align:start position:0%
+is a very rare event that is true or
+ 
+
+ align:start position:0%
+is a very rare event that is true or
+what else could you be hitting a proton
+
+ align:start position:0%
+what else could you be hitting a proton
+ 
+
+ align:start position:0%
+what else could you be hitting a proton
+hydrogen that's right so it can only be
+
+ align:start position:0%
+hydrogen that's right so it can only be
+ 
+
+ align:start position:0%
+hydrogen that's right so it can only be
+let's say you can only have the
+
+ align:start position:0%
+let's say you can only have the
+ 
+
+ align:start position:0%
+let's say you can only have the
+probability of the neutron coming ending
+
+ align:start position:0%
+probability of the neutron coming ending
+ 
+
+ align:start position:0%
+probability of the neutron coming ending
+up with any energy for the case of
+
+ align:start position:0%
+up with any energy for the case of
+ 
+
+ align:start position:0%
+up with any energy for the case of
+hydrogen incidentally this is why we
+
+ align:start position:0%
+hydrogen incidentally this is why we
+ 
+
+ align:start position:0%
+hydrogen incidentally this is why we
+fill light water reactors with hydrogen
+
+ align:start position:0%
+fill light water reactors with hydrogen
+ 
+
+ align:start position:0%
+fill light water reactors with hydrogen
+the goal is to get the neutrons as slow
+
+ align:start position:0%
+the goal is to get the neutrons as slow
+ 
+
+ align:start position:0%
+the goal is to get the neutrons as slow
+as possible as quick as possible
+
+ align:start position:0%
+as possible as quick as possible
+ 
+
+ align:start position:0%
+as possible as quick as possible
+interesting sentence to say there right
+
+ align:start position:0%
+interesting sentence to say there right
+ 
+
+ align:start position:0%
+interesting sentence to say there right
+we want the neutrons to be as low energy
+
+ align:start position:0%
+we want the neutrons to be as low energy
+ 
+
+ align:start position:0%
+we want the neutrons to be as low energy
+as possible as rapidly as possible and
+
+ align:start position:0%
+as possible as rapidly as possible and
+ 
+
+ align:start position:0%
+as possible as rapidly as possible and
+the best way to do that is to fill the
+
+ align:start position:0%
+the best way to do that is to fill the
+ 
+
+ align:start position:0%
+the best way to do that is to fill the
+reactor with hydrogen because then any
+
+ align:start position:0%
+reactor with hydrogen because then any
+ 
+
+ align:start position:0%
+reactor with hydrogen because then any
+collision could in theory get the
+
+ align:start position:0%
+collision could in theory get the
+ 
+
+ align:start position:0%
+collision could in theory get the
+neutron down to zero energy without
+
+ align:start position:0%
+neutron down to zero energy without
+ 
+
+ align:start position:0%
+neutron down to zero energy without
+water or something with the same mass as
+
+ align:start position:0%
+water or something with the same mass as
+ 
+
+ align:start position:0%
+water or something with the same mass as
+a neutron like another Neutron there's
+
+ align:start position:0%
+a neutron like another Neutron there's
+ 
+
+ align:start position:0%
+a neutron like another Neutron there's
+no way that that Neutron can slow down
+
+ align:start position:0%
+no way that that Neutron can slow down
+ 
+
+ align:start position:0%
+no way that that Neutron can slow down
+by very much so even though we're gonna
+
+ align:start position:0%
+by very much so even though we're gonna
+ 
+
+ align:start position:0%
+by very much so even though we're gonna
+keep it as this generalized function
+
+ align:start position:0%
+keep it as this generalized function
+ 
+
+ align:start position:0%
+keep it as this generalized function
+note that in reality it's this pretty
+
+ align:start position:0%
+note that in reality it's this pretty
+ 
+
+ align:start position:0%
+note that in reality it's this pretty
+simple function it changes a little bit
+
+ align:start position:0%
+simple function it changes a little bit
+ 
+
+ align:start position:0%
+simple function it changes a little bit
+as there can be a forward scattering
+
+ align:start position:0%
+as there can be a forward scattering
+ 
+
+ align:start position:0%
+as there can be a forward scattering
+bias for some Neutron reactions but we
+
+ align:start position:0%
+bias for some Neutron reactions but we
+ 
+
+ align:start position:0%
+bias for some Neutron reactions but we
+are not going to deal with that this
+
+ align:start position:0%
+are not going to deal with that this
+ 
+
+ align:start position:0%
+are not going to deal with that this
+year you will deal with that next year
+
+ align:start position:0%
+year you will deal with that next year
+ 
+
+ align:start position:0%
+year you will deal with that next year
+in 22:05 so I've been saying a lot oh
+
+ align:start position:0%
+in 22:05 so I've been saying a lot oh
+ 
+
+ align:start position:0%
+in 22:05 so I've been saying a lot oh
+well we're not gonna go into this topic
+
+ align:start position:0%
+well we're not gonna go into this topic
+ 
+
+ align:start position:0%
+well we're not gonna go into this topic
+because if you're gonna see it in 2202
+
+ align:start position:0%
+because if you're gonna see it in 2202
+ 
+
+ align:start position:0%
+because if you're gonna see it in 2202
+which is quantum now I switch gears to
+
+ align:start position:0%
+which is quantum now I switch gears to
+ 
+
+ align:start position:0%
+which is quantum now I switch gears to
+say we're not going to go into the way
+
+ align:start position:0%
+say we're not going to go into the way
+ 
+
+ align:start position:0%
+say we're not going to go into the way
+this function changes cuz you'll see it
+
+ align:start position:0%
+this function changes cuz you'll see it
+ 
+
+ align:start position:0%
+this function changes cuz you'll see it
+next year in 2205 which is Neutron
+
+ align:start position:0%
+next year in 2205 which is Neutron
+ 
+
+ align:start position:0%
+next year in 2205 which is Neutron
+physics but for now I want you to be
+
+ align:start position:0%
+physics but for now I want you to be
+ 
+
+ align:start position:0%
+physics but for now I want you to be
+prepared for 2205 so we'll put on in
+
+ align:start position:0%
+prepared for 2205 so we'll put on in
+ 
+
+ align:start position:0%
+prepared for 2205 so we'll put on in
+scattering as one of our gains
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there's a last one I want to make you
+
+ align:start position:0%
+there's a last one I want to make you
+ 
+
+ align:start position:0%
+there's a last one I want to make you
+aware of we very briefly touched upon it
+
+ align:start position:0%
+aware of we very briefly touched upon it
+ 
+
+ align:start position:0%
+aware of we very briefly touched upon it
+but I wouldn't be surprised if no one
+
+ align:start position:0%
+but I wouldn't be surprised if no one
+ 
+
+ align:start position:0%
+but I wouldn't be surprised if no one
+remembers because it was for like ten
+
+ align:start position:0%
+remembers because it was for like ten
+ 
+
+ align:start position:0%
+remembers because it was for like ten
+seconds it's what's called photo fission
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what this means is you have some
+
+ align:start position:0%
+what this means is you have some
+ 
+
+ align:start position:0%
+what this means is you have some
+reaction that would in comes a gamma and
+
+ align:start position:0%
+reaction that would in comes a gamma and
+ 
+
+ align:start position:0%
+reaction that would in comes a gamma and
+out goes fission this actually does
+
+ align:start position:0%
+out goes fission this actually does
+ 
+
+ align:start position:0%
+out goes fission this actually does
+start to happen around three or four MeV
+
+ align:start position:0%
+start to happen around three or four MeV
+ 
+
+ align:start position:0%
+start to happen around three or four MeV
+for isotopes like uranium-235 and in our
+
+ align:start position:0%
+for isotopes like uranium-235 and in our
+ 
+
+ align:start position:0%
+for isotopes like uranium-235 and in our
+reactor whatever whatever shape we
+
+ align:start position:0%
+reactor whatever whatever shape we
+ 
+
+ align:start position:0%
+reactor whatever whatever shape we
+decide it is there are tons of gamma
+
+ align:start position:0%
+decide it is there are tons of gamma
+ 
+
+ align:start position:0%
+decide it is there are tons of gamma
+rays flying about in all directions at
+
+ align:start position:0%
+rays flying about in all directions at
+ 
+
+ align:start position:0%
+rays flying about in all directions at
+very high energy does anyone remember
+
+ align:start position:0%
+very high energy does anyone remember
+ 
+
+ align:start position:0%
+very high energy does anyone remember
+where they come from anyone remember the
+
+ align:start position:0%
+where they come from anyone remember the
+ 
+
+ align:start position:0%
+where they come from anyone remember the
+fission timeline that we drew on Friday
+
+ align:start position:0%
+fission timeline that we drew on Friday
+ 
+
+ align:start position:0%
+fission timeline that we drew on Friday
+so what we said there was right away
+
+ align:start position:0%
+so what we said there was right away
+ 
+
+ align:start position:0%
+so what we said there was right away
+let's say fission happens and almost
+
+ align:start position:0%
+let's say fission happens and almost
+ 
+
+ align:start position:0%
+let's say fission happens and almost
+instantly you get your fission product
+
+ align:start position:0%
+instantly you get your fission product
+ 
+
+ align:start position:0%
+instantly you get your fission product
+one and fission product two and they
+
+ align:start position:0%
+one and fission product two and they
+ 
+
+ align:start position:0%
+one and fission product two and they
+move around for a little while
+
+ align:start position:0%
+move around for a little while
+ 
+
+ align:start position:0%
+move around for a little while
+and then some of them will emit some
+
+ align:start position:0%
+and then some of them will emit some
+ 
+
+ align:start position:0%
+and then some of them will emit some
+neutrons and then some of them will
+
+ align:start position:0%
+neutrons and then some of them will
+ 
+
+ align:start position:0%
+neutrons and then some of them will
+start to emit gamma rays betas and
+
+ align:start position:0%
+start to emit gamma rays betas and
+ 
+
+ align:start position:0%
+start to emit gamma rays betas and
+whatever else they're gonna do until
+
+ align:start position:0%
+whatever else they're gonna do until
+ 
+
+ align:start position:0%
+whatever else they're gonna do until
+they finally lose all their kinetic
+
+ align:start position:0%
+they finally lose all their kinetic
+ 
+
+ align:start position:0%
+they finally lose all their kinetic
+energy and stop in the surrounding fuel
+
+ align:start position:0%
+energy and stop in the surrounding fuel
+ 
+
+ align:start position:0%
+energy and stop in the surrounding fuel
+creating the heat that actually powers
+
+ align:start position:0%
+creating the heat that actually powers
+ 
+
+ align:start position:0%
+creating the heat that actually powers
+the turbine and makes steam to make
+
+ align:start position:0%
+the turbine and makes steam to make
+ 
+
+ align:start position:0%
+the turbine and makes steam to make
+electricity and so it's from these
+
+ align:start position:0%
+electricity and so it's from these
+ 
+
+ align:start position:0%
+electricity and so it's from these
+gammas as well as any of the gammas from
+
+ align:start position:0%
+gammas as well as any of the gammas from
+ 
+
+ align:start position:0%
+gammas as well as any of the gammas from
+the decay products of the fission
+
+ align:start position:0%
+the decay products of the fission
+ 
+
+ align:start position:0%
+the decay products of the fission
+products that lead to a huge flux of
+
+ align:start position:0%
+products that lead to a huge flux of
+ 
+
+ align:start position:0%
+products that lead to a huge flux of
+gamma rays firing out from all sides in
+
+ align:start position:0%
+gamma rays firing out from all sides in
+ 
+
+ align:start position:0%
+gamma rays firing out from all sides in
+the reactor that's one of the main
+
+ align:start position:0%
+the reactor that's one of the main
+ 
+
+ align:start position:0%
+the reactor that's one of the main
+things that you actually have to shield
+
+ align:start position:0%
+things that you actually have to shield
+ 
+
+ align:start position:0%
+things that you actually have to shield
+in a nuclear reactor since we talked
+
+ align:start position:0%
+in a nuclear reactor since we talked
+ 
+
+ align:start position:0%
+in a nuclear reactor since we talked
+about all sorts of different shielding
+
+ align:start position:0%
+about all sorts of different shielding
+ 
+
+ align:start position:0%
+about all sorts of different shielding
+and all sorts of ways that you have to
+
+ align:start position:0%
+and all sorts of ways that you have to
+ 
+
+ align:start position:0%
+and all sorts of ways that you have to
+shield things you know from seeing the
+
+ align:start position:0%
+shield things you know from seeing the
+ 
+
+ align:start position:0%
+shield things you know from seeing the
+MIT reactor which you all did that
+
+ align:start position:0%
+MIT reactor which you all did that
+ 
+
+ align:start position:0%
+MIT reactor which you all did that
