Theory of the Linear Fokker-Planck Collision Operator

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Abstract
The linearized Fokker‐Planck collision integral with coulomb interaction is expanded in terms of surface spherical harmonics. The radial part of the distribution function is shown to be governed by a set of decoupled differential‐integral equations. The differential operators are shown to be self‐adjoint while the integral operators are symmetric and completely continuous. The spectrum of the eigenvalues contains, on top of discrete points, a continuous part ranging from zero to minus infinity. The discrete part of the spectrum is obtained by requiring that the corresponding eigenvectors have a definite asymptotic behavior at large velocity. A variation principle is constructed for the computation of the discrete spectrum.

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