Excitation of accelerating wakefields in inhomogeneous plasmas

The excitation of the wakefields in an inhomogeneous plasma by a short laser pulse is investigated theoretically. A general equation for the wake excitation in transversely nonuniform plasma is derived. This equation is applied to the step-function density profile model of hollow channel laser wakefield accelerator [1], [2]. A more realistic model, in which the transition between the evacuated channel and the homogeneous surrounding plasma occurs over a finite radial extent, is then analyzed. It is shown that the excited channel mode can interact resonantly with the plasma electrons inside the channel wall, leading to secular growth of the electric field. This eventually results in wavebreaking and the dissipation of the accelerating mode. We introduce an effective quality factor Q for the hollow channel laser wakefield geometry. This resonance limits the number of electron bunches that can be accelerated in the wake of single laser pulse.