# Multi-GeV Laser Wakefield Electron Acceleration with PW Lasers
## 3 Multi-GeV LWFA with PW-Class Lasers
### Dual-Stage LWFA with PW Laser at UQBF  
In this section, we review the dual-stage LWFA with the PW lasers at the Ultrashort Quantum Beam Facility (UQBF), Advanced Photonics Research Institute (APRI), GIST. The APRI group successfully constructed two PW beamlines in 2012 by using the CPA scheme and Ti:Sapphire amplification media. The first beamline produced energy of 30 J and a pulse duration of 30 fs [17], and the second beamline did 45 J [30] and the same pulse duration. The PW laser at UQBF was used for LWFA experiments to produce multi-GeV electron beams. As discussed in Section 2, the achievable electron energy can be increased by increasing the laser power and lowering plasma density. However, the self-injection of electron bunches into plasma waves can be prohibited by reducing the plasma density. Thus, the plasma medium density and profile should be carefully designed to maximize the electron energy: the acceleration length should be maximized while keeping self-injection occurring. One solution can be to combine gas media of different lengths and densities called dual-stage or cascaded acceleration. The dual-stage LWFA experiments were performed by focusing the PW laser onto a dual gas jet medium consisting of 4-mm and 10-mm helium gas jets [18]. The first 4-mmhelium jet acted as an injector stage, and the second 10-mm jet boosted electron energy. Laser pulses with an energy of 25 J were focused with a 4-m long concave spherical mirror, as shown in Figure 2a. The wavefront aberration of the laser pulse was corrected using a deformable mirror installed before the compressor. The laser pulse was stretched to 60 fs with a positive chirp by detuning the compressor grating. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Shot** & & & \\ \hline \hline \(\mathrm{E_{peak}}\) (GeV) & \(2.0\pm 0.1\) & \(1.8\pm 0.1\) & \(0.95\pm 0.1\) \\ Energy spread (\%) & 10 & 8 & 11 \\ Divergence (mrad) & \(0.6\pm 0.1\) & \(0.5\pm 0.1\) & \(0.5\pm 0.1\) \\ Charge in peak (pC) & \(63\pm 8\) & \(34\pm 5\) & \(13\pm 2\) \\ Plasma density (\(10^{47}\) cm\({}^{-3}\)) & \(4.8\pm 0.1\) & \(3.4\pm 0.1\) & \(2.1\pm 0.1\) \\ Laser energy (J) & \(100\pm 5\) & \(120\pm 6\) & \(129\pm 6\) \\ Laser pulse duration (fs) & \(160\pm 10\) & \(150\pm 10\) & \(160\pm 10\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Experimental results for three different laser shots from the Texas PW laser [11]. Reproduced with permission from [[PERSON]], [_Nat. Commun_]; published by [macmillan Publishers Limited], [2013]. Figure 2: (a) Experimental layout for dual-stage LWFA with a PW laser pulse, (b) schematic drawing of the dual-stage target, and (c) the experimental result with the dual-stage target [18]. In figure (c), the red line shows the electron spectrum from the first target, and the black line shows the spectrum after the second target. In the dual-stage LWFA, several issues should be properly treated to obtain a high-energy electron beam. Firstly, a self-injection should happen in the first medium, and the resulting electron bunch should have sufficient energy when entering the plasma wave in the second medium. Secondly, the electron beam and driving laser pulses should be properly coupled into the second medium. Thirdly, the electron beam should be accelerated in the second medium without an additional electron injection. The first 4-mm helium gas jet was optimized to obtain a 400 MeV electron beam by tuning the gas pressure to have an electron density of 2 \(\times\) 10\({}^{18}\) electrons/cm\({}^{3}\). No electron beam signal was observed when the second jet was used alone with densities below 1 \(\times\) 10\({}^{18}\) electrons/cm\({}^{3}\). A significant enhancement of electron energy was observed with the dual gas jet target having electron densities of 2 \(\times\) 10\({}^{18}\) electrons/cm\({}^{3}\) for the 4-mm jet and 0.8 \(\times\) 10\({}^{18}\) electrons/cm\({}^{3}\) for the 10-mm jet. The gap between the two jets was about 2 mm, and the laser focus was at the middle of the gap.