Sheath broadening by the lower-hybrid-drift instability in post-implosion theta pinches

Theoretical and numerical studies of anomalous transport due to the lower-hybrid-drift instability show that this mode can cause significant diffusion in post-implosion theta pinches where T i ≫ T e and the electron drift velocity is below the ion thermal speed. Numerical results show that the diffusion scales with the simple diffusion velocity V D ∼ (c 2 ν an /ω 2 pe ) [∂ℓnB z /∂x] = − (c 2 ν an β/2ω pe 2 ) [∂ℓnn/∂x], where ν an is the anomalous collision frequency for the lower-hybrid-drift instability, estimated from quasilinear theory. (Here, B z is the magnetic field, n is the density, and β = 8πnT i /B z 2 is the local value of beta.) Moreover, the time evolution of the sheath width in the numerical calculation agrees well with the simple theoretical estimate [L n (t)/L n (t=0)] 4 = 1 + 4[V D (t=0)/L n (t = 0)]t, where L n (t) is the density sheath width [L n ≅ −(∂ℓnn/∂x) −1 ]. This simple formula for lower-hybrid-drift sheath broadening is valid for 0.5 r Li < L n < 0.5 (m i /m e ) 1/2 r Li , where r Li is the ion Larmor radius.