## 2 Hybrid Combinations of LWFA and PWFA
### Trojan Horse--Plasma Photocathode Injection
A low energy spread is also crucial for key applications, e.g., for photon science drivers. It should be noted that the added level of complexity of hybrid LWFA-PWFA in various configurations when compared to, e.g., single-stage LWFA must not be confused with limited feasibility! On the contrary, the Trojan Horse scheme, which promises highest output beam quality and tunability, is composed such that the individual building blocks are all well controllable due to threshold effects: The preionization of the PWFA stage requires deploying laser pulse intensity sufficient to ionize the low ionization threshold component such as hydrogen, and excess intensity does not change the produced local plasma yield once 100% of the hydrogen is ionized. This acts as a bandpass filter against shot-to-shot laser intensity jitter. Figure 11: Potential setup of a “triple-hybrid” system where the laser system generates the electron bunch driver for PWFA via LWFA, is used to preionize the PWFA stage, and for witness bunch generation via the Trojan Horse mechanism. Further, by operating at low plasma densities and hence large blowouts, the release position of electrons inside the blowout can be very stable and tunable: for example, for a blowout of \(\approx 500\) um size, the center of the blowout can be hit reliably with better than 1% stability shot-by-shot when assuming a plasma photocathode laser vs. electron driver beam time-of-arrival (and pointing) jitter of \(<\)30 fs. A sensitivity analysis of realistic timing, pointing and laser intensity jitter (to be published) confirms the expectation that near-constant charge bunches with tens of nmrad normalized emittance values and corresponding ultrahigh brightness values can stably be achieved shot-by-shot. When operating at such reduced plasma densities, the accelerating fields still amount to tens of GV/m, and next to injection stability the moderate fields are also advantageous because the reduced field gradient inside the blowout leads to a reduced residual energy spread [17]. While \(\approx\) 30 fs laser-electron beam timing stability can be reached at state-of-the-art linac-driven FEL facilities, using a split-off laser pulse from the LWFA system in the hybrid approach can assumedly be delivered with a synchronization stability at or better than the 1-fs level. In the hybrid LWFA-PWFA variant, at present the major sources of shot-to-shot-jitter of the LWFA output are pointing, energy, energy spread, charge and current. However, energy spread and energy jitter is rather uncritical for any of the hybrid approaches for reasons discussed above, and as regards driver current jitter, the Trojan Horse scheme has unique advantages due to the injection process being to a large degree decoupled from a varying wakefield strength and shape shot-by-shot. Even if the drive beam current jitters substantially from shot-to-shot, and as a direct consequence the excited wakefield strength, the plasma photocathode-produced witness beam charge is completely independent from this, as it is only a function of the laser pulse and high-ionization-threshold medium (e.g., helium) density. Due to the parabolic shape of the trapping potential around the center of the blowout and the corresponding longitudinal electric wakefield, this laser-gated injection process has a further auto-stabilizing function even in case of drive beam shot-to-shot jitter. The approach therefore combines prospects for highest beam quality with ultrahigh tunability as well as potentially very high stability compared to other plasma wakefield approaches. The first demonstration of (linac-driven) Trojan Horse could be realized at SLAC FACET in the E210 programme, using plasma torch injection as a stepping stone (to be published). This was realized under boundary conditions of incoming beam jitter as well as blowout size which have been rather unfavourable and will be much improved e.g., for SLAC FACET-II, which confirms and fosters expectations as regards controllability and impact of this method in the future.