# Betatron Radiation and Bremsstrahlung in the Interaction of Intense Laser Pulse with Solid Target
## 3 Results  
### Effect of the Preplasma Scalelength  
From Figure 1c,f, we see that the preplasma scalelength \(L\) affects the laser energy transfer to the electrons and thus the radiation. For 3.0 \(\upmu\)m \(<L<15.0\)\(\upmu\)m, the energy conversion rate \(\eta_{c0}\) from the laser to preplasma electrons is high, but that (\(\eta_{c1}\)) from the laser to slab electrons is very low. For 0.15 \(\upmu\)m \(<L<3.0\)\(\upmu\)m, \(\eta_{c0}\) decreases rapidly with \(L\), but \(\eta_{c1}\) increases. Despite the differences in detail, the dependence (on the interaction parameters) of the energy conversion rate (\(\eta_{\gamma,s}\)) from the laser to synchrotron radiation is similar to that of \(\eta_{c0}\). That is, synchrotron radiation is mainly produced by the laser-driven preplasma electrons, and the laser-to-bremsstrahlung energy conversion rate \(\eta_{\gamma,b}\) is not sensitive to \(L\) for 0.5 \(\upmu\)m \(<L<5.0\)\(\upmu\)m. For the extreme case \(L=15.0\)\(\upmu\)m, bremsstrahlung photons are produced by the laser-accelerated preplasma electrons as they propagate through the slab, because no laser energy is transferred to the slab electrons with the initial solid-slab electron spectrum hardly changed, as showed by Figure 1b. Figure 1e shows that for \(L=1.5\)\(\upmu\)m the bremsstrahlung photon number is much larger than that for \(L=15.0\)\(\upmu\)m. Moreover, one can see that the slab-electron spectrum for \(L=1.5\)\(\upmu\)m is much wider, suggesting that deposition of the laser energy in the slab electrons tends to enhance \(\eta_{\gamma,b}\). This is because in this case more relativistic electrons are produced which give rise to bremsstrahlung as they pass through the solid slab. For \(a_{0}\gg 1\), the LPI contains two stages: for \(0.05n_{c}<n_{e}<a_{0}n_{c}\), the laser can propagate in the preplasma and many of the affected electrons are accelerated by the laser fields to relativistic energies and emit high-energy photons. In the second stage, for \(n_{e}>a_{0}n_{c}\), the laser is cut off around \(n_{e}\sim a_{0}n_{c}\) and reflected. Electrons in the cut-off region (skin layer) can also be accelerated and emit high-energy photons as they interact with the laser light. Simulation results show that for given laser parameters, the laser energy deposition in the first and second stages are different as \(L\) changes. For long preplasmas with \(L=15.0,5.0\), and 3.0 \(\upmu\)m, almost all the laser energy is deposited in the preplasma, and the second stage of the interaction is negligible. As an example of the mechanisms and relative importance of synchrotron radiation and bremsstrahlung in the different parameter regimes, it may be instructive to consider the case \(L=5.0\) um in more detail. With the slab located in \(35\) um \(<x<40\) um, a long preplasma of density \(0.05n_{c}<n_{e}<a_{0}n_{c}\) is located in \(3.0\) um \(<x<32.4\) um. As the laser pulse propagates through the preplasma, its ponderomotive force displaces the background electrons, forming a positive channel with bounding sheaths of elevated density, as can be seen in Figure 2a. Figure 2c shows that these electrons are readily accelerated to relativistic energies by the laser light, and they can continuously gain energy by direct laser acceleration (DLA) as they co-propagate with the laser, as well as emit high-energy photons, as shown in Figure 2d,e. Figure 2b shows that at around \(t=50T_{L}\), the laser is cut off near \(x=28\) um, but the co-moving relativistic electrons continue to move forward. Figure 2f shows that at about \(t=50T_{L}\), \(\eta_{e0}\sim 0.85\) and \(\eta_{7,s}\sim 0.0016\). That is, most of the laser energy is converted into that of preplasma electrons, and with only a small amount into that of the synchrotron photons. Both \(\eta_{e0}\) and \(\eta_{7,s}\) become saturated shortly after the laser propagation is cut off. That is, the photons here are from synchrotron (more precisely, betatron) radiation rather than inverse-Compton scattering.