Theory of nonlinear diffusion of plasma across the magnetic field of a toroidal multipole

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Abstract
A phenomenological derivation of a one‐dimensional model of crossfield plasma diffusion in toroidal multipole geometry is presented. Experimental studies have shown previously that this one‐dimensional model describes the observed density profile shape and decay in the Wisconsin levitated octupole in certain regimes. Simplified mathematical studies of the model (which did not give adequate attention to geometrical effects) have also shown that a stable profile should evolve from an arbitrary initial particle distribution. Here, a numerical treatment and a discussion of the effects of multipole geometry are given. Comparison is made with experimental results. Finally, analytical studies give additional evidence that the observed rapid evolution toward a stable profile should be expected theoretically. It is concluded that the phenomenological model is generally useful for determining diffusion coefficient magnitude and scaling with density once the density profiles have been determined experimentally.

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