Nonlinear dynamics of kink-unstable spheromak equilibria

Abstract

The nonlinear evolution of several kink-unstable, force-free equilibria inside a cylindrical flux conserver is studied by solving the nonlinear, three-dimensional, time-dependent equations of resistive magnetohydrodynamics (MHD). The stability properties of the equilibria are controlled by the slope, α, of the linear λ(ψ) profile (where λ=μ0J⋅B/B2 and ψ is the poloidal flux). Very unstable configurations (with α well beyond the stability threshold) are observed to fully relax toward the Taylor state, as predicted by relaxation theory. In contrast, marginally unstable cases undergo only partial relaxation. Since we consider decaying plasmas without open flux (no driving), the partial relaxation process is a result of the dynamics of marginally unstable configurations. The effect of the Lundquist number, S, on a fixed initial condition (a fixed α) is studied. Increasing S leads to a higher level of fluctuations and poloidal flux amplification. However, it is found that, despite the stronger activity, the final level of relaxation is determined only by the initial slope α (for the high S regime considered here). The nonaxisymmetric activity produced by the instability is studied. The relaxation event begins with a dominant n=1 kink mode responsible for poloidal flux amplification and ends with a low activity period (of several tens of Alfvén times) which produces a current redistribution process that flattens the λ profile. Finally, the MHD dynamo field is investigated.