Numerical calculation of neoclassical distribution functions and current profiles in low collisionality, axisymmetric plasmas
Abstract
A new code, the Neoclassical IonElectron 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 driftkinetic equations (DKEs) with linearized FokkerPlanckLandau collision operators. Solvability conditions on the DKEs determine the relevant nonadiabatic 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 »
 Authors:

 Program in Plasma Physics, Princeton University, Princeton, New Jersey 085430451 (United States)
 Princeton Plasma Physics Laboratory, Princeton, New Jersey 085430451 (United States)
 Plasma Science and Fusion Center, Massachusetts Institute of Technology, Cambridge, Massachusetts 021394307 (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 1070664X
 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; FOKKERPLANCK 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 IonElectron 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 driftkinetic equations (DKEs) with linearized FokkerPlanckLandau collision operators. Solvability conditions on the DKEs determine the relevant nonadiabatic 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, 183204 (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., M3DC{sup 1}[S. C. Jardin et al., Comput. Sci. Discovery 5, 014002 (2012)]).},
doi = {10.1063/1.4747501},
journal = {Physics of Plasmas},
issn = {1070664X},
number = 8,
volume = 19,
place = {United States},
year = {2012},
month = {8}
}