# Multi-GeV Laser Wakefield Electron Acceleration with PW Lasers
## 4 Perspective of LWFA with PW Lasers  
In this section, we will discuss the current difficulties of LWFA with PW lasers and the future perspective of LWFA with upcoming multi-PW lasers. We reviewed several experimental results on LWFA with PW laser pulses. Overall, PW lasers demonstrated multi-GeV LWFA in the energy range from 2-8 GeV with divergence of about 1 mrad, the beam charge in the order of 10 pC, and energy spread of about 10%. The rapid progress of high-power lasers enabled the development of high-energy electron beams with high bunch charge and small beam emittance. Although PW lasers began to appear a decade ago, and the expectations on LWFA have been quite promising, experimental results were relatively rare. The advancement of LWFA with PW lasers was retarded due to the technological difficulties in operating PW lasers and the growing complexity of experimental setups. LWFA uses highly nonlinear processes in a plasma medium with micrometer scale acceleration structures. Thus, tiny defects of laser pulses and the plasma media can significantly deteriorate the acceleration processes. As laser power and system size increase, the elimination of the flaws is getting more difficult. The recent development of high-power laser reached 10 PW peak powers [38], and 100-GeV electron acceleration with LWFA is not an absurd goal. However, the massive scale of the LWFA experimental system with the 10-PW lasers can make it challenging to realize a 100-GeV electron beam. From the estimation with Equation (1), a 10-PW laser with 250 J energy can produce a 100 GeV electron beam by focusing the laser pulse with F/# > 150 onto a 10-m length plasma medium with an electron density of about 10\({}^{16}\) electrons/cm\({}^{3}\). If the beam size of the 10 PW laser is about half a meter, then the LWFA experimental system, including the focusing system, acceleration medium, and detection system, should be more than 100 m to achieve 100 GeV. The 10 PW laser should have the beam pointing stability below 1 mrad before the focusing mirror for its pulse to be properly guided along the 10-m plasma channel. The plasma medium also has to be well designed and fabricated to be transversally profiled for a deep electron density gradient to guide the 10-PW laser pulse with a longitudinal uniformity over 10 m. For that reason, engineering efforts should be devoted to constructing more stable 10-PW lasers with a clean focal spot as well as a long plasma channel medium with substantially profiled electron density distribution. The electron injection at such a low electron density is problematic. The self-injection process occurs when the laser intensity and the plasma density are high enough to induce the wave breaking of the plasma wave. The self-injection, empirically, happens when the laser power is higher than the critical power, \(P_{c}\approx 17\left(\frac{\omega_{\rm B}}{\omega_{p}}\right)^{2}\) GW [29]; that is, the laser power where relativistic self-focusing dominates over diffraction. For the plasma with an electron density of 10\({}^{16}\) electrons/cm\({}^{3}\), the critical power is about 3 PW. However, the laser pulse duration should be stretched to be more than 150 fs to prevent too quick etching, and the laser power on target would be below 2 PW. At this condition, self-injection is not possible. Recently, electron injection mechanisms, such as ionization injection [39; 40; 41], density shock injection [42; 43], and nanoparticle insertion [44; 45], have been proposed and demonstrated. Because the laser should propagate 10 m for 100 GeV acceleration, the electron injection process should not degrade laser properties and should occur only at the beginning of the medium. Thus, the electron injection mechanism for 100 GeV LWFA should be chosen carefully to maintain the laser quality and induce localized injection at the beginning.