Quasilinear ballooning mode saturation

Abstract

At small amplitudes, resistive ballooning modes form a quasilinear sheet current, which opposes the magnetic flux reconnection. In the ensuing Rutherford regime [Phys. Fluids 16, 1903 (1973)] the sheet current at each resonance surface decays. To remain in a quasistatic equilibrium, magnetic islands form and thereby flatten the pressure at each resonance surface. For local instabilities, a spectrum of modes are excited, each flattening the pressure gradient at its resonance surface. The resulting averaged quasilinear pressure profile has a Cantor setlike structure. Using the equivalence of harmonics, the calculation of the saturated amplitudes is reformulated as a nonlinear eigenvalue problem of an integral differential equation with the quasimode formalism.