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Title: On Ideal Stability of Cylindrical Localized Interchange Modes

Abstract

Stability of cylindrical localized ideal pressure-driven interchange plasma modes is revisited. Converting the underlying eigenvalue problem into the form of the Schroedinger equation gives a new simple way of deriving the Suydam stability criterion and calculating the growth rates of unstable modes. Near the marginal stability limit the growth rate is exponentially small and the mode has a double-peak structure.

Authors:
Publication Date:
Research Org.:
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
942022
Report Number(s):
UCRL-JRNL-231049
Journal ID: ISSN 0863-1042; CPPHEP; TRN: US0807512
DOE Contract Number:
W-7405-ENG-48
Resource Type:
Journal Article
Resource Relation:
Journal Name: Contributions to Plasma Physics, vol. 47, no. 6, August 30, 2007, pp. 447-450; Journal Volume: 47; Journal Issue: 6
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION; EIGENVALUES; PLASMA; SCHROEDINGER EQUATION; STABILITY

Citation Formats

Umansky, M V. On Ideal Stability of Cylindrical Localized Interchange Modes. United States: N. p., 2007. Web. doi:10.1002/ctpp.200710058.
Umansky, M V. On Ideal Stability of Cylindrical Localized Interchange Modes. United States. doi:10.1002/ctpp.200710058.
Umansky, M V. Tue . "On Ideal Stability of Cylindrical Localized Interchange Modes". United States. doi:10.1002/ctpp.200710058. https://www.osti.gov/servlets/purl/942022.
@article{osti_942022,
title = {On Ideal Stability of Cylindrical Localized Interchange Modes},
author = {Umansky, M V},
abstractNote = {Stability of cylindrical localized ideal pressure-driven interchange plasma modes is revisited. Converting the underlying eigenvalue problem into the form of the Schroedinger equation gives a new simple way of deriving the Suydam stability criterion and calculating the growth rates of unstable modes. Near the marginal stability limit the growth rate is exponentially small and the mode has a double-peak structure.},
doi = {10.1002/ctpp.200710058},
journal = {Contributions to Plasma Physics, vol. 47, no. 6, August 30, 2007, pp. 447-450},
number = 6,
volume = 47,
place = {United States},
year = {Tue May 15 00:00:00 EDT 2007},
month = {Tue May 15 00:00:00 EDT 2007}
}
  • Ideal magnetohydrodynamic theory for localized interchange modes is developed for toroidal plasmas with anisotropic pressure. The work extends the existing theories of Johnson and Hastie [Phys. Fluids 31, 1609 (1988)], etc., to the low n mode case, where n is the toroidal mode number. Also, the plasma compressibility is included, so that the coupling of the parallel motion to perpendicular one, i.e., the so-called apparent mass effect, is investigated in the anisotropic pressure case. The singular layer equation is obtained, and the generalized Mercier's criterion is derived.
  • The stabilization of cylindrical plasmas by resistive walls combined with plasma rotation is analyzed. Perturbations with a single mode rational surface q=m/n in a finitely conducting plasma are treated by the {open_quotes}resistive kink{close_quotes} dispersion relation of Coppi {ital et al.} [Sov. J. Plasma Phys. {bold 2}, 533 (1976)]. The possibilities for stabilization of ideal and resistive instabilities are explored systematically in different regions of parameter space. The study confirms that an ideal instability can be stabilized by a close-fitting wall and a rotation velocity on the order of resistive growth rates [J. M. Finn, Phys. Plasmas {bold 2}, 3782 (1995)].more » However, the region in parameter space where such stabilization occurs is very small and appears to be difficult to exploit in experiments. The overall conclusion from the cylindrical plasma model is that resistive modes can readily be wall stabilized, whereas complete wall stabilization is hard to achieve for plasmas that are ideally unstable with the wall at infinity. {copyright} {ital 1997 American Institute of Physics.}« less
  • Eigenmode analysis of a magnetic-shear-localized ideal magnetohydrodynamic interchange instability in the presence of plasma compressibility indicates the marginal stability criterion (D{sub I}=1/4) is not affected by the compressibility effects. Above the marginal stability criterion, plasma compressibility causes a significant reduction in the growth rate of an ideal interchange instability.
  • Pressure-driven ideal modes cannot completely interchange flux tubes of a sheared magnetic field; instead, they saturate, forming new helical equilibria. These equilibria are studied both analytically and numerically with reduced magnetohydrodynamic equations in a flux-conserving Lagrangian representation. For unstable localized modes, the structure of the nonlinear layer generated around the resonant flux surface depends on the value of Mercier parameter {ital D}{sub M}. The shape of magnetic surfaces in the vicinity of resonance is changed significantly even close to the instability threshold. However, the radial width of the affected layer becomes exponentially small near the threshold. The appearance of sheetmore » currents and islandlike structures along the resonant flux surface may be of interest for the description of forced reconnection in models with finite resistivity. This study also includes the case of ballooning instability by representing nonlocal driving terms through the matching parameter {Delta}{prime}, which defines the outer boundary conditions for the interchange layer.« less