## 2 Hybrid Combinations of LWFA and PWFA
### Plasma Torch--All Optical Density Downramp Injection  
Density downramp injection is an attractive method of bunch generation both for LWFA and PWFA, as it can realize localized and tunable injection of electrons into the plasma wave. It relies on a localized elongation of the plasma cavity on the plasma density downramp, which facilities injection and trapping of plasma electrons into the plasma cavity. Density downramp injection is a state-of-the-art injection method for LWFA, where modern implementations even allow increasingly stable generation even of double bunches [24], which could be used, e.g., for electron energy afterburners [4]. While the use of a sharp density downramp for localized injection had been first suggested for PWFA [25], it has not been realized for PWFA until recently in context of the E210 collaboration at SLAC FACET (to be published). One reason for this is the much poorer availability of PWFA driver beams when compared to high-power laser pulses for LWFA. Another one is the higher Lorentz factor \(\gamma\) of electron beam driven plasma waves compared to LWFA, which increases the threshold of injection as pointed out above, and a further one is the general practical complexity and difficulty when generating downramps hydrodynamically, in particular in multi-component gas mixtures. However, in such multi-component mixtures with gases with lower and higher ionization thresholds, or in PWFA which relies on self-ionization of the supporting gas/plasma medium, plasma downramps can be generated optically, as suggested in [23; 26]. In this approach, the plasma density spike and downramp are generated by an additional laser pulse, which generates plasma in the path of the electron beam driver by tunneling ionization of a gas component with higher ionization threshold. For example, in a hydrogen-helium gas mixture, preionized hydrogen can be used to support the wakefield, and helium with its substantially higher ionization threshold is ionized by a laser pulse which generates a plasma column or \"plasma torch\" perpendicular to the driver electron beam path on top of the preionized hydrogen. Figure 9 visualizes this approach by particle-in-cell simulations with the code VSim. The electron beam driver (black) propagates to the right through a hydrogen plasma channel, and encounters a perpendicular helium plasma torch (grey black). This plasma torch constitutes sharp local plasma density up- and downramps, and, when the electron beam driver arrives, this leads to a local distortion of the plasma wave such that plasma electrons are robustly injected at the desired position in the laboratory frame. Tuning of the laser pulse parameters and helium density allows exploring and optimizing [27] this all-optically-triggered plasma downramp injection in a wide parameter range, including the production of high-brightness electron witness beams. Owing to the extremely steep density downramp gradients, which this method allows to produce, injection can be achieved with comparably low driver beam currents of the order of 1 kA. Timing of the plasma torch injection method is uncritical, because the plasma torch filament, being generated by a laser pulse just above the ionization threshold, is rather cold and does not change much over a wide timing window of at least tens of ps, ultimately until recombination sets in. It is important to emphasize that the laser pulse required to generate the optical density spike can be of sub-mJ class for typical pulse durations of tens of femtoseconds, as the intensity required to tunnel ionize even helium sufficiently, the element with highest (first) ionization threshold, for Ti:sapphire lasers amounts to few \(10^{15}\,\mathrm{W}/\mathrm{cm}^{2}\). At these intensities and corresponding power levels, laser pulses are far more manageable than those with relativistic intensities such as required for LWFA.