Transient amplification of shear Alfvén waves and concomitant development of the gravitational instability

Making use of the ideal magnetohydrodynamic description in a plasma slab model, the transient amplification of shear Alfvén waves and their concomitant development into gravitational (ballooning) instabilities as the plasma pressure is increased are studied. When applied to tokamak geometry, for β<β_c/2, it is found that the curvature effect has a negligibly small influence on the evolution of the shear Alfvén waves. (Here, β is the ratio of plasma pressure to magnetic pressure, β_c =Rr_n/L_s² is the critical beta, R is the major radius, r_n is the plasma density length scale, and L_s is the magnetic shear length scale.) The curvature effect becomes dominant, however, for β≳(3/4)β_c, and the instability exhibits very strong growth whenever β≳1.1β_c.