An analytic solution to the steady‐state double adiabatic equations

20 moment transport equations applicable to low β plasmas of thermal origin in rotating planetary magnetospheres are presented. An analytic solution is found for a set of simplified equations describing the steady‐state transport of collisionless plasma neglecting heat flow effects, which is also known as the double adiabatic situation [ Chew et al., 1956]. The new element of this analytic solution is a closed form solution for the variation of the parallel flow velocity, u ∥ , along magnetic field lines. The solution is significantly different from the often used assumption that, in the collisionless regime, the divergence of the parallel flow velocity is negligible (cf. [ Burgers , 1969]). It is shown that only T⟂/B remains constant along the field line (as predicted by earlier calculations), while the density, parallel temperature and parallel Mach number vary as n/B∝1/u ∥ , T ∥ ⧜1/u ∥ ², and M ∥ ⧜u ∥ ², respectively (in contrast to earlier predictions of n/B=const, T ∥ =const, and M ∥ =const. ).