Numerical calculation of neoclassical distribution functions and current profiles in low collisionality, axisymmetric plasmas

Journal Article · Wed Aug 15 00:00:00 EDT 2012 · Physics of Plasmas

DOI:https://doi.org/10.1063/1.4747501· OSTI ID:22086043

Lyons, B C ^[1]; Jardin, S C ^[2]; Ramos, J J ^[3]

---

1. Program in Plasma Physics, Princeton University, Princeton, New Jersey 08543-0451 (United States)
2. Princeton Plasma Physics Laboratory, Princeton, New Jersey 08543-0451 (United States)
3. Plasma Science and Fusion Center, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139-4307 (United States)

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 electrons 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 {psi} defines a flux surface, {theta} is the poloidal angle, v is the magnitude of the velocity referenced to the mean flow velocity, and {lambda} is the dimensionless magnetic moment parameter. We expand h in finite elements in both v and {lambda}. The Rosenbluth potentials, {Phi} and {Psi}, which define the integral part of the collision operator, are expanded in Legendre series in cos{chi}, where {chi} is the pitch angle, Fourier series in cos{theta}, and finite elements in v. At each {psi}, we solve a block tridiagonal system for h{sub i} (independent of f{sub e}), then solve another block tridiagonal system for h{sub e} (dependent on f{sub i}). 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, 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-C{sup 1}[S. C. Jardin et al., Comput. Sci. Discovery 5, 014002 (2012)]).

• OSTI ID: 22086043
• Journal Information: Physics of Plasmas, Vol. 19, Issue 8; Other Information: (c) 2012 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 1070-664X
• Country of Publication: United States
• Language: English

Related Subjects

70 PLASMA PHYSICS AND FUSION TECHNOLOGY
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
AXIAL SYMMETRY
BANANA REGIME
BOOTSTRAP CURRENT
DISTRIBUTION FUNCTIONS
FINITE ELEMENT METHOD
FOKKER-PLANCK EQUATION
INCLINATION
KINETIC EQUATIONS
MAGNETIC MOMENTS
MAGNETIC SURFACES
MAGNETOHYDRODYNAMICS
MHD EQUILIBRIUM
NEOCLASSICAL TRANSPORT THEORY
PHASE SPACE