Polarized Ultrashort Brilliant Multi-GeV $\gamma$ Rays via Single-Shot Laser-Electron Interaction

Generation of circularly polarized (CP) and linearly polarized (LP) $\gamma$ rays via the single-shot interaction of an ultraintense laser pulse with a spin-polarized counterpropagating ultrarelativistic electron beam has been investigated in nonlinear Compton scattering in the quantum radiation-dominated regime. For the process simulation, a Monte Carlo method is developed which employs the electron-spin-resolved probabilities for polarized photon emissions. We show efficient ways for the transfer of the electron polarization to the high-energy photon polarization. In particular, multi-GeV CP (LP) $\gamma$ rays with polarization of up to about 95% can be generated by a longitudinally (transversely) spin-polarized electron beam, with a photon flux meeting the requirements of recent proposals for the vacuum birefringence measurement in ultrastrong laser fields. Such high-energy, high-brilliance, high-polarization $\gamma$ rays are also beneficial for other applications in high-energy physics, and laboratory astrophysics.

Figure 1

Scenarios of generating CP and LP $\gamma$ rays via nonlinear Compton scattering. (a) An arbitrarily polarized (AP) laser pulse propagating along $+z$ direction and head-on colliding with a longitudinally spin-polarized (LSP) electron bunch produces CP $\gamma$ rays. (b) An elliptically polarized (EP) laser pulse propagating along $+z$ direction and colliding with a transversely spin-polarized (TSP) electron bunch produces LP $\gamma$ rays. The major axis of the polarization ellipse is along the $x$ axis.

Figure 2

(a) Angle-resolved photon number density ${\log }_{10}(d^2{N}_p/d{\theta }_{x}d{\theta }_y)({\mathrm{mrad}}^{-2})$ vs deflection angles, ${\theta }_x=p_x/p_z$ and ${\theta }_y=p_y/p_z$. (b) Distribution of average circular polarization for all emitted photons $\overline{P^{\mathrm{CP}}}=\overline{{\xi }_2}$. (c) Degree of circular polarization of $\gamma$-photons $P_{\gamma }^{\mathrm{CP}}={\xi }_2$ and energy density of $\gamma$ photons ${\log }_{10}(d{N}_{\gamma }/d{ϵ}_{\gamma })$ vs $\gamma$-photon energy ${ϵ}_{\gamma }$: via the Monte Carlo method (gray, thick, solid), via the spin-resolved average method of Eq. (6) (red, dash dotted), and via the average method summed up by ${\mathit{S}}_f$ at each simulation step (blue, dashed), respectively. (d) $P_{\gamma }^{\mathrm{CP}}$ vs the energy ratio parameter $\delta ={ϵ}_{\gamma }/{ϵ}_e$: via the Monte Carlo method (gray, thick, solid), and only considering the first photon emission (FPE) calculated numerically (green, thin, solid, using the instantaneous $\chi$ parameter) and analytically (black, dashed, employing the constant average parameter of $\chi =1.41$) via the average method (summing over ${\mathit{S}}_f$), respectively. In (b) the observation frame can be chosen following [57]. In (c) and (d) the basis vectors of the observation frame ${\widehat{\mathbf{o}}}_1$, ${\widehat{\mathbf{o}}}_2$, and ${\widehat{\mathbf{o}}}_3$ are along the $x$ axis, $-y$ axis, and $-z$ axis, respectively. The laser and other electron beam parameters are given in the text.

Figure 3

LP $\gamma$-ray emission with a left-handed EP laser with $a_0=100$, $\tau =5T_0$, ellipticity $\epsilon =|E_y|/|E_x|=0.05$, ${ϵ}_0=2\mathrm{GeV}$, initial average spin of electrons $({\overline{S}}_x,{\overline{S}}_y,{\overline{S}}_z)=(0,1,0)$ with 100% polarization, and other laser and electron beam parameters are the same as those in Fig. 2: (a) ${\log }_{10}(d^2{N}_p/d{\theta }_{x}d{\theta }_y)({\mathrm{mrad}}^{-2})$ vs ${\theta }_x$ and ${\theta }_y$; (b) Average linear polarization for all emitted photons $\overline{P^{\mathrm{LP}}}=\sqrt{{\xi }_1^2+{\xi }_3^2}$ vs ${\theta }_x$ and ${\theta }_y$; (c) ${\log }_{10}(d{N}_{\gamma }/d{ϵ}_{\gamma })$ into -10 mrad $<{\theta }_y<0$ (red, solid) and into $0<{\theta }_y<10\mathrm{mrad}$ (blue, dash dotted), respectively, and the relative difference $\mathrm{\Delta }{\mathcal{N}}_{\gamma }\equiv (d{N}_{\gamma }^{{\theta }_y<0}/d{ϵ}_{\gamma }-d{N}_{\gamma }^{{\theta }_y>0}/d{ϵ}_{\gamma })/(d{N}_{\gamma }^{{\theta }_y<0}/d{ϵ}_{\gamma }+d{N}_{\gamma }^{{\theta }_y>0}/d{ϵ}_{\gamma }$) (black, dotted) vs ${ϵ}_{\gamma }$. (d) Linear polarization of $\gamma$ photons $P_{\gamma }^{\mathrm{LP}}$ (employing ${\xi }_3$) vs ${ϵ}_{\gamma }$. In (c) and (d), $-10\mathrm{mrad}$ $<{\theta }_x<10\mathrm{mrad}$. The red, solid (blue, dash dotted) and black, dotted (green, dashed) curves indicate the results of -10 mrad $<{\theta }_y<0$ ($0<{\theta }_y<10\mathrm{mrad}$), calculated numerically and analytically (with average $\chi \approx 0.7$), respectively. In (d) the basis vectors of the observation frame ${\widehat{\mathbf{o}}}_1$, ${\widehat{\mathbf{o}}}_2$, and ${\widehat{\mathbf{o}}}_3$ are along the $x$ axis, $-y$ axis, and $-z$ axis, respectively.