Equation of State of the Kappa-Distributed Solar Wind Particles in the Earth’s Magnetopause

We provide a non-adiabatic equation of state of a space plasma based on the kappa distribution. Our formulation generalizes the polytropic gamma index. An analytic expression is deduced for gamma. Then, the equation of state is derived. The model is applied to describe the electron solar wind in the Earth’s magnetopause. A relationship between the plasma pressure and electron concentration is fitted by our equation of state. It is found that: (i) the value of the kappa index is slightly larger than its lower limit, 3/2, thereby actually characterizing electrons in the ambient solar wind; (ii) the electron concentration varies between 2 and 4 particles per cubic centimeter at a null electric potential; (iii) the electron temperature varies between 1.1 and 1.5 million degrees kelvin. Further applications of our theory are briefly addressed.