# Betatron Radiation and Bremsstrahlung in the Interaction of Intense Laser Pulse with Solid Target
## 3 Results
### Effect of Laser Intensity and Spot Size
It should however be noted that this may overestimate \(\eta_{7,b}\) and the bremsstrahlung duration since lateral escape of electrons and light is precluded. The results are shown in Figure 5e. For example, for \(a_{0}=18\) (orange curve), the peak value of \(d\eta_{7,b}/dt\sim 5.00\times 10^{-6}\) fs\({}^{-1}\). Around \(t=1085T_{L}\), it decreases to \(\sim\)1.83\(\times 10^{-6}\) fs\({}^{-1}\), or \(\exp(-1)\) of the peak value, and the corresponding \(\eta_{7,b}\) is \(\sim\)0.17%. Note that the bremsstrahlung pulse lasts \(\sim\)1000\(T_{L}\), much longer than that (\(\tau_{d}=9T_{L}\)) of the driving laser pulse. The results for \(a_{0}=6\) and 38 are similar, with the long-time behavior of \(\eta_{7,b}\) reaching 0.1\(\sim\)0.2%, respectively, and the bremsstrahlung duration lasting much longer than the laser pulse. With the preplasma scalelength \(L\) fixed, \(\eta_{7,s}\) depends mainly on \(\alpha\) and the electron energy. Electron energy gain by DLA during the first-stage of interaction depends strongly on \(a_{0}\), as can be seen in Figure 6a. These high-energy electrons emit photons by synchrotron radiation during the first-stage of the interaction, as shown in Figure 6b. The photon density (green curve) for \(a_{0}=38\) is appreciably larger than that (orange curve) for \(a_{0}=18\) due to the higher electron energy, the photon density (blue curve in the inset) for \(a_{0}=6\) is almost negligible. This is consistent with the \(\eta_{7,s}\) levels of these three cases. Figure 6c shows the longitudinal distribution of bremsstrahlung photons of these three cases up to \(160T_{L}\)Bremsstrahlung photons arise mainly from the slab region. Different from synchrotron radiation, where radiation power depends strongly on the electron energy, radiation power of bremsstrahlung is independent of electron energy. Thus, the bremsstrahlung photon densities \(a_{0}=38\) and 18 are not much different, but their electron energy spectra are clearly different in high-energy regions (\(>\)20 MeV), as shown in Figure 6c and the inset in Figure 6d. The reason why the photon density of \(a_{0}=6\) case (the blue curve in Figure 6c) is at a relatively low level is that the bremsstrahlung pulse is delayed, as can be seen in Figure 5d. The conversion efficiency \(\eta_{\gamma,b}\) depends on the number of times the relativistic electrons traverse the slab, which depends mainly on relativistic electrons with lower energy, since they are more numerous and more easily trapped by the electrostatic sheath fields. Figure 6d shows the average number \(\langle N_{\text{cross}}\rangle\) of times that electrons of different energies traverse the slab up to \(t=160T_{L}\). For the \(>\)20 MeV electrons, \(\langle N_{\text{cross}}\rangle\sim 1\), since such high-energy electrons can propagate through the slab without being trapped. For the \(<\)20 MeV electrons, \(\langle N_{\text{cross}}\rangle\) increases with decreases in electron energy, indicating that electrons of lower energies can be trapped in the slab and can traverse it many times. Up to \(t=160T_{L}\), \(\langle N_{\text{cross}}\rangle\) for \(a_{0}=38\) (solid green curve) and \(a_{0}=18\) (solid orange curve), and thus \(\eta_{\gamma,b}\), are not much different. The \(\langle N_{\text{cross}}\rangle\) for \(a_{0}=6\) case (solid blue line) is small because rising of the laser pulse is relatively slow with \(\tau_{d}=81T_{L}\). At \(t=200T_{L}\), the difference of \(\langle N_{\text{cross}}\rangle\) between \(a_{0}=6\) and 38 becomes smaller, as can be seen from the dashed curves in Figure 6d. This is consistent with the result that \(\eta_{\gamma,b}\) for these three cases are similar. Figure 5: (Color online) (**a–d**) Energy-conversion efficiency versus \(t\), from laser to: all electrons (\(\eta_{e}\), blue solid curves), preplasma electrons only (\(\eta_{e0}\), blue dashed curves), synchrotron radiation photons (\(\eta_{\gamma,s}\), orange curves), and bremsstrahlung photons (\(\eta_{\gamma,b}\), green curves).