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Hybrid FRC equilibria with Fokker-Planck distributions

Author: Loren C Steinhauer
Requested Type: Poster Only
Submitted: 2009-12-04 10:53:00

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University of Washington
14700 N.E. 95th St., Ste 100
Redmond, WA   98011
USA

Abstract Text:
Field-reversed configurations (FRC) are highly-kinetic plasmas where the ion gyroradius is a significant fraction of the overall plasma size. This is especially so near the O-point and X-points where the gyroradius goes to infinity, and in the edge region where the gyroradius is comparable to the density gradient length scale. While kinetic effects have been investigated in the context of stability, generally overlooked is the fact that kinetics also affect the equilibrium. FRC equilibria are investigated using a hybrid formulation, i.e. ions governed by the Vlasov equation and electrons as a warm, massless fluid. In axisymmetric equilibria, the ion distribution is expressible as a function of the Hamiltonian and the canonical angular momentum. Kinetic ion equilibria were originally analyzed for Astrons [Lovelace 1978]. For FRCs the distribution function is assumed to have a “thermal” dependence on the Hamiltonian. Its dependence on the canonical angular momentum (Ptheta) is a solution to the steady Fokker-Planck equation including an end-loss “sink” in the unconfined region in Ptheta and an artificial source to maintain steady state in the confined region. Using this solution the important moments are expressible as analytic functions of the radius coordinate and the magnetic flux variable. Equilibrium is found by combining this result with Ampere’s law, which calls for the azimuthal current density moment. This equation is readily solvable in 1D or 2D by an iterative procedure. Solutions for elongated FRCs (1D) are presented and the implications discussed.

Characterization: A1

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