ISSN:
1089-7674
Source:
AIP Digital Archive
Topics:
Physics
Notes:
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(R1/2M), where RM is the magnetic Reynolds number.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.870468
