Dependence of Single- and Multi-Helicity States on Θ and the Hartmann number in the Force-free Visco-resistive MHD Model

Converged computations with the DEBS code indicate that, within the force-free resistive MHD model in a doubly periodic cylinder with perfectly conducting boundary conditions, the appearance of single-helicity or multihelicity states is determined primarily by the Hartmann number, and is relatively independent of the pinch parameter or the degree of field reversal. 1 Similarity Scaling in Visco-resistive MHD Many aspects of RFP dynamics are well described with the force-free visco-resistive MHD model[1]. In MKS units, the equations of this model are dV dt = 1 ρ J×B+ ν∇V , (1) and ∂B ∂t = ∇× (V ×B) + η μ0 ∇B , (2) where ν = μ/ρ is the kinematic viscosity, η is the resistivity, μ0J = ∇ × B and d/dt ≡ ∂/∂t +V · ∇V. These equations admit non-solenoidal flows (∇ ·V 6= 0), so that the implied stress tensor Π = ν∇V is neither symmetric nor invariant