Describing the flow of fully ionized, magnetized gases:: improved gyrotropic transport equations

We have developed a new set of transport equations for magnetized, fully ionized gases designed to cover the entire regime from collision-dominated to collisionless flow. The equations are based on a skewed bi-Maxwellian velocity distribution function and describe number density, n, flow velocity, u, parallel and perpendicular temperature; T-parallel to and T-perpendicular to, and heat flow, q. We choose a velocity distribution function f(v) = f(bM)(1 + phi) where f(bM) is a bi-Maxwellian and the 'skewness', phi, is proportional to c(3) instead of the more commonly used phi proportional to c (c equivalent to vertical bar v - u vertical bar). We find transport coefficients (heat flux and thermal force) in the collision-dominated limit that are in good agreement with results from classical transport theory. The equations also describe, reasonably well, the flow of collisionless, ionized crases. and should therefore be well suited to describe the transition region-corona-solar wind system and other fully ionized, expanding stellar atmospheres.