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Title: Behavior of perturbed plasma displacement near regular and singular X-points for compressible ideal magnetohydrodynamic stability analysis

Abstract

The ideal magnetohydrodynamic (MHD) stability analysis of axisymmetric plasma equilibria is simplified if magnetic coordinates, such as Boozer coordinates ({psi}{sub T} radial, i.e., toroidal flux divided by 2{pi}, {theta} poloidal angle, {phi} toroidal angle, with Jacobian {radical}(g){proportional_to}1/B{sup 2}), are used. The perturbed plasma displacement {xi}-vector is Fourier expanded in the poloidal angle, and the normal-mode equation {delta}W{sub p}({xi}-vector*,{xi}-vector)={omega}{sup 2}{delta}W{sub k}({xi}-vector*,{xi}-vector) (where {delta}W{sub p} and {delta}W{sub k} are the perturbed potential and kinetic plasma energies and {omega}{sup 2} is the eigenvalue) is solved through a 1D radial finite-element method. All magnetic coordinates are however plagued by divergent metric coefficients, if magnetic separatrices exist within (or at the boundary of) the plasma. The ideal MHD stability of plasma equilibria in the presence of magnetic separatrices is therefore a disputed problem. We consider the most general case of a simply connected axisymmetric plasma, which embeds an internal magnetic separatrix--{psi}{sub T}={psi}{sub T}{sup X}, with rotational transform {iota}slantslash({psi}{sub T}{sup X})=0 and regular X-points (B-vector{ne}0)--and is bounded by a second magnetic separatrix at the edge--{psi}{sub T}={psi}{sub T}{sup max}, with {iota}slantslash({psi}{sub T}{sup max}){ne}0--that includes a part of the symmetry axis (R=0) and is limited by two singular X-points (B-vector=0). At the embedded separatrix, the ideal MHD stabilitymore » analysis requires the continuity of the normal plasma perturbed displacement variable, {xi}{sup {psi}}={xi}-vector{center_dot}{nabla}-vector{psi}{sub T}; the other displacement variables, the binormal {eta}{sup {psi}}={xi}-vector{center_dot}({nabla}-vector{theta}-{iota}slantslash{nabla}-vector{phi}) and the parallel {mu}=-{radical}(g){xi}-vector{center_dot}{nabla}-vector{phi}, can instead be discontinuous everywhere. The permissible asymptotic limits of ({xi}{sup {psi}},{eta}{sup {psi}},{mu}) are calculated for the unstable ({omega}{sup 2}<0) eigenvectors, imposing the regularity of {delta}W{sub p}, {delta}W{sub k}, and {xi}-vector at the embedded separatrix and at the edge separatrix. An intensified numerical radial mesh following Boozer magnetic coordinates is set up; it requires a logarithmic fit to the rotational transform near the embedded magnetic separatrix, a minimum distance between the radial mesh and both separatrices, and finally an extended spectrum of poloidal mode numbers in the Boozer angle. The numerical results are compared 'a posteriori' with the permissible asymptotic limits for the perturbed displacement: the radial displacement variable {xi}{sup {psi}} is found to be always near its most unstable asymptotic limit, while the full range of permissible asymptotic behaviors can be obtained for the binormal and the parallel displacement variables.« less

Authors:
; ; ;  [1]
  1. Associazione EURATOM-ENEA sulla Fusione, CR Frascati, C.P. 65-00044, Frascati, Rome (Italy)
Publication Date:
OSTI Identifier:
20860191
Resource Type:
Journal Article
Journal Name:
Physics of Plasmas
Additional Journal Information:
Journal Volume: 13; Journal Issue: 8; Other Information: DOI: 10.1063/1.2220008; (c) 2006 American Institute of Physics; 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; AXIAL SYMMETRY; BOUNDARY LAYERS; COORDINATES; EIGENFUNCTIONS; EIGENVALUES; EIGENVECTORS; FINITE ELEMENT METHOD; MAGNETOHYDRODYNAMICS; PLASMA; PLASMA CONFINEMENT; PLASMA INSTABILITY; RADIATION TRANSPORT; ROTATIONAL TRANSFORM; STABILITY; VECTORS

