Generation of Collimated Bright Gamma Rays with Controllable Angular Momentum Using Intense Laguerre-Gaussian Laser Pulses

A scheme to produce mega-electron-volt- (MeV) level gamma rays with a high level of brilliance, a small divergence angle, and controllable angular momentum from Laguerre-Gaussian (LG) laser-pulse interactions with underdense plasma is proposed. Three-dimensional particle-in-cell simulations show that the gamma photon beam acquires angular momentum from the helically distributed relativistic electrons driven by the LG laser and the self-generated fields in the plasma bubble created by the laser. The divergence angle and the orbital angular momentum (OAM) of the gamma photons can be controlled by manipulating the laser parameters. It is found that a 1-MeV helical gamma-ray pulse with peak brightness $2.23\times {10}^{24}\mathrm{photons}/\mathrm{s}/{\mathrm{mm}}^2/{\mathrm{mrad}}^2/0.1\mathrm{\%}\mathrm{BW}$ and angular momentum $7.1\times {10}^{-15}\mathrm{kg}{\mathrm{m}}^2/\mathrm{s}$, as well as a $<{10}^{\circ }$ divergence angle, can be generated by a $2\times {10}^{22}\mathrm{W}/{\mathrm{cm}}^2$ right-hand circularly polarized LG laser pulse. Such bright gamma rays with OAM offer an additional degree of freedom, which is relevant for understanding quantum-electrodynamics phenomena involving angular momentum, astrophysical phenomena, time-resolved probing of the nucleus, the generation of a vortical positron beam, etc.

Figure 1

(a) The isosurfaces of the normalized electric field $e{E}_y/m_e\omega c$ (green, for isosurface value $7$) of the $l=1$ LG laser light and the normalized energy density ${\mathcal{E}}_{\mathrm{photon}}/n_c{m}_e{c}^2$ (red, for isosurface value $16.5$) of the generated gamma photons at $t=100T_0$ at $x=61.5\mu \mathrm{m}$. The isosurface of the radiating trapped electron is similar to the latter. The transverse ($y$-$z$ plane) distributions of the normalized (b) laser electric field and (c) photon energy density.

Figure 2

(a) The transverse ($z=0$ plane) profile of the electron density normalized by $n_c$ along the laser propagation direction $x$, at $t=100T_0$. One can see (around $y=0$, $x=60\mu \mathrm{m}$) the helical betatron-oscillating electron bunches. Since during the process the structure also rotates around the center axis (i.e., $r=0$), the resulting electron density distribution has a helical structure (not shown), similar to that of the energy density of the photons emitted by these electrons given by the red isosurface in Fig. 1. (b) The normalized acceleration field $e(E_r-c{B}_{\theta })/m_e\omega c$. (c) The trajectories of four typical electrons starting from different radial locations. Here, one can clearly see the focusing and collimation effects. (d) The angular distribution of the accelerated electrons in the $x$-$y$ plane. Here, the radius represents the electron energy normalized by its maximum value and the polar angle $\varphi =0$ is in the laser propagation, or $x$, direction. The color code is for the electron number $N_e$.

Figure 3

(a) The evolution of the energy gain of three typical electrons from the longitudinal $W_x=-{\int }_0^{t}e{v}_x{E}_{x}dt$ (blue curves) and the transverse $W_{\perp }=-{\int }_0^{t}e(v_y{E}_y+v_z{E}_z)dt$ (red curves) fields. (b) The evolution of the normalized (by the laser frequency ${\omega }_0$) frequencies ${\omega }_B$ and ${\omega }_L$ of the electron betatron oscillations and the laser in the electron comoving frame, respectively, as experienced by the electron.

Figure 4

(a) The energy spectra of the helical electron beam for laser topological charges $l=0$ (no OAM, red curve), $l=1$ (blue curve), and $l=2$ (green curve) in the plasma bubble at $100T_0$. (b) The energy spectra of the gamma photons for $0.1\mathrm{\%}$ bandwidth. In all cases, the slope of the high-energy part is approximately $-0.71$, in agreement with that of typical synchrotron radiation. The critical energy is around $E_{\mathrm{ph}}=2\times {10}^5\mathrm{eV}$ (note that we have not tracked the lower-energy photons). (c) The energy distribution in the $x$-$y$ plane of the gamma photons for $l=0,1$, and 2 [same color code as in (a)]. Here, the polar angle is given by $\varphi =\arctan (p_y/p_x)$ and the radius represents the photon energy normalized by the maximum value, which is from the laser with $l=1$. Recall that the laser propagates in the $x$, or $\varphi =0$, direction. (d) The $y$-$z$, or transverse, plane energy distribution (given by the color bar) of energetic ($\mathcal{E}\ge 1\mathrm{MeV}$) gamma photons for $l=1$. Here, the polar angle is $\mathrm{\Psi }=\arctan (p_y/p_z)$ and the radial coordinate is for the $x$-$y$-plane polar angle, e.g., ${20}^{\circ }$, ${40}^{\circ }$, and ${60}^{\circ }$.

Figure 5

(a)–(c) The $y$-$z$ cross-section view of the photon energy densities (in units of $n_c{m}_e{c}^2$) at $x=61.5\mu \mathrm{m}$ for $\sigma =1$ and $l=0,1$, and 2, respectively. (d) The evolution of the angular momentum of the gamma photons for $l=0,1$, and 2. (e) The dependence of the angular momentum of the gamma photons on the topological charge. The green curve is a linear fit.

Figure 6

The dependence of the (a) electron and (b) photon angular momentum on the laser amplitude $a_0$ at $100T_0$ for $l=2$ with the same self-similar parameter $S=n_e/a_l{n}_c$. The angular momenta of the electrons and photons are normalized by $\lambda m_{e}c=2.18\times {10}^{-28}\mathrm{kg}{\mathrm{m}}^2/\mathrm{s}$.