Series expansion of electrostatic potential radiated by a point source in isotropic Maxwellian plasma


  • C. Béghin


A new algebraic approach is proposed to calculate the electrostatic potential distributed around a point source in isotropic Maxwellian plasma. The method derives a power series expansion of the radial distance from the source with frequency-dependent coefficients. Distance and frequency are normalized to the Debye length and to the plasma frequency, respectively, so that the expression keeps its entire generality whatever the experimental conditions might be. The proposed method is based upon the Mittag-Lefler expansion of the inverse of the plasma dispersion function for the infinite series of Landau poles. After mathematical clarification of the validity of this expansion, a significant correction of the previous works leads to a self-consistent interpretation of the true contribution of the higher-order poles at large distance from the source. The power series expansion is compared to the classical so-called “Landau wave approximation” which is proved to include in reality the contribution of higher-order poles independently from the plasma temperature. For practical use the power expansion is needed to obtain a precise result at distances from the source shorter than about 15 Debye lengths, while the Landau wave approximation gives correct results at larger distances. This work provides all necessary baselines for precise three-dimensional modeling of mutual impedance devices to be used in space plasma experiments where the Debye length is comparable to the spacecraft size.