Superexponentially damped Vlasov Plasma Oscillations in the Fourier Transformed Velocity Space

The Landau (exponentially) damped solutions of the Vlasov-Poisson equation Fourier transformed with respect to velocity are genuine eigenmodes corresponding to complex eigenvalues. In addition there exist solutions decaying faster than exponentially which exhibit no oscillatory behaviour. We give a new characterization of the initial conditions that give rise to these solutions and demonstrate them numerically.