Moment-Fourier approach to ion parallel fluid closures and transport for a toroidally confined plasma

Ji, Jeong-Young; Held, Eric D.; Andrew Spencer, J.; Na, Yong-Su

doi:10.1088/1361-6587/acb3f8

Title: Moment-Fourier approach to ion parallel fluid closures and transport for a toroidally confined plasma

Journal Article · Thu Feb 09 00:00:00 EST 2023 · Plasma Physics and Controlled Fusion

DOI:https://doi.org/10.1088/1361-6587/acb3f8· OSTI ID:1991370

^[1]; Held, Eric D. ^[1]; Andrew Spencer, J. ^[1]; Na, Yong-Su ^[2]

Utah State University, Logan, UT (United States)
Seoul National University (Korea, Republic of)

A general method of solving the drift kinetic equation is developed for an axisymmetric magnetic field. Expanding a distribution function in general moments, a set of ordinary differential equations is obtained. Successively expanding the moments and magnetic-field involved quantities in Fourier series, a set of linear algebraic equations is obtained. The set of full (Maxwellian and non-Maxwellian) moment equations is solved to express the first-order density, temperature, and flow velocity in terms of radial gradients of the zeroth-order pressure and temperature. Closure relations that connect parallel heat flux density and viscosity to the radial gradients and parallel gradients of temperature and flow velocity are also obtained by solving the non-Maxwellian moment equations. The closure relations combined with the linearized fluid equations reproduce the same solution obtained directly from the full moment equations. Furthermore, the method can be generalized to derive closures and transport for an electron-ion plasma and a multi-ion plasma in a general magnetic field.

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Research Organization:: Utah State Univ., Logan, UT (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Fusion Energy Sciences (FES)

Grant/Contract Number:: SC0022048; FG02-04ER54746

OSTI ID:: 1991370

Alternate ID(s):: OSTI ID: 1992376

Journal Information:: Plasma Physics and Controlled Fusion, Vol. 65, Issue 3; ISSN 0741-3335

Publisher:: IOP ScienceCopyright Statement

Country of Publication:: United States

Language:: English

References (28)

