Phase-controlled direct laser acceleration enabled by longitudinal variation of the laser-driven quasi-static plasma magnetic field

Abstract

Direct laser acceleration (DLA) enables energy transfer from an ultra-high-intensity laser to plasma electrons and underpins many laser-driven particle and radiation-source concepts. A laser-driven azimuthal plasma magnetic field is a key player in this process: it confines energetic electrons, induces betatron oscillations, and makes possible a resonant interaction between the betatron motion and the laser field. While this betatron resonance can enhance electron energy gain, the gain itself generally drives frequency detuning and promotes largely reversible energy exchange that limits net acceleration. Here we show, using a test-electron model with prescribed fields, that a slow longitudinal increase of the quasi-static plasma magnetic field qualitatively changes DLA by introducing hysteresis in the ratio of the betatron frequency to the laser frequency experienced by the electron, so that this ratio depends on the prior evolution of the electron even at the same energy. This hysteresis enables phase control of the electron-laser energy exchange and suppresses the usual reversibility of DLA, allowing electrons to retain the acquired energy and sustain energy gain without intermittent losses.

Figures (22)

• Figure 1: Schematic of the plasma current filament used in the test-electron model, with the return current that typically flows on the periphery gong.pre.2020 not shown. The filament has both longitudinal and radial current density components. The brown surface is an isosurface of the current-density magnitude $|\bm{j}|$. The black arrows indicate the local direction of the current-density vector $\bm{j}$. The blue circles show the azimuthal magnetic field produced by the filament, with several cross sections illustrating its variation along the laser propagation direction. The black curve is an example of a flat electron trajectory in this field, with a characteristic forward drift.
• Figure 2: Maximum $\gamma$, denoted as $\gamma_{\max}$, attained by an electron in a longitudinally uniform plasma magnetic field as a function of the relative superluminosity $\delta u$ and the conserved quantity $S$. The horizontal dashed line marks $\delta u_{\max}$, the value of $\delta u$ that yields the highest $\gamma_{\max}$. The scan is for $a_0 = 8$ and $\alpha = 1.4$.
• Figure 3: $\gamma_{\max}$ as a function of $S$ at $\delta u = \delta u_{\max}$, where $\delta u_{\max}$ is the value of $\delta u$ that yields the highest $\gamma_{\max}$ in the scan shown in \ref{['fig:duScan']}. The green marker highlights the value of $S$ corresponding to the trajectory analyzed in \ref{['fig:alphaConstFreq']} and \ref{['fig:alphaConstPhase']}.
• Figure 4: Frequency ratio $\langle \omega' \rangle / \omega_{\beta}$ as a function of $\gamma$ for $S = 9.5$ and $\delta u = \delta u_{\max}$ ($\alpha = 1.4$, $a_0 = 8$). The solid curve is the analytical result given by \ref{['eq:freq_ratio']} and the blue round markers are the values obtained during numerical integration of the equations of motion. The horizontal dashed line marks the betatron resonance, $\langle \omega' \rangle = \omega_{\beta}$. The round gray and square red markers indicate the values of $\gamma$ at which this resonance condition is satisfied.
• Figure 5: Electron dynamics for the case with $S = 9.5$ and $\delta u = \delta u_{\max}$ ($\alpha = 1.4$ and $a_0 = 8$). (a) $\gamma$ as a function of the longitudinal position $x$. (b) Electron trajectory $y(x)$, with the color indicating $\gamma/a_0$. The dashed lines show $\pm y_*$, where $y_*$ is the amplitude of the betatron oscillations given by \ref{['eq:y_*']}. (c) Phase offset between the laser phase and the betatron phase, $[\xi - \psi]_{y=0}$, evaluated on the axis. The gray and red markers indicate locations where $\langle \omega' \rangle = \omega_{\beta}$.