Debye shielding of an electron in various plasma distributions

A single test electron in a plasma experiences a force arising from its induced potential due to the shielding by charges around the test charge. This electric potential can be obtained by solving the Poisson equation or computing the dielectric permittivity. We obtain the length of a test electron’s shielding (or Debye length) for the various distribution functions in a plasma by calculating the dielectric permittivity. As the Maxwellian distribution function leads to a Yukawa-type potential, other distributions give the same potential type but with different damping distances. The results agreed with the formerly known results obtained by solving the Poisson equation. Distributions with twisted waves or orbital angular momentum may lead to a Coulomb potential in certain limits in the absence of ions.