Pitch Angle Diffusion in a Magnetic Mirror Geometry

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Abstract
The diffusion in pitch angle produced by Coulomb scattering of charged particles in a magnetic mirror is derived by geometrical arguments neglecting energy loss. The resultant diffusion equation in particle pitch angle and time agrees with the more fundamental Fokker‐Planck equation when energy loss is neglected. The diffusion coefficient may be defined as the inverse of a ``lifetime'' and for particles in the Van Allen radiation belt it is compared to the energy loss time neglecting pitch angle diffusion. It is shown that both energy loss and pitch angle diffusion must, in general, be considered simultaneously. However, the special problem of the early diffusion of mirror points of a monoenergetic group of electrons injected at very low pitch angle is discussed, and it is shown that significant changes in mirror altitude take place before energy loss is appreciable. Thus the present analysis has a limited but potentially important application to such problems of low injection as the Argus experiment.