Formation and sustainment of electrostatically driven spheromaks in the resistive magnetohydrodynamic model

Abstract

The nonlinear time-dependent equations of resistive magnetohydrodynamics are solved in simply connected domains to investigate spheromak formation and sustainment with electrostatic current drive. Spheromak magnetic fields are generated in three-dimensional computations as the nonlinear state resulting from an unstable pinch. Perturbations convert continuously supplied toroidal magnetic flux into poloidal magnetic flux, leading to “flux amplification” of field embedded in the electrodes. Relaxation of the axisymmetric component of the parallel current profile can be substantial, and the final nonlinear state is steady over a wide range of parameters. However, for sufficiently large values of Lundquist number or sufficiently large applied potential, nonsteady final states are observed with periodic relaxation events in some cases. Under most conditions, the saturated configuration exhibits chaotic scattering of the magnetic field lines. Conditions just above the marginal point of pinch instability sustain large closed flux surfaces in steady state; a weakly kinked pinch current threads the toroidal region of closed flux surfaces and imposes stellarator-like helical transform. Closed flux surfaces also form during decay, due to reduced fluctuation levels and average toroidal current driven directly by inductive electric field.