MHD Simulations of single helicity and quasi-single helicity states in Reversed Field Pinches

We present a systematic MHD study of single helicity (SH) states and quasi-single helicity (QSH) states in RFPs. We begin with cylindrical paramagnetic pinch equilibria with uniform resistivity, characterized by a single dimensionless parameter proportional to the toroidal electric field, or the RFP toroidal current parameter $\Theta$. For sufficiently high $\Theta$, there are several unstable $m=1$ ideal MHD instabilities, typically one of which is nonresonant, with 1/n just above $q(r=0)$. We evolve these modes nonlinearly to saturation for low Hartmann number H. We then obtain the $m=k=0$ quasilinear profiles, which typically have toroidal field reversal, and study their stability. For typical cases, these profiles may remain unstable to tearing modes, but only for sufficiently high $H$. For lower $H$ these states are stable. We show results indicating the proximity of these thresholds to the thresholds between SH and QSH behavior.