Polytropic indices in collisionless plasmas: Theory and measurements

Abstract

All theories and models based upon fluid methods are dependent upon p pairs of parameters (p=1 for MHD) which are the polytropic indices γ⫽ and γ⊥ of each of the p fluid populations, and their results can sometimes be greatly affected by changes in these indices. For these fluid descriptions of collisionless plasmas, there was no general method up to now for determining the right values γ⫽ and γ⊥ to be injected, depending on the local physical situation. Are the different populations isothermal (γ⫽ = γ⊥ = 1), isobaric (γ⫽ = γ⊥ = 0), adiabatic (γ⫽ = γ⊥ = 5/3 if the variations are isotropic, but this hypothesis of isotropy is generally not verified in a magnetoplasma) or anything else? These choices may be made by going back to complete kinetic calculations in each specific situation, thereby losing the ease of the fluid methods. This paper shows that the use of polytropic laws is justified for plasma variations belonging to any linear low‐frequency wave, and it provides the correct values to be used for the polytropic indices in these cases, thanks to a general kinetic calculation. In these terms, the polytropic indices γ⫽ and γ⊥ must be considered as the interface between kinetic and fluid sides of the physics. The dependence of the indices upon the mode and upon the particle population considered is emphasized. An experimental case concerning a fast magnetosonic mode observed on board the Giotto spacecraft close to comet Halley is completely analyzed from this point of view. Electron measurements are used, simultaneously with magnetic field ones, and all the correlations between the four parameters p⫽, p⊥, n, and Bz are explained; for doing so, the theory is made more sophisticated to account for the fact that the coldest and densest part of the electron distribution function is not, in this case, accessible to the detector.