Citation Formats

Alladio, F, Mancuso, A, Micozzi, P, Rogier, F, and ONERA-CERT/DTIM/M2SN 2, avenue Edouard Belin-BP 4025-31055, Toulouse Cedex 4. Behavior of perturbed plasma displacement near regular and singular X-points for compressible ideal magnetohydrodynamic stability analysis. United States: N. p., 2006. Web. doi:10.1063/1.2220008.
Alladio, F, Mancuso, A, Micozzi, P, Rogier, F, & ONERA-CERT/DTIM/M2SN 2, avenue Edouard Belin-BP 4025-31055, Toulouse Cedex 4. Behavior of perturbed plasma displacement near regular and singular X-points for compressible ideal magnetohydrodynamic stability analysis. United States. https://doi.org/10.1063/1.2220008
Alladio, F, Mancuso, A, Micozzi, P, Rogier, F, and ONERA-CERT/DTIM/M2SN 2, avenue Edouard Belin-BP 4025-31055, Toulouse Cedex 4. 2006. "Behavior of perturbed plasma displacement near regular and singular X-points for compressible ideal magnetohydrodynamic stability analysis". United States. https://doi.org/10.1063/1.2220008.
@article{osti_20860191,
title = {Behavior of perturbed plasma displacement near regular and singular X-points for compressible ideal magnetohydrodynamic stability analysis},
author = {Alladio, F and Mancuso, A and Micozzi, P and Rogier, F and ONERA-CERT/DTIM/M2SN 2, avenue Edouard Belin-BP 4025-31055, Toulouse Cedex 4},
abstractNote = {The ideal magnetohydrodynamic (MHD) stability analysis of axisymmetric plasma equilibria is simplified if magnetic coordinates, such as Boozer coordinates ({psi}{sub T} radial, i.e., toroidal flux divided by 2{pi}, {theta} poloidal angle, {phi} toroidal angle, with Jacobian {radical}(g){proportional_to}1/B{sup 2}), are used. The perturbed plasma displacement {xi}-vector is Fourier expanded in the poloidal angle, and the normal-mode equation {delta}W{sub p}({xi}-vector*,{xi}-vector)={omega}{sup 2}{delta}W{sub k}({xi}-vector*,{xi}-vector) (where {delta}W{sub p} and {delta}W{sub k} are the perturbed potential and kinetic plasma energies and {omega}{sup 2} is the eigenvalue) is solved through a 1D radial finite-element method. All magnetic coordinates are however plagued by divergent metric coefficients, if magnetic separatrices exist within (or at the boundary of) the plasma. The ideal MHD stability of plasma equilibria in the presence of magnetic separatrices is therefore a disputed problem. We consider the most general case of a simply connected axisymmetric plasma, which embeds an internal magnetic separatrix--{psi}{sub T}={psi}{sub T}{sup X}, with rotational transform {iota}slantslash({psi}{sub T}{sup X})=0 and regular X-points (B-vector{ne}0)--and is bounded by a second magnetic separatrix at the edge--{psi}{sub T}={psi}{sub T}{sup max}, with {iota}slantslash({psi}{sub T}{sup max}){ne}0--that includes a part of the symmetry axis (R=0) and is limited by two singular X-points (B-vector=0). At the embedded separatrix, the ideal MHD stability analysis requires the continuity of the normal plasma perturbed displacement variable, {xi}{sup {psi}}={xi}-vector{center_dot}{nabla}-vector{psi}{sub T}; the other displacement variables, the binormal {eta}{sup {psi}}={xi}-vector{center_dot}({nabla}-vector{theta}-{iota}slantslash{nabla}-vector{phi}) and the parallel {mu}=-{radical}(g){xi}-vector{center_dot}{nabla}-vector{phi}, can instead be discontinuous everywhere. The permissible asymptotic limits of ({xi}{sup {psi}},{eta}{sup {psi}},{mu}) are calculated for the unstable ({omega}{sup 2}<0) eigenvectors, imposing the regularity of {delta}W{sub p}, {delta}W{sub k}, and {xi}-vector at the embedded separatrix and at the edge separatrix. An intensified numerical radial mesh following Boozer magnetic coordinates is set up; it requires a logarithmic fit to the rotational transform near the embedded magnetic separatrix, a minimum distance between the radial mesh and both separatrices, and finally an extended spectrum of poloidal mode numbers in the Boozer angle. The numerical results are compared 'a posteriori' with the permissible asymptotic limits for the perturbed displacement: the radial displacement variable {xi}{sup {psi}} is found to be always near its most unstable asymptotic limit, while the full range of permissible asymptotic behaviors can be obtained for the binormal and the parallel displacement variables.},
doi = {10.1063/1.2220008},
url = {https://www.osti.gov/biblio/20860191}, journal = {Physics of Plasmas},
issn = {1070-664X},
number = 8,
volume = 13,
place = {United States},
year = {2006},
month = {8}
}