Numerical Calculation of Neoclassical Distribution Functions and Current Profiles in Low Collisionality, Axisymmetric Plasmas
Authors: B.C. Lyons, S.C. Jardin, and J.J. Ramos
Abstract:
A new code, the Neoclassical Ion-Electron Solver (NIES), has been written to solve for stationary,
axisymmetric distribution functions (f ) in the conventional banana regime for both ions and elec
trons using a set of drift-kinetic equations (DKEs) with linearized Fokker-Planck-Landau collision
operators. Solvability conditions on the DKEs determine the relevant non-adiabatic pieces of f
(called h ). We work in a 4D phase space in which Ψ defines a flux surface, θ is the poloidal angle,
v is the total velocity referenced to the mean flow velocity, and λ is the dimensionless magnetic
moment parameter. We expand h in finite elements in both v and λ . The Rosenbluth potentials,
φ and ψ, which define the integral part of the collision operator, are expanded in Legendre series
in cos χ , where χ is the pitch angle, Fourier series in cos θ , and finite elements in v . At each ψ ,
we solve a block tridiagonal system for hi (independent of fe ), then solve another block tridiagonal
system for he (dependent on fi ). We demonstrate that such a formulation can be accurately and
efficiently solved. NIES is coupled to the MHD equilibrium code JSOLVER [J. DeLucia, et al., J.
Comput. Phys. 37 , pp 183-204 (1980).] allowing us to work with realistic magnetic geometries.
The bootstrap current is calculated as a simple moment of the distribution function. Results are
benchmarked against the Sauter analytic formulas and can be used as a kinetic closure for an MHD
code (e.g., M3D-C1 [S.C. Jardin, et al ., Computational Science & Discovery, 4 (2012).]).
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Submitted to: Physics of Plasmas (May 2012)
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Download PPPL-4775 (pdf KB pp)
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