Double‐polytropic closure in the magnetosheath

Abstract

The magnetosheath plasma is usually neither isotropic nor adiabatic. This paper contains an attempt to decribe its thermodynamic properties in terms of two polytropic laws, p⟂/ρBγ⟂−1 = C⟂ and p∥Bγ∥−1 / ργ∥ = C∥, such that for γ⟂ = 2, γ∥ = 3 the usual Chew‐Goldberger‐Low double‐adiabatic expressions are recovered and for γ⟂ = 1, γ∥ = 1 double‐isothermal conditions are obtained. Using data from the AMPTE/IRM spacecraft, we show that the subsolar magnetosheath plasma may be better described by the double‐polytropic laws than by the mirror instability threshold, in particular in the low beta region near the magnetopause. The inferred polytropic exponents vary from event to event but are typically in the ranges of γ⟂ = 0.94 ± 0.10 and γ∥ =1.14 ± 0.13 for the 29 cases we have examined.

Space charge saturated sheath regime and electron temperature saturation in Hall thrusters

“…The notion of the effective polytropic exponent is used extensively in the problems of astrophysical, solar, and magnetospheric plasmas. [36][37][38] In our case, the effective γ falls quite reasonably between the limiting values that correspond to the isothermal (γ=1) and adiabatic approximations (γ=5/3). This implies that the electron heat conduction is neither zero nor infinite, but takes a finite value.…”

Effects of Hall current and electron temperature anisotropy on proton fire-hose instabilities

“…As indicated, the growth rate for both slow and intermediate fire hose in case (c) is enhanced due to the additional contribution from electron temperature anisotropy. As a result, the slow fire hose no longer grows faster than the intermediate fire hose as in curves a, b, and d, in accordance with the condition in (17). Due to smaller ion pressure anisotropy of b k;i À b ?…”

“…As revealed by many satellite observations, both ions and electrons have distinct temperatures and the associated temperature anisotropies. 17,18 While the widely used hybrid model treats the ions as particles and the electrons as a fluid but in most cases neglects the electron inertia and their temperature anisotropy as well. In this paper, the proton FHI is examined within the framework of linear two-fluid theory by retaining the ion inertia and electron temperature anisotropy but neglecting the electron inertia in the model; in particular, both ions and electrons are allowed to have separate thermal pressures and the associated energy equations.…”

“…The doublepolytropic laws are adopted as the energy equations, which have been shown to provide a viable closure for not only the ions but also the electrons of collisionless space plasmas. 17 Note that the MHD model with double-polytropic closure may also give rise to the correct mirror and compressible fire-hose instability criteria for the special case of c ? ¼ 2, c jj ¼ 1=2, thus removing the deficiency associated with the standard Chew-Goldberger-Low-(CGL)MHD model.…”

Application of the bounded anisotropy model for the dayside magnetosheath

“…There are two competitive approaches to explain the observed ion temperature anisotropy in the magnetosheath. In the first approach, nonideal MHD effects, such as the heat fluxes and the imperfect conductivity, are supposed to be responsible for the decrease of the temperature anisotropy [Hau et al, 1993;Hau, 1996]. In this case, the following equations (called the double polytropic model) were proposed' …”