Extended 3D MHD simulations of q-profile evolution spheromaks

The profile evolution of spheromaks from S$\sim $10$^{3}$ to S$\sim $107 is examined by use of the NIMROD code [1] for the PBX (minor radius, a$\sim $6cm, B$\mathbin{\lower.3ex\hbox{$\buildrel<\over {\smash{\scriptstyle\sim}\vphantom{_x}}$}} $0.1T) and ACE (a$\sim $10cm, B$\mathbin{\lower.3ex\hbox{$\buildrel<\over {\smash{\scriptstyle\sim}\vphantom{_x}}$}} $0.5T) experiments [2], and a next-step device that compresses a plasma from a0$\simeq $0.5m to af=0.15m (with a convergence ratio, C=a0/af of 3), and following usual adiabatic scaling relations to Te$\sim $5keV. q-profile evolution is determined mainly by resistive decay, observing the evolution of toroidal modes as mode-rational surfaces enter the plasma and grow islands (like [3][4]). However, at high S, resistive dissipation times are long, so dq/dr is compared with tilt growth rate for conformal walls to the no wall limit. Evidence of pressure-limiting behavior is presented. Dynamic simulations of spheromaks undergoing a compression are also presented, and predicted effects [5] of toroidal rotation are examined due to conservation of momentum during compression. \\[4pt][1] C. R. Sovinec, et al J. Comput. Phys. 195, 355 (2004)\\[0pt][2] S. Woodruff et al Proc. ICC 2010\\[0pt] [3] H. S. Mclean \textit{et al} Physics of Plasmas, v 13, n 5, p 56105-1-8 (2006)\\[0pt] [4] B. Cohen et al Phys. Plasmas 12, 056106 (2005)\\[0pt] [5] D. D. Ryutov UCRL-JRNL-227066 (2007)