# Conceptual and Technical Design Aspects of Accelerators for External Injection in LWFA
## 1 Introduction
A net energy gain of the electron bunch in a single stage up to 4 GeV [6] has already been shown. Moreover the possibility of staging this acceleration process has recently been experimentally demonstrated [7]. In Dielectric Laser Acceleration (DLA) laser pulses with wavelength in the \(\mu\)m scale are coupled (typically perpendicularly) to a micro-structure made from a dielectric material such as SiO\({}_{2}\) or Si [8]. Due to the short length of the acceleration channel in the longitudinal direction, compared to the typical electron bunch length in linear accelerators, only energy modulation experiments have been realized so far, proving an energy gain of part of the electrons in the bunch of the order of tens of keV [9]. Nevertheless, as shown in Table 1, gradients of the order of the GV/m have been experimentally demonstrated. In THz based acceleration a mJ THz laser is longitudinally coupled to a metallic structure loaded with dielectrics [10]. This technique should in principle allow gradients of GV/m but is presently limited by the lack of high power THz sources. Research and development on novel acceleration methods using laser drivers has spread out rapidly in the last decades [11; 12; 13; 14; 15; 16]. Ultimately the goal of this research is the complete miniaturization of an accelerator, i.e., starting from beam generation, continuing with beam acceleration and compression and including possibly even radiation generation. The injector is normally the most sensitive part of an accelerator and the control of beam generation via e.g., internal injection in plasmas or via the design of an electron source with sufficient brightness is a challenging task, especially for the DLA and THz driven techniques, which operate in regimes where the injector \(\alpha\) parameter, i.e., the normalized accelerating field strength, is very low [17; 18]. The study of externally injected beams is therefore very important to allow the sole characterization of the accelerator using a stable, well characterized and ideally tunable electron source. This justifies the effort invested in the production of high-brightness ultra-short electron bunches by using conventional RF technology. Moreover on the theoretical side the existence of such conventional sources of ultra-short beams opens up the possibility of benchmarking beam dynamics simulation codes widely used in the accelerator field in this new regime. In the past this study was partially not possible also due to the lack of beam diagnostics capable of detecting with sufficient resolution the ultra-short and low charge bunches but the technical progresses made in the last few years bring us closer to accomplishing this. This article is organized as follows. We will restrict ourselves to the analysis of e-bunch shaping techniques for providing ultra-short electron probes for LWFA acceleration with external injection. This study will cover both beam dynamics aspects, such as bunch generation and compression, and technical aspects, such as beam control and characterization. In the next Section we shall give an overview of the requirements of the electron bunch to be properly matched (longitudinally and transversely) with the plasma channel. In Section 3 we shall give an overview of the methods to control bunch length compression in a linear acceleration with special emphasis on the ultimate limitations to achieve ultra-short electron bunches. Section 4 will present the design of the SINBAD-ARES linac at DESY as an example of accelerator for the production of ultra-short electron bunches. We will show how the design of the SINBAD-ARES linac satisfies the requirements for generating high brightness LWFA probes. In Section 5 we shall discuss stability problems related to the synchronization of the electron bunch with the laser driving the plasma and we shall give an overview concerning the challenges for beam diagnostics and control. Finally we shall come to the conclusions.