## 2 Hybrid Combinations of LWFA and PWFA
To control LWFA-PWFA staging, and to extend the acceleration distance in the PWFA stage, e.g., in view of head erosion, the PWFA stage needs to be preionized. In [15], the diffracting remnant of the LWFA laser pulse was used--as long as one does not exceed the dephasing limit, this laser pulse fraction arrives in the PWFA stage earlier than the LWFA-generated electron beam and can tunnel ionize the gas in the PWFA stage. The laser remnant intensity has to exceed the tunneling ionization threshold, but should also not be too high, otherwise the plasma electrons are heated. Selective full ionization of hydrogen, but not helium, was observed in [15]. However, the laser pulse diffraction of the remnant laser pulse cannot be mitigated, and the distance over which suitable ionization is achieved is limited. The laser intensity at this point is below the relativistic self-focusing threshold, so that this mitigation mechanism is not present. On the contrary, ionization defocusing may play a significant role, which further reduces the length over which the LWFA remnant pulse may be useful for ionizing the PWFA stage. Long-range preionization, for example with an axilens in counterpropagating geometry as suggested in [17], is required over and beyond an initial ionization distance provided by the LWFA remnant, in order to fully unlock the long acceleration distances which PWFA enables. Figure 7: An electron double bunch from an LWFA stage is put into a second, higher density plasma stage, where it acts as a driver-witness pair PWFA energy afterburner. The right hand side shows a later snapshot during the PWFA acceleration, where plasma lensing has pinched both driver and witness bunch. The top plots shows the electron density, the middle plots the transverse electric field, and the bottom plots show the longitudinal wakefields. Visualization adapted from [4]. Next to acceleration as a goal, hybrid LWFA-PWFA systems do also allow to investigate various basic PWFA-specific features and challenges in compact setups, such as PWFA plasma dynamics and ion motion [18] or may allow innovative light sources applications [1; 19]. In addition to huge energy gains in single accelerator stages, the low electric fields of the PWFA driver allows realizing a unique set of electron injection methods, such as plasma photocathodes also known as Trojan Horse [20; 21], wakefield-induced ionization (WII) injection [22], and optical density downramp injection also known as plasma torch [23]. These methods allow boosting the quality of electron bunches by many orders of magnitude, and therefore may pave the way to high performance key applications, such as for hard X-ray light sources or for potential building blocks for high energy physics research. Figure 8 summarizes various options of injection on the right hand side. The central gateway building block here is PWFA, either driven by electron beams from linacs, or from LWFA. In the following, the three injection methods are discussed briefly. In addition to the general idea of utilizing LWFA-generated bunches for PWFA, these are currently explored in the Strathclyde/DESY-led Work Package 14: \"Hybrid Laser-electron-beam driven acceleration\" of EuPRAXIA, the EU H2020 design study for a European Plasma Research Accelerator with eXcellence In Applications (2015-2019). Hybrid LWFA-PWFA and the Trojan Horse method, specifically, has been supported by RadiaBeam Technology's US DOE-funded \"Plasma Photocathode Beam Brightness Transformer for Laser-Plasma Wakefield Accelerators\" (2013-2016) in a Strathclyde-RadiaBeam-UCLA-centered collaboration. Here, the work was broken down into the plasma photocathode research on the one hand, which was developed within the \"E210: Trojan Horse PWFA\" experimental programme (2012-2017) at the SLAC FACET linac, and R&D on the exploitation of LWFA-generated electron bunches for PWFA on the other hand. Figure 8 visualizes the underlying conceptual approaches.