Transient excitation of linear space-charge waves by a punctual source in a drifting cold plasma

Abstract

We study the effects of a uniform drift on the excitation emanating from an external antenna immersed in a cold modelled plasma. Instead of the well-known approach based on the steady-state regime approximation, the causal and transient evolution of the excited plasma waves is investigated. A comprehensive description of the computational method is proposed. We show that a technique based on the Heaviside direct operational method turns out to be very effective in order to handle the integrodifferential expression for the solution. Making use of a pure analytical calculation, an exact algebraic expression for the plasma response is inferred. The solution takes the form of a combination of Bessel's functions and series of Lommel's functions. Then some specific analysis of the result allow us to gain more understanding on the dynamics of the fast and slow space-charge waves. A special attention is paid to the analysis of the extended singularity of the wave field and the secular behaviour of the fast wave mode at the resonant excitation.