Resonant excitation of plasma waves in a plasma channel

We demonstrate resonant excitation of a plasma wave by a train of short laser pulses guided in a pre-formed plasma channel, for parameters relevant to a plasma-modulated plasma accelerator (P-MoPA). We show experimentally that a train of $N\approx 10$ short pulses, of total energy $\sim 1$ J, can be guided through $110$ mm long plasma channels with on-axis densities in the range ${10}^{17}-{10}^{18}$ cm${}^{-3}$. The spectrum of the transmitted train is found to be strongly red-shifted when the plasma period is tuned to the intra-train pulse spacing. Numerical simulations are found to be in excellent agreement with the measurements and indicate that the resonantly excited plasma waves have an amplitude in the range $3$ - $10$ GV m${}^{-1}$, corresponding to an accelerator stage energy gain of order $1$ GeV.