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Title: Verification of continuum drift kinetic equation solvers in NIMROD

Abstract

Verification of continuum solutions to the electron and ion drift kinetic equations (DKEs) in NIMROD [C. R. Sovinec et al., J. Comp. Phys. 195, 355 (2004)] is demonstrated through comparison with several neoclassical transport codes, most notably NEO [E. A. Belli and J. Candy, Plasma Phys. Controlled Fusion 54, 015015 (2012)]. The DKE solutions use NIMROD's spatial representation, 2D finite-elements in the poloidal plane and a 1D Fourier expansion in toroidal angle. For 2D velocity space, a novel 1D expansion in finite elements is applied for the pitch angle dependence and a collocation grid is used for the normalized speed coordinate. The full, linearized Coulomb collision operator is kept and shown to be important for obtaining quantitative results. Bootstrap currents, parallel ion flows, and radial particle and heat fluxes show quantitative agreement between NIMROD and NEO for a variety of tokamak equilibria. In addition, velocity space distribution function contours for ions and electrons show nearly identical detailed structure and agree quantitatively. A Θ-centered, implicit time discretization and a block-preconditioned, iterative linear algebra solver provide efficient electron and ion DKE solutions that ultimately will be used to obtain closures for NIMROD's evolving fluid model.

Authors:
;  [1];  [2];  [3];  [4]
  1. Utah State University, Logan, Utah 84322-4415 (United States)
  2. Tech-X Corporation, Boulder, Colorado 80303 (United States)
  3. General Atomics, San Diego, California 92186-5608 (United States)
  4. Program in Plasma Physics, Princeton University, Princeton, New Jersey 08543-0451 (United States)
Publication Date:
OSTI Identifier:
22408212
Resource Type:
Journal Article
Journal Name:
Physics of Plasmas
Additional Journal Information:
Journal Volume: 22; Journal Issue: 3; Other Information: (c) 2015 AIP Publishing LLC; 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; 97 MATHEMATICAL METHODS AND COMPUTING; ALGEBRA; BOOTSTRAP CURRENT; COLLISIONS; COULOMB FIELD; DISTRIBUTION FUNCTIONS; ELECTRONS; FINITE ELEMENT METHOD; FOURIER ANALYSIS; HEAT FLUX; INCLINATION; IONS; ITERATIVE METHODS; KINETIC EQUATIONS; NEOCLASSICAL TRANSPORT THEORY; NIMROD; ONE-DIMENSIONAL CALCULATIONS; TOKAMAK DEVICES; VELOCITY; VERIFICATION

Citation Formats

Held, E. D., Ji, J. -Y., Kruger, S. E., Belli, E. A., and Lyons, B. C. Verification of continuum drift kinetic equation solvers in NIMROD. United States: N. p., 2015. Web. doi:10.1063/1.4914165.
Held, E. D., Ji, J. -Y., Kruger, S. E., Belli, E. A., & Lyons, B. C. Verification of continuum drift kinetic equation solvers in NIMROD. United States. https://doi.org/10.1063/1.4914165
Held, E. D., Ji, J. -Y., Kruger, S. E., Belli, E. A., and Lyons, B. C. Sun . "Verification of continuum drift kinetic equation solvers in NIMROD". United States. https://doi.org/10.1063/1.4914165.
@article{osti_22408212,
title = {Verification of continuum drift kinetic equation solvers in NIMROD},
author = {Held, E. D. and Ji, J. -Y. and Kruger, S. E. and Belli, E. A. and Lyons, B. C.},
abstractNote = {Verification of continuum solutions to the electron and ion drift kinetic equations (DKEs) in NIMROD [C. R. Sovinec et al., J. Comp. Phys. 195, 355 (2004)] is demonstrated through comparison with several neoclassical transport codes, most notably NEO [E. A. Belli and J. Candy, Plasma Phys. Controlled Fusion 54, 015015 (2012)]. The DKE solutions use NIMROD's spatial representation, 2D finite-elements in the poloidal plane and a 1D Fourier expansion in toroidal angle. For 2D velocity space, a novel 1D expansion in finite elements is applied for the pitch angle dependence and a collocation grid is used for the normalized speed coordinate. The full, linearized Coulomb collision operator is kept and shown to be important for obtaining quantitative results. Bootstrap currents, parallel ion flows, and radial particle and heat fluxes show quantitative agreement between NIMROD and NEO for a variety of tokamak equilibria. In addition, velocity space distribution function contours for ions and electrons show nearly identical detailed structure and agree quantitatively. A Θ-centered, implicit time discretization and a block-preconditioned, iterative linear algebra solver provide efficient electron and ion DKE solutions that ultimately will be used to obtain closures for NIMROD's evolving fluid model.},
doi = {10.1063/1.4914165},
url = {https://www.osti.gov/biblio/22408212}, journal = {Physics of Plasmas},
issn = {1070-664X},
number = 3,
volume = 22,
place = {United States},
year = {2015},
month = {3}
}