Scaling of accelerating gradients and dephasing effects in channel-guided laser wakefield accelerators

Future wakefield accelerator (LWFA) experiments are expected to operate in the short pulse resonant regime and employ some form of laser guiding, such as a preformed plasma channel. Performance of an LWFA may be characterized by the maximum axial electric field E_m, the dephasing length L_d, and the corresponding dephasing limited energy gain W_d. Dephasing is characterized by the normalized phase slippage rate Δβ_p, of the wakefield relative to a particle moving at the velocity of light. This paper presents analytical models for all of these quantities and compares them with results from simulations of channel-guided LWFAs. The simulations generally confirm the scaling predicted by the analytical models, agreeing within a few percent in most cases. The results show that with the proper choice of laser and channel parameters, the pulse will propagate at a nearly constant spot size r_M over many Rayleigh lengths and generate large accelerating electric fields. The spot size correction to the slippage rate is shown to be important in the LWFA regime, whereas Δβ_p, is essentially independent of laser intensity. An example is presented of a 25-TW, 100-fs laser pulse that produces a dephasing limited energy gain in excess of 1 GeV