Absolute and convective ion beam instability studied through Green's function

A Vlasov plasma with a double-humped, unstable ion velocity distribution function is considered. A δ function in space is assumed as the initial perturbation and the plasma response to this perturbation is calculated, i.e., the Green's function for the problem is found. The response can be divided into two parts: a self-similar, damped part of the form t−1h(x/t), and an unstable, exponentially growing part. The conditions for absolute and convective growth of the latter are discussed.