Local and global Fokker–Planck neoclassical calculations showing flow and bootstrap current modification in a pedestal Landreman, Matt; Ernst, Darin R. Plasma Physics and Controlled Fusion, Vol. 54, Issue 11 https://doi.org/10.1088/0741-3335/54/11/115006	journal	October 2012
The M3D- C ¹ approach to simulating 3D 2-fluid magnetohydrodynamics in magnetic fusion experiments Jardin, S. C.; Ferraro, N.; Luo, X. Journal of Physics: Conference Series, Vol. 125 https://doi.org/10.1088/1742-6596/125/1/012044	journal	July 2008
Plasma Transport in Toroidal Confinement Systems Rosenbluth, M. N. Physics of Fluids, Vol. 15, Issue 1 https://doi.org/10.1063/1.1693728	journal	January 1972
Nonlinear magnetohydrodynamics simulation using high-order finite elements Sovinec, C. R.; Glasser, A. H.; Gianakon, T. A. Journal of Computational Physics, Vol. 195, Issue 1 https://doi.org/10.1016/j.jcp.2003.10.004	journal	March 2004
Verification of continuum drift kinetic equation solvers in NIMROD Held, E. D.; Kruger, S. E.; Ji, J. -Y. Physics of Plasmas, Vol. 22, Issue 3 https://doi.org/10.1063/1.4914165	journal	March 2015
Effect of finite aspect ratio on the neoclassical ion thermal conductivity in the banana regime Chang, C. S. Physics of Fluids, Vol. 25, Issue 9 https://doi.org/10.1063/1.863934	journal	January 1982
BOUT++: A framework for parallel plasma fluid simulations Dudson, B. D.; Umansky, M. V.; Xu, X. Q. Computer Physics Communications, Vol. 180, Issue 9 https://doi.org/10.1016/j.cpc.2009.03.008	journal	September 2009
Neoclassical transport of impurities in tokamak plasmas Hirshman, S. P.; Sigmar, D. J. Nuclear Fusion, Vol. 21, Issue 9 https://doi.org/10.1088/0029-5515/21/9/003	journal	September 1981
Nonlinear gyrokinetic Coulomb collision operator Jorge, R.; Frei, B. J.; Ricci, P. Journal of Plasma Physics, Vol. 85, Issue 6 https://doi.org/10.1017/S0022377819000734	journal	November 2019
Moment approach to deriving parallel heat flow for general collisionality Ji, Jeong-Young; Held, Eric D.; Sovinec, Carl R. Physics of Plasmas, Vol. 16, Issue 2 https://doi.org/10.1063/1.3079072	journal	February 2009
Benchmarking NIMROD continuum kinetic formulations through the steady-state poloidal flow Jepson, J. R.; Hegna, C. C.; Held, E. D. Physics of Plasmas, Vol. 28, Issue 8 https://doi.org/10.1063/5.0054978	journal	August 2021
An Eulerian method for the solution of the multi-species drift-kinetic equation Belli, E. A.; Candy, J. Plasma Physics and Controlled Fusion, Vol. 51, Issue 7 https://doi.org/10.1088/0741-3335/51/7/075018	journal	June 2009
New velocity-space discretization for continuum kinetic calculations and Fokker–Planck collisions Landreman, Matt; Ernst, Darin R. Journal of Computational Physics, Vol. 243 https://doi.org/10.1016/j.jcp.2013.02.041	journal	June 2013
Exact linearized Coulomb collision operator in the moment expansion Ji, Jeong-Young; Held, Eric D. Physics of Plasmas, Vol. 13, Issue 10 https://doi.org/10.1063/1.2356320	journal	October 2006
A framework for moment equations for magnetized plasmas Ji, Jeong-Young; Held, Eric D. Physics of Plasmas, Vol. 21, Issue 4 https://doi.org/10.1063/1.4869999	journal	April 2014
Ion closure theory for high collisionality revisited Ji, Jeong-Young; Held, Eric D. Physics of Plasmas, Vol. 22, Issue 6 https://doi.org/10.1063/1.4922755	journal	June 2015
Plasma transport in a torus of arbitrary aspect ratio Hazeltine, R. D.; Hinton, F. L.; Rosenbluth, M. N. The Physics of Fluids, Vol. 16, Issue 10 https://doi.org/10.1063/1.1694191	journal	October 1973
A drift-kinetic analytical model for scrape-off layer plasma dynamics at arbitrary collisionality Jorge, R.; Ricci, P.; Loureiro, N. F. Journal of Plasma Physics, Vol. 83, Issue 6 https://doi.org/10.1017/S002237781700085X	journal	November 2017
Some properties of the M3D-C1 form of the three-dimensional magnetohydrodynamics equations Breslau, J.; Ferraro, N.; Jardin, S. Physics of Plasmas, Vol. 16, Issue 9 https://doi.org/10.1063/1.3224035	journal	September 2009
Recursive derivation of drift-kinetic equation Hazeltine, R. D. Plasma Physics, Vol. 15, Issue 1 https://doi.org/10.1088/0032-1028/15/1/009	journal	January 1973
Ion thermal conductivity and ion distribution function in the banana regime Taguchi, M. Plasma Physics and Controlled Fusion, Vol. 30, Issue 13 https://doi.org/10.1088/0741-3335/30/13/009	journal	December 1988
Kinetic calculation of neoclassical transport including self-consistent electron and impurity dynamics Belli, E. A.; Candy, J. Plasma Physics and Controlled Fusion, Vol. 50, Issue 9 https://doi.org/10.1088/0741-3335/50/9/095010	journal	July 2008
The JOREK non-linear extended MHD code and applications to large-scale instabilities and their control in magnetically confined fusion plasmas Hoelzl, Matthias; Huijsmans, Guido; Pamela, Stanislas Nuclear Fusion https://doi.org/10.1088/1741-4326/abf99f	journal	April 2021
Accurate numerical, integral methods for computing drift-kinetic Trubnikov-Rosenbluth potentials Spencer, J. Andrew; Adair, Brett; Held, Eric D. Journal of Computational Physics, Vol. 450 https://doi.org/10.1016/j.jcp.2021.110862	journal	February 2022
Full Coulomb collision operator in the moment expansion Ji, Jeong-Young; Held, Eric D. Physics of Plasmas, Vol. 16, Issue 10 https://doi.org/10.1063/1.3234253	journal	October 2009
Ion parallel closures Ji, Jeong-Young; Lee, Hankyu Q.; Held, Eric D. Physics of Plasmas, Vol. 24, Issue 2 https://doi.org/10.1063/1.4977054	journal	February 2017
Theory of plasma transport in toroidal confinement systems Hinton, F. L.; Hazeltine, R. D. Reviews of Modern Physics, Vol. 48, Issue 2 https://doi.org/10.1103/RevModPhys.48.239	journal	April 1976
Full linearized Fokker–Planck collisions in neoclassical transport simulations Belli, E. A.; Candy, J. Plasma Physics and Controlled Fusion, Vol. 54, Issue 1 https://doi.org/10.1088/0741-3335/54/1/015015	journal	December 2011

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Title: Moment-Fourier approach to ion parallel fluid closures and transport for a toroidally confined plasma

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