Linear spectrum of magnetostatic and thermally conducting planar plasmas

Abstract

The linear spectrum of 1-D magnetostatic and thermally conducting equilibrium plasmas is analyzed. It is found that the influence of thermal conduction is fundamentally different on the various parts of the linear spectrum of ideal magnetohydrodynamics and that it is by far the most profound for the slow magnetoacoustic part. The ideal Alfvén continuous spectrum is unaffected by thermal conduction. However, the ideal slow continuous spectrum is replaced by the isothermal slow continuous spectrum. This new continuous spectrum owes its existence to thermal conduction but is independent of κ and involves a different range of continuum frequencies. In addition to these two continuous parts, the spectrum consists of discrete slow and fast magnetoacoustic modes and thermal modes. The point eigenvalues of the fast magnetoacoustic modes are slightly distorted in proportion to κ. However, the point eigenvalues of the slow magnetoacoustic modes lie on well-defined curves in the complex plane that are independent of κ and controlled by the ideal slow and isothermal slow continua. The discrete slow magnetoacoustic spectrum hangs, as it were, on the ideal slow and isothermal slow continua and is determined by the nonuniformity of the equilibrium. The thermal modes are the result of the inclusion of the nonideal effect of thermal conduction in the energy equation.