+there's like six feet of lead and
+
+ align:start position:0%
+there's like six feet of lead and
+ 
+
+ align:start position:0%
+there's like six feet of lead and
+concrete shielding around the reactor
+
+ align:start position:0%
+concrete shielding around the reactor
+ 
+
+ align:start position:0%
+concrete shielding around the reactor
+it's not there to shield the alphas and
+
+ align:start position:0%
+it's not there to shield the alphas and
+ 
+
+ align:start position:0%
+it's not there to shield the alphas and
+the beta's because those don't really
+
+ align:start position:0%
+the beta's because those don't really
+ 
+
+ align:start position:0%
+the beta's because those don't really
+make it out of the water it's not there
+
+ align:start position:0%
+make it out of the water it's not there
+ 
+
+ align:start position:0%
+make it out of the water it's not there
+to shield the soft x-rays that betas
+
+ align:start position:0%
+to shield the soft x-rays that betas
+ 
+
+ align:start position:0%
+to shield the soft x-rays that betas
+make from bremsstrahlung
+
+ align:start position:0%
+make from bremsstrahlung
+ 
+
+ align:start position:0%
+make from bremsstrahlung
+it's also not there to shield the
+
+ align:start position:0%
+it's also not there to shield the
+ 
+
+ align:start position:0%
+it's also not there to shield the
+neutrons because the neutrons don't
+
+ align:start position:0%
+neutrons because the neutrons don't
+ 
+
+ align:start position:0%
+neutrons because the neutrons don't
+really get out they bounce around or get
+
+ align:start position:0%
+really get out they bounce around or get
+ 
+
+ align:start position:0%
+really get out they bounce around or get
+absorbed in the water the fuel the
+
+ align:start position:0%
+absorbed in the water the fuel the
+ 
+
+ align:start position:0%
+absorbed in the water the fuel the
+reflector it's there to shield the
+
+ align:start position:0%
+reflector it's there to shield the
+ 
+
+ align:start position:0%
+reflector it's there to shield the
+high-energy gamma rays because the only
+
+ align:start position:0%
+high-energy gamma rays because the only
+ 
+
+ align:start position:0%
+high-energy gamma rays because the only
+thing that stops high-energy gamma rays
+
+ align:start position:0%
+thing that stops high-energy gamma rays
+ 
+
+ align:start position:0%
+thing that stops high-energy gamma rays
+is lots of mass in between the source
+
+ align:start position:0%
+is lots of mass in between the source
+ 
+
+ align:start position:0%
+is lots of mass in between the source
+and you so we know there's tons of
+
+ align:start position:0%
+and you so we know there's tons of
+ 
+
+ align:start position:0%
+and you so we know there's tons of
+gammas all about so let's say there's
+
+ align:start position:0%
+gammas all about so let's say there's
+ 
+
+ align:start position:0%
+gammas all about so let's say there's
+also going to be some gamma ray flux
+
+ align:start position:0%
+also going to be some gamma ray flux
+ 
+
+ align:start position:0%
+also going to be some gamma ray flux
+there'll be some gamma ray energy and
+
+ align:start position:0%
+there'll be some gamma ray energy and
+ 
+
+ align:start position:0%
+there'll be some gamma ray energy and
+there'll be some cross-section for photo
+
+ align:start position:0%
+there'll be some cross-section for photo
+ 
+
+ align:start position:0%
+there'll be some cross-section for photo
+fission as a function of the incoming
+
+ align:start position:0%
+fission as a function of the incoming
+ 
+
+ align:start position:0%
+fission as a function of the incoming
+gamma ray energy spectrum now I'm adding
+
+ align:start position:0%
+gamma ray energy spectrum now I'm adding
+ 
+
+ align:start position:0%
+gamma ray energy spectrum now I'm adding
+terms to the ones that you'll see in the
+
+ align:start position:0%
+terms to the ones that you'll see in the
+ 
+
+ align:start position:0%
+terms to the ones that you'll see in the
+reading because drawing them out in math
+
+ align:start position:0%
+reading because drawing them out in math
+ 
+
+ align:start position:0%
+reading because drawing them out in math
+is actually fairly instructive they all
+
+ align:start position:0%
+is actually fairly instructive they all
+ 
+
+ align:start position:0%
+is actually fairly instructive they all
+follow the same pattern so instead of
+
+ align:start position:0%
+follow the same pattern so instead of
+ 
+
+ align:start position:0%
+follow the same pattern so instead of
+just showing you one of each and saying
+
+ align:start position:0%
+just showing you one of each and saying
+ 
+
+ align:start position:0%
+just showing you one of each and saying
+memorize we'll develop a whole lot of
+
+ align:start position:0%
+memorize we'll develop a whole lot of
+ 
+
+ align:start position:0%
+memorize we'll develop a whole lot of
+these and you'll find out that they all
+
+ align:start position:0%
+these and you'll find out that they all
+ 
+
+ align:start position:0%
+these and you'll find out that they all
+actually look almost the same anyone
+
+ align:start position:0%
+actually look almost the same anyone
+ 
+
+ align:start position:0%
+actually look almost the same anyone
+else can anyone else think of any
+
+ align:start position:0%
+else can anyone else think of any
+ 
+
+ align:start position:0%
+else can anyone else think of any
+possible gains of neutrons where else
+
+ align:start position:0%
+possible gains of neutrons where else
+ 
+
+ align:start position:0%
+possible gains of neutrons where else
+could they come from yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the neutron birth spectrum is
+
+ align:start position:0%
+so the neutron birth spectrum is
+ 
+
+ align:start position:0%
+so the neutron birth spectrum is
+included in fission so our new is in
+
+ align:start position:0%
+included in fission so our new is in
+ 
+
+ align:start position:0%
+included in fission so our new is in
+there our kya V is in there and that's a
+
+ align:start position:0%
+there our kya V is in there and that's a
+ 
+
+ align:start position:0%
+there our kya V is in there and that's a
+new of II that's all accounted for in
+
+ align:start position:0%
+new of II that's all accounted for in
+ 
+
+ align:start position:0%
+new of II that's all accounted for in
+the fission term and we'll see how we
+
+ align:start position:0%
+the fission term and we'll see how we
+ 
+
+ align:start position:0%
+the fission term and we'll see how we
+put that together to math and if no one
+
+ align:start position:0%
+put that together to math and if no one
+ 
+
+ align:start position:0%
+put that together to math and if no one
+else has any ideas that's good because
+
+ align:start position:0%
+else has any ideas that's good because
+ 
+
+ align:start position:0%
+else has any ideas that's good because
+neither do I now what about the lost
+
+ align:start position:0%
+neither do I now what about the lost
+ 
+
+ align:start position:0%
+neither do I now what about the lost
+terms there aren't too many of these as
+
+ align:start position:0%
+terms there aren't too many of these as
+ 
+
+ align:start position:0%
+terms there aren't too many of these as
+long as you lump them correctly so what
+
+ align:start position:0%
+long as you lump them correctly so what
+ 
+
+ align:start position:0%
+long as you lump them correctly so what
+sort of ways could neutrons be lost from
+
+ align:start position:0%
+sort of ways could neutrons be lost from
+ 
+
+ align:start position:0%
+sort of ways could neutrons be lost from
+our energy group yep
+
+ align:start position:0%
+our energy group yep
+ 
+
+ align:start position:0%
+our energy group yep
+scatter out yep they can undergo any
+
+ align:start position:0%
+scatter out yep they can undergo any
+ 
+
+ align:start position:0%
+scatter out yep they can undergo any
+kind of scattering reaction and they
+
+ align:start position:0%
+kind of scattering reaction and they
+ 
+
+ align:start position:0%
+kind of scattering reaction and they
+will probably change direction and
+
+ align:start position:0%
+will probably change direction and
+ 
+
+ align:start position:0%
+will probably change direction and
+energy what else well we've got to lift
+
+ align:start position:0%
+energy what else well we've got to lift
+ 
+
+ align:start position:0%
+energy what else well we've got to lift
+up on the board right there right
+
+ align:start position:0%
+up on the board right there right
+ 
+
+ align:start position:0%
+up on the board right there right
+capture decision because in order to
+
+ align:start position:0%
+capture decision because in order to
+ 
+
+ align:start position:0%
+capture decision because in order to
+undergo fission you actually have to
+
+ align:start position:0%
+undergo fission you actually have to
+ 
+
+ align:start position:0%
+undergo fission you actually have to
+lose a neutron and so on and so on and
+
+ align:start position:0%
+lose a neutron and so on and so on and
+ 
+
+ align:start position:0%
+lose a neutron and so on and so on and
+so on what I want to do to simplify
+
+ align:start position:0%
+so on what I want to do to simplify
+ 
+
+ align:start position:0%
+so on what I want to do to simplify
+things is this it's a lot simpler just
+
+ align:start position:0%
+things is this it's a lot simpler just
+ 
+
+ align:start position:0%
+things is this it's a lot simpler just
+to track the total cross-section the
+
+ align:start position:0%
+to track the total cross-section the
+ 
+
+ align:start position:0%
+to track the total cross-section the
+probability of any interaction at all
+
+ align:start position:0%
+probability of any interaction at all
+ 
+
+ align:start position:0%
+probability of any interaction at all
+whatsoever because any interaction will
+
+ align:start position:0%
+whatsoever because any interaction will
+ 
+
+ align:start position:0%
+whatsoever because any interaction will
+cause the neutron to either change
+
+ align:start position:0%
+cause the neutron to either change
+ 
+
+ align:start position:0%
+cause the neutron to either change
+energy and angle or disappear even if it
+
+ align:start position:0%
+energy and angle or disappear even if it
+ 
+
+ align:start position:0%
+energy and angle or disappear even if it
+makes some other ones so we can simplify
+
+ align:start position:0%
+makes some other ones so we can simplify
+ 
+
+ align:start position:0%
+makes some other ones so we can simplify
+this to just the total cross-section
+
+ align:start position:0%
+this to just the total cross-section
+ 
+
+ align:start position:0%
+this to just the total cross-section
+term and there's only one other way that
+
+ align:start position:0%
+term and there's only one other way that
+ 
+
+ align:start position:0%
+term and there's only one other way that
+neutrons can leave our energy angle and
+
+ align:start position:0%
+neutrons can leave our energy angle and
+ 
+
+ align:start position:0%
+neutrons can leave our energy angle and
+volume group what would that be so any
+
+ align:start position:0%
+volume group what would that be so any
+ 
+
+ align:start position:0%
+volume group what would that be so any
+reaction takes care of energy and angle
+
+ align:start position:0%
+reaction takes care of energy and angle
+ 
+
+ align:start position:0%
+reaction takes care of energy and angle
+what about volume how did neutrons leave
+
+ align:start position:0%
+what about volume how did neutrons leave
+ 
+
+ align:start position:0%
+what about volume how did neutrons leave
+the control volume
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's simpler than it may sound they just
+
+ align:start position:0%
+it's simpler than it may sound they just
+ 
+
+ align:start position:0%
+it's simpler than it may sound they just
+go they just move the neutrons are
+
+ align:start position:0%
+go they just move the neutrons are
+ 
+
+ align:start position:0%
+go they just move the neutrons are
+always moving right we'll call that
+
+ align:start position:0%
+always moving right we'll call that
+ 
+
+ align:start position:0%
+always moving right we'll call that
+leakage because every neutrons got a
+
+ align:start position:0%
+leakage because every neutrons got a
+ 
+
+ align:start position:0%
+leakage because every neutrons got a
+speed like we've showed up here where
+
+ align:start position:0%
+speed like we've showed up here where
+ 
+
+ align:start position:0%
+speed like we've showed up here where
+the flux of neutrons the number of
+
+ align:start position:0%
+the flux of neutrons the number of
+ 
+
+ align:start position:0%
+the flux of neutrons the number of
+neutrons moving through some surface per
+
+ align:start position:0%
+neutrons moving through some surface per
+ 
+
+ align:start position:0%
+neutrons moving through some surface per
+second is just their velocity times the
+
+ align:start position:0%
+second is just their velocity times the
+ 
+
+ align:start position:0%
+second is just their velocity times the
+number that are there for there to be a
+
+ align:start position:0%
+number that are there for there to be a
+ 
+
+ align:start position:0%
+number that are there for there to be a
+neutron flux there has to be a velocity
+
+ align:start position:0%
+neutron flux there has to be a velocity
+ 
+
+ align:start position:0%
+neutron flux there has to be a velocity
+which means the neutrons are moving so
+
+ align:start position:0%
+which means the neutrons are moving so
+ 
+
+ align:start position:0%
+which means the neutrons are moving so
+the neutrons even without undergoing any
