Diffusion in Finite Media

Consider, then, a homogeneous slab of width a in the x direction and 

there is specified a uniform distribution of isotropic sources of strength go neutrons per unit area per unit time. Because of the finite extent of the x dimension, and the nonsymmetry of the problem, there will be a nonuniform distribution of the neutron population along the x direction the dependence on the y and z directions for given x, however, will be uniform. Thus, the flux is given by the function (x), and the appropriate differ- 

We seek two specific solutions to this problem, one based on boundary condition (5,57a) and the other on (5.576). In each case we require also a condition on the source plane which, when used with either (5.57a) or (5.576), yields the arbitrary constants Ai and Bi or Az and Bi, 

The boundary conditions to be used in the first case, namely, that the return current from the vacuum be zero at the source-free face of the slab, are 

We use for the partial currents the expressions (5.49). It is easily shown that the application of these conditions to the second of the general solutions given above yields the flux / i(x)  

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