Three-dimensional simulation of ∇ T i-driven turbulence and transport

Abstract

The anomalous transport of ion thermal energy in a heated plasma slab confined by a uniform, straight magnetic field B_z has been investigated in three‐dimensional (3‐D) fluid simulations. Convection flows are driven unstable by ∇T_i and nonlinearly develop into narrow streams which carry cold edge plasma into the hot center. The convective flows undergo a sharp transition from laminar to turbulent behavior as the thermal energy confined in the slab is increased beyond a critical level. This transition is reminiscent of similar behavior in Rayleigh–Bénard convection in heated fluids. The convective thermal transport increases sharply as this turbulence threshold is exceeded. The structure of the flow patterns and associated transport also depend strongly on the physical dimensions of the confined plasma (L_x,L_y,L_z) =(a,2πa,2πR) compared with the ion Larmor radius ρ_i. For α=a²/Rρ_i>1, the dominant flows have k_yρ_i ∼a/R and produce an anomalous cross field thermal transport χ_⊥i that scales as v_ia²/R . In the opposite limit α=a²/Rρ_i k_ya∼1 and the transport is given by χ_⊥i∼ρ_iv_i, the Bohm scaling. Close to marginal stability, the transport is greatly reduced. These simulations imply that ion thermal transport in any straight field system such as a tandem mirror or a stellarator with weak shear and nearly rational fields will be strongly anomalous if the ∇T_i threshold for instability is exceeded.