+
+ align:start position:0%
+the neutrons even without undergoing any
+ 
+
+ align:start position:0%
+the neutrons even without undergoing any
+reaction could just move out of our
+
+ align:start position:0%
+reaction could just move out of our
+ 
+
+ align:start position:0%
+reaction could just move out of our
+control volume and then they're gone and
+
+ align:start position:0%
+control volume and then they're gone and
+ 
+
+ align:start position:0%
+control volume and then they're gone and
+that's all there is for gain and loss
+
+ align:start position:0%
+that's all there is for gain and loss
+ 
+
+ align:start position:0%
+that's all there is for gain and loss
+terms so let's see if we can do this all
+
+ align:start position:0%
+terms so let's see if we can do this all
+ 
+
+ align:start position:0%
+terms so let's see if we can do this all
+on one board I want to start putting
+
+ align:start position:0%
+on one board I want to start putting
+ 
+
+ align:start position:0%
+on one board I want to start putting
+this table right here into math that
+
+ align:start position:0%
+this table right here into math that
+ 
+
+ align:start position:0%
+this table right here into math that
+we'll be able to abstract simplify and
+
+ align:start position:0%
+we'll be able to abstract simplify and
+ 
+
+ align:start position:0%
+we'll be able to abstract simplify and
+then solve but not today not solve today
+
+ align:start position:0%
+then solve but not today not solve today
+ 
+
+ align:start position:0%
+then solve but not today not solve today
+so if we want to track the change in the
+
+ align:start position:0%
+so if we want to track the change in the
+ 
+
+ align:start position:0%
+so if we want to track the change in the
+number of neutrons as a function of time
+
+ align:start position:0%
+number of neutrons as a function of time
+ 
+
+ align:start position:0%
+number of neutrons as a function of time
+let's start writing down the gain terms
+
+ align:start position:0%
+let's start writing down the gain terms
+ 
+
+ align:start position:0%
+let's start writing down the gain terms
+so how do we describe the number of
+
+ align:start position:0%
+so how do we describe the number of
+ 
+
+ align:start position:0%
+so how do we describe the number of
+neutrons produced from fission what sort
+
+ align:start position:0%
+neutrons produced from fission what sort
+ 
+
+ align:start position:0%
+neutrons produced from fission what sort
+of terms do we have to include and Jared
+
+ align:start position:0%
+of terms do we have to include and Jared
+ 
+
+ align:start position:0%
+of terms do we have to include and Jared
+started kicking us off so what would you
+
+ align:start position:0%
+started kicking us off so what would you
+ 
+
+ align:start position:0%
+started kicking us off so what would you
+say
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yep so the neutron birth spectrum
+
+ align:start position:0%
+yep so the neutron birth spectrum
+ 
+
+ align:start position:0%
+yep so the neutron birth spectrum
+there's going to be some probability
+
+ align:start position:0%
+there's going to be some probability
+ 
+
+ align:start position:0%
+there's going to be some probability
+that a neutron is born in our energy
+
+ align:start position:0%
+that a neutron is born in our energy
+ 
+
+ align:start position:0%
+that a neutron is born in our energy
+group e because we're tracking how many
+
+ align:start position:0%
+group e because we're tracking how many
+ 
+
+ align:start position:0%
+group e because we're tracking how many
+neutrons are in our little de energy
+
+ align:start position:0%
+neutrons are in our little de energy
+ 
+
+ align:start position:0%
+neutrons are in our little de energy
+group what else matters in terms of
+
+ align:start position:0%
+group what else matters in terms of
+ 
+
+ align:start position:0%
+group what else matters in terms of
+fission yep number of fissions so if we
+
+ align:start position:0%
+fission yep number of fissions so if we
+ 
+
+ align:start position:0%
+fission yep number of fissions so if we
+want to write number of fission's we
+
+ align:start position:0%
+want to write number of fission's we
+ 
+
+ align:start position:0%
+want to write number of fission's we
+have to write that as a reaction rate so
+
+ align:start position:0%
+have to write that as a reaction rate so
+ 
+
+ align:start position:0%
+have to write that as a reaction rate so
+let's take those two terms right there
+
+ align:start position:0%
+let's take those two terms right there
+ 
+
+ align:start position:0%
+let's take those two terms right there
+so we'll have Sigma fission in this case
+
+ align:start position:0%
+so we'll have Sigma fission in this case
+ 
+
+ align:start position:0%
+so we'll have Sigma fission in this case
+we're gonna write e prime times flux of
+
+ align:start position:0%
+we're gonna write e prime times flux of
+ 
+
+ align:start position:0%
+we're gonna write e prime times flux of
+our e prime Omega prime T why did I
+
+ align:start position:0%
+our e prime Omega prime T why did I
+ 
+
+ align:start position:0%
+our e prime Omega prime T why did I
+write in Omega prime here just from a
+
+ align:start position:0%
+write in Omega prime here just from a
+ 
+
+ align:start position:0%
+write in Omega prime here just from a
+physical reason yeah precisely that's
+
+ align:start position:0%
+physical reason yeah precisely that's
+ 
+
+ align:start position:0%
+physical reason yeah precisely that's
+right so the neutrons are going to be
+
+ align:start position:0%
+right so the neutrons are going to be
+ 
+
+ align:start position:0%
+right so the neutrons are going to be
+produced from some other energy group
+
+ align:start position:0%
+produced from some other energy group
+ 
+
+ align:start position:0%
+produced from some other energy group
+for example the fission birth spectrum
+
+ align:start position:0%
+for example the fission birth spectrum
+ 
+
+ align:start position:0%
+for example the fission birth spectrum
+right here starts out where did it go I
+
+ align:start position:0%
+right here starts out where did it go I
+ 
+
+ align:start position:0%
+right here starts out where did it go I
+knew I drew it somewhere at 1 MeV but
+
+ align:start position:0%
+knew I drew it somewhere at 1 MeV but
+ 
+
+ align:start position:0%
+knew I drew it somewhere at 1 MeV but
+most of the neutrons that cause fission
+
+ align:start position:0%
+most of the neutrons that cause fission
+ 
+
+ align:start position:0%
+most of the neutrons that cause fission
+to happen are way down below one easy so
+
+ align:start position:0%
+to happen are way down below one easy so
+ 
+
+ align:start position:0%
+to happen are way down below one easy so
+it's different energy neutrons that
+
+ align:start position:0%
+it's different energy neutrons that
+ 
+
+ align:start position:0%
+it's different energy neutrons that
+cause neutrons to be born in our energy
+
+ align:start position:0%
+cause neutrons to be born in our energy
+ 
+
+ align:start position:0%
+cause neutrons to be born in our energy
+group that's why we're using a prime and
+
+ align:start position:0%
+group that's why we're using a prime and
+ 
+
+ align:start position:0%
+group that's why we're using a prime and
+not e it's some other energy group and
+
+ align:start position:0%
+not e it's some other energy group and
+ 
+
+ align:start position:0%
+not e it's some other energy group and
+so we also have to account for all
+
+ align:start position:0%
+so we also have to account for all
+ 
+
+ align:start position:0%
+so we also have to account for all
+possible other energy groups so if we
+
+ align:start position:0%
+possible other energy groups so if we
+ 
+
+ align:start position:0%
+possible other energy groups so if we
+want to write this right we'll say this
+
+ align:start position:0%
+want to write this right we'll say this
+ 
+
+ align:start position:0%
+want to write this right we'll say this
+could be as low as 0 evey to our maximum
+
+ align:start position:0%
+could be as low as 0 evey to our maximum
+ 
+
+ align:start position:0%
+could be as low as 0 evey to our maximum
+energy and there's going to be some D
+
+ align:start position:0%
+energy and there's going to be some D
+ 
+
+ align:start position:0%
+energy and there's going to be some D
+Omega prime D prime D V we'll also have
+
+ align:start position:0%
+Omega prime D prime D V we'll also have
+ 
+
+ align:start position:0%
+Omega prime D prime D V we'll also have
+to account for all possible angles and
+
+ align:start position:0%
+to account for all possible angles and
+ 
+
+ align:start position:0%
+to account for all possible angles and
+integrate over our entire volume it's
+
+ align:start position:0%
+integrate over our entire volume it's
+ 
+
+ align:start position:0%
+integrate over our entire volume it's
+get it's going to get it's going to look
+
+ align:start position:0%
+get it's going to get it's going to look
+ 
+
+ align:start position:0%
+get it's going to get it's going to look
+ugly quick but it's all going to be
+
+ align:start position:0%
+ugly quick but it's all going to be
+ 
+
+ align:start position:0%
+ugly quick but it's all going to be
+understandable so what this says is that
+
+ align:start position:0%
+understandable so what this says is that
+ 
+
+ align:start position:0%
+understandable so what this says is that
+we have to account for
+
+ align:start position:0%
+we have to account for
+ 
+
+ align:start position:0%
+we have to account for
+the reaction rate of fission from all
+
+ align:start position:0%
+the reaction rate of fission from all
+ 
+
+ align:start position:0%
+the reaction rate of fission from all
+other energy neutrons inside our volume
+
+ align:start position:0%
+other energy neutrons inside our volume
+ 
+
+ align:start position:0%
+other energy neutrons inside our volume
+from other energies and other angles and
+
+ align:start position:0%
+from other energies and other angles and
+ 
+
+ align:start position:0%
+from other energies and other angles and
+account for every other possible energy
+
+ align:start position:0%
+account for every other possible energy
+ 
+
+ align:start position:0%
+account for every other possible energy
+because they can all make fission happen
+
+ align:start position:0%
+because they can all make fission happen
+ 
+
+ align:start position:0%
+because they can all make fission happen
+what else is missing in terms of
+
+ align:start position:0%
+what else is missing in terms of
+ 
+
+ align:start position:0%
+what else is missing in terms of
+describing the number of neutrons made
+
+ align:start position:0%
+describing the number of neutrons made
+ 
+
+ align:start position:0%
+describing the number of neutrons made
+from fission yep there's the number of
+
+ align:start position:0%
+from fission yep there's the number of
+ 
+
+ align:start position:0%
+from fission yep there's the number of
+neutrons made provision so we have to
+
+ align:start position:0%
+neutrons made provision so we have to
+ 
+
+ align:start position:0%
+neutrons made provision so we have to
+put in our Neutron multiplication factor
+
+ align:start position:0%
+put in our Neutron multiplication factor
+ 
+
+ align:start position:0%
+put in our Neutron multiplication factor
+and in this case normalize think someone
+
+ align:start position:0%
+and in this case normalize think someone
+ 
+
+ align:start position:0%
+and in this case normalize think someone
+had mentioned solid angle we normalize
+
+ align:start position:0%
+had mentioned solid angle we normalize
+ 
+
+ align:start position:0%
+had mentioned solid angle we normalize
+over all possible angles with an over
+
+ align:start position:0%
+over all possible angles with an over
+ 
+
+ align:start position:0%
+over all possible angles with an over
+4pi in there and this right here is the
+
+ align:start position:0%
+4pi in there and this right here is the
+ 
+
+ align:start position:0%
+4pi in there and this right here is the
+fission term so this tells us the number
+
+ align:start position:0%
+fission term so this tells us the number
+ 
+
+ align:start position:0%
+fission term so this tells us the number
+of neutrons gained in terms of a
+
+ align:start position:0%
+of neutrons gained in terms of a
+ 
+
+ align:start position:0%
+of neutrons gained in terms of a
+reaction rate times the number of
+
+ align:start position:0%
+reaction rate times the number of
+ 
+
+ align:start position:0%
+reaction rate times the number of
+neutrons for each of those reactions
+
+ align:start position:0%
+neutrons for each of those reactions
+ 
+
+ align:start position:0%
+neutrons for each of those reactions
+times the probability that there just
+
+ align:start position:0%
+times the probability that there just
+ 
+
+ align:start position:0%
+times the probability that there just
+happened to be born in the energy group
+
+ align:start position:0%
+happened to be born in the energy group
+ 
+
+ align:start position:0%
+happened to be born in the energy group
+that we're tracking so is there any term
+
+ align:start position:0%
+that we're tracking so is there any term
+ 
+
+ align:start position:0%
+that we're tracking so is there any term
+here that's unclear to folks yeah on the
+
+ align:start position:0%
+here that's unclear to folks yeah on the
+ 
+
+ align:start position:0%
+here that's unclear to folks yeah on the
+first integral that's zero electron
+
+ align:start position:0%
+first integral that's zero electron
+ 
+
+ align:start position:0%
