Astron. Nachr. 320 (1999) 2, 87–93 Adiabatic indices in a convecting anisotropic plasma M.I. Pudovkin, St. Petersburg, Russia Institute of Physics, University of St. Petersburg C.-V. Meister, Potsdam, Germany Astrophysical Institute Potsdam B.P. Besser, Graz, ¨ Osterreich Institut f¨ ur Weltraumforschung, ¨ Osterreichische Akademie der Wissenschaften Received 1999 January 15; accepted 1999 April 15 Adiabatic indices for a non-dissipative anisotropic convecting plasma are analyzed, and general expressions for the effective adiabatic index and the partial adiabatic indices parallel (γ ‖ ) and perpendicular (γ⊥) to the magnetic field are obtained. It is shown that, in the general case, the value of the effective adiabatic index is not an universal constant and depends on the plasma temperature anisotropy and on the properties of the plasma motion. The values of γ⊥ and γ ‖ are shown to be independent of the plasma parameters being completely determined by the characteristics of the plasma flow. Key words: Convecting anisptropic plasma – adiabatic indices 1. Introduction The system of MHD equations describing the motion of a plasma and the evolution of the magnetic field and plasma parameters in one-fluid approximation is usually closed by the thermodynamic equations of state in the form d dt  p ρ γ  =0, or d dt  T n γ-1  =0, (1) where γ, p, T , ρ and n designate the polytropic index, particle pressure, temperature, mass density, and particle density, respectively. For an adiabatic process in a monoatomic isotropic gas or non-magnetized plasma, γ = c p c V = 5 3 (c p and c V are the specific heats at constant pressure p and constant volume V ). For the rarefied cosmic plasma when the degrees of freedom in the respective directions parallel and perpen- dicular to the magnetic field are split and, correspondingly, plasma heating or cooling in these directions proceed independently, the situation is more complicated. This problem was considered in detail by Sturrock (1994), Baumjohann & Treumann (1996), and others. Following their analyses, we write the Boltzmann-Vlasov equation for the velocity distribution function f (t, r,v) as ∂f ∂t + v r ∂f ∂ r + q m  E r + ε rst c v s B t  ∂f ∂v r =  ∂f ∂t  c . (2) The symbols are standard; and ε rst is the Levi-Civita symbol. After multiplication of Eq. (2) by mv 2 /2 and integration over dv (adding the resulting expressions for electrons and ions), Sturrock (1994) obtained the energy transfer equations in the form 1 2 d dt p ss + 1 2 p ss ∂u r ∂x r + p rs ∂u r ∂x s + n 2 ∂ ∂x r  m e 〈w 2 e w e,r 〉 + m p 〈w 2 p w p,r 〉  (3)