Computation of resistive instabilities by matched asymptotic expansions
Here, we present a method for determining the linear resistive magnetohydrodynamic (MHD) stability of an axisymmetric toroidal plasma, based on the method of matched asymptotic expansions. The plasma is partitioned into a set of ideal MHD outer regions, connected through resistive MHD inner regions about singular layers where q = m/n, with m and n toroidal mode numbers, respectively, and q the safety factor. The outer regions satisfy the ideal MHD equations with zerofrequency, which are identical to the EulerLagrange equations for minimizing the potential energy delta W. The solutions to these equations go to infinity at the singular surfaces. The inner regions satisfy the equations of motion of resistive MHD with a finite eigenvalue, resolving the singularity. Both outer and inner regions are solved numerically by newly developed singular Galerkin methods, using specialized basis functions. These solutions are matched asymptotically, providing a complex dispersion relation which is solved for global eigenvalues and eigenfunctions in full toroidal geometry. The dispersion relation may have multiple complex unstable roots, which are found by advanced rootfinding methods. These methods are much faster and more robust than the previous numerical methods. The new methods are applicable to more challenging highpressure and strongly shaped plasmamore »
 Authors:

^{[1]}
;
^{[2]};
^{[2]}
 Fusion Theory and Computation, Inc., Kingston, WA (United States)
 Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
 Publication Date:
 Report Number(s):
 PPPL5292
Journal ID: ISSN 1070664X; TRN: US1701243
 Grant/Contract Number:
 AC0209CH11466; FG0205ER54811; SC0016106
 Type:
 Accepted Manuscript
 Journal Name:
 Physics of Plasmas
 Additional Journal Information:
 Journal Volume: 23; Journal Issue: 11; Journal ID: ISSN 1070664X
 Publisher:
 American Institute of Physics (AIP)
 Research Org:
 Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States); Fusion Theory and Computation, Inc., Kingston, WA (United States)
 Sponsoring Org:
 USDOE Office of Science (SC), Fusion Energy Sciences (FES) (SC24)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; 01 COAL, LIGNITE, AND PEAT; resistive MHD instabilities
 OSTI Identifier:
 1340151
 Alternate Identifier(s):
 OSTI ID: 1332585; OSTI ID: 1418992
Glasser, A. H., Wang, Z. R., and Park, J. K.. Computation of resistive instabilities by matched asymptotic expansions. United States: N. p.,
Web. doi:10.1063/1.4967862.
Glasser, A. H., Wang, Z. R., & Park, J. K.. Computation of resistive instabilities by matched asymptotic expansions. United States. doi:10.1063/1.4967862.
Glasser, A. H., Wang, Z. R., and Park, J. K.. 2016.
"Computation of resistive instabilities by matched asymptotic expansions". United States.
doi:10.1063/1.4967862. https://www.osti.gov/servlets/purl/1340151.
@article{osti_1340151,
title = {Computation of resistive instabilities by matched asymptotic expansions},
author = {Glasser, A. H. and Wang, Z. R. and Park, J. K.},
abstractNote = {Here, we present a method for determining the linear resistive magnetohydrodynamic (MHD) stability of an axisymmetric toroidal plasma, based on the method of matched asymptotic expansions. The plasma is partitioned into a set of ideal MHD outer regions, connected through resistive MHD inner regions about singular layers where q = m/n, with m and n toroidal mode numbers, respectively, and q the safety factor. The outer regions satisfy the ideal MHD equations with zerofrequency, which are identical to the EulerLagrange equations for minimizing the potential energy delta W. The solutions to these equations go to infinity at the singular surfaces. The inner regions satisfy the equations of motion of resistive MHD with a finite eigenvalue, resolving the singularity. Both outer and inner regions are solved numerically by newly developed singular Galerkin methods, using specialized basis functions. These solutions are matched asymptotically, providing a complex dispersion relation which is solved for global eigenvalues and eigenfunctions in full toroidal geometry. The dispersion relation may have multiple complex unstable roots, which are found by advanced rootfinding methods. These methods are much faster and more robust than the previous numerical methods. The new methods are applicable to more challenging highpressure and strongly shaped plasma equilibria and generalizable to more realistic inner region dynamics. In the thermonuclear regime, where the outer and inner regions overlap, they are also much faster and more accurate than the straightthrough methods, which treat the resistive MHD equations in the whole plasma volume.},
doi = {10.1063/1.4967862},
journal = {Physics of Plasmas},
number = 11,
volume = 23,
place = {United States},
year = {2016},
month = {11}
}