+first integral that's zero electron
+volts because supposedly you could have
+
+ align:start position:0%
+volts because supposedly you could have
+ 
+
+ align:start position:0%
+volts because supposedly you could have
+a neutron at zero evey which has a very
+
+ align:start position:0%
+a neutron at zero evey which has a very
+ 
+
+ align:start position:0%
+a neutron at zero evey which has a very
+high cross section of that so it should
+
+ align:start position:0%
+high cross section of that so it should
+ 
+
+ align:start position:0%
+high cross section of that so it should
+probably induce fission in reality there
+
+ align:start position:0%
+probably induce fission in reality there
+ 
+
+ align:start position:0%
+probably induce fission in reality there
+might be some actual minimum temperature
+
+ align:start position:0%
+might be some actual minimum temperature
+ 
+
+ align:start position:0%
+might be some actual minimum temperature
+but there is a nonzero probability that
+
+ align:start position:0%
+but there is a nonzero probability that
+ 
+
+ align:start position:0%
+but there is a nonzero probability that
+you could have a neutron at rest it's
+
+ align:start position:0%
+you could have a neutron at rest it's
+ 
+
+ align:start position:0%
+you could have a neutron at rest it's
+just not very large the top bound is
+
+ align:start position:0%
+just not very large the top bound is
+ 
+
+ align:start position:0%
+just not very large the top bound is
+Emax whatever your maximum Neutron
+
+ align:start position:0%
+Emax whatever your maximum Neutron
+ 
+
+ align:start position:0%
+Emax whatever your maximum Neutron
+energy is this is usually around 10 MeV
+
+ align:start position:0%
+energy is this is usually around 10 MeV
+ 
+
+ align:start position:0%
+energy is this is usually around 10 MeV
+for most fission reactors that Emax is
+
+ align:start position:0%
+for most fission reactors that Emax is
+ 
+
+ align:start position:0%
+for most fission reactors that Emax is
+going to be this point right here the
+
+ align:start position:0%
+going to be this point right here the
+ 
+
+ align:start position:0%
+going to be this point right here the
+highest energy at which neutrons can be
+
+ align:start position:0%
+highest energy at which neutrons can be
+ 
+
+ align:start position:0%
+highest energy at which neutrons can be
+born by any process and so this term
+
+ align:start position:0%
+born by any process and so this term
+ 
+
+ align:start position:0%
+born by any process and so this term
+right here is going to serve as a
+
+ align:start position:0%
+right here is going to serve as a
+ 
+
+ align:start position:0%
+right here is going to serve as a
+template for all the other gain and loss
+
+ align:start position:0%
+template for all the other gain and loss
+ 
+
+ align:start position:0%
+template for all the other gain and loss
+terms so I think this is the hardest one
+
+ align:start position:0%
+terms so I think this is the hardest one
+ 
+
+ align:start position:0%
+terms so I think this is the hardest one
+that we had to develop from the
+
+ align:start position:0%
+that we had to develop from the
+ 
+
+ align:start position:0%
+that we had to develop from the
+beginning
+
+ align:start position:0%
+beginning
+ 
+
+ align:start position:0%
+beginning
+now let's develop the term for let's
+
+ align:start position:0%
+now let's develop the term for let's
+ 
+
+ align:start position:0%
+now let's develop the term for let's
+just go with external sources pretty
+
+ align:start position:0%
+just go with external sources pretty
+ 
+
+ align:start position:0%
+just go with external sources pretty
+easy
+
+ align:start position:0%
+easy
+ 
+
+ align:start position:0%
+easy
+there's gonna be some source making
+
+ align:start position:0%
+there's gonna be some source making
+ 
+
+ align:start position:0%
+there's gonna be some source making
+neutrons it's something that you would
+
+ align:start position:0%
+neutrons it's something that you would
+ 
+
+ align:start position:0%
+neutrons it's something that you would
+just impose like say alright I have a
+
+ align:start position:0%
+just impose like say alright I have a
+ 
+
+ align:start position:0%
+just impose like say alright I have a
+californium source giving off this many
+
+ align:start position:0%
+californium source giving off this many
+ 
+
+ align:start position:0%
+californium source giving off this many
+neutrons well then you know how many
+
+ align:start position:0%
+neutrons well then you know how many
+ 
+
+ align:start position:0%
+neutrons well then you know how many
+neutrons that's giving off and that
+
+ align:start position:0%
+neutrons that's giving off and that
+ 
+
+ align:start position:0%
+neutrons that's giving off and that
+one's done that's easy so we've done
+
+ align:start position:0%
+one's done that's easy so we've done
+ 
+
+ align:start position:0%
+one's done that's easy so we've done
+fission we've done external now that
+
+ align:start position:0%
+fission we've done external now that
+ 
+
+ align:start position:0%
+fission we've done external now that
+we've done fission let's tackle photo
+
+ align:start position:0%
+we've done fission let's tackle photo
+ 
+
+ align:start position:0%
+we've done fission let's tackle photo
+fission so what would the photo fission
+
+ align:start position:0%
+fission so what would the photo fission
+ 
+
+ align:start position:0%
+fission so what would the photo fission
+cross-section look like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's going to look awfully similar so
+
+ align:start position:0%
+it's going to look awfully similar so
+ 
+
+ align:start position:0%
+it's going to look awfully similar so
+what sort of things do you need to know
+
+ align:start position:0%
+what sort of things do you need to know
+ 
+
+ align:start position:0%
+what sort of things do you need to know
+if it's a fission reaction well what do
+
+ align:start position:0%
+if it's a fission reaction well what do
+ 
+
+ align:start position:0%
+if it's a fission reaction well what do
+we have up here to start reading things
+
+ align:start position:0%
+we have up here to start reading things
+ 
+
+ align:start position:0%
+we have up here to start reading things
+off I heard a murmur was that yep so
+
+ align:start position:0%
+off I heard a murmur was that yep so
+ 
+
+ align:start position:0%
+off I heard a murmur was that yep so
+you're gonna have to have some flux in
+
+ align:start position:0%
+you're gonna have to have some flux in
+ 
+
+ align:start position:0%
+you're gonna have to have some flux in
+this case we want to know what's the
+
+ align:start position:0%
+this case we want to know what's the
+ 
+
+ align:start position:0%
+this case we want to know what's the
+flux of gamma rays because photo fission
+
+ align:start position:0%
+flux of gamma rays because photo fission
+ 
+
+ align:start position:0%
+flux of gamma rays because photo fission
+starts off with a gamma that ends up
+
+ align:start position:0%
+starts off with a gamma that ends up
+ 
+
+ align:start position:0%
+starts off with a gamma that ends up
+with a fission and it's also going to be
+
+ align:start position:0%
+with a fission and it's also going to be
+ 
+
+ align:start position:0%
+with a fission and it's also going to be
+in our volume it's going to matter what
+
+ align:start position:0%
+in our volume it's going to matter what
+ 
+
+ align:start position:0%
+in our volume it's going to matter what
+the energy of those gammas is they'll
+
+ align:start position:0%
+the energy of those gammas is they'll
+ 
+
+ align:start position:0%
+the energy of those gammas is they'll
+all be traveling in some direction at
+
+ align:start position:0%
+all be traveling in some direction at
+ 
+
+ align:start position:0%
+all be traveling in some direction at
+some time what else do we need uh yeah
+
+ align:start position:0%
+some time what else do we need uh yeah
+ 
+
+ align:start position:0%
+some time what else do we need uh yeah
+if we're gonna be going over all angles
+
+ align:start position:0%
+if we're gonna be going over all angles
+ 
+
+ align:start position:0%
+if we're gonna be going over all angles
+yep you need the 4pi what else do we
+
+ align:start position:0%
+yep you need the 4pi what else do we
+ 
+
+ align:start position:0%
+yep you need the 4pi what else do we
+have a reaction rate yet no well what's
+
+ align:start position:0%
+have a reaction rate yet no well what's
+ 
+
+ align:start position:0%
+have a reaction rate yet no well what's
+missing that's right
+
+ align:start position:0%
+missing that's right
+ 
+
+ align:start position:0%
+missing that's right
+we need a cross-section and in this case
+
+ align:start position:0%
+we need a cross-section and in this case
+ 
+
+ align:start position:0%
+we need a cross-section and in this case
+instead of just fission or neutron
+
+ align:start position:0%
+instead of just fission or neutron
+ 
+
+ align:start position:0%
+instead of just fission or neutron
+fission we'll put in the gamma fission
+
+ align:start position:0%
+fission we'll put in the gamma fission
+ 
+
+ align:start position:0%
+fission we'll put in the gamma fission
+cross-section and so now we have a
+
+ align:start position:0%
+cross-section and so now we have a
+ 
+
+ align:start position:0%
+cross-section and so now we have a
+reaction rate for a single reaction
+
+ align:start position:0%
+reaction rate for a single reaction
+ 
+
+ align:start position:0%
+reaction rate for a single reaction
+we've got to integrate over all of our
+
+ align:start position:0%
+we've got to integrate over all of our
+ 
+
+ align:start position:0%
+we've got to integrate over all of our
+gamma-ray energies over all angles over
+
+ align:start position:0%
+gamma-ray energies over all angles over
+ 
+
+ align:start position:0%
+gamma-ray energies over all angles over
+our volume what else is missing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+besides our D Omega de gamma D volume it
+
+ align:start position:0%
+besides our D Omega de gamma D volume it
+ 
+
+ align:start position:0%
+besides our D Omega de gamma D volume it
+should look awfully similar because the
+
+ align:start position:0%
+should look awfully similar because the
+ 
+
+ align:start position:0%
+should look awfully similar because the
+terms are basically exactly the same
+
+ align:start position:0%
+terms are basically exactly the same
+ 
+
+ align:start position:0%
+terms are basically exactly the same
+with just different cross sections and
+
+ align:start position:0%
+with just different cross sections and
+ 
+
+ align:start position:0%
+with just different cross sections and
+energies in there so what's missing
+
+ align:start position:0%
+energies in there so what's missing
+ 
+
+ align:start position:0%
+energies in there so what's missing
+between the photo fission and the
+
+ align:start position:0%
+between the photo fission and the
+ 
+
+ align:start position:0%
+between the photo fission and the
+neutron fission one sure there might be
+
+ align:start position:0%
+neutron fission one sure there might be
+ 
+
+ align:start position:0%
+neutron fission one sure there might be
+some different birth spectrum for gammas
+
+ align:start position:0%
+some different birth spectrum for gammas
+ 
+
+ align:start position:0%
+some different birth spectrum for gammas
+and there might be some different
+
+ align:start position:0%
+and there might be some different
+ 
+
+ align:start position:0%
+and there might be some different
+multiplication factor for gammas between
+
+ align:start position:0%
+multiplication factor for gammas between
+ 
+
+ align:start position:0%
+multiplication factor for gammas between
+neutron fission and photo fission but
+
+ align:start position:0%
+neutron fission and photo fission but
+ 
+
+ align:start position:0%
+neutron fission and photo fission but
+these terms should look exactly the same
+
+ align:start position:0%
+these terms should look exactly the same
+ 
+
+ align:start position:0%
+these terms should look exactly the same
+because in every case you're looking at
+
+ align:start position:0%
+because in every case you're looking at
+ 
+
+ align:start position:0%
+because in every case you're looking at
+some reaction rate between either the
+
+ align:start position:0%
+some reaction rate between either the
+ 
+
+ align:start position:0%
+some reaction rate between either the
+neutrons and fission or the gammas and
+
+ align:start position:0%
+neutrons and fission or the gammas and
+ 
+
+ align:start position:0%
+neutrons and fission or the gammas and
+fission and you need to know at what
+
+ align:start position:0%
+fission and you need to know at what
+ 
+
+ align:start position:0%
+fission and you need to know at what
+energy they're born how many are made
+
+ align:start position:0%
+energy they're born how many are made
+ 
+
+ align:start position:0%
+energy they're born how many are made
+all the angles and integrate over all
+
+ align:start position:0%
+all the angles and integrate over all
+ 
+
+ align:start position:0%
+all the angles and integrate over all
+the variables that we care about and
+
+ align:start position:0%
+the variables that we care about and
+ 
+
+ align:start position:0%
+the variables that we care about and
+this is part of why I'm adding these
+
+ align:start position:0%
+this is part of why I'm adding these
+ 
+
+ align:start position:0%
+this is part of why I'm adding these
+extra terms because they end up looking
+
+ align:start position:0%
+extra terms because they end up looking
