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Problem is from Introduction to Nuclear Engineering by John R. Lamarsh

5. An infinite diffusing system (see Section 5.6) has two point sources, located at r=0 and at r=Rcm. Derive the neutron flux and current at a point exactly on the line between the two sources and at a distance of 54 R from the origin. 5.6 SOLUTIONS OF THE DIFFUSION EQUATION Some simple diffusion problems are now considered to illustrate how the diffusion equation may be solved subject to the prior boundary conditions. These methods are applied in Chapter 6 to calculations of reactor properties. Infinite Planar Source Consider first an infinite planar source emitting S neutrons per cm/sec in an infi- nite diffusing medium. Examining Fig. 5.3, one sees that there is no variation in the y or z direction that could cause the flux to change. The flux in this case can only be a function of xthe distance from the plane. Also on further examination, one sees that the problem has symmetry about the x = 0 plane. The solution can then be divided into one for x > 0 and one for x 0 and one for x