Mathematics
Scientific paper
Dec 1986
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1986nascp2442..461v&link_type=abstract
In NASA. Goddard Space Flight Center Coronal and Prominence Plasmas p 461-463 (SEE N87-20871 13-92)
Mathematics
Ballooning Modes, Magnetic Fields, Magnetohydrodynamic Stability, Mathematical Models, Solar Corona, Flow Velocity, Linear Equations, Pressure Gradients, Topology, Vectors (Mathematics)
Scientific paper
The equations describing the linear evolution of resistive ballooning modes are obtained by using a modified WKB expansion in the short perpendicular wavelength, while variations of the perturbations along the field are described by a slowly varying amplitude, on which the tying boundary conditions are imposed. In general, given an equilibrium, there are certain ranges of magnetic surfaces for which the system predicts instability even without dissipation. The main conclusion is that within the resistive MHD approximation cylindrically symmetric arcades with pressure falling with radius are unstable to resistive localized modes; the growth rates, close to ideal marginal stability, are large, so that it would appear that energy could be released during 10 to 100 Alfven times. The wavelength of the modes is expected to be limited by the ion gyroradius, when stabilizing drift effects must be taken into account. The nonlinear evolution of resistive ballooning modes should be studied to assess their overall relevance to the violent and rapidly evolving phenomena observed on the sun.
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