Analysis of dephasingless plasma wakefield photon acceleration

The propagating density gradients of a plasma wakefield may frequency upshift a trailing witness laser pulse, a process known as `photon acceleration'. In uniform plasma, the witness laser will eventually dephase because of group delay. In this work we present the analysis of the wake response to an ultra-relativistic drive beam. The solution for the driven wake is parametrized by drive-beam parameters and background plasma density. This parametrization couples to the frequency shift equation, leading to phase matching conditions for the pulse using a tailored density profile. The solution to these coupled equations generically tends to zero density and infinite laser frequency. Provided the wake can be sustained, the solution to this 1D model has no asymptotic limit to the achievable frequency shift. This model is studied with fully self-consistent 1D particle-in-cell (PIC) simulations, more than 40 times frequency shifts were demonstrated. In quasi-3D PIC simulations frequency shifts up to ten times were observed, limited only by simulation resolution and non-optimized driver evolution. Simulations demonstrate that the frequency shift is robust to perturbations in the tailored plasma density profile.