Synchrotron radiation from ultrahigh-intensity laser-plasma interactions and competition with Bremsstrahlung in thin foil targets

The emission of high-energy photons is one of the major effects of relativistic laser-plasma interactions, which underpins a wide range of applications, from plasma diagnostics to radiography to nuclear physics and quantum electrodynamics studies. In the case of solid targets, such emission is usually dominated by Bremsstrahlung and radiative transitions of excited ions, yet one expects prolific synchrotron emission to kick in and eventually prevail at high enough laser intensities, such as those contemplated at various facilities under construction worldwide. In this paper, by means of advanced, self-consistent particle-in-cell numerical simulations, we present a detailed analysis of x-ray and $\gamma$-ray radiation under previously unexplored interaction conditions, involving ultrathin targets partially transparent to the laser light, yet accessible to multipetawatt laser systems during their early operation phase. We first examine the characteristics of synchrotron radiation from laser-driven plasmas of varying density and size. In particular, we show and explain the dependence of the angular distribution of the radiated photons on the transparency or opacity of the plasma. We then study the competition of the synchrotron and Bremsstrahlung emissions in copper foil targets irradiated with ${10}^{22}\mathrm{W}{\mathrm{cm}}^{-2}$, 50-fs laser pulses. Synchrotron emission is observed to be maximized for target thicknesses of a few tens of nanometers, close to the relativistic transparency threshold, and to be superseded by Bremsstrahlung in targets a few microns thick. At their best efficiency, both mechanisms are found to radiate about 1% of the laser energy into photons with energies above 10 keV. Their energy and angular spectra are thoroughly analyzed in light of the ultrafast target expansion, the influence of which has been overlooked so far. Our results demonstrate that even using solid materials of relatively high atomic number and not-so-extreme laser pulse intensities, synchrotron radiation can be a strongly dominant and efficient source of energetic photons provided the targets are thin enough.

Figure 1

Interaction of a semi-infinite, electromagnetic plane wave ($I_L={10}^{22}\mathrm{W}{\mathrm{cm}}^{-2}$) with a semi-infinite, relativistically undercritical ${\mathrm{C}}^{6+}$ plasma ($n_{e0}=17n_c$). (a) Longitudinal lineouts of the $E_y$ (purple) and $B_z$ (blue) field components and of the electron density $n_e$ (green). (b) $x\text{−}{p}_x$ electron phase space (averaged along $y$). (c) $x\text{−}{p}_y$ electron phase space (averaged over $y$). In (b) and (c) the red curve plots a longitudinal lineout of the synchrotron radiated power density ($P_{\gamma }$). All quantities are recorded 36 fs after the on-target laser peak.

Figure 2

Angle-resolved synchrotron radiated energy ($d{\mathcal{E}}_{\gamma }/d{\theta }_{\gamma }$) in a uniform ${\mathrm{C}}^{6+}$ plasma slab with $n_e=17n_c$, irradiated at a ${10}^{22}\mathrm{W}{\mathrm{cm}}^{-2}$ laser intensity. Three cases are considered: a semi-infinite laser wave in a semi-infinite plasma (blue), a 30-fs laser pulse in a semi-infinite plasma (green), and a 30-fs laser pulse in a 1-$\mu \mathrm{m}$ plasma (red). Angles are defined as ${\theta }_{\gamma }=arccos\left(k_{\gamma ,x}/k_{\gamma }\right)\in \left(0,\pi \right)$ (${\mathbf{k}}_{\gamma }$ is the photon wave vector) and are symmetrized relative to ${\theta }_{\gamma }=0$. The laser-to-photon energy conversion efficiency, ${\eta }_{\gamma }\equiv {\mathcal{E}}_{\gamma }/{\mathcal{E}}_L$, is indicated in each case.

