BIFURCATION ANALYSIS FOR SYMMETRIC EQUILIBRIA WITH LOCALISED MAGNETIC SHEAR IN 2D RRMHD

摘要

For reduced resistive magnetohydrodynamics we consider the class of symmetric equilibria ψ_e~α(x) = ψ_0~α/cosh~2 αx with no motion and analyse the sequence of bifurcations varying the aspect ratio ∈ of the domain as a control parameter of the magnetic shear. The stability threshold in the inviscid case ∈_0 scales linearly with α. Destabilization happens because of a symmetry-breaking bifurcation, occurring at ∈_c < ∈_0 because of viscosity, which originates a stable equilibrium with a small magnetic island and vortices. For α = 1 the equilibrium disappears by tangent bifurcation at a critical value ∈_P. Above ∈_P, no stationary solutions with small island exist and the system very rapidly develops an island of macroscopic size. Differently, for α = 2, i.e. for higher magnetic shear at x = 0, the equilibrium with small island does not disappear, but becomes unstable at ∈_P.= 2.437. Below this value a stable equilibrium of weaker symmetry has been detected, with magnetic island of essentially the same size but velocity field with different topology and strongly enhanced. The phenomenology is observed for the first time in RRMHD and is of interest because connected with experimental evidences in fusion plasmas.