+ 
+
+ align:start position:0%
+extra terms because they end up looking
+all exactly the same it's the integral
+
+ align:start position:0%
+all exactly the same it's the integral
+ 
+
+ align:start position:0%
+all exactly the same it's the integral
+of a reaction rate times some stuff
+
+ align:start position:0%
+of a reaction rate times some stuff
+ 
+
+ align:start position:0%
+of a reaction rate times some stuff
+that's all that every single one of
+
+ align:start position:0%
+that's all that every single one of
+ 
+
+ align:start position:0%
+that's all that every single one of
+these terms is going to be so we've got
+
+ align:start position:0%
+these terms is going to be so we've got
+ 
+
+ align:start position:0%
+these terms is going to be so we've got
+photo fission
+
+ align:start position:0%
+photo fission
+ 
+
+ align:start position:0%
+photo fission
+now let's tackle in scattering so how do
+
+ align:start position:0%
+now let's tackle in scattering so how do
+ 
+
+ align:start position:0%
+now let's tackle in scattering so how do
+we represent scattering in the same way
+
+ align:start position:0%
+we represent scattering in the same way
+ 
+
+ align:start position:0%
+we represent scattering in the same way
+that we represented fission what do we
+
+ align:start position:0%
+that we represented fission what do we
+ 
+
+ align:start position:0%
+that we represented fission what do we
+start with inside the integral
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+reaction rate yes so we're going to have
+
+ align:start position:0%
+reaction rate yes so we're going to have
+ 
+
+ align:start position:0%
+reaction rate yes so we're going to have
+some scattering cross-section and if
+
+ align:start position:0%
+some scattering cross-section and if
+ 
+
+ align:start position:0%
+some scattering cross-section and if
+it's in scattering it means it's coming
+
+ align:start position:0%
+it's in scattering it means it's coming
+ 
+
+ align:start position:0%
+it's in scattering it means it's coming
+from a different energy
+
+ align:start position:0%
+from a different energy
+ 
+
+ align:start position:0%
+from a different energy
+hence the prime will have our flux and
+
+ align:start position:0%
+hence the prime will have our flux and
+ 
+
+ align:start position:0%
+hence the prime will have our flux and
+here's where we're gonna bring in our
+
+ align:start position:0%
+here's where we're gonna bring in our
+ 
+
+ align:start position:0%
+here's where we're gonna bring in our
+scattering kernel because there's some
+
+ align:start position:0%
+scattering kernel because there's some
+ 
+
+ align:start position:0%
+scattering kernel because there's some
+probability that the neutron scatters in
+
+ align:start position:0%
+probability that the neutron scatters in
+ 
+
+ align:start position:0%
+probability that the neutron scatters in
+from a different group and then we'll
+
+ align:start position:0%
+from a different group and then we'll
+ 
+
+ align:start position:0%
+from a different group and then we'll
+have our D Omega D prime DV is this
+
+ align:start position:0%
+have our D Omega D prime DV is this
+ 
+
+ align:start position:0%
+have our D Omega D prime DV is this
+complete yet
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we've now accounted for one other energy
+
+ align:start position:0%
+we've now accounted for one other energy
+ 
+
+ align:start position:0%
+we've now accounted for one other energy
+e prime now how do we account for all
+
+ align:start position:0%
+e prime now how do we account for all
+ 
+
+ align:start position:0%
+e prime now how do we account for all
+possible other energies scattering into
+
+ align:start position:0%
+possible other energies scattering into
+ 
+
+ align:start position:0%
+possible other energies scattering into
+our energy group yep again same
+
+ align:start position:0%
+our energy group yep again same
+ 
+
+ align:start position:0%
+our energy group yep again same
+integrals we integrate over all possible
+
+ align:start position:0%
+integrals we integrate over all possible
+ 
+
+ align:start position:0%
+integrals we integrate over all possible
+energies over all possible angles and
+
+ align:start position:0%
+energies over all possible angles and
+ 
+
+ align:start position:0%
+energies over all possible angles and
+over our volume hopefully these terms
+
+ align:start position:0%
+over our volume hopefully these terms
+ 
+
+ align:start position:0%
+over our volume hopefully these terms
+are looking very similar in every case
+
+ align:start position:0%
+are looking very similar in every case
+ 
+
+ align:start position:0%
+are looking very similar in every case
+it's a volume angle energy integral of a
+
+ align:start position:0%
+it's a volume angle energy integral of a
+ 
+
+ align:start position:0%
+it's a volume angle energy integral of a
+reaction rate and all that saying is
+
+ align:start position:0%
+reaction rate and all that saying is
+ 
+
+ align:start position:0%
+reaction rate and all that saying is
+there's some rate that these reactions
+
+ align:start position:0%
+there's some rate that these reactions
+ 
+
+ align:start position:0%
+there's some rate that these reactions
+are occurring which is either a gain
+
+ align:start position:0%
+are occurring which is either a gain
+ 
+
+ align:start position:0%
+are occurring which is either a gain
+rate or a loss rate we integrate over
+
+ align:start position:0%
+rate or a loss rate we integrate over
+ 
+
+ align:start position:0%
+rate or a loss rate we integrate over
+whatever volume energy and angle we're
+
+ align:start position:0%
+whatever volume energy and angle we're
+ 
+
+ align:start position:0%
+whatever volume energy and angle we're
+tracking and that's all there is to it
+
+ align:start position:0%
+tracking and that's all there is to it
+ 
+
+ align:start position:0%
+tracking and that's all there is to it
+so we've got in scattering now let's
+
+ align:start position:0%
+so we've got in scattering now let's
+ 
+
+ align:start position:0%
+so we've got in scattering now let's
+tackle the ni n reactions there's only
+
+ align:start position:0%
+tackle the ni n reactions there's only
+ 
+
+ align:start position:0%
+tackle the ni n reactions there's only
+going to be one little difference but I
+
+ align:start position:0%
+going to be one little difference but I
+ 
+
+ align:start position:0%
+going to be one little difference but I
+want you guys to tell me what sort of
+
+ align:start position:0%
+want you guys to tell me what sort of
+ 
+
+ align:start position:0%
+want you guys to tell me what sort of
+things are going to be the same as all
+
+ align:start position:0%
+things are going to be the same as all
+ 
+
+ align:start position:0%
+things are going to be the same as all
+the other terms that we have here so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what do we start off with in this in the
+
+ align:start position:0%
+what do we start off with in this in the
+ 
+
+ align:start position:0%
+what do we start off with in this in the
+inside the integral
+
+ align:start position:0%
+inside the integral
+ 
+
+ align:start position:0%
+inside the integral
+a reaction rate how we write that yep a
+
+ align:start position:0%
+a reaction rate how we write that yep a
+ 
+
+ align:start position:0%
+a reaction rate how we write that yep a
+cross-section there's going to be some
+
+ align:start position:0%
+cross-section there's going to be some
+ 
+
+ align:start position:0%
+cross-section there's going to be some
+cross-section for let's call it an
+
+ align:start position:0%
+cross-section for let's call it an
+ 
+
+ align:start position:0%
+cross-section for let's call it an
+n-by-n reaction as a function of energy
+
+ align:start position:0%
+n-by-n reaction as a function of energy
+ 
+
+ align:start position:0%
+n-by-n reaction as a function of energy
+times a flux will be our normal
+
+ align:start position:0%
+times a flux will be our normal
+ 
+
+ align:start position:0%
+times a flux will be our normal
+integrated over all angles all energies
+
+ align:start position:0%
+integrated over all angles all energies
+ 
+
+ align:start position:0%
+integrated over all angles all energies
+and our volume so we have a reaction
+
+ align:start position:0%
+and our volume so we have a reaction
+ 
+
+ align:start position:0%
+and our volume so we have a reaction
+rate what do we have to then integrate
+
+ align:start position:0%
+rate what do we have to then integrate
+ 
+
+ align:start position:0%
+rate what do we have to then integrate
+that reaction right over to get all the
+
+ align:start position:0%
+that reaction right over to get all the
+ 
+
+ align:start position:0%
+that reaction right over to get all the
+neutrons in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+same things as everything else exactly
+
+ align:start position:0%
+same things as everything else exactly
+ 
+
+ align:start position:0%
+same things as everything else exactly
+integrate over all possible energies
+
+ align:start position:0%
+integrate over all possible energies
+ 
+
+ align:start position:0%
+integrate over all possible energies
+integrate over all possible angles
+
+ align:start position:0%
+integrate over all possible angles
+ 
+
+ align:start position:0%
+integrate over all possible angles
+integrate over our volume looks quite
+
+ align:start position:0%
+integrate over our volume looks quite
+ 
+
+ align:start position:0%
+integrate over our volume looks quite
+similar the only thing we haven't dealt
+
+ align:start position:0%
+similar the only thing we haven't dealt
+ 
+
+ align:start position:0%
+similar the only thing we haven't dealt
+with is this I term right here because
+
+ align:start position:0%
+with is this I term right here because
+ 
+
+ align:start position:0%
+with is this I term right here because
+there can be there are actually n to n
+
+ align:start position:0%
+there can be there are actually n to n
+ 
+
+ align:start position:0%
+there can be there are actually n to n
+reactions + 3 n + 4 N and so on so there
+
+ align:start position:0%
+reactions + 3 n + 4 N and so on so there
+ 
+
+ align:start position:0%
+reactions + 3 n + 4 N and so on so there
+are probabilities that let's say you in
+
+ align:start position:0%
+are probabilities that let's say you in
+ 
+
+ align:start position:0%
+are probabilities that let's say you in
+goes one Neutron out comes three
+
+ align:start position:0%
+goes one Neutron out comes three
+ 
+
+ align:start position:0%
+goes one Neutron out comes three
+neutrons but no fission actually
+
+ align:start position:0%
+neutrons but no fission actually
+ 
+
+ align:start position:0%
+neutrons but no fission actually
+happened you just blast a few of them
+
+ align:start position:0%
+happened you just blast a few of them
+ 
+
+ align:start position:0%
+happened you just blast a few of them
+out so I think all we'd really have to
+
+ align:start position:0%
+out so I think all we'd really have to
+ 
+
+ align:start position:0%
+out so I think all we'd really have to
+do is sum over I equals 1 oh I'm sorry I
+
+ align:start position:0%
+do is sum over I equals 1 oh I'm sorry I
+ 
+
+ align:start position:0%
+do is sum over I equals 1 oh I'm sorry I
+equals 2 because a neutron going in and
+
+ align:start position:0%
+equals 2 because a neutron going in and
+ 
+
+ align:start position:0%
+equals 2 because a neutron going in and
+then the same Neutron going out that's
+
+ align:start position:0%
+then the same Neutron going out that's
+ 
+
+ align:start position:0%
+then the same Neutron going out that's
+just scattering and what would be the
+
+ align:start position:0%
+just scattering and what would be the
+ 
+
+ align:start position:0%
+just scattering and what would be the
+maximum probably 4 because the
+
+ align:start position:0%
+maximum probably 4 because the
+ 
+
+ align:start position:0%
+maximum probably 4 because the
+probability of an increasing I or more
+
+ align:start position:0%
+probability of an increasing I or more
+ 
+
+ align:start position:0%
+probability of an increasing I or more
+neutrons coming out gets lower and lower
+
+ align:start position:0%
+neutrons coming out gets lower and lower
+ 
+
+ align:start position:0%
+neutrons coming out gets lower and lower
+as you go in fact these reactions don't
+
+ align:start position:0%
+as you go in fact these reactions don't
+ 
+
+ align:start position:0%
+as you go in fact these reactions don't
+even turn on until the end-to-end
+
+ align:start position:0%
+even turn on until the end-to-end
+ 
+
+ align:start position:0%
+even turn on until the end-to-end
+reaction turns on at around like 1 MeV
+
+ align:start position:0%
+reaction turns on at around like 1 MeV
+ 
+
+ align:start position:0%
+reaction turns on at around like 1 MeV
+this one turns on and around like 5 MeV
+
+ align:start position:0%
+this one turns on and around like 5 MeV
+ 
+
+ align:start position:0%
+this one turns on and around like 5 MeV
+this one turns on at like 12 MeV I was
+
+ align:start position:0%
+this one turns on at like 12 MeV I was
+ 
+
+ align:start position:0%
+this one turns on at like 12 MeV I was
+just looking up these cross-sections
+
+ align:start position:0%
+just looking up these cross-sections
+ 
+
+ align:start position:0%
+just looking up these cross-sections
+before class so if you have a reaction
+
+ align:start position:0%
+before class so if you have a reaction
+ 
+
+ align:start position:0%
+before class so if you have a reaction
