Asymptotic and numerical analysis of perpendicular transport in low-beta plasmas

Kinetic physics, including finite Larmor radius (FLR) effects, are known to affect the physics of magnetized plasma fluid phenomena such as the Kelvin-Helmholtz and Rayleigh-Taylor instabilities. Accurately incorporating FLR effects into fluid simulations requires moment closures for the heat flux and stress tensor, including the gyroviscous stress in collisionless magnetized plasmas. However, the most commonly used gyroviscous stress tensor closure (Braginskii Rev. Plasma Phys., 1965) is based on a strongly collisional assumption for the asymptotic expansion of the kinetic equation in the so-called fast-dynamics ordering. A formal asymptotic analysis of the Vlasov equation in the slow-dynamics or drift ordering is performed in a new ``semi-fluid'' formalism, which integrates in v_⊥ to obtain a five-moment system which requires a heat flux and stress tensor closure. The leading-order perpendicular transport physics is determined via a Hilbert expansion of the kinetic equation, and the stress tensor is found to be a second-order quantity in the expansion parameter. A numerically affordable approximation to the stress tensor closure is proposed which adjusts the Braginskii closure to account for temperature gradient-driven stress. Continuum kinetic simulations of a family of sheared-flow configurations with variable magnetization and temperature gradients are used to validate the predictions of the drift ordering semi-fluid expansion. The expected convergence with magnetization is observed, and residuals are examined and discussed in terms of their relationship to higher-order terms in the expansion. The adjusted Braginskii closure is found to accurately correct for the over- and under-estimation committed by the Braginskii gyroviscous stress tensor closure in the presence of temperature gradients.