What Factors Affect Neutron Flux in a Finite Medium?

damyoro
Messages
11
Reaction score
0
Deaar all
good morning

I am very interested to the flux in a slab of extrapolated thickness a, containing distributed sources of neutron. A I have an example in which the source is given as s(x)=S(x+a/2) where S is a constant and x distance from the center of the slab.
You mentioned in one of your post that you would do it but I could find.
I would really appreciate any help of reference from you
Thank you in advance
 
Physics news on Phys.org
I wanted to add the reference of the book : Introduction to Nuclear reactor theory by John R. Lamarsh

CHp5 Problem
a)By using the diffusion equation for a planar source located at x', show that the diffusion kernel for an infinite slab of thickness a is given by

G(x,x^' )=L/(Dsinh(a/L)) {█(sinh 1/L (a/2-x)sinh 1/L (a/2+x^' ),x>x',
sinh 1/L (a/2+x)sinh 1/L (a/2-x^' ),x<x'
b) using this kernel calculate the flux in a slab containing uniformly distributed souces emitting S neutrons/cm3.sec
 
What have you tried so far? This looks to be a homework problem.
 
You are right and thank you for your reply
This is my try
general solution is C=A*e^(-x/L)+Be^(x/L)
And I use as boundary conditions φ(a/2)==0
and as source condition
J(a/2-x')=J(x') +1
What I found is the following
Ф+(x,x^' )=-(Le^((x-a/2)/L))/2D[cosh x^'/L-cosh((x^'-a/2)/L) ] +(Le^((-x+a/2)/L))/(2*D[cosh x^'/L-cosh((x^'-a/2)/L) ] )

I really tried hard but until now I could not get it right.
One of my problems is to find the conditions for determining the constants.

thank you in advance
 
Hi, I had an exam and I completely messed up a problem. Especially one part which was necessary for the rest of the problem. Basically, I have a wormhole metric: $$(ds)^2 = -(dt)^2 + (dr)^2 + (r^2 + b^2)( (d\theta)^2 + sin^2 \theta (d\phi)^2 )$$ Where ##b=1## with an orbit only in the equatorial plane. We also know from the question that the orbit must satisfy this relationship: $$\varepsilon = \frac{1}{2} (\frac{dr}{d\tau})^2 + V_{eff}(r)$$ Ultimately, I was tasked to find the initial...
The value of H equals ## 10^{3}## in natural units, According to : https://en.wikipedia.org/wiki/Natural_units, ## t \sim 10^{-21} sec = 10^{21} Hz ##, and since ## \text{GeV} \sim 10^{24} \text{Hz } ##, ## GeV \sim 10^{24} \times 10^{-21} = 10^3 ## in natural units. So is this conversion correct? Also in the above formula, can I convert H to that natural units , since it’s a constant, while keeping k in Hz ?
Back
Top