Radiative and reconnection instabilities: filaments and flares

The linear interaction of the radiative cooling (Field, 1965) and resistive tearing (Furth, Killeen and Rosenbluth, 1963) instabilities in sheared magnetic fields, which may lead to solar coronal filaments and flares, respectively, is studied. The dynamics and energetics are shown to be coupled by Coulomb resistivity eta(T) and/or by plasma compressibility, and the resulting MHD system is solved numerically to provide growth rates and eigenfunctions. Magnetic tearing in an inviscid and incompressible plasma is first treated. The local evolution of the temperature (and thus of the resistivity) is described by an energy equation which includes Joule heating and optically-thin radiation R(rho,T). Without radiation, there are two distinct solutions above a critical value of the magnetic Reynolds number S, a tearing-like and a Joule-heating mode. Below this point, the growth rates coalesce into a conjugate pair. It is demonstrated that, although the energetics are significantly affected by compressional effects, the dynamics are not, leaving the tearing mode relatively unaffected. Inhibition of plasma condensation in the radiative mode by perpendicular thermal conduction, most important in the short wavelength limit, is then demonstrated. Finally, results are applied to the characteristic unstable phenomena of solar activity, and are applied to the interrelations between filaments and flares