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 language | English (US) |
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Pages (from-to) | 3151-3160 |
Number of pages | 10 |
Journal | Physics of Plasmas |
Volume | 1 |
Issue number | 10 |
DOIs | |
State | Published - Jan 1 1994 |
Externally published | Yes |
Bibliographical note
Generated from Scopus record by KAUST IRTS on 2022-09-13ASJC Scopus subject areas
- Condensed Matter Physics