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An analytic solution to the steady‐state double adiabatic equations
Author(s) -
Gombosi Tamas I.
Publication year - 1991
Publication title -
geophysical research letters
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.007
H-Index - 273
eISSN - 1944-8007
pISSN - 0094-8276
DOI - 10.1029/91gl01614
Subject(s) - physics , adiabatic process , steady state (chemistry) , flow (mathematics) , mach number , plasma , zonal flow (plasma) , magnetic field , constant (computer programming) , moment (physics) , field (mathematics) , classical mechanics , quantum electrodynamics , mechanics , thermodynamics , quantum mechanics , mathematics , chemistry , computer science , pure mathematics , tokamak , programming language
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. ).