# Betatron Radiation and Bremsstrahlung in the Interaction of Intense Laser Pulse with Solid Target
## 3 Results
### Effect of the Preplasma Scalelength
In this case, the synchrtron radiation dominates since \(\eta_{7,s}\gg\eta_{7,b}\). For medium-length preplasmas with \(L=1.5\) um and \(0.5\) um, the laser energy is deposited in both the first and second stages of the LPI. As an example, we consider the case \(L=0.5\) um in more detail. The slab is located in \(20\) um \(<x<25\) um, the preplasma region with density \(0.05n_{c}<n_{e}<a_{0}n_{c}\) is located in \(16.8\) um \(<x<19.74\) um. As shown in Figure 3a, from the beginning of the LPI to \(t\sim 35T_{L}\), \(\eta_{e0}\) remains roughly the same as \(\eta_{e}\) (\(\eta_{e0}+\eta_{e1}=\eta_{e}\)). However, \(\eta_{e}\) continues to increase even though \(\eta_{e0}\) is saturated at \(t\sim 35T_{L}\), and becomes saturated only at \(t\sim 40T_{L}\). That is, before \(t\sim 35T_{L}\), the LPI is in the first-stage, and from \(t\sim 35T_{L}\) to \(t\sim 40T_{L}\), the LPI is in the second-stage. Similar to the long preplasma case, during the first-stage, the laser pulse propagates in preplasma, as shown in Figure 3b. Figure 3d,e show that a small number of electrons can be accelerated to relativistic energies by DLA. Figure 3f shows that these electrons can emit high-energy photons by betatron  
Figure 1: (Color online) Energy spectra of the (**a**) preplasma electrons, (**b**) slab electrons, (**d**) synchrotron photons, and (**e**) bremsstrahlung photons, for \(L=0.15\), \(0.5\), \(1.5\), and \(15\) μm. (**c**) The laser-to-electron energy conversion efficiency \(\eta_{e}\) versus the preplasma scalelength \(L\). (**f**) the laser-to-photon energy conversion efficiency \(\eta_{\gamma}\) versus \(L\). In (**c**), the orange and blue curves represent the energy conversion efficiencies \(\eta_{e0}\) and \(\eta_{e1}\) in the preplasma and slab, respectively. In (**f**), the orange and blue curves denote \(\eta_{7,s}\) and \(\eta_{7,b}\) of the synchrotron-radiation photons and bremsstrahlung photons, respectively. radiation. However, the orange curve in Figure 3a shows that \(\eta_{\gamma,s}\sim 0.02\%\), much less than that in long preplasma case. During the second-stage interaction, the laser pulse propagation is cut off at dense plasma boundary with the laser pulse being reflected, as shown in Figure 3c. However, the laser electric field can still penetrate into the skin layer of the dense plasma and accelerate the surface electrons there to relativistic energies. The black curve in Figure 3g shows that with the expulsion of these energetic electrons, an electrostatic sheath field is built up. Figure 3g,h show that electrons on the front surface are then accelerated by both the laser electric field and the sheath field until the end of the second-stage interaction. Relativistic electrons accelerated in both the first and second stages can emit high-energy photons by bremsstrahlung, as can be seen in Figure 3i. After the laser pulse is fully reflected at \(t\sim 40T_{L}\), \(\eta_{\gamma,s}\) tends to saturate, but \(\eta_{\gamma,b}\) continues to increase, as shown in Figure 3a, due to bouncing of the energetic electrons trapped between the electrostatic sheath fields at the front and back slab surfaces. Eventual saturation of bremsstrahlung shall be discussed later. For the short preplasma with \(L=0.15\) um, the slab is located in \(5.0\) um\(~{}<x<10.0\) um, with the region \(0.05n_{c}<n_{e}<a_{0}n_{c}\) in \(4.04\) um\(~{}<x<4.92\) um. After only about one cycle in the preplasma, the laser pulse begins to interact with the slab. There is almost no laser energy loss in the preplasma, so that the first interaction stage is ignorable. However, the laser is reflected after penetrating only about a skin depth into the slab, as shown in Figure 4a. Nevertheless, the laser fields can accelerate the surface electrons to \(\sim\)10 MeV in just one cycle (\(6T_{L}<t<6T_{L}+2\tau_{d}\)), corresponding to the rapid-rising stage of \(\eta_{e1}\) shown in Figure 4d. Interaction between the laser pulse with the slab ends at around \(t=24T_{L}\), when \(\eta_{e1}\) becomes saturated at about 27%.