Magnetothermal instabilities in coronal arcades

The normal mode spectrum for the linearized MHD equations is investigated for a plasma in a cylindrical equilibrium. The equations describing these normal modes are solved numerically using a finite element code. The ballooning equations that describe localized modes are manipulated and a dispersion relation derived. It is shown that as the axial wave numberk is increased, the fundamental thermal and Alfvén modes can coalesce to form overstable magnetothermal modes. The ratio between the magnetic and thermal terms is varied and the existence of the magnetothermal modes examined. The corresponding growth rates are predicted by a WKB solution to the ballooning equations. The existence of these magnetothermal modes may be significant in the eruption of prominences into solar flares.