Calculations of polytropic coefficient for the Tonks–Langmuir Electron‐ion plasma with non‐Maxwellian electron distributions

Abstract

AbstractThe dynamics of the Tonks and Langmuir‐type bounded plasma requires a closure relation to make the system of equations self‐consistent. Fluid equations are obtained from the moments of velocity distribution function. The two most frequently used closure relations are (a) completely neglecting ion temperature, and (b) setting a constant value for the ion polytropic coefficient. It has been shown that, for a Maxwellian source, either of these assumptions leads to erroneous results. Here, the premise of polytropic coefficient being a function of the potential is extended to a nonthermal plasma. Two different cases for the electron velocity distribution function are studied, namely (a) the Kappa distribution, and (b) the Cairns distribution. Number density (ni) and temperature (Ti) for the ions are numerically calculated, for respective spectral indices. The polytropic coefficient is then calculated as a function of the potential, using the relation γi = 1 + (ni/Ti)(dTi/dni). It is concluded that better approximations, vetted by kinetic means, to the polytropic coefficient are crucial for appropriate closure of fluid equations. Present work will be useful in fusion devices where non‐Maxwellian electrons may exist due to various physical phenomena.