Production of high-angular-momentum electron beams in laser-plasma interactions

It was shown that in the interactions of ultra-intense circularly polarized laser pulse with the near-critical plasmas, the angular momentum can be transferred efficiently from the laser beam to electrons through the resonance acceleration process. The transferred angular momentum increases almost linearly with the acceleration time $t_a$ when the electrons are resonantly accelerated by the laser field. In addition, it is shown analytically that the averaged angular momentum of electrons is proportional to the laser amplitude $a_L$, and the total angular momentum of the accelerated electron beam is proportional to the square of the laser amplitude $a_L^2$ for a fixed parameter of $\frac{n_e}{n_c{a}_L}$. These results are verified by three-dimensional particle-in-cell simulations. This regime provides an efficient and compact alternative for the production of high angular momentum electron beams, which may have many potential applications in condensed-matter spectroscopy, new electron microscopes, and bright x-ray vortex generation.

Figure 1

The single-particle simulation results based on Eqs. (1) and (2). (a) The maximum energy gain $\mathrm{\Delta }{\gamma }_{\max }/{\gamma }_0$ of the electron for different ${\gamma }_0$, where $\mathrm{\Delta }{\gamma }_{\max }=({\gamma }_{\max }-{\gamma }_0)/{\gamma }_0$. The inset figure shows the time evolution of the Lorentz factor for typical resonant electron with ${\gamma }_0=0.75a_L^2{n}_c/n_e$. (b) The time evolution of the electron transverse momentum ($p_z$ and $p_y$) for typical resonant electron. (c) The comparison of the variation of the transverse velocity ($d{v}_y/cdt$) and the longitudinal velocity ($d{v}_x/cdt$) for the resonant electron. (d) The comparison of the variation of the lorentz factor and the transverse velocities for the resonant electron, where ${\eta }_y=|\frac{1}{\gamma }\frac{d\gamma }{dt}|/|\frac{1}{v_y}\frac{d{v}_y}{dt}|$ and ${\eta }_z=|\frac{1}{\gamma }\frac{d\gamma }{dt}|/|\frac{1}{v_z}\frac{d{v}_z}{dt}|$. The initial parameters in panels (b–d) correspond to $n_e/a_L{n}_c=0.002,a_L=10$, and ${\gamma }_0=0.75a_L^2{n}_c/n_e$, and the initial conditions are $x\left(0\right),y\left(0\right),z\left(0\right)=0,p_y\left(0\right),p_z\left(0\right)=0$, and $p_x\left(0\right)=\sqrt{{\gamma }_0^2-1}$.

Figure 2

(a, b) The typical trajectory of the high-energy betatron electron in CP and LP cases, respectively. (c) The time evolutions of electron energy in CP and LP cases, respectively. The energy is in units of $\mathrm{MeV}$. (d) The corresponding time evolutions of the angular momentum of the tracing electrons in CP and LP cases, respectively. The angular momentum of electron is in units of $\lambda m_{e}c$.

Figure 3

The 3D PIC simulation results at $50T_L$. (a) The laser field $E_y$ normalized by $m_e\omega c/e$; (b) the electron density $n_e$, normalized by the critical density $n_c$; (c) the electron energy density normalized by $n_c\mathrm{MeV}$; (d) 3D isosurface distribution of electron energy density with isosurface value $100n_c\mathrm{MeV}$ for CP case; (e) 3D isosurface distribution of electron energy density with isosurface value $100n_c\mathrm{MeV}$ for the LP case.

Figure 4

(a) and (b) The transverse and axial quasistatic magnetic fields $B_z,B_x$ normalized by $m_e{\omega }_0/e$ at $28T_L$. The black line in (a) shows the transverse profile of the static magnetic field at $15\mu \mathrm{m}$, and the parameter $S=\frac{n_e}{n_c{a}_L}$ is fixed as 0.078 with $a_L=64$.

Figure 5

3D isosurface distribution of photon energy density with isosurface value $11n_c\mathrm{MeV}$ at $28T_L$. In the simulations, the parameter $S=\frac{n_e}{n_c{a}_L}$ is fixed as 0.078 with $a_L=64$.

Figure 6

The angular momentum evolution of electrons and total particles changing with time in $x$ direction in the unit of $\lambda m_{e}c$. The blue and red lines are the angular momenta of total particles generated by CP and LP laser, respectively. The green and black lines are the angular momenta of electrons generated by CP and LP laser, respectively.

Figure 7

(a) The total angular momentum of the electrons in the unit of $\lambda m_{e}c$ at $50T_L$, where the fitted curve is in form of the power function as $L_{\mathrm{total}}=b{a}_L^d$ and the fitting coefficients correspond to $b=(2.20\pm 0.91)\times {10}^9$ and $d=2.17\pm 0.17$. (b) The averaged angular momentum of the trapped electrons in the plasma channel in the unit of $\lambda m_{e}c$ at $50T_L$, where the fitted curve is in the form of the power function as $L_{\mathrm{averaged}}=b{a}_L^d$ and the coefficients are $b=0.35\pm 0.07$ and $d=1.37\pm 0.08$. Here the small quantities behind the plus-minus sign refer to the standard errors of the fitting coefficients.

Figure 8

(a, b) The electron transverse momentum $p_y,p_z$ normalized by $m_{e}c$. (c, f) The typical trajectory of the electrons. (d) The time evolution of the Lorentz factor of the electron. (e) The time evolution of the angular momentum of the electron. The red-dashed line represents the electron only interacting with the laser field in vacuum, and the blue-solid line represents the electron interacting with both the laser field and the quasistatic magnetic fields, The initial parameters are $n_e/a_L{n}_c=0.002,a_L=10$, and ${\gamma }_0=0.75a_L^2{n}_c/n_e$, and the initial conditions are $x\left(0\right),y\left(0\right),z\left(0\right)=0,p_y,p_z=0$, and $p_x\left(0\right)=\sqrt{{\gamma }_0^2-1}$.