# Betatron Radiation and Bremsstrahlung in the Interaction of Intense Laser Pulse with Solid Target
## 4 Discussion  
We have shown by simulating with different parameter combinations that synchrotron radiation dominates when \(\alpha<1\) and bremsstrahlung dominates if \(\alpha>1\). The dependence of \(\alpha\) on the major parameters \(a_{0}\) and \(L\) may be obtained by noting the interdependence of the laser and preplasma parameters. For a laser with a fixed energy and focal spot, we obtain \(\alpha\propto 1/a_{0}^{2}L\), where we have noted that \(l_{L}\propto a_{0}^{2}\). Figure 7a shows a map of \(\alpha(a_{0},L)\). One can see that for fixed \(L\) (\(a_{0}\)), reducing \(a_{0}\) (\(L\)) can change the dominant radiation mechanism from synchrotron radiation to bremsstrahlung. On the other hand, for laser pulse with fixed energy and intensity, we obtain \(\alpha\propto(r_{0}L)^{-1}\sqrt{1+\left(c\lambda L/2\pi r_{0}^{2}\right)^{2}}\), as shown in Figure 7b. Thus, for fixed \(L\) (\(r_{0}\)), reducing \(r_{0}\) (\(L\)) can change the dominant radiation mechanism from synchrotron radiation to bremsstrahlung. In Figure 7, the cases simulated in the preceding sections are marked by stars.  
Figure 6: (Color online) Results for \(L=0.5\)\(\upmu\)m. (**a**) Energy gain of typical electrons in the transverse direction. The blue, orange, and green curves are for \(a_{0}=6,18\), and 38, respectively. The vertical dashed lines in (**b**,**c**) mark the position of the solid target. (**b**) Longitudinal distribution of the synchrotron radiation photon density at \(t=160T_{L}\), obtained by summing along transverse direction. The inset shows the blue curve (which is of much smaller magnitude) more clearly. (**c**) Longitudinal distribution of bremsstrahlung photon density at \(t=160T_{L}\), obtained by summing along transverse direction. (**d**) Average number of times different-energy electrons traverse the slab from \(21T_{L}\) to \(160T_{L}\) (the dashed curves are up to \(200T_{L}\)). The inset shows the energy spectra of all electrons.  
In summary, we employ the PIC simulation code EPOCH including a Monte-Carlo implementation for bremsstrahlung to investigate electron acceleration and the subsequent synchrotron radiation and bremsstrahlung processes in the interaction of intense laser pulses with solid-density targets. The energy-conversion efficiencies of synchrotron radiation and bremsstrahlung are investigated in the moderate laser intensity range \(10^{19}\lesssim I\lesssim 10^{21}\) W/cm\({}^{2}\) as a function of the laser and plasma parameters. It is found that the laser pulse and the transparent preplasma widths are important parameters determining the two radiation processes, and that the dominant radiation mechanism can be controlled by tailoring the parameter \(\alpha=c\tau_{d}/\Delta x_{1}\), or the laser contrast, intensity, and spot size. Our findings can thus assist in controlling the radiation type in LPI research and applications.  
Conceptualization, simulation, data analysis and writing--original draft preparation, L.L. and R.L.; writing--review and editing, L.L., R.L., M.Y. and T.H.; methodology and software, H.Z.; validation and supervision, L.J., K.J., S.W. and B.Q.; project administration, C.Z. and X.H. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Natural Science Foundation of China (Grants No. 11875092, No. 12175154, No. 12005149, and No. 12205201), the Natural Science Foundation of Top Talent of SZTU (Grant No. 2019020801001), and the Shenzhen Science and Technology Program (Grant No. RCYX20221008092851073).  
Not applicable.  
The data that support the findings of this study are available from the corresponding author upon reasonable request.  
The epoch code is used under UK EPSRC contract (EP/G055165/1 and EP/G056803/1).  
The authors declare no conflict of interest.  
The following abbreviations are used in this manuscript:  
LPI Laser-plasma interaction PIC Particle-in-cell MC Monte-Carlo FWHM Full Width at Half Maximum DLA Direct laser acceleration 1D one-dimension 2D two-dimension fs femto second