Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-27T22:38:03.492Z Has data issue: false hasContentIssue false
  • English
  • Français

Gyrokinetic Simulation of Magnetic Compressional Modes in General Geometry

Published online by Cambridge University Press:  20 August 2015

Peter Porazik  and
Zhihong Lin
Peter Porazik*
Affiliation:
Department of Physics and Astronomy, University of California, Irvine, CA 92697, USA
Zhihong Lin*
Affiliation:
Department of Physics and Astronomy, University of California, Irvine, CA 92697, USA
*
Email:pporazik@uci.edu
Corresponding author.Email:zhihongl@uci.edu
Get access

Abstract

A method for gyrokinetic simulation of low frequency (lower than the cyclotron frequency) magnetic compressional modes in general geometry is presented. The gyrokinetic-Maxwell system of equations is expressed fully in terms of the compressional component of the magnetic perturbation, δB∥, with finite Larmor radius effects. This introduces a “gyro-surface” averaging of δB∥ in the gyrocenter equations of motion, and similarly in the perpendicular Ampere’s law, which takes the form of the perpendicular force balance equation. The resulting system can be numerically implemented by representing the gyro-surface averaging by a discrete sum in the configuration space. For the typical wavelength of interest (on the order of the gyroradius), the gyro-surface averaging can be reduced to averaging along an effective gyro-orbit. The phase space integration in the force balance equation can be approximated by summing over carefully chosen samples in the magnetic moment coordinate, allowing for an efficient numerical implementation.

Keywords

02.60.-x02.70.-c52.65.TtFinite Larmor radius effectsgyrokinetic simulationcompressional modesgyro-surface average
Type
Research Article
Information
Communications in Computational Physics , Volume 10 , Issue 4 , October 2011 , pp. 899 - 911
Copyright
Copyright © Global Science Press Limited 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Antonsen, T. M. J. and Lane, B., Kinetic equations for low frequency instabilities in inhomo-geneous plasmas, Phys. Fluids., 23 (1980), 1205–1214.Google Scholar
[2]Belova, E. V., Denton, R. E. and Chan, A. A., Hybrid simulations of the effects of energetic particles on low-frequency mhd waves, J. Comput. Phys., 136 (1997), 324–336.Google Scholar
[3]Brizard, A., Nonlinear gyrokinetic maxwell-vlasov equations using magnetic coordinates, J. Plasma. Phys., 41 (1989), 541–559.Google Scholar
[4]Brizard, A., Nonlinear gyrofluid description of turbulent magnetized plasmas, Phys. Fluids. B., 4 (1992), 1213–1228.Google Scholar
[5]Brizard, A. J. and Hahm, T. S., Foundations of nonlinear gyrokinetic theory, Rev. Mod. Phys., 79 (2007), 421–468.Google Scholar
[6]Cary, J. R. and Brizard, A. J., Hamiltonian theory of guiding-center motion, Rev. Mod. Phys., 81 (2009), 693–738.Google Scholar
[7]Catto, P. J., Linearized gyro-kinetics, Plasma. Phys., 20 (1978), 719–722.Google Scholar
[8]Chen, L. and Hasegawa, A., Kinetic theory of geomagnetic pulsations I-internal excitations by energetic particles, J. Geophys. Res., 96 (1991), 1503–1512.Google Scholar
[9]Crabtree, C. and Chen, L., Finite gyroradius theory of drift compressional modes, Geophys. Res. Lett., 31 (2004), L17804.Google Scholar
[10]Frieman, E. A. and Chen, L., Nonlinear gyrokinetic equations for low-frequency electromagnetic waves in general plasma equilibria, Phys. Fluids., 25 (1982), 502–508.Google Scholar
[11]Hahm, T. S., Wang, L. and Madsen, J., Fully electromagnetic nonlinear gyrokinetic equations for tokamak edge turbulence, Phys. Plasmas., 16 (2009), 022305.Google Scholar
[12]Hasegawa, A., Drift mirror instability in the magnetosphere, Phys. Fluids., 12 (1969), 2642–2650.Google Scholar
[13]Hasegawa, A., Plasma instabilities in the magnetosphere, Rev. Geophys., 9 (1971), 703–772.Google Scholar
[14]Holod, I., Zhang, W. L., Xiao, Y. and Lin, Z., Electromagnetic formulation of global gyrokinetic particle simulation in toroidal geometry, Phys. Plasmas., 16 (2009), 122307.Google Scholar
[15]Joiner, N., Hirose, A. and Dorland, W., Parallel magnetic field perturbations in gyrokinetic simulations, Phys. Plasmas., 17 (2010), 072104.Google Scholar
[16]Kotschenreuther, M., Rewoldt, G. and Tang, W. M., Comparison of initial value and eigenvalue codes for kinetic toroidal plasma instabilities, Comput. Phys. Commun., 88 (1995), 128–140.Google Scholar
[17]Lee, W. W., Gyrokinetic particle simulation model, J. Comput. Phys., 72 (1987), 243–269.Google Scholar
[18]Lee, W. W. and Qin, H., Alfven waves in gyrokinetic plasmas, Phys. Plasmas., 10 (2003), 3196–3203.Google Scholar
[19]Lin, Y., Wang, X., Lin, Z. and Chen, L., A gyrokinetic electron and fully kinetic ion plasma simulation model, Plasma. Phys. Control. Fusion., 47 (2005), 657.Google Scholar
[20]Lin, Z., Hahm, T. S., Lee, W. W., Tang, W. M. and White, R. B., Turbulent transport reduction by zonal flows: massively parallel simulations, Science., 281 (1998), 1835–1837.Google Scholar
[21]Lin, Z. and Lee, W. W., Method for solving the gyrokinetic poisson equation in general geometry, Phys. Rev. E., 52 (1995), 5646–5652.Google Scholar
[22]Parker, S. E., Chen, Y., Wan, W., Cohen, B. I. and Nevins, W. M., Electromagnetic gyrokinetic simulations, Phys. Plasmas., 11 (2004), 2594–2599.Google Scholar
[23]Porazik, P. and Lin, Z., Gyrokinetic particle simulation of drift-compressional modes in dipole geometry, sumbitted to Phys. Plasmas., (2011).Google Scholar
[24]Qin, H., Tang, W. M., Lee, W. W. and Rewoldt, G., Gyrokinetic perpendicular dynamics, Phys. Plasmas., 6 (1999), 1575–1588.Google Scholar
[25]Qu, H., Lin, Z. and Chen, L., Gyrokinetic theory and simulation of mirror instability, Phys. Plasmas., 14 (2007), 042108.Google Scholar
[26]Rosenbluth, M. N., Magnetic trapped-particle modes, Phys. Rev. Lett., 46 (1981), 1525–1528.Google Scholar
[27]Rutherford, P. H. and Frieman, E. A., Drift instabilities in general magnetic field configurations, Phys. Fluids., 11 (1968), 569–585.CrossRefGoogle Scholar