## 2 Hybrid Combinations of LWFA and PWFA
### Trojan Horse--Plasma Photocathode Injection  
The Trojan Horse [28], also known as plasma photocathode injection method, is related to plasma torch injection. However, here the laser pulse needs to arrive very shortly after the electron beam driver, such that additional electrons via ionization of the higher ionization threshold medium are released approximately in the center of the blowout. Then, these electrons, which initially have negligible residual momentum due to the low laser intensity, are then rapidly accelerated in the forward direction by the plasma wakefield, which allows realizing particularly low emittance values. This can be achieved in various geometries between driver electron beam and release laser [20], e.g., in perpendicular or collinear geometry [21]. Figure 10 visualizes for collinear geometry how the process works in co-moving (left) frame and laboratory frame (right). The laser pulse focuses to intensities exceeding the ionization threshold of the higher ionization threshold medium (e.g., helium) in the center of the electron beam driven blowout, and releases helium electrons, represented by the green ellipse, at arbitrary position within the blowout. The center of the blowout is particularly interesting, because here the longitudinal wakefield is zero and the corresponding trapping potential is maximized: electrons released here harness the full accelerating field of the wakefield, which optimizes the use of the driver-excited wakefield for trapping. It is also  
Figure 9: Plasma torch injection in PIC-simulations with VSim. The drive beam (black) propagates to the right and drives a plasma wave based on preionized hydrogen. A laser pulse has generated a helium-based plasma torch perpendicular to the drive beam propagation axis, constitutes a density ramp and triggers density downramp injection. an ideal position because here, longitudinal and transverse plasma wakefields are zero, and hence the laser-controlled release rate of helium electrons is completely decoupled from the wakefield excitation process. The witness bunch generation is therefore much more decoupled from drive beam jitter than in other schemes. One can also release with transverse longitudinal offset at other positions within the blowout, simply by shifting the release laser pulse with respect to the wakefield center. If one releases farther away from the center, however, transverse and longitudinal plasma wakefields may have to be taken into account for the tunneling ionization rates as superposition of laser and plasma wakefields. Because the trapping potential parabolic shape is flat at its maximum in the middle of the blowout, this position is also robust against longitudinal (i.e., timing) jitter of the release laser pulse. This may be important in context of linac-driven Trojan Horse, where there is no intrinsic synchronization between electron and laser beam. Finally, the center blowout position is also favourable because it allows to realize a robust dark-current free PWFA, when the trapping region is confined to the area around the center of the blowout [29]. The plasma photocathode therefore allows uniquely tunable electron bunch generation. As regards obtainable beam quality, the key advantage is that the release laser pulse requires intensities just above the ionization threshold of comparably low ionization levels. In practice, e.g., a Ti:sapphire laser pulse at an intensity of \(\approx 10^{15}\,\mathrm{W/cm^{2}}\) is sufficient to liberate electrons from helium, similar as for plasma torch injection. The ponderomotive force of such a laser pulse is comparably low, which in turn means that the residual transverse momentum of the released electrons is low--the released electrons are not transversally pushed out by the laser pulse, but simply remain on axis, fall back and catch up with the plasma wave. This is in contrast to LWFA, where the laser pulse _has_ to be intense enough to expel electrons off axis, and to excite the plasma wave.