Flux of Parallel Flow Momentum by Parallel Shear Flow Driven Instability

Abstract

The flux of parallel momentum by parallel shear flow driven instability is calculated with the self-consistent mode dispersion. The result indicates that the diffusive component has two characteristic terms: ν_D1 ∼ ṽ_x² /γ₍₀₎ and ν_D2 ∼ ṽ_x² /(k_∥²D_∥) where ṽ_x is the fluctuation radial velocity, γ₍₀₎ is the growth rate of the mode, k_∥ is the parallel wave number, and D_∥ is the electron diffusivity along the magnetic field. ν_D1 results when the parallel flow shear is above the threshold, while ν_D2 is important around the marginal state. Since typically ν_D1 ≫ ν_D2 ∼ D_n, where D_n is the particle diffusivity, the Prandtl number (≡ ν/D_n) becomes large when parallel flow shear driven instability occurs. This feature may explain the experimental observation on the difference between profiles of density and toroidal flow in edge and SOL plasmas.