The General Solution to Vlasov Equation and Linear Landau Damping

A general solution to linearized Vlasov equation for an electron electrostatic wave in a homogeneous unmagnetized plasma is derived. The quasi-linear diffusion coefficient resulting from this solution is a continuous function of omega in contrast to that derived from the traditional Vlasov treatment. The general solution is also equivalent to the Landau treatment of the plasma normal oscillations, and hence leads to the well-known Landau damping.