+that doesn't happen beyond your highest
+
+ align:start position:0%
+that doesn't happen beyond your highest
+ 
+
+ align:start position:0%
+that doesn't happen beyond your highest
+Neutron energy you probably don't need
+
+ align:start position:0%
+Neutron energy you probably don't need
+ 
+
+ align:start position:0%
+Neutron energy you probably don't need
+to worry about it but the reason I had
+
+ align:start position:0%
+to worry about it but the reason I had
+ 
+
+ align:start position:0%
+to worry about it but the reason I had
+us write all these extra equations and I
+
+ align:start position:0%
+us write all these extra equations and I
+ 
+
+ align:start position:0%
+us write all these extra equations and I
+think that the the t-shirt for this
+
+ align:start position:0%
+think that the the t-shirt for this
+ 
+
+ align:start position:0%
+think that the the t-shirt for this
+department needs some updating to
+
+ align:start position:0%
+department needs some updating to
+ 
+
+ align:start position:0%
+department needs some updating to
+include these extra terms because
+
+ align:start position:0%
+include these extra terms because
+ 
+
+ align:start position:0%
+include these extra terms because
+they're all the same term it is in every
+
+ align:start position:0%
+they're all the same term it is in every
+ 
+
+ align:start position:0%
+they're all the same term it is in every
+case it's an integral over all of our
+
+ align:start position:0%
+case it's an integral over all of our
+ 
+
+ align:start position:0%
+case it's an integral over all of our
+stuff of a reaction rate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Dease tough times some multiplier every
+
+ align:start position:0%
+Dease tough times some multiplier every
+ 
+
+ align:start position:0%
+Dease tough times some multiplier every
+single term in this equation follows the
+
+ align:start position:0%
+single term in this equation follows the
+ 
+
+ align:start position:0%
+single term in this equation follows the
+exact same pattern so what I hope and I
+
+ align:start position:0%
+exact same pattern so what I hope and I
+ 
+
+ align:start position:0%
+exact same pattern so what I hope and I
+would expect out of you guys is that if
+
+ align:start position:0%
+would expect out of you guys is that if
+ 
+
+ align:start position:0%
+would expect out of you guys is that if
+I were to give you this table of
+
+ align:start position:0%
+I were to give you this table of
+ 
+
+ align:start position:0%
+I were to give you this table of
+possible reactions you would be able to
+
+ align:start position:0%
+possible reactions you would be able to
+ 
+
+ align:start position:0%
+possible reactions you would be able to
+recreate this neutron transport equation
+
+ align:start position:0%
+recreate this neutron transport equation
+ 
+
+ align:start position:0%
+recreate this neutron transport equation
+using this template to know that every
+
+ align:start position:0%
+using this template to know that every
+ 
+
+ align:start position:0%
+using this template to know that every
+single reaction is just multiplier times
+
+ align:start position:0%
+single reaction is just multiplier times
+ 
+
+ align:start position:0%
+single reaction is just multiplier times
+integral of stuff of a reaction rate D
+
+ align:start position:0%
+integral of stuff of a reaction rate D
+ 
+
+ align:start position:0%
+integral of stuff of a reaction rate D
+stuff where the reaction rate is just a
+
+ align:start position:0%
+stuff where the reaction rate is just a
+ 
+
+ align:start position:0%
+stuff where the reaction rate is just a
+cross section times the flux that's all
+
+ align:start position:0%
+cross section times the flux that's all
+ 
+
+ align:start position:0%
+cross section times the flux that's all
+there is to it not bad when you see that
+
+ align:start position:0%
+there is to it not bad when you see that
+ 
+
+ align:start position:0%
+there is to it not bad when you see that
+everything follows the same pattern
+
+ align:start position:0%
+everything follows the same pattern
+ 
+
+ align:start position:0%
+everything follows the same pattern
+right that's the basis behind most of
+
+ align:start position:0%
+right that's the basis behind most of
+ 
+
+ align:start position:0%
+right that's the basis behind most of
+the hideous equations that you see in
+
+ align:start position:0%
+the hideous equations that you see in
+ 
+
+ align:start position:0%
+the hideous equations that you see in
+all physics everywhere is if there are
+
+ align:start position:0%
+all physics everywhere is if there are
+ 
+
+ align:start position:0%
+all physics everywhere is if there are
+additive or subtractive terms they
+
+ align:start position:0%
+additive or subtractive terms they
+ 
+
+ align:start position:0%
+additive or subtractive terms they
+better be in the same units and so
+
+ align:start position:0%
+better be in the same units and so
+ 
+
+ align:start position:0%
+better be in the same units and so
+they're going to follow some sort of a
+
+ align:start position:0%
+they're going to follow some sort of a
+ 
+
+ align:start position:0%
+they're going to follow some sort of a
+similar template not too scary when you
+
+ align:start position:0%
+similar template not too scary when you
+ 
+
+ align:start position:0%
+similar template not too scary when you
+think of it that way so let's now come
+
+ align:start position:0%
+think of it that way so let's now come
+ 
+
+ align:start position:0%
+think of it that way so let's now come
+up with the lost terms I should have
+
+ align:start position:0%
+up with the lost terms I should have
+ 
+
+ align:start position:0%
+up with the lost terms I should have
+planned these boards better keep these
+
+ align:start position:0%
+planned these boards better keep these
+ 
+
+ align:start position:0%
+planned these boards better keep these
+ones here so we keep a template and
+
+ align:start position:0%
+ones here so we keep a template and
+ 
+
+ align:start position:0%
+ones here so we keep a template and
+we'll have a - well how do we write the
+
+ align:start position:0%
+we'll have a - well how do we write the
+ 
+
+ align:start position:0%
+we'll have a - well how do we write the
+anything reaction using this template
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+how many neutrons undergo a reaction
+
+ align:start position:0%
+how many neutrons undergo a reaction
+ 
+
+ align:start position:0%
+how many neutrons undergo a reaction
+when one Neutron undergoes a reaction
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah one so our multiplier is one we
+
+ align:start position:0%
+yeah one so our multiplier is one we
+ 
+
+ align:start position:0%
+yeah one so our multiplier is one we
+don't have to worry about it we have our
+
+ align:start position:0%
+don't have to worry about it we have our
+ 
+
+ align:start position:0%
+don't have to worry about it we have our
+integral of stuff so we'll have to
+
+ align:start position:0%
+integral of stuff so we'll have to
+ 
+
+ align:start position:0%
+integral of stuff so we'll have to
+integrate over all possible volumes
+
+ align:start position:0%
+integrate over all possible volumes
+ 
+
+ align:start position:0%
+integrate over all possible volumes
+angles and energy and what's on the
+
+ align:start position:0%
+angles and energy and what's on the
+ 
+
+ align:start position:0%
+angles and energy and what's on the
+inside yep
+
+ align:start position:0%
+inside yep
+ 
+
+ align:start position:0%
+inside yep
+total cross-section as a function of
+
+ align:start position:0%
+total cross-section as a function of
+ 
+
+ align:start position:0%
+total cross-section as a function of
+energy times the flux DS stuff save time
+
+ align:start position:0%
+energy times the flux DS stuff save time
+ 
+
+ align:start position:0%
+energy times the flux DS stuff save time
+so don't worry even though the boards
+
+ align:start position:0%
+so don't worry even though the boards
+ 
+
+ align:start position:0%
+so don't worry even though the boards
+are laid out funny on the pictures of
+
+ align:start position:0%
+are laid out funny on the pictures of
+ 
+
+ align:start position:0%
+are laid out funny on the pictures of
+the blackboard that will put on the
+
+ align:start position:0%
+the blackboard that will put on the
+ 
+
+ align:start position:0%
+the blackboard that will put on the
+stellar site I'll Photoshop these and
+
+ align:start position:0%
+stellar site I'll Photoshop these and
+ 
+
+ align:start position:0%
+stellar site I'll Photoshop these and
+arrange them so that they're all in
+
+ align:start position:0%
+arrange them so that they're all in
+ 
+
+ align:start position:0%
+arrange them so that they're all in
+sequence and you can see everything and
+
+ align:start position:0%
+sequence and you can see everything and
+ 
+
+ align:start position:0%
+sequence and you can see everything and
+then there's the last term to account
+
+ align:start position:0%
+then there's the last term to account
+ 
+
+ align:start position:0%
+then there's the last term to account
+for that's the leakage term this one is
+
+ align:start position:0%
+for that's the leakage term this one is
+ 
+
+ align:start position:0%
+for that's the leakage term this one is
+a little different it's the only one
+
+ align:start position:0%
+a little different it's the only one
+ 
+
+ align:start position:0%
+a little different it's the only one
+that's a little different and in this
+
+ align:start position:0%
+that's a little different and in this
+ 
+
+ align:start position:0%
+that's a little different and in this
+case we're going to say that our little
+
+ align:start position:0%
+case we're going to say that our little
+ 
+
+ align:start position:0%
+case we're going to say that our little
+volume element also has a surface to it
+
+ align:start position:0%
+volume element also has a surface to it
+ 
+
+ align:start position:0%
+volume element also has a surface to it
+and if the neutrons leave the surface
+
+ align:start position:0%
+and if the neutrons leave the surface
+ 
+
+ align:start position:0%
+and if the neutrons leave the surface
+then they're go then they leave the
+
+ align:start position:0%
+then they're go then they leave the
+ 
+
+ align:start position:0%
+then they're go then they leave the
+volume so in this case we'll have a
+
+ align:start position:0%
+volume so in this case we'll have a
+ 
+
+ align:start position:0%
+volume so in this case we'll have a
+surface integral of our Neutron flouts
+
+ align:start position:0%
+surface integral of our Neutron flouts
+ 
+
+ align:start position:0%
+surface integral of our Neutron flouts
+say our Neutron flux D s because there's
+
+ align:start position:0%
+say our Neutron flux D s because there's
+ 
+
+ align:start position:0%
+say our Neutron flux D s because there's
+no reaction happening when neutrons just
+
+ align:start position:0%
+no reaction happening when neutrons just
+ 
+
+ align:start position:0%
+no reaction happening when neutrons just
+move right they just go and so well we'd
+
+ align:start position:0%
+move right they just go and so well we'd
+ 
+
+ align:start position:0%
+move right they just go and so well we'd
+also have to multiply by our normal
+
+ align:start position:0%
+also have to multiply by our normal
+ 
+
+ align:start position:0%
+also have to multiply by our normal
+vector because every flux is going to
+
+ align:start position:0%
+vector because every flux is going to
+ 
+
+ align:start position:0%
+vector because every flux is going to
+have a certain number of neutrons moving
+
+ align:start position:0%
+have a certain number of neutrons moving
+ 
+
+ align:start position:0%
+have a certain number of neutrons moving
+in a certain direction let's say we were
+
+ align:start position:0%
+in a certain direction let's say we were
+ 
+
+ align:start position:0%
+in a certain direction let's say we were
+tracking the flow of neutrons through
+
+ align:start position:0%
+tracking the flow of neutrons through
+ 
+
+ align:start position:0%
+tracking the flow of neutrons through
+this surface right here and if we had a
+
+ align:start position:0%
+this surface right here and if we had a
+ 
+
+ align:start position:0%
+this surface right here and if we had a
+flux going in exactly this direction
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+through this surface and this is the
+
+ align:start position:0%
+through this surface and this is the
+ 
+
+ align:start position:0%
+through this surface and this is the
+normal vector in this case flux which is
+
+ align:start position:0%
+normal vector in this case flux which is
+ 
+
+ align:start position:0%
+normal vector in this case flux which is
+a vector dotted with a normal vector is
+
+ align:start position:0%
+a vector dotted with a normal vector is
+ 
+
+ align:start position:0%
+a vector dotted with a normal vector is
+just the flux which is to say that if
+
+ align:start position:0%
+just the flux which is to say that if
+ 
+
+ align:start position:0%
+just the flux which is to say that if
+the flux and the normal vector are
+
+ align:start position:0%
+the flux and the normal vector are
+ 
+
+ align:start position:0%
+the flux and the normal vector are
+aligned in the same way then every
+
+ align:start position:0%
+aligned in the same way then every
+ 
+
+ align:start position:0%
+aligned in the same way then every
+Neutron going through the surface is
+
+ align:start position:0%
+Neutron going through the surface is
+ 
+
+ align:start position:0%
