# Multi-GeV Laser Wakefield Electron Acceleration with PW Lasers
## 3 Multi-GeV LWFA with PW-Class Lasers
### LWFA with Capillary Discharge Plasmas at LBNL  
Laser propagation through a plasma medium is a highly complicated process. To increase the electron energy for a given laser power, the elongation of laser propagation is a critical issue in LWFA research. Most experiments were performed with self-guiding schemes that provide a much longer propagation length than the Rayleigh range by balancing relativistic self-focusing and diffraction. For increasing the electron energy, the plasma density should be lower, and the medium length should be longer. However, the elongation of laser-propagation length by relativistic self-guiding is getting more difficult as plasma density is lowered because the critical power for self-guiding increases as the plasma density decreases. Thus, the elongation of the laser propagation through the plasma medium is an essential technique to increase electron energy with PW laser pulses. One of the solutions is guiding the laser pulse with a plasma channel. The plasma channel guiding utilizes a refractive index gradient in the transverse direction like optical fibers. It can contain high-intensity laser pulses in the relativistic regime due to the extremely high-intensity limit of the plasma medium. Several groups developed plasma channel technology [34; 35; 36], and the research group at Lawrence Berkley National Laboratory successfully applied the plasma channel to enhance the electron energy [16; 32; 33]. The first successful application of a plasma channel to LWFA demonstrated 1 GeV electron acceleration by focusing a 40 TW laser pulse to a 3.3 cm plasma channel [37]. The plasma channel was formed in a pre-ionized hydrogen plasma confined in a capillary tube. The capillary tube was fabricated on a sapphire block by laser machining: two gas inlets and a central tube with a few-hundred-microns diameter. The hydrogen gas was fully ionized by a high-voltage electric pulse applied to the electrodes at both ends of the capillary tube. The pre-formed plasma had a hyperbolic electron density profile in the transverse direction that can guide an intense laser pulse. The capillary discharge medium has an obvious advantage of elongated laser propagation through the plasma medium. Table 2 summarizes the successful demonstrations of electron energy enhancement with capillary discharge plasma channels and sub-PW [19] and PW lasers [12]. The enhancement of electron energy with the laser power is not straightforward, even though the plasma channel can guide the driving laser pulse to a long distance. Since 1-GeV electron beam was produced with a laser power below 100-TW, as seen in experiment 1 in Table 2, a 1-PW laser pulse should have the capability to generate a 10-GeV electron beam. Despite the use of sub-PW laser pulses, a 4.2-GeV electron beam was produced with a 9 cm capillary discharge plasma channel because of the nonlinear evolution of laser pulses with a top-hat profile. The nonlinear propagation in the plasma can assist the self-injection process but disturb smooth laser propagation in the plasma channel. For increasing electron energy in LWFA further, a longer laser propagation through a plasma with a lower plasma density is essential. However, the nonlinear laser propagation can prohibit the increase of electron energy by limiting long and smooth laser propagation through a plasma medium with an extremely low electron density below 5 \(\times\) 10\({}^{17}\) electrons/cm\({}^{3}\). Although experiment 2 in Table 2 was performed with an almost perfectly focused laser beam of Strehl ratio of about 0.8, the top-hat laser profile in the near field, ordinarily formed by the laser amplification, induced a nonlinear laser propagation and hindered the additional increase of electron energy. The nonlinear laser propagation problem has been mitigated by steepening the transversal electron density gradient of the plasma channel. A nanosecond laser, focused on