Kinetic Stress and Particle Transport by Stochastic Fields and Turbulence

It is general wisdom that stochastic magnetic fields affect the electron heat transport in a tokamak. In the L-H transition, with resonant magnetic perturbation (RMP), the transport of ion heat, particles, toroidal momentum can also be influenced by stochastic fields due to RMP. A well-known model from Finn et al. discussed how toroidal flow is affected under the influence of stochastic fields. However, they merely have an Elsässer-like variable of parallel rotation and particle density—no explicit momentum and particle density transport presented. Moreover, they didn’t mention the kinetic stress which is critical in toroidal flow damping. 

We propose a model to analytically derive the toroidal momentum transport and particle transport—we calculate the real diffusivity of particle and parallel momentum. Also, the physics of kinetic stress (K) and compressible heat, which play important roles in momentum and particle evolution, are further analyzed. We address this magnetic geometry effect to understand this “tail wagging the dog” feedback. Besides recovering the effective diffusivity Deff  = C_sD_M in ‘stochastic field regime’, where C_s is sound speed and D_M is the familiar stochastic field diffusivity of Rosenbluth et al., we obtain a hybrid turbulent viscosity  D_ν = C_s²Σ_k |b_x,k |² /k⊥D_T in ‘strong turbulent regime’ such that Κ=-D_ν ∂_x〈u_z〉, where D_T is turbulent fluid diffusivity. This indicates that the actual diffusivity D_ν describes how the mean flow is scattered perpendicularly by the synergy of stochastic fields and the strongly turbulent flow. Finally, there are several implications of those results for the physics of the kinetic stress and toroidal rotation. Discussions of these will be presented.