Fourier Transform Methods in Linear Transport Theory

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Abstract
We generalize a three‐dimensional Fourier transform method presented previously, to solve various forms of the linearized transport equation in planar geometry. Infinite‐space problems are in general easily treated by our procedures. Half‐space problems may also be solved analytically in, at least, the following cases: (i) separable scattering kernel (arbitrary particle speed); (ii) one‐speed, anistropic scattering with rotation‐invariant kernel; (iii) one‐dimensional energy‐dependent kernel of Kac; (iv) multigroup transport with down scattering only. The general importance of recursion relations to problems with nonseparable kernels is emphasized. A comparison is made between our methods and the two‐dimensional singular eigenfunction approach, and a criterion is presented for the analytic solubility of any problem of the general form considered.