+Neutron going through the surface is
+tracked as going through the surface to
+
+ align:start position:0%
+tracked as going through the surface to
+ 
+
+ align:start position:0%
+tracked as going through the surface to
+take the opposite example what about the
+
+ align:start position:0%
+take the opposite example what about the
+ 
+
+ align:start position:0%
+take the opposite example what about the
+situation where you have a surface here
+
+ align:start position:0%
+situation where you have a surface here
+ 
+
+ align:start position:0%
+situation where you have a surface here
+and you have a mono directional flux of
+
+ align:start position:0%
+and you have a mono directional flux of
+ 
+
+ align:start position:0%
+and you have a mono directional flux of
+neutrons in this direction and that is
+
+ align:start position:0%
+neutrons in this direction and that is
+ 
+
+ align:start position:0%
+neutrons in this direction and that is
+your surface normal what does the flux
+
+ align:start position:0%
+your surface normal what does the flux
+ 
+
+ align:start position:0%
+your surface normal what does the flux
+dotted with the surface normal vector
+
+ align:start position:0%
+dotted with the surface normal vector
+ 
+
+ align:start position:0%
+dotted with the surface normal vector
+equal zero just a dot product between
+
+ align:start position:0%
+equal zero just a dot product between
+ 
+
+ align:start position:0%
+equal zero just a dot product between
+the direction that your neutrons are
+
+ align:start position:0%
+the direction that your neutrons are
+ 
+
+ align:start position:0%
+the direction that your neutrons are
+moving and the normal vector saying does
+
+ align:start position:0%
+moving and the normal vector saying does
+ 
+
+ align:start position:0%
+moving and the normal vector saying does
+it go out of the surface at all so for
+
+ align:start position:0%
+it go out of the surface at all so for
+ 
+
+ align:start position:0%
+it go out of the surface at all so for
+these two limiting cases in this case
+
+ align:start position:0%
+these two limiting cases in this case
+ 
+
+ align:start position:0%
+these two limiting cases in this case
+the flux is just listed what is it the
+
+ align:start position:0%
+the flux is just listed what is it the
+ 
+
+ align:start position:0%
+the flux is just listed what is it the
+number of neutrons leaving the surface
+
+ align:start position:0%
+number of neutrons leaving the surface
+ 
+
+ align:start position:0%
+number of neutrons leaving the surface
+is the flux in this case no neutrons
+
+ align:start position:0%
+is the flux in this case no neutrons
+ 
+
+ align:start position:0%
+is the flux in this case no neutrons
+leave the surface because they're not
+
+ align:start position:0%
+leave the surface because they're not
+ 
+
+ align:start position:0%
+leave the surface because they're not
+actually going through the surface it's
+
+ align:start position:0%
+actually going through the surface it's
+ 
+
+ align:start position:0%
+actually going through the surface it's
+a good time to mention again that these
+
+ align:start position:0%
+a good time to mention again that these
+ 
+
+ align:start position:0%
+a good time to mention again that these
+units of flux are in neutrons per
+
+ align:start position:0%
+units of flux are in neutrons per
+ 
+
+ align:start position:0%
+units of flux are in neutrons per
+centimeter squared per second which is
+
+ align:start position:0%
+centimeter squared per second which is
+ 
+
+ align:start position:0%
+centimeter squared per second which is
+to say the number of particles traveling
+
+ align:start position:0%
+to say the number of particles traveling
+ 
+
+ align:start position:0%
+to say the number of particles traveling
+through this area in centimeters squared
+
+ align:start position:0%
+through this area in centimeters squared
+ 
+
+ align:start position:0%
+through this area in centimeters squared
+every second I know we've gone over it
+
+ align:start position:0%
+every second I know we've gone over it
+ 
+
+ align:start position:0%
+every second I know we've gone over it
+before but I want you to keep these
+
+ align:start position:0%
+before but I want you to keep these
+ 
+
+ align:start position:0%
+before but I want you to keep these
+units in mind because now they actually
+
+ align:start position:0%
+units in mind because now they actually
+ 
+
+ align:start position:0%
+units in mind because now they actually
+have a little more physical significance
+
+ align:start position:0%
+have a little more physical significance
+ 
+
+ align:start position:0%
+have a little more physical significance
+and that's why we have this flux times
+
+ align:start position:0%
+and that's why we have this flux times
+ 
+
+ align:start position:0%
+and that's why we have this flux times
+normal vector DS that describes the
+
+ align:start position:0%
+normal vector DS that describes the
+ 
+
+ align:start position:0%
+normal vector DS that describes the
+number of neutrons that get through the
+
+ align:start position:0%
+number of neutrons that get through the
+ 
+
+ align:start position:0%
+number of neutrons that get through the
+surface the last thing we'll do because
+
+ align:start position:0%
+surface the last thing we'll do because
+ 
+
+ align:start position:0%
+surface the last thing we'll do because
+everything else is a volume integral we
+
+ align:start position:0%
+everything else is a volume integral we
+ 
+
+ align:start position:0%
+everything else is a volume integral we
+want this to be a volume integral
+
+ align:start position:0%
+want this to be a volume integral
+ 
+
+ align:start position:0%
+want this to be a volume integral
+because we're going to simplify this in
+
+ align:start position:0%
+because we're going to simplify this in
+ 
+
+ align:start position:0%
+because we're going to simplify this in
+terms of getting rid of all the volume
+
+ align:start position:0%
+terms of getting rid of all the volume
+ 
+
+ align:start position:0%
+terms of getting rid of all the volume
+stuff we're going to use what's called
+
+ align:start position:0%
+stuff we're going to use what's called
+ 
+
+ align:start position:0%
+stuff we're going to use what's called
+the divergence theorem I hear some
+
+ align:start position:0%
+the divergence theorem I hear some
+ 
+
+ align:start position:0%
+the divergence theorem I hear some
+snickering because I remember this is
+
+ align:start position:0%
+snickering because I remember this is
+ 
+
+ align:start position:0%
+snickering because I remember this is
+probably something that where you were
+
+ align:start position:0%
+probably something that where you were
+ 
+
+ align:start position:0%
+probably something that where you were
+told in 1801 or eight - no - this exists
+
+ align:start position:0%
+told in 1801 or eight - no - this exists
+ 
+
+ align:start position:0%
+told in 1801 or eight - no - this exists
+use it in a few problems moving on that
+
+ align:start position:0%
+use it in a few problems moving on that
+ 
+
+ align:start position:0%
+use it in a few problems moving on that
+sound about right
+
+ align:start position:0%
+sound about right
+ 
+
+ align:start position:0%
+sound about right
+this is
+
+ align:start position:0%
+this is
+ 
+
+ align:start position:0%
+this is
+you actually use it so the divergence
+
+ align:start position:0%
+you actually use it so the divergence
+ 
+
+ align:start position:0%
+you actually use it so the divergence
+theorem says that the integral of some
+
+ align:start position:0%
+theorem says that the integral of some
+ 
+
+ align:start position:0%
+theorem says that the integral of some
+variable f D s through some volume
+
+ align:start position:0%
+variable f D s through some volume
+ 
+
+ align:start position:0%
+variable f D s through some volume
+element of surface is the same as the
+
+ align:start position:0%
+element of surface is the same as the
+ 
+
+ align:start position:0%
+element of surface is the same as the
+volume integral of how does this go del
+
+ align:start position:0%
+volume integral of how does this go del
+ 
+
+ align:start position:0%
+volume integral of how does this go del
+dot F DV and this is going to be quite
+
+ align:start position:0%
+dot F DV and this is going to be quite
+ 
+
+ align:start position:0%
+dot F DV and this is going to be quite
+important because one it gives us a
+
+ align:start position:0%
+important because one it gives us a
+ 
+
+ align:start position:0%
+important because one it gives us a
+volume integral so this is a be a volume
+
+ align:start position:0%
+volume integral so this is a be a volume
+ 
+
+ align:start position:0%
+volume integral so this is a be a volume
+integral of our del dot flux DV so now
+
+ align:start position:0%
+integral of our del dot flux DV so now
+ 
+
+ align:start position:0%
+integral of our del dot flux DV so now
+everything's in the same units and if we
+
+ align:start position:0%
+everything's in the same units and if we
+ 
+
+ align:start position:0%
+everything's in the same units and if we
+were to say forget about our little
+
+ align:start position:0%
+were to say forget about our little
+ 
+
+ align:start position:0%
+were to say forget about our little
+volume element let's just assume an
+
+ align:start position:0%
+volume element let's just assume an
+ 
+
+ align:start position:0%
+volume element let's just assume an
+infinite reactor every single volume
+
+ align:start position:0%
+infinite reactor every single volume
+ 
+
+ align:start position:0%
+infinite reactor every single volume
+integral in terms instantly disappears
+
+ align:start position:0%
+integral in terms instantly disappears
+ 
+
+ align:start position:0%
+integral in terms instantly disappears
+because we wrote these equations to be
+
+ align:start position:0%
+because we wrote these equations to be
+ 
+
+ align:start position:0%
+because we wrote these equations to be
+identical for any DV anywhere inside
+
+ align:start position:0%
+identical for any DV anywhere inside
+ 
+
+ align:start position:0%
+identical for any DV anywhere inside
+this reactor if the reactor is then
+
+ align:start position:0%
+this reactor if the reactor is then
+ 
+
+ align:start position:0%
+this reactor if the reactor is then
+infinite then all of those volume terms
+
+ align:start position:0%
+infinite then all of those volume terms
+ 
+
+ align:start position:0%
+infinite then all of those volume terms
+disappear and that's the first
+
+ align:start position:0%
+disappear and that's the first
+ 
+
+ align:start position:0%
+disappear and that's the first
+simplification that we'll make in the
+
+ align:start position:0%
+simplification that we'll make in the
+ 
+
+ align:start position:0%
+simplification that we'll make in the
+next class but right here on these five
+
+ align:start position:0%
+next class but right here on these five
+ 
+
+ align:start position:0%
+next class but right here on these five
+boards we've developed the neutron
+
+ align:start position:0%
+boards we've developed the neutron
+ 
+
+ align:start position:0%
+boards we've developed the neutron
+transport equation which is the absolute
+
+ align:start position:0%
+transport equation which is the absolute
+ 
+
+ align:start position:0%
+transport equation which is the absolute
+most general highest escalated form of
+
+ align:start position:0%
+most general highest escalated form of
+ 
+
+ align:start position:0%
+most general highest escalated form of
+how do you track neutrons through any
+
+ align:start position:0%
+how do you track neutrons through any
+ 
+
+ align:start position:0%
+how do you track neutrons through any
+volume any direction any energy at any
+
+ align:start position:0%
+volume any direction any energy at any
+ 
+
+ align:start position:0%
+volume any direction any energy at any
+time and we'll spend Thursday and Friday
+
+ align:start position:0%
+time and we'll spend Thursday and Friday
+ 
+
+ align:start position:0%
+time and we'll spend Thursday and Friday
+simplifying this to something that we
+
+ align:start position:0%
+simplifying this to something that we
+ 
+
+ align:start position:0%
+simplifying this to something that we
+can solve the other reason that we use
+
+ align:start position:0%
+can solve the other reason that we use
+ 
+
+ align:start position:0%
+can solve the other reason that we use
+this divergence theorem is because we're
+
+ align:start position:0%
+this divergence theorem is because we're
+ 
+
+ align:start position:0%
+this divergence theorem is because we're
+going to make an approximation this
+
+ align:start position:0%
+going to make an approximation this
+ 
+
+ align:start position:0%
+going to make an approximation this
+crazy-looking thing right here we will
+
+ align:start position:0%
+crazy-looking thing right here we will
+ 
+
+ align:start position:0%
+crazy-looking thing right here we will
+make an approximation called the
+
+ align:start position:0%
+make an approximation called the
+ 
+
+ align:start position:0%
+make an approximation called the
+diffusion approximation where we assume
+
+ align:start position:0%
+diffusion approximation where we assume
+ 
+
+ align:start position:0%
+diffusion approximation where we assume
+that neutrons are like a gas that just
+
+ align:start position:0%
+that neutrons are like a gas that just
+ 
+
+ align:start position:0%
+that neutrons are like a gas that just
+diffuse away from each other and that's
+
+ align:start position:0%
+diffuse away from each other and that's
+ 
+
