A numerical assessment of the Lundquist number requirement for relaxation current drive

Numerical simulations of a decaying, unstable spheromak equilibrium are conducted with the resistive magnetohydrodynamic code NIMROD [A. H. Glasser et al., Plasma Phys. Controlled Fusion 41, A747 (1999)] in a “bowtie” flux conserver geometry. The magnetic Lundquist number, S, is varied over one order of magnitude and the minimum value needed for relaxation current drive is identified, based on poloidal flux generation results. The results can be understood as a two-stage relaxation process with two governing time scales—the Alfvén time governing the growth of the unstable mode, and the Sweet–Parker reconnection time governing the relaxation toward the Taylor state. An analytic energy cascade model based on helicity conservation explains the NIMROD results. Implications for relaxation current drive in sustained spheromaks are discussed.