Generalized fluid equations for parallel transport in collisional to weakly collisional plasmas

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Abstract
A new set of two‐fluid equations that are valid from collisional to weakly collisional limits is derived. Starting from gyrokinetic equations in flux coordinates with no zero‐order drifts, a set of moment equations describing plasma transport along the field lines of a space‐ and time‐dependent magnetic field is derived. No restriction on the anisotropy of the ion distribution function is imposed. In the highly collisional limit, these equations reduce to those of Braginskii, while in the weakly collisional limit they are similar to the double adiabatic or Chew, Goldberger, and Low (CGL) equations [Proc. R. Soc. London, Ser. A 2 3 6, 112 (1956)]. The new set of equations also exhibits a physical singularity at the sound speed. This singularity is used to derive and compute the sound speed. Numerical examples comparing these equations with conventional transport equations show that in the limit where the ratio of the mean free path λ to the scale length of the magnetic field gradient LB approaches zero, there is no significant difference between the solution of the new and conventional transport equations. However, conventional fluid equations, ordinarily expected to be correct to the order (λ/LB)2, are found to have errors of order (λ/Lu)2 =(λ/LB)2/(1−M2)2, where Lu is the scale length of the flow velocity gradient and M is the Mach number. As such, the conventional equations may contain large errors near the sound speed (M≊1).