Spheromak aspect-ratio effects on poloidal flux amplification

A short experimental run at the end of SSPX operation examined the effect of increasing the flux conserver length-to-aspect ration, L/R, from 1 to 1.2, thereby reducing the formation threshold for $\lambda _{gun} =\mu _0 I_{gun} /\Psi _{gun} $ from 10 m$^{-1}$ to $\approx $ 7.5 m$^{-1}$ with a corresponding increase in power efficiency [1]. Resistive MHD (NIMROD) simulations of flux amplification which agreed well with experiment at L/R=1 [2] agree fairly well with L/R=1.2 and have been extended to L/R=1.6, just under the tilt-mode stability limit (1.67) for an isolated spheromak. At the longest length, helicity injection changes from a chaotic relaxation process to a steady, high amplitude n=1 mode which opens the field lines throughout most of the flux conserver. Calculations are presented to elucidate the characteristics of the chaos for the standard flux-conserver dimensions. Comparisons are made among the simulations to determine the ``optimum'' L/R based on a trade-off between spheromak buildup efficiency and low mode activity. [1] R. D. Wood, et al., submitted to Phys. Rev. Letters. [2] E. B. Hooper, et al., Nucl. Fusion \textbf{47}, 1064 (2007).