# Betatron Radiation and Bremsstrahlung in the Interaction of Intense Laser Pulse with Solid Target
## 3 Results
### Effect of the Preplasma Scalelength
However, the electrons trapped between the sheath fields at the slab's surfaces can emit high-energy bremsstrahlung photons as they bounce back and forth, as can be seen in Figure 4b,c. Thus, bremsstrahlung lasts much longer than the laser pulse duration, as can be seen from the evolution of \(\eta_{\gamma,b}\) shown in Figure 4d. As mentioned, the low level (\(<\)0.01%) of \(\eta_{\gamma,s}\) is because no laser energy is deposited in the first-stage interaction (i.e., with the preplasma). Figure 2: (Color online) Results for \(L=5.0\) μm. Density (normalized by \(n_{c}\)) of the preplasma electrons at (**a**) \(t=40T_{L}\) and (**b**) \(t=50T_{L}\), where the black curves are for the normalized laser electric field \(eE_{y}/m_{e}\omega_{0}c\) at \(y=0\). (**c**) Trajectories of typical preplasma electrons. The color bar is for \(\gamma\), showing the energy gain process. The vertical dashed lines mark the target slab. (**d**) Energy gain by the electrons shown in (**c**), where the blue and orange curves show their energy gain \(\Gamma_{j}=-\int_{0}^{t}ev_{j}E_{j}dt/m_{e}c^{2}\), \(j=x,y\), in the longitudinal and transverse directions, respectively. (**e**) Density of the synchrotron photons at \(t=55T_{L}\). (**f**) Evolution of \(\eta_{e0}\) (blue curve) and \(\eta_{\gamma,s}\) (orange curve). Figure 4: (Color online) Results for the case \(L=0.15\) μm. (**a**) Normalized total electron density \(n_{e}/n_{c}\) (color bar) at \(t=15T_{L}\), and the normalized laser electric field \(eE_{y}/m_{e}\omega_{0}c\) (black curve) on the axis \(y=0\). (**b**) Trajectories and energy \(\gamma_{e1}\) of typical slab electrons, and the normalized longitudinal electric field \(eE_{x}/m_{e}\omega_{0}c\) (black curve) on the axis. (**c**) Density of bremsstrahlung photons at \(t=75T_{L}\). (**d**) Evolution of \(\eta_{e1}\) (blue curve) and \(\eta_{\gamma,b}\) (orange curve). The vertical dashed lines in (**b**,**c**) mark the position of the slab. The dashed lines in (**d**) mark the laser-to-electron energy-conversion efficiency saturated at \(t=25T_{L}\). Figure 3: (Color online) Results for \(L=0.5\) μm. (**a**) Evolution of the energy conversion efficiencies: \(\eta_{e}\) (blue solid curve), \(\eta_{e0}\) (blue dashed curve), \(\eta_{\gamma,s}\) (orange curve), and \(\eta_{\gamma,b}\) (green curve). (**b**) Distribution of the total electron density (normalized by \(n_{c}\)) at \(t=30T_{L}\), and the normalized laser electric field \(eE_{y}/m_{e}\omega_{0}c\) (black curve) on \(y=0\). (**c**) Same as (**b**), but for \(t=35T_{L}\). (**d**) Trajectories of typical preplasma electrons with their local energy given by the color bar. (**e**) Energy gain of the electrons in (**d**), where the blue and orange curves show the energy gain in the longitudinal and transverse directions, respectively. (**f**) Density of the synchrotron photons at \(t=80T_{L}\). (**g**) Trajectories of the slab electrons with their local energy given by the color bar. The black curve shows the normalized longitudinal electric field \(eE_{x}/m_{e}\omega_{0}c\) (right vertical-axis label) on the \(y=0\) axis. (**h**) Energy gain \(\Gamma\) of the electrons in (**g**), where the blue and orange curves show the energy gain in the longitudinal and transverse directions, respectively. (**i**) Distribution of the bremsstrahlung photons at \(t=80T_{L}\). The vertical dashed lines in (**d**,**g**,**f**,**i**) mark the target slab.