A NECESSARY CONDITION FOR THE STABILITY OF A CLASS OF 3-DIMENSIONAL LAMINATED EQUILIBRIA

A necessary condition is derived for the ideal magnetohydrodynamic sta bility of a class of three-dimensional laminated isothermal equilibria presented by Chou, Low, & Bhattacharjee (1993). The condition is deri ved by the use of a particular destabilizing trial function known as a '' ballooning mode.'' This choice of trial function allows the necess ary condition to be found by the solution of four coupled first-order ordinary differential equations that may be integrated along individua l field lines. Here the boundary conditions model the line-tying effec t of the dense photosphere. The necessary condition for stability toge ther with the sufficient condition derived by Chou gives a bound on ma rginal stability, the tightness of the bound depending on the paramete r regime. For the case of penumbral loops, considered by Chou, an appr oximate lower and upper bound on the critical value of the plasma beta for this model can be found. The upper bound on beta, however, is sma ller than that determined from observations.