## 4 Compact, High Efficiency Laser System  
### Diode -Pumped Yb:YAG Chirped-Pulse Amplification Laser  
As mentioned above, the invention of CPA together with the Ti:sapphire gain material has opened a route to experimental inquiries of laser-matter interactions in the relativistic regime. The Ti:sapphire CPA lasers in widespread use are pumped by lamp pumped green lasers, which are limited in the system size. However, one can overcome this limitation and also benefit from the improved stability and maintenance effort, which are required for many applications. Among several laser gain materials for short pulse amplification, the Yb:YAG is one of the most attractive materials for compact high intensity CPA lasers because of Yb\({}^{3+}\) ion's excellent spectroscopic and material properties for amplifying short pulses and for being pumped with commercially available near-infrared high power LD [110, 111]. The LD pumped laser systems can be significantly more compact than similar lamp pumped laser systems. Features of the thin-disk geometry which are suitable for Yb:YAG laser material are very low thermal lens effects owing to efficient cooling with a good volume to surface ratio and the temperature gradient that is predominantly parallel to the beam direction, allowing for \begin{table}
\begin{tabular}{c c c c} \hline
**Parameters** & **E (150 MeV) + PWLaser** & **E (1.25 GeV) +PWLaser** & **E (10 GeV) +PWlaser** \\ \hline \(\gamma_{e}\) & 300 & 2500 & \(2\times 10^{4}\) \\ \(\gamma_{e}\) & 0.05 & 0.5 & 2.5 \\ \(\chi_{s}\) & 0.01 & 0.05 & 1 \\ \(\alpha_{\mathrm{rad}}=(\varepsilon_{\mathrm{rad}}\,\gamma_{\mathrm{e}})^{-1/3}\) & 60 & 30 & 15 \\ \hline \end{tabular}
\end{table} 
Table 1: Peak values of the invariants \(\gamma_{e}\) and \(\gamma_{s}\) for a 30 fs PW laser pulse (_a_ = 100) interacting with electron beams of different energy (150 MeV, 1.25 GeV, and 10 GeV). \(a_{\mathrm{rad}}\) is the normalized laser field at which the radiation friction effects come into play. high spatial beam quality. Furthermore, it exhibits simple power scalability. Power can be increased by simply increasing the pump and seed diameters on the amplifier disk [110,111]. As noted above, ASE can generate unwanted preformed plasma and influence laser-plasma interactions driven by short pulses. OPCPA is becoming increasingly popular as a front end preamplifier system that can significantly reduce the ASE background level, improving the temporal contrast. OPCPA also provides broadband amplification [11], avoiding the strong gain narrowing in Yb:YAG. Thus, an OPCPA/Yb:YAG thin-disk CPA laser system is the most promising candidate for realizing a compact high-spatiotemporal-quality, high intensity laser system [11,112]. The laser system consists of an oscillator, an aberration-free stretcher, an OPCPA preamplifier, a multi-pass Yb:YAG ceramic thin disk amplifier, and a compressor. At a 40 MHz repetition-rate the oscillator delivered 20 nJ pulses of 5.5 nm bandwidth at a 1029 nm central wavelength. The near transform-limited pulse duration of 220 fs were stretched to about 1 ns with a pulse energy reduced to 12 nJ using an Offner stretcher of 60% efficiency. Stretched pulses were subsequently amplified and then compressed by a grating pair. Following the stretcher and prior to amplification a commercial pulse selector extracted 10 Hz seed pulses that were synchronized to a Nd:YAG 532 nm pump laser. The gain of a three-stage (BBO) OPCPA preamplifier increased the output pulse energy to 3.5 mJ. Following preamplification the laser pulse energy was further increased by a Yb:YAG (7 at. %) ceramic thin disk amplifer. This thin disk is of 0.6 mm thickness and is mounted on a 1.0 mm thick YAG (undoped) disk of diameter of 14 mm. The Yb:YAG disk was pumped by the Q-CW fiber coupled LD unit at an energy of 2 J with 2 ms pump pulse duration (kW peak power). As shown in Figure 23, after 20 passes across the thin disk, we achieved the maximum output energy of 98.6 mJ with bandwidth of 2.2 nm (FWHM) and at 10 Hz.