## 3 Applications with J-KAREN Laser System
### Xuv Electromagnetic Wave Generation via Flying Mirror  
In this subsection, we review the flying mirror experiment, which produced extreme ultraviolet electromagnetic pulse. An intense, ultra-short laser pulse (driver) can generate a wake wave in an underdense plasma. When the intensity is high enough, the wake wave becomes nonlinear and its density profile forms a cusp shape. The phase velocity of the wake wave is approximately equal to the group velocity of the driver laser, _i.e._, \(v_{ph}\) = \(c\) {1 - (\(\omega_{p}/\omega_{L}\))\({}^{2}\)}\({}^{1/2}\), where \(c\) is the light speed in free space,  
Figure 14: **(a)** A typical image of an energy distribution of the electron bunch at n\({}_{\rm e}\) = 1.0 \(\times\) 10\({}^{19}\) cm\({}^{-3}\), and a projection of the image onto the energy axis; **(b)** The monoenergetic electron bunch has a peak energy of 134 MeV and an energy spread of 3.5%. \(\omega_{p}\) and \(\omega_{L}\) are the plasma and laser frequencies, respectively. Thus, the wake wave or density cusp works as a partially reflecting, moving mirror at a relativistic velocity; thus this is referred to relativistic flying mirror (RFM) [85]. When another laser pulse (source) directs to the RFM properly, it can be reflected. Because of the relativistic motion of the RFM, the frequency of the reflected pulse is upshifted to \(\approx\) 4\(\gamma_{ph}^{2}\omega_{s}^{2}\) and the pulse duration is compressed down to \(\approx\tau_{s}\left/\left(4\gamma_{ph}^{2}\right)\right.\)due to the double Doppler effect, where \(\gamma_{ph}=\left\{1-\left(\
u_{ph}/c\right)^{2}\right\}^{-1/2}\) is the Lorentz factor associated with the RFM, \(\omega_{s}\) and \(\tau_{s}\) are the frequency and the pulse duration of the source pulse, respectively. After the proof-of-principle experiment [86], we conducted an improved experiment with head-on configuration using the J-KAREN laser system [87]. Here we describe the summary of the experiment. In the experiment, the head-on configuration was adopted and this required the laser system modification due to possible returning pulses. The returning pulses are transmitted laser pulses through the target medium (He gas) and may cause damage in the laser optics. The estimated laser energies of the returning pulses are shown in Figure 15. The energies are estimated assuming the transmission through the target is 100% (the worst case). By installing Faraday isolators, Pockels cells, and a spatial filter we confirmed that even in the worst case there is no damage in the laser chain. In the flying mirror experiment with J-KAREN laser system, 420 mJ, 27 fs driver pulses and 42 mJ, 34 fs source pulses are focused onto the helium gas-jet target by off-axis parabolic mirrors. The estimated peak irradiances in vacuum for the driver and source pulses are 6.5 \(\times\) 10\({}^{18}\) W/cm\({}^{2}\) and 1.2 \(\times\) 10\({}^{17}\) W/cm\({}^{2}\), respectively. The maximum plasma density is \(\left(4.7\pm 1.3\right)\times\) 10\({}^{19}\) cm\({}^{-3}\) at the absolute stagnation pressure of 2.1 MPa. By directing the source pulse, we have obtained the reflected laser spectrum in the extreme ultraviolet (XUV) region as shown in Figure 16 with a normal-incidence XUV spectrograph consisting of a spherical focusing mirror with broadband reflection, a transmission grating (5000 gr/mm), optical blocking filters, and a back-illuminated charge-coupled-device (CCD). Figure 15: A schematic of head-on laser system. FI: Faraday isolator; PC: Pockels cell; SF: spatial filter; STR: pulse stretcher; COMP: pulse compressor; TRPT: laser transport. Typical energies in the laser chain and estimated energies of returning pulses are shown. The estimated photon number is (1.05 \(\pm\) 0.03) \(\times\) 10\({}^{9}\) photons in the spectral range from 12.8 to 22.0 nm assuming that the reflection is result of one flying mirror. The reflectivity of the mirror is approximately half of the theoretical expectation (as seen in Figure 16). The expected pulse duration is 520-920 as.