A New Approach to Compute Linear Landau Damping

Abstract

We present a semi-analytical method for calculating exact time-domain solutions to linear Landau-damping problems. Unlike traditional residue-based approaches, our framework avoids the need to compute complex zeros of the dielectric function. We illustrate the method for an electrostatic, unmagnetized plasma with kinetic ions and adiabatic electrons by deriving the response of both the ion density and the ion distribution function to an initial density perturbation. We further show that the construction can be formally extended to linear Vlasov-Maxwell problems with a uniform background magnetic field and a Maxwellian equilibrium distribution.