The pseudospectrum of the resistive magnetohydrodynamics operator: Resolving the resistive Alfvén paradox

D. Borba, K. S. Riedel, W. Kerner, G. T.A. Huysmans, M. Ottaviani, P. J. Schmid

Research output: Contribution to journalArticlepeer-review

25 Scopus citations

Abstract

The "Alfvén paradox" is that as resistivity decreases, the discrete eigenmodes do not converge to the generalized eigenmodes of the ideal Alfvén continuum. To resolve the paradox, the ε-pseudospectrum of the resistive magnetohydrodynamic (RMHD) operator is considered. It is proven that for any ε, the ε-pseudospectrum contains the Alfvén continuum for sufficiently small resistivity. Formal ε-pseudoeigenmodes are constructed using the formal Wentzel-Kramers-Brillouin-Jeffreys solutions, and it is shown that the entire stable half-annulus of complex frequencies with ρ|ω|2=|k·B(x)|2 is resonant to order ε, i.e., belongs to the ε-pseudospectrum. The resistive eigenmodes are exponentially ill-conditioned as a basis and the condition number is proportional to exp(RM1/2), where RM is the magnetic Reynolds number. © 1994 American Institute of Physics.
Original languageEnglish (US)
Pages (from-to)3151-3160
Number of pages10
JournalPhysics of Plasmas
Volume1
Issue number10
DOIs
StatePublished - Jan 1 1994
Externally publishedYes

Bibliographical note

Generated from Scopus record by KAUST IRTS on 2022-09-13

ASJC Scopus subject areas

  • Condensed Matter Physics

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