Figure 3

Interaction of a semi-infinite, electromagnetic plane wave ($I_L={10}^{22}\mathrm{W}{\mathrm{cm}}^{-2}$) with a semi-infinite, relativistically overcritical ${\mathrm{C}}^{6+}$ plasma ($n_{e0}=100n_c$). (a1–a3) Longitudinal lineouts of the $E_y$ (purple) and $B_z$ (blue) field components and of the electron density $n_e$ (green). (b1–b3) $x\text{−}{p}_x$ electron phase space (averaged along $y$) (red). (c1–c3) $x\text{−}{p}_y$ electron phase space (averaged along $y$). In (b1)–(b3) and (c1)–(c3), the red curve plots a lineout of the synchrotron radiated power density, $P_{\gamma }$ (red). The three columns correspond to the interaction times: (a1–c1) $t=4$ fs, (a2–c2) 36 fs, and (a3–c3) 100 fs.

Figure 4

Same as Fig. 2 for a ${\mathrm{C}}^{6+}$ plasma with $n_e=100n_c$.

Figure 5

Two-dimensional PIC simulations of an ultraintense (${10}^{22}\mathrm{W}{\mathrm{cm}}^{-2}$), ultrashort (50-fs), and tightly focused (5-$\mu \mathrm{m}$) laser pulse interacting with a copper foil target. (a) Synchrotron (red triangles) and Bremsstrahlung (cyan triangles) conversion efficiencies into $>10$-keV photons as a function of the target thickness. (b) Laser absorption (blue triangles) and transmission (green triangles) as a function of the target thickness.

Figure 6

Time evolution of the angle-resolved (a) synchrotron and (b) Bremsstrahlung power spectrum from a 32-nm-thick Cu foil target. The dashed line at $t\simeq 0$ fs indicates both the laser pulse maximum and the onset of relativistic transparency.

Figure 7

A 32-nm-thick copper foil target: spatial distributions of the modulus of the magnetic field $|B_z|$ (blue color map) and the electron density $n_e$ (blue color map) at $t=12$ fs after the on-target laser peak. The closed red curves are isocontour lines (at $P_{\gamma }={10}^{23}\mathrm{W}{\mathrm{cm}}^{-3}$) of the synchrotron radiated power density.

Figure 8

Same as Fig. 6, from a 5-$\mu \mathrm{m}$-thick copper foil target.

Figure 9

Same as Fig. 7, from a 5-$\mu \mathrm{m}$-thick copper foil target.

Figure 10

Time-integrated (a) synchrotron and (b) Bremsstrah- lung energy-angle spectra from a 5-$\mu \mathrm{m}$-thick Cu target. The result is expressed as $\mathrm{J}/\mathrm{keV}/\mathrm{rad}$ instead of $\mathrm{J}/\mathrm{keV}/\mathrm{rad}/\mu \mathrm{m}$, as we assumed the third dimension $z$ to be 5 $\mu \mathrm{m}$.

Figure 11

(a) Time evolution of the longitudinal ($T_x$) and transverse ($T_y$) electron temperatures in a 5-$\mu \mathrm{m}$-thick Cu target. We distinguish between the (‘bulk') electrons initially contained in the preionized ${\mathrm{Cu}}^{25+}$ layer and the (‘ionized') electrons originating from the surface hydrogen layers and subsequent ionization of the Cu ions. (b) Space-integrated $p_x\text{−}{p}_y$ electron distribution at $t=+250\mathrm{fs}$.

Figure 12

Variations in the synchrotron radiation with the Cu target thickness: (a) Energy-resolved and (b) angle-resolved radiated energy spectra for $>10$-keV photon energies. In (b), the energy densities at thicknesses of $\le 0.1$ $\mu \mathrm{m}$ (lower half-plane) have been multiplied by a factor of 2 for visibility.

Figure 13

Variations in the Bremsstrahlung radiation with the Cu target thickness. (a) Energy-resolved and (b, c) angle-resolved radiated energy spectra for (b) $>10$-keV and (c) $>5$-MeV photon energies. In (b) and (c), the energy densities at thicknesses of $\le 0.1$ $\mu \mathrm{m}$ (upper half-planes) have been multiplied by factors of 200 and 20, respectively.