Plasma rotation driven by lasers with zero angular momentum

TL;DR

This work demonstrates that plasmas can acquire angular momentum from lasers carrying zero angular momentum density through local pump depletion that creates a trailing long-wavelength vector-potential offset. Using analytical arguments and 1D/3D PIC simulations (OSIRIS), the authors show that electron transverse momentum follows canonical momentum transfer $p_y = A_y$ (and $p_ heta = e A_ heta$ in azimuthal geometry), while total angular momentum is balanced by ions and wakefields, consistent with angular-momentum conservation. The angular momentum of high-energy electrons is tunable via laser phase, the laser-to-plasma frequency ratio $rac{ω_0}{ω_p}$, and polarization (azimuthal vs radial), enabling controlled transverse electron dynamics and providing potential signatures in betatron radiation and wakefield diagnostics. The findings have implications for manipulating angular momentum in laser-plasma interactions and for designing compact sources with tailored angular-momentum properties.

Abstract

We present a novel mechanism in which plasma electrons and ions optically acquire angular momentum during local pump depletion of an azimuthally polarized laser, despite the laser carrying none. Using theoretical considerations and multi-dimensional particle-in-cell simulations, we find that this process is enabled by a strong frequency downshift at the gradually eroding laser pulse front. We further show that the angular momentum gained by the plasma electrons is compensated by the ions and by the combined electromagnetic fields of the laser and nonlinear plasma wave. By varying key laser parameters such as phase, frequency, and polarization, we demonstrate that the transverse momentum of high-energy electrons can be effectively controlled.

Figures (5)

• Figure 1: One-dimensional OSIRIS simulation results at time $t \approx 116/\omega_p$ showcase the frequency downshift of the laser electric field $E_y$, which manifests in the vector potential $A_y$ amid local pump depletion, enabling the plasma electrons to acquire transverse momentum in the nonlinear wakefield behind the main laser pulse. (a) The frequency of the laser electric field (envelope of $E_y$ in red) drops at the leading edge (Wigner distribution of $E_y$), which resides in a steep electron charge density spike (grey line). (b) The normalized amplitude of the low $k$-spectrum of the vector potential $A_y$ (blue line) surpasses that of the laser's electric field $E_y = -\partial A_y/\partial t$ (red line). (c) The vector potential $A_y$ (blue line) exhibits a long wavelength offset trailing the laser pulse ($(z-ct) \lesssim 25 \, c/\omega_p$ in the co-moving frame), where the electrons acquire transverse momentum, following canonical momentum conservation $p_y = A_y$ (highlighted in the inset).
• Figure 2: One-dimensional OSIRIS simulations show self-injected electron transverse momentum oscillations in a nonlinear wakefield, with increasing magnitude and a period linked to the laser's leading-edge erosion. (a) The electrons' position, $z - ct$ in the co-moving frame, and longitudinal momentum, $p_z$, at time $\approx 116/\omega_p$, show high-energy electrons with $p_z > 140 \, m_e c$ concentrated at $(z-ct) \approx 16 \, c/\omega_p$, with their transverse momentum around $p_y \approx 0.25 \, m_e c$, as highlighted in the inset (orange dots). (b) The time evolution of the mean transverse momentum of the high-energy electrons, $\langle p_y \rangle$, represented by orange dots, aligns well with the corresponding vector potential at their position, $\langle A_y \rangle$, shown as a blue line. The black-circled position corresponds to the time step of subplot (a). (c) The time evolution of the vector potential $A_y$ in the co-moving frame illustrates the erosion of the leading edge and the development of an oscillating long-wavelength offset. The oscillation half-period, $T/2 \approx 25/\omega_p$, is highlighted by dashed lines, illustrating the connection between the erosion of the leading edge, the long-wavelength offset, and the transverse momentum of the electrons shown in (b).
• Figure 3: Three-dimensional OSIRIS simulation results at $t \approx 150/\omega_p$ illustrate the angular momentum gain of plasma electrons in a nonlinear wakefield, driven by an azimuthally polarized laser pulse -- facilitated by the development of a long-wavelength offset in the laser's azimuthal vector potential due to local pump depletion. (a) The hollow intensity laser pulse (orange isosurfaces) with azimuthal polarization (black arrows) drives a donut-shaped nonlinear wakefield in the bubble regime (gray isosurfaces). Projections show the spatial distribution of the electron charge density, highlighting increased density at the laser pulse front. The blue and orange arrows indicate the direction of rotation of the electrons belonging to the electron sheath composing the donut-shaped bubble (blue) and the injected electrons inside the bubble (orange). The illustrated box dimensions are $20 \times 20 \times 20 \, (c/\omega_p)^3$. (b) The vector potential $A_\theta$ (yellow-purple colormap) exhibits a long-wavelength offset trailing the laser pulse ($z \lesssim 25 \, c/\omega_p$). Electrons in the inner and outer current sheaths (blue dots) and the self-injected electrons (orange dots) acquire azimuthal momentum following canonical momentum conservation, $p_\theta = A_\theta$, (see inset). (c) The high-energy ($>200 \, m_e c^2$) injected electrons form a ring in both configuration and transverse momentum space, exhibiting a well-defined angular momentum with a mean value of $\langle p_\theta \rangle \approx -2 m_e c$ (dashed line).
• Figure 4: Three-dimensional OSIRIS simulation results showing the evolution of angular momentum components, as defined in Eq. \ref{['Eq:totalAngular']}. (a) Angular momentum gained by the plasma electrons and ions (orange line) is compensated by that of the combined wakefield and laser fields (blue line). Individual contributions from electrons and ions are indicated in orange by crosses and a dashed line. The horizontal black line labeled "T" indicates the oscillation period. (b) The angular momentum acquired by protons and heavier ions is independent of their mass. This trend deviates for lighter species, as their motion influences local pump depletion and wakefield formation. We compare positively charged species with ten (blue line) and one hundred (purple line) times the electron mass, a mixed gas of protons (green line) and alpha particles (grey-dotted) and their sum (black line), protons (orange-dotted), ions with twice the proton mass (green dashed line), and ions with ten times the proton mass (black diamonds).
• Figure 5: Three-dimensional OSIRIS simulation results demonstrate how adjustments of laser parameters allow for the control of angular (transverse) momentum of high-energy electrons ($> 80\%$ of the maximum energy) under local pump depletion. (a) to (c) show the time evolution of the mean azimuthal momentum $\langle p_\theta \rangle$, mean radial momentum $\langle p_r \rangle$, and mean longitudinal momentum $\langle p_z \rangle$, respectively, for different laser and plasma parameters. Orange dots correspond to the reference case with $\theta_0 = 0$, $\omega_0/\omega_p = 8$ and azimuthal polarization; orange squares correspond to a change in the initial laser phase, $\theta_0 = 180^\circ$; purple diamonds represent a change in the laser-to-plasma frequency ratio, $\omega_0 / \omega_p = 6$; and blue triangles illustrate the transition to radial polarization. Note that the phase change affects only $p_\theta$, such that the points overlap in (b) and (c).