Nonlinear Compton scattering of an ultraintense laser pulse in a plasma

Laser pulses traveling through a plasma can feature group velocities significantly differing from the speed of light in vacuum. This modifies the well-known Volkov states of an electron inside a strong laser-field from the vacuum case and, consequently, all quantum electrodynamical effects triggered by the electron. Here we present an in-depth study of the basic process of photon emission by an electron scattered from an intense short laser pulse inside a plasma, labeled nonlinear Compton scattering, based on modified Volkov solutions derived from first principles. Consequences of the nonlinear, plasma-dressed laser dispersion on the Compton spectra of emitted photons and implications for high-intensity laser-plasma experiments are pointed out. From a quantitative numerical evaluation we find the plasma to effectively suppress emission of low-frequency photons, whereas the emission of high-frequency photons is enhanced. The emission's angular distribution, on the other hand, is found to remain qualitatively unchanged with respect to the vacuum case.

Figure 1

(a) Integrated spectra for $I_L={10}^{22}\text{W}/{\text{cm}}^2$ for different plasma densities. (b) Total emitted energy compared to the vacuum limit (dashed red) with a quadratic fit (solid blue).

Figure 2

Angular spectra of the Compton scattered signal for a laser pulse with $I_L={10}^{22}\text{W}/{\text{cm}}^2$ $\left(\xi \approx 70\right)$ and a plasma density of $n_e={10}^{18}{\mathrm{cm}}^{-3}$ compared to the vacuum boundary angle ${\theta }_1^{\text{vac}}$ (white dotted line).

Figure 3

(a) Integrated spectra for $I_L={10}^{22}\text{W}/{\text{cm}}^2$ for forward emission $\left({\theta }_1\le {\theta }_1^{\text{vac}}/2\right)$ for different plasma densities. (b) Total emitted energy compared to the vacuum limit (dashed red) with a linear fit (solid blue). The arrows denote the position of the Compton peaks which are compared with the harmonics of the anti-Stokes mode in Fig. 5.

Figure 4

The photon energy spectrum ($d\mathcal{E}/d{\omega }_1$, in eV) with photon energy $({\epsilon }_{\mathrm{ph}}={\omega }_1)$ at $\xi =100$. The spectrum is similar to Fig. 3 but is plotted at a fixed angle $\theta =1/\xi$ instead of being integrated over a cone ${\theta }_1\le {\theta }_1^{\text{vac}}/2$ as in Fig. 3. Legends show the plasma densities (in ${\mathrm{cm}}^{-3}$) on a ${\log }_{10}$ scale.

Figure 5

Difference (color bar in eV) between the Compton spectrum peaks (marked by arrows in Fig. 3) and the corresponding harmonics of the anti-Stokes mode (also in eV) ${\omega }_n^{+}=n({\omega }_L+{\omega }_p)$, with $n=1,2,3$ (for different Compton peaks) at different plasma densities and $\xi =100$.