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

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 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.more » 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)]).« less

Authors:
 [1];  [2];  [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)
Publication Date:
OSTI Identifier:
22086043
Resource Type:
Journal Article
Journal Name:
Physics of Plasmas
Additional Journal Information:
Journal Volume: 19; Journal Issue: 8; Other Information: (c) 2012 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1070-664X
Country of Publication:
United States
Language:
English
Subject:
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

Citation Formats

Lyons, B C, Jardin, S C, and Ramos, J J. Numerical calculation of neoclassical distribution functions and current profiles in low collisionality, axisymmetric plasmas. United States: N. p., 2012. Web. doi:10.1063/1.4747501.
Lyons, B C, Jardin, S C, & Ramos, J J. Numerical calculation of neoclassical distribution functions and current profiles in low collisionality, axisymmetric plasmas. United States. doi:10.1063/1.4747501.
Lyons, B C, Jardin, S C, and Ramos, J J. Wed . "Numerical calculation of neoclassical distribution functions and current profiles in low collisionality, axisymmetric plasmas". United States. doi:10.1063/1.4747501.
@article{osti_22086043,
title = {Numerical calculation of neoclassical distribution functions and current profiles in low collisionality, axisymmetric plasmas},
author = {Lyons, B C and Jardin, S C and Ramos, J J},
abstractNote = {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)]).},
doi = {10.1063/1.4747501},
journal = {Physics of Plasmas},
issn = {1070-664X},
number = 8,
volume = 19,
place = {United States},
year = {2012},
month = {8}
}