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Neutron Flux in a sub-critical reactor

  1. Nov 2, 2016 #1
    Hi everyone,

    I am supposed to derive the neutron flux equation provided for region A of my reactor. Just wondering if anyone can help me out since I stuck on the derivation for [1/r - 1/R2]; S/4πD aspect is very similar to a solving the constant for a point source spherical reactor

    Here is my reactor diagram consisting of nested spheres (sorry, this is my first time posting):

    Sphere 1 --> Lead target with radius of R0 (Target-region)
    Sphere 2 --> Actinide Fuel surrounding lead target; has outer radius of R1 (A-region)
    Sphere 3 --> Reflector surrounding the fuel with outer radius of R2 (E-region)

    Neutron Flux vanished at R2 and the flux at A-region is given as:

    Φ(r) = S/4πD [1/r - 1/R2]

    My attempts at deriving this equation always leaves me with exponential terms if I'm assuming I'm solving the diffusion equation for a finite spherical reactor with a point source. Can anyone help me?
  2. jcsd
  3. Nov 7, 2016 #2
    Thanks for the thread! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post? The more details the better.
  4. Nov 9, 2016 #3


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    Staff Emeritus
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    Assuming symmetry, the current at the center of the Pb is zero. The current at the boundaries/interfaces on one side must equal that on the other side.
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