+ align:start position:0%
+diffuse away from each other and that's
+gonna make solving this really really
+
+ align:start position:0%
+gonna make solving this really really
+ 
+
+ align:start position:0%
+gonna make solving this really really
+easy it's gonna go from some
+
+ align:start position:0%
+easy it's gonna go from some
+ 
+
+ align:start position:0%
+easy it's gonna go from some
+second-order differential or
+
+ align:start position:0%
+second-order differential or
+ 
+
+ align:start position:0%
+second-order differential or
+differential integral equation to just
+
+ align:start position:0%
+differential integral equation to just
+ 
+
+ align:start position:0%
+differential integral equation to just
+an equation that you can solve with
+
+ align:start position:0%
+an equation that you can solve with
+ 
+
+ align:start position:0%
+an equation that you can solve with
+algebra yep
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+probably yep
+
+ align:start position:0%
+probably yep
+ 
+
+ align:start position:0%
+probably yep
+overall II overall Omega and that flux
+
+ align:start position:0%
+overall II overall Omega and that flux
+ 
+
+ align:start position:0%
+overall II overall Omega and that flux
+is gonna be of our e omega t absolutely
+
+ align:start position:0%
+is gonna be of our e omega t absolutely
+ 
+
+ align:start position:0%
+is gonna be of our e omega t absolutely
+just to make sure everything's in the
+
+ align:start position:0%
+just to make sure everything's in the
+ 
+
+ align:start position:0%
+just to make sure everything's in the
+same units every term has a fairly
+
+ align:start position:0%
+same units every term has a fairly
+ 
+
+ align:start position:0%
+same units every term has a fairly
+similar template the only difference is
+
+ align:start position:0%
+similar template the only difference is
+ 
+
+ align:start position:0%
+similar template the only difference is
+leakage there's no reaction here every
+
+ align:start position:0%
+leakage there's no reaction here every
+ 
+
+ align:start position:0%
+leakage there's no reaction here every
+single other term constitutes a reaction
+
+ align:start position:0%
+single other term constitutes a reaction
+ 
+
+ align:start position:0%
+single other term constitutes a reaction
+and they all follow this template so I
+
+ align:start position:0%
+and they all follow this template so I
+ 
+
+ align:start position:0%
+and they all follow this template so I
+will stop here because it is 5 of C if
+
+ align:start position:0%
+will stop here because it is 5 of C if
+ 
+
+ align:start position:0%
+will stop here because it is 5 of C if
+anyone has any quick questions on what
+
+ align:start position:0%
+anyone has any quick questions on what
+ 
+
+ align:start position:0%
+anyone has any quick questions on what
+you've got here I'll make sure to get
+
+ align:start position:0%
+you've got here I'll make sure to get
+ 
+
+ align:start position:0%
+you've got here I'll make sure to get
+all of this on the board images so you
+
+ align:start position:0%
+all of this on the board images so you
+ 
+
+ align:start position:0%
+all of this on the board images so you
+guys can take a look at it and I'll
+
+ align:start position:0%
+guys can take a look at it and I'll
+ 
+
+ align:start position:0%
+guys can take a look at it and I'll
+project it up on the screen so that we
+
+ align:start position:0%
+project it up on the screen so that we
+ 
+
+ align:start position:0%
+project it up on the screen so that we
+can make some simplifications based on
+
+ align:start position:0%
+can make some simplifications based on
+ 
+
+ align:start position:0%
+can make some simplifications based on
+what we see here on Thursday yeah the
+
+ align:start position:0%
+what we see here on Thursday yeah the
+ 
+
+ align:start position:0%
+what we see here on Thursday yeah the
+neutron birth spectrum says that if you
+
+ align:start position:0%
+neutron birth spectrum says that if you
+ 
+
+ align:start position:0%
+neutron birth spectrum says that if you
+have any old fission event what's the
+
+ align:start position:0%
+have any old fission event what's the
+ 
+
+ align:start position:0%
+have any old fission event what's the
+probability of those neutrons being born
+
+ align:start position:0%
+probability of those neutrons being born
+ 
+
+ align:start position:0%
+probability of those neutrons being born
+at different energies what this says is
+
+ align:start position:0%
+at different energies what this says is
+ 
+
+ align:start position:0%
+at different energies what this says is
+that they're born between 1 and 10 MeV
+
+ align:start position:0%
+that they're born between 1 and 10 MeV
+ 
+
+ align:start position:0%
+that they're born between 1 and 10 MeV
+with a peak at around 2 MeV but if you
+
+ align:start position:0%
+with a peak at around 2 MeV but if you
+ 
+
+ align:start position:0%
+with a peak at around 2 MeV but if you
+want to track the number of neutrons in
+
+ align:start position:0%
+want to track the number of neutrons in
+ 
+
+ align:start position:0%
+want to track the number of neutrons in
+every energy group you need to know
+
+ align:start position:0%
+every energy group you need to know
+ 
+
+ align:start position:0%
+every energy group you need to know
+where they begin good question so if any
+
+ align:start position:0%
+where they begin good question so if any
+ 
+
+ align:start position:0%
+where they begin good question so if any
+of the terms here are unclear what they
+
+ align:start position:0%
+of the terms here are unclear what they
+ 
+
+ align:start position:0%
+of the terms here are unclear what they
+physically mean because that's what I'm
+
+ align:start position:0%
+physically mean because that's what I'm
+ 
+
+ align:start position:0%
+physically mean because that's what I'm
+most interested in you guys knowing
+
+ align:start position:0%
+most interested in you guys knowing
+ 
+
+ align:start position:0%
+most interested in you guys knowing
+please do ask either on Piazza on email
+
+ align:start position:0%
+please do ask either on Piazza on email
+ 
+
+ align:start position:0%
+please do ask either on Piazza on email
+on Thursday yeah the big end and the
+
+ align:start position:0%
+on Thursday yeah the big end and the
+ 
+
+ align:start position:0%
+on Thursday yeah the big end and the
+little end which one the curse of one or
+
+ align:start position:0%
+little end which one the curse of one or
+ 
+
+ align:start position:0%
+little end which one the curse of one or
+this one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay the little end and the non cursive
+
+ align:start position:0%
+okay the little end and the non cursive
+ 
+
+ align:start position:0%
+okay the little end and the non cursive
+one little n is the number of neutrons
+
+ align:start position:0%
+one little n is the number of neutrons
+ 
+
+ align:start position:0%
+one little n is the number of neutrons
+in a volume at a certain energy going in
+
+ align:start position:0%
+in a volume at a certain energy going in
+ 
+
+ align:start position:0%
+in a volume at a certain energy going in
+a direction at a certain time big n
+
+ align:start position:0%
+a direction at a certain time big n
+ 
+
+ align:start position:0%
+a direction at a certain time big n
+right here is just number density number
+
+ align:start position:0%
+right here is just number density number
+ 
+
+ align:start position:0%
+right here is just number density number
+of atoms per centimeter cubed cursive n
+
+ align:start position:0%
+of atoms per centimeter cubed cursive n
+ 
+
+ align:start position:0%
+of atoms per centimeter cubed cursive n
+is the number of neutrons at an energy
+
+ align:start position:0%
+is the number of neutrons at an energy
+ 
+
+ align:start position:0%
+is the number of neutrons at an energy
+in a volume we don't care where they're
+
+ align:start position:0%
+in a volume we don't care where they're
+ 
+
+ align:start position:0%
+in a volume we don't care where they're
+going and the reason I write these terms
+
+ align:start position:0%
+going and the reason I write these terms
+ 
+
+ align:start position:0%
+going and the reason I write these terms
+up here is we are going to switch from
+
+ align:start position:0%
+up here is we are going to switch from
+ 
+
+ align:start position:0%
+up here is we are going to switch from
+lowercase to capital or angular ly
+
+ align:start position:0%
+lowercase to capital or angular ly
+ 
+
+ align:start position:0%
+lowercase to capital or angular ly
+dependent to angular ly independent by
+
+ align:start position:0%
+dependent to angular ly independent by
+ 
+
+ align:start position:0%
+dependent to angular ly independent by
+making a simple approximation to say we
+
+ align:start position:0%
+making a simple approximation to say we
+ 
+
+ align:start position:0%
+making a simple approximation to say we
+don't care what direction they're going
+
+ align:start position:0%
+don't care what direction they're going
+ 
+
+ align:start position:0%
+don't care what direction they're going
+we just care if they're there but in
+
+ align:start position:0%
+we just care if they're there but in
+ 
+
+ align:start position:0%
+we just care if they're there but in
+real complex neutron physics problems
+
+ align:start position:0%
+real complex neutron physics problems
+ 
+
+ align:start position:0%
+real complex neutron physics problems
+like the one solved in the computational
+
+ align:start position:0%
+like the one solved in the computational
+ 
+
+ align:start position:0%
+like the one solved in the computational
+reactor physics group you need to know
+
+ align:start position:0%
+reactor physics group you need to know
+ 
+
+ align:start position:0%
+reactor physics group you need to know
+all the angles and you need to know the
+
+ align:start position:0%
+all the angles and you need to know the
+ 
+
+ align:start position:0%
+all the angles and you need to know the
+probability or the cross section that a
+
+ align:start position:0%
+probability or the cross section that a
+ 
+
+ align:start position:0%
+probability or the cross section that a
+neutron coming in at this angle leaves
+
+ align:start position:0%
+neutron coming in at this angle leaves
+ 
+
+ align:start position:0%
+neutron coming in at this angle leaves
+at that angle and imparts a certain
+
+ align:start position:0%
+at that angle and imparts a certain
+ 
+
+ align:start position:0%
+at that angle and imparts a certain
+energy because they're all different the
+
+ align:start position:0%
+energy because they're all different the
+ 
+
+ align:start position:0%
+energy because they're all different the
+purposes of this class I just want you
+
+ align:start position:0%
+purposes of this class I just want you
+ 
+
+ align:start position:0%
+purposes of this class I just want you
+to know that they exist and the first
+
+ align:start position:0%
+to know that they exist and the first
+ 
+
+ align:start position:0%
+to know that they exist and the first
+thing we will do is simplify them away
+
+ align:start position:0%
+thing we will do is simplify them away
+ 
+
+ align:start position:0%
+thing we will do is simplify them away
+but this way you'll be fully prepared
+
+ align:start position:0%
+but this way you'll be fully prepared
+ 
+
+ align:start position:0%
+but this way you'll be fully prepared
+for 22:05 and a lifetime of reactor
+
+ align:start position:0%
+for 22:05 and a lifetime of reactor
+ 
+
+ align:start position:0%
+for 22:05 and a lifetime of reactor
+physics if you so choose who here's done
+
+ align:start position:0%
+physics if you so choose who here's done
+ 
+
+ align:start position:0%
+physics if you so choose who here's done
+a year up in the computational reactor
+
+ align:start position:0%
+a year up in the computational reactor
+ 
+
+ align:start position:0%
+a year up in the computational reactor
+physics group just one okay I recommend
+
+ align:start position:0%
+physics group just one okay I recommend
+ 
+
+ align:start position:0%
+physics group just one okay I recommend
+more they they tend to be the biggest
+
+ align:start position:0%
+more they they tend to be the biggest
+ 
+
+ align:start position:0%
+more they they tend to be the biggest
+group in the department they've got like
+
+ align:start position:0%
+group in the department they've got like
+ 
+
+ align:start position:0%
+group in the department they've got like
+twenty grad students and probably more
+
+ align:start position:0%
+twenty grad students and probably more
+ 
+
+ align:start position:0%
+twenty grad students and probably more
+your ops than that so try it out it's
+
+ align:start position:0%
+your ops than that so try it out it's
+ 
+
+ align:start position:0%
+your ops than that so try it out it's
+what makes us us us nukes right is
+
+ align:start position:0%
+what makes us us us nukes right is
+ 
+
+ align:start position:0%
+what makes us us us nukes right is
+neutrons and tracking them to ridiculous
+
+ align:start position:0%
+neutrons and tracking them to ridiculous
+ 
+
+ align:start position:0%
+neutrons and tracking them to ridiculous
+proportions okay definitely wanna let
+
+ align:start position:0%
+proportions okay definitely wanna let
+ 
+
+ align:start position:0%
+proportions okay definitely wanna let
+you guys go cuz it's one of so I'll see
+
+ align:start position:0%
+you guys go cuz it's one of so I'll see
+ 
+
+ align:start position:0%
+you guys go cuz it's one of so I'll see
+you all on Thursday
\ No newline at end of file