# Betatron Radiation and Bremsstrahlung in the Interaction of Intense Laser Pulse with Solid Target
## 3 Results
### Effect of Laser Intensity and Spot Size  
For fixed laser parameters, the parameter \(\alpha\) changes from \(\ll\)1 to \(\gg\)1 as the preplasma width is reduced. We found that with increasing \(\alpha\), synchrotron radiation is suppressed and bremsstrahlung becomes dominant. A similar behavior also appears if the preplasma scalelength is fixed but the laser pulse parameter is varied. The change in laser pulse duration \(\tau_{d}\) can directly change \(\alpha\). For a laser pulse of fixed energy, we have \(\tau_{d}a_{0}^{2}\tau_{0}^{2}=\) constant. In the 2D cases considered, this relation becomes \(\tau_{d}a_{0}^{2}\tau_{0}=\) constant. Thus, the parameter \(\alpha\), or the radiation mechanism, can be controlled by tailoring \(a_{0}\) and/or \(r_{0}\). For long preplasmas (say \(L=5.0\) um), synchrotron radiation is dominant since \(\eta_{7,s}\gg\eta_{7,b}\). In this case, \(\alpha\ll 1\) for \(a_{0}=18\), \(r_{0}=3.0\) um, and \(\tau_{d}=9T_{L}\). Synchrotron radiation suppression can thus be achieved by increasing \(\alpha\), such as by keeping \(a_{0}\) unchanged and decreasing \(r_{0}\), or keeping \(r_{0}\) unchanged and decreasing \(a_{0}\), as shown in Figure 5a. Relative to the original case (orange curve with triangle marks), \(\eta_{7,s}\) decreases with decreasing \(r_{0}\) (\(r_{0}=1.0\) um, orange curve with squares) and decreasing \(a_{0}\) (\(a_{0}=6\), orange curve with circles), but \(\eta_{e}\) for these three cases (blue curves) are not so different. In fact, for all the three cases, \(\eta_{e0}\sim\eta_{e}\) (the blue dashed and solid curves in Figure 5a overlap). This indicates that in all the three cases almost all of the laser energy is transferred to the preplasma electrons. If \(a_{0}\) or \(r_{0}\) is decreased, \(\eta_{7,s}\) can be reduced to a level comparable with \(\eta_{7,b}\), as shown in Figure 5b. In fact, for \(r_{0}=1.0\) um, we have \(\eta_{7,s}\sim 0.03\%\) (orange and green curves with squares). For \(a_{0}=6\), (orange and green curves with circles), we see that \(\eta_{7,s}<0.01\%\), and \(\eta_{7,b}\) overtakes \(\eta_{7,s}\). It is of interest to note that although the laser pulse parameters are quite different in these three cases, the bremsstrahlung power from them are not much different, namely \(d\eta_{7,b}/dt=1.53\times 10^{-6}\) fs\({}^{-1}\) for \(a_{0}=18\), \(r_{0}=3.0\) um, \(d\eta_{7,b}/dt=1.43\times 10^{-6}\) fs\({}^{-1}\) for \(a_{0}=18\), \(r_{0}=1.0\) um, and \(d\eta_{7,b}/dt=1.03\times 10^{-6}\) fs\({}^{-1}\) for \(a_{0}=6\), \(r_{0}=3.0\) um. For the medium-width preplasma, such as \(L=0.5\) um, we have \(\eta_{7,s}\sim 0.02\%\), and \(\eta_{7,b}\) with a steady growth rate of \(5.40\times 10^{-6}\) fs\({}^{-1}\) overtakes \(\eta_{7,s}\), as shown in Figure 5d by the orange and green curves with circles. In this case, \(\alpha>1\) for \(a_{0}=18\), \(r_{0}=3.0\) um, and \(\tau_{d}=9T_{L}\). Keeping \(r_{0}\) unchanged, the variation of \(\eta_{7,s}\) with \(a_{0}\) is shown in Figure 5c. Increasing \(a_{0}\) from 18 to 38 causes \(\alpha\) to change from \(>\)1 to \(<\)1, with \(\eta_{7,s}\) reaching a high level of 0.1% (orange curve with squares). Decreasing \(a_{0}\) from \(a_{0}=18\) to \(a_{0}=6\) causes \(\alpha\) to change from \(>\)1 to \(\gg\)1, with \(\eta_{7,s}\) becoming negligible (orange curve with triangles). As \(a_{0}\) decreases, \(\eta_{e0}/\eta_{e}\) also decreases, as shown by the blue curves in Figure 5c. Similar to that for \(L=5.0\) um, although the laser parameters are different, the bremsstrahlung radiation power are not very different, namely, \(d\eta_{7,b}/dt=5.40\times 10^{-6}\) fs\({}^{-1}\) for \(a_{0}=18\), \(d\eta_{7,b}/dt=4.76\times 10^{-6}\) fs\({}^{-1}\) for \(a_{0}=38\), and \(d\eta_{7,b}/dt=5.01\times 10^{-6}\) fs\({}^{-1}\) for \(a_{0}=6\) as shown in the panel (d). It is convenient to measure the long-time behavior of bremsstrahlung by the attenuation of \(d\eta_{7,b}/dt\) to \(\exp(-1)\) of its peak value. To save computation time we carried out 1D simulations for this purpose.