Behavior of perturbed plasma displacement near regular and singular Xpoints 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 normalmode 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 finiteelement 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 Xpoints (Bvector{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}0that includes a part of the symmetry axis (R=0) and is limited by two singular Xpoints (Bvector=0). At the embedded separatrix, the ideal MHD stabilitymore »
 Authors:

 Associazione EURATOMENEA sulla Fusione, CR Frascati, C.P. 6500044, 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 1070664X
 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 ONERACERT/DTIM/M2SN 2, avenue Edouard BelinBP 402531055, Toulouse Cedex 4. Behavior of perturbed plasma displacement near regular and singular Xpoints 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, & ONERACERT/DTIM/M2SN 2, avenue Edouard BelinBP 402531055, Toulouse Cedex 4. Behavior of perturbed plasma displacement near regular and singular Xpoints for compressible ideal magnetohydrodynamic stability analysis. United States. https://doi.org/10.1063/1.2220008
Alladio, F, Mancuso, A, Micozzi, P, Rogier, F, and ONERACERT/DTIM/M2SN 2, avenue Edouard BelinBP 402531055, Toulouse Cedex 4. 2006.
"Behavior of perturbed plasma displacement near regular and singular Xpoints 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 Xpoints for compressible ideal magnetohydrodynamic stability analysis},
author = {Alladio, F and Mancuso, A and Micozzi, P and Rogier, F and ONERACERT/DTIM/M2SN 2, avenue Edouard BelinBP 402531055, 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 normalmode 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 finiteelement 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 Xpoints (Bvector{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}0that includes a part of the symmetry axis (R=0) and is limited by two singular Xpoints (Bvector=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 = {1070664X},
number = 8,
volume = 13,
place = {United States},
year = {2006},
month = {8}
}