Steady-state magnetohydrodynamic clump turbulence

The turbulent steady state of the magnetohydrodynamic (MHD) clump instability [Phys. Fluids 31, 2122 (1988)] is investigated. The steady state is determined by the balance between clump growth by turbulent mixing and clump decay by field line stochasticity. The turbulent fields driving the mixing are generated self-consistently from Ampère’s law and conserve the magnetic helicity. In the steady state, the mean current and magnetic field satisfy J0=μB0, where μ depends on the mean-square fluctuation level. Above this critical point (J0>μB0), the plasma is MHD clump unstable. MHD clump instability is a dynamical route to the force-free, Taylor state. For the steady state to exist, μ must exceed a threshold on the order of that required for B0z field reversal. Steady-state MHD clump turbulence corresponds to field reversed Taylor states. From the μ threshold condition, the steady-state fluctuation spectrum (δBrms/B) is calculated and shown to increase with mean driving current as θ3, where θ is the pinch parameter.