Nonlinear driven resonance in magnetic self-organization and the feasibility of a spheromak reactor

A Taylor relaxed plasma (${\bf j}=k{\bf B}$ with $k$ a constant) under external magnetic helicity injection encounters resonances in spatial frequencies of its force-free eigenmodes. Such driven resonance underlies the physics of magnetic self-organization and determines the flux amplification in laboratory helicity injection applications. Here we show that for partially relaxed plasmas where the deviation from the fully relaxed Taylor state, for example, a flux-dependent $k$, is a function of the normalized flux $\chi/\chi_{a}$ with $\chi_{a}$ the poloidal flux at the magnetic axis, a modified driven resonance persists even if $k(\chi)$ has an order-unity variation across the flux surfaces. We will also explain why experimentally accessing such nonlinear resonance appears to hold the key for a potential spheromak reactor. Ref. X.Z.Tang, Phys. Rev. Lett. {\bf 98}, 175001 (2007).