## 2 Hybrid Combinations of LWFA and PWFA
### Trojan Horse--Plasma Photocathode Injection
The low residual transverse momentum of electrons released by the plasma photocathode process is crucial, because it means the thermal emittance of produced electrons is very small [21; 30]. The release laser can in principle be realized at arbitrary frequency [20; 28], e.g., frequency-multiplied. This could be useful because then the electric field \(E_{0}\) which is needed for tunneling ionization is reached at a lower laser intensity, due to the \(E_{0}=a_{0}\times 3.2\times 10^{-12}\,\mathrm{V/m}\,/\lambda[\mu\mathrm{m}]\) scaling with the normalized light amplitude \(a_{0}\). Therefore, if operating at frequency-doubled laser light, i.e., at \(\lambda\approx 400\) nm, \(a_{0}\) can be decreased by a factor of 2, which further reduces the residual transverse momentum and thermal emittance contribution. The use of higher frequency light also has impact on the minimum obtainable spot size of a Gaussian laser pulse, and on the Rayleigh length, which has to be taken into account when calculating thermal emittance and phase mixing. However, at higher frequencies, multi-photon-ionization becomes relevant [31], which may limit the range of applicability of shorter wavelength injector pulses, and of all-optical two-colour variations such as mentioned in [32; 33] and explored in [34]. The latter approaches have a different set of challenges and limitations,  
Figure 10: **(a)** Collinear Trojan Horse schematic in the co-moving frame; and **(b)** laboratory frame. The laser focusing pulse releases ultracold electrons (green) from the high ionization threshold medium, which then briefly fall back and are trapped in the back part of the accelerating blowout. e.g., as regards dephasing (in particular for longer wavelength \(\lambda\) driver pulses due to \(L_{d}\approx\lambda_{p}^{3}/\lambda^{2}\)) and diffraction of the driver beam, practical limitations in context of drive beam laser availability, tunability and parameter range, and may require gas-dynamic confinement of the high-ionization threshold component as in [34]. Key advantages of the Trojan Horse method are:  
* The far-reaching decoupling of wakefield excitation from laser-based ionization injection with low-power laser pulses offers robustness and tunability, including use of different gas species for wakefield excitation and injection, respectively. * The unprecedented range of emittance and brightness of the obtainable electron beam: A key factor here is the residual transverse momentum of the released electrons, which means the (thermal) emittance scales with laser spot size and the normalized release laser amplitude \(a_{0}\)[21; 30]. Because electrons can be released in the center of the blowout, a minimum drive beam current of 5-6 kA is sufficient to allow for trapping. Such currents are straightforwardly obtainable as output from LWFA systems. Such an LWFA-PWFA-TH system constitutes a triple-hybrid approach, as it would make use of the laser system for generating the electron beam driver in LWFA, for preionization of the PWFA stage, and for witness bunch generation. Figure 11 visualizes this potential setup. The preionization laser here is focused by an axilens and applied in counter-propagating geometry to allow a well-defined and wide plasma channel, and the plasma photocathode release laser has intrinsic synchronization with the electron drive beam--this hybrid setup therefore harnesses fully the advantages of being initially LWFA-driven. Trojan Horse allows for tens of nm-rad scale normalized emittance values, kA-scale currents and hence in combination for unprecedented 5D-brightness. By employing tailored beam loading mechanisms [17], the energy spread of the produced electron bunches can potentially be controlled and reduced to sub-0.01% values in one and the same plasma stage. This is important, as this reduces the challenges associated with extraction and transport of electron beams from the plasma stage and for beam quality and emittance preservation substantially.