Nonlinear screening effect in an ultrarelativistic degenerate electron positron gas

Abstract

Nonlinear screening process in an ultrarelativistic degenerate electron-positron gas has been investigated by deriving a generalized nonlinear Poisson equation for the electrostatic potential. In the simple one-dimensional case, the nonlinear Poisson equation leads to Debye-like Coulomb-like solutions at distances larger less than the characteristic length. When the electrostatic energy is larger than the thermal energy, this nonlinear Poisson equation converts into the relativistic Thomas–Fermi equation whose asymptotic solution in three dimensions shows that the potential field goes to zero at infinity much more slowly than the Debye potential. The possibility of the formation of a bound state in electron-positron plasma is also indicated. Further, it is investigated that the strong spatial fluctuations of the potential field may reduce the screening length and that the root mean square of this spatial fluctuating potential goes to zero for large r rather slowly as compared to the case of the Debye potential