Retrieving Transient Magnetic Fields of Ultrarelativistic Laser Plasma via Ejected Electron Polarization

Interaction of an ultrastrong short laser pulse with nonprepolarized near-critical density plasma is investigated in an ultrarelativistic regime, with an emphasis on the radiative spin polarization of ejected electrons. Our particle-in-cell simulations show explicit correlations between the angle resolved electron polarization and the structure and properties of the transient quasistatic plasma magnetic field. While the magnitude of the spin signal is the indicator of the magnetic field strength created by the longitudinal electron current, the asymmetry of electron polarization is found to gauge the islandlike magnetic distribution which emerges due to the transverse current induced by the laser wave front. Our studies demonstrate that the spin degree of freedom of ejected electrons could potentially serve as an efficient tool to retrieve the features of strong plasma fields.

Figure 1

(a) The interaction scheme: The laser pulse impinges on unpolarized plasma (the electron density is shown in gray shades); accelerated and radiatively polarized electrons due to spin flips form outgoing polarized bunches. The red (blue) dots represent the electrons with spin $s_z=1$ ($-1$) and the lines show their movement tendency. The green line shows a typical electron trajectory with a spin-flip marked by a pentagram. (b) and (c) Snapshots of the electron SP distribution in spatial $(x,y)$ coordinates and transverse $(y,\theta )$ phase space, respectively. The green lines in (b) profile the laser field $E_y$ at slice $y=0$. (d) Angular distribution of electron number $dN/d{\theta }_f$ and SP $⟨s_z⟩$. (e) $\delta ⟨s_z⟩$ and $dN/d{ϵ}_e$ vs electron energy ${ϵ}_e$. All parameters are indicated in the text.

Figure 2

The ${\overline{B}}_z$ obtained from (a) analytical theory and (b) PIC simulations, where the black arrows denote the direction of electric current $\mathit{j}$. (c) Probabilities $\mathcal{P}$ of electron spin-flip after emitting a photon with ${\chi }_{\mathrm{ph}}$. The $\uparrow \downarrow$ represents the spin flip from parallel to antiparallel with respect to the magnetic field direction. The blue line profiles the photon emission probability $d^2{N}_{\mathrm{ph}}/d{\chi }_{\mathrm{ph}}dt$ with a bandwidth accounting for the influence of electron spin. (d) The number distribution of all emitted photons $N_{\mathrm{ph}}$ (gray) and emission associated with spin flips $N_{\mathrm{sf}}$ (yellow). (e) The spatial dependent SP differentiate $d{s}_z/dx$ contributed by the cases of $\kappa \lessgtr 1$ for electrons with final angle ${\theta }_f>0$ and ${\theta }_f<0$, respectively. (f) The angular dependence of spin-flip occurrence, where the result of condition $\kappa >1$ is multiplied by 10 for better visibility.

Figure 3

(a) The red (blue) dots present the electron spin-flip from $s_z=-1$ (1) to 1 ($-1$) in the plasma field dominant regime ($\kappa >1$) and the histogram exhibits its dependence on the transverse coordinate $d{\tilde{N}}_{sf}/dy$. The magenta line refers to a typical electron trajectory and its time evolution of $p_x$ is in (b). (c) The typical electron trajectory for the regime $\kappa <1$ and its corresponding momentum evolution in (d). The spin flips of electron trajectories in (a)–(d) are marked by yellow circles. (e) and (f) Spin flips with $\kappa <1$ for electrons with final angle ${\theta }_f>0$ and ${\theta }_f<0$, where the solid black (dashed lime) lines profile the simulated (analytically derived) dependence of net electron SP $s_z$ on the coordinate $y$.

Figure 4

The dependence of (a) electron SP $\delta ⟨s_z⟩$ and (b) the leading order QPMF ${\overline{B}}_{z,1}$ on $a_0$. (c) The correlation between $\delta ⟨s_z⟩$ and ${\overline{B}}_{z,1}$. In (a)–(c), the dots refer to the simulation results with different laser CEP ${\varphi }_0$ while the dashed black line denotes the theory. (d) The dependence of $\mathrm{\Delta }⟨s_z⟩$ on ${\varphi }_0$ for different $a_0$. (e) The dependence of $\mathrm{\Delta }{⟨s_z⟩}_a$ and $b_2$ on $a_0$. (f) The correlation between the amplitude of the SP asymmetry $\mathrm{\Delta }{⟨s_z⟩}_a$ and the secondary QPMF $b_2$.

Figure 5

(a) The ${\overline{B}}_z$ predicted by the model based on the sign of $\mathrm{\Delta }⟨s_z⟩$ and $\mathrm{\Delta }⟨\theta ⟩$. The valid range of the model is illustrated in the white region of the parameter space in (b) $a_0=350$ and (c) $n_e=5n_c$, where the circles (triangles) mark the simulation results of ${\overline{B}}_z$ with no more (more) than two islands on each side of $y=0$. (d) The ${\overline{B}}_z$ obtained from simulation for the case of $a_0=350$, $n_e=5n_c$, and $l_0=20\mu \mathrm{m}$.