Radiation reaction effects on particle dynamics in intense counterpropagating laser pulses

TL;DR

This work demonstrates that radiation reaction can reversibly alter the dominant direction of proton motion in an underdense plasma subjected to counterpropagating circularly polarized laser pulses. Using 1D (and select 2D) PIC simulations, the authors show that RR can detach electrons from the beat wave formed during pulse overlap, converting the initial electron dynamics into a net charge-separation field that drives ion motion in the opposite direction. They develop a simple threshold framework, with inequalities in terms of $R_\\lambda$, $R_a$, pulse duration, and the RR parameter $r_c w / R_\\lambda$, which broadly predict reversal when RR is strong enough to detrap electrons without destroying the overall beat-wave coherence. The results are corroborated by simulations and extended to 2D, and an experimental procedure is proposed to observe the transition to radiation-dominated dynamics via proton signatures. Overall, the study provides a practical diagnostic of RR effects in intense laser-plasma interactions and clarifies the parameter space where RR drives qualitative changes in ion acceleration.

Abstract

In high-intensity laser-plasma interactions, particles can lose a substantial fraction of their energy by emitting radiation. Using particle-in-cell simulations, we study the impact of radiation reaction on the dynamics of an underdense plasma target struck by counterpropagating circularly polarized laser pulses. By varying the relative wavelengths and intensities of the pulses, we find a range of parameters where radiation reaction can detrap electrons from the interference beat wave. The resulting charge separation field and the dominant direction of ion expulsion are thus reversed by radiative effects. Based on the electron dynamics during the interaction, we estimate the bounds on the parameter regime where the reversal occurs. The bounds take the form of three simple inequalities which depend only on the wavelength, normalized vector potential, and pulse duration ratios of the two lasers as well as the product of the pulse duration with a dimensionless radiation reaction parameter. Our estimates, which predict whether radiation reaction will change the final ion direction for a given set of laser parameters, broadly agree with the simulated results. Finally, we outline an experimental procedure by which the reversal could be used to observe the transition to radiation-dominated dynamics.

Figures (8)

• Figure 1: Schematic. (a) Circularly polarized laser pulses strike an initially stationary thin underdense plasma at normal incidence from both sides. The outer lines on each pulse represent the pulse envelope, while the interior sinusoidal curve represents one electric field component. (b) Longitudinal motion (blue arrows) of an accelerating electron (blue circle) under the influence of pulse 2 only. (c) Longitudinal motion of the same electron as it encounters pulse 1. The electron's longitudinal momentum is reduced to zero and it is turned around. (d) Standing wave electric field amplitude (gray curve, upper) resulting from the interference of pulses 1 and 2 (purple and red curves, lower) in the zero-momentum frame where $\lambda_1=\lambda_2$. The panel on the right shows the motion of a single electron trapped in the standing wave, oscillating between the sides of the potential well. As time proceeds, the pulses increase in amplitude. The pink sinusoid and arrow represent a high-energy emitted photon, corresponding to the radiative losses. (e) Longitudinal proton motion (gray circle and arrow) after the pulses have passed through the plasma. The protons are pulled by the charge separation field ($E_x$, green arrows) produced by the early electron dynamics. Here we show a representative case where the electrons moved with the beat wave, i.e. in the same direction as the higher-frequency pulse. The true direction in a given configuration depends on $R_a$ and $R_\lambda$, as well as whether radiation reaction is significant.
• Figure 2: 1D simulation results. (a) Distribution of electron number density over time for simulations without radiation reaction. Pulse 1 ($\lambda_1=0.4$ µ m, $a_1=100$) is incident from the left, while pulse 2 ($R_\lambda=3$, $R_a=5$) is incident from the right. (b) Same conditions as (a), but with radiation reaction enabled in the simulation. The density evolution shows a clear change in favored direction compared to (a). (c) Results of a scan over $R_a$, showing $\zeta$ (measured at $t=45$, $\sim60$ fs after the pulse peaks pass each other) for electrons ($e^-$) and protons ($p^+$). The vertical dashed line indicates $R_a=5$, corresponding to the conditions of panels (a) and (b). There is evidently a range of $R_a$ for which $\zeta_{p^+}$ changes signs when radiation reaction is considered.
• Figure 3: (a) Average electron $d\gamma/dt$ vs time in the initial acceleration stage for $\sim 100$ macroparticles with initial positions $10.9\lesssim x_0 \lesssim 12.5$ from the simulation with $R_\lambda=3$, $R_a=5$, and radiation reaction disabled. Eq. (\ref{['eq:dgdt']}) agrees with the PIC results until $t \gtrsim -18$, when the electrons begin to feel pulse 1. (b) Average local pulse normalized vector potentials $a_1g_1$ and $a_2g_2$ and normalized momentum $p_x$ over time for the same electrons as in (a). Once the electrons feel pulse 1, and especially during the stopping process ($-13\lesssim t \lesssim -10$, around the time when $a_1g_1$ becomes dominant), the amplitude of pulse 1 rises rapidly while that of pulse 2 rises by only about a factor of 2. (c) Numerically estimated $\sqrt{\kappa^2-1}$ for randomly sampled electrons across the right half of the plasma, compared to the PIC results for $a_1g_1$ at the time $t_{\text{stop}}$ when each electron's $p_x$ reaches 0. Color indicates the electron's initial position, with lighter color corresponding to a position further from the center. The dashed line represents a slope of 1, following Eq. (\ref{['eq:a1g1']}). The electrons generally follow the predicted trend.
• Figure 4: (a) Individual electron trajectories without (blue) and with (orange) radiation reaction for the simulation with $R_\lambda=3$ and $R_a=5$. The dash-dotted green line corresponds to $v_{ZMF}$ (Eq. (\ref{['eq:vZMF']})), which well-approximates the average velocity of the trapped electrons without radiation reaction. The oscillations seen in the trapped electron trajectories correspond to the oscillations within the potential wells as discussed in Section \ref{['sec:resultsbeat']}. The inclusion of radiation reaction does not substantially impact the trajectories until the trapping stage, at which point it enables the majority of particles to escape the beat wave. (b) Individual electron momenta over time from $-10\lesssim t \lesssim -4$ for three representative electron macroparticles, without (blue) and with (orange) radiation reaction. Radiation reaction leads to a decrease in $\hat{\mathbf{x}}$ momentum, nudging the electrons out of their trapped trajectories.
• Figure 5: Simulation results for an $R_a$ and $R_\lambda$ parameter scan, showing $\zeta_{p^+}$ (a) without and (b) with radiation reaction. (c) Comparison of the sign of $\zeta_{p^+}$ across the scans. The two symbols ($+,-$) represent the sign of $\zeta_{p^+}$ at the corresponding points in panels (a) and (b), i.e. the blue upward triangle corresponds to $\zeta_{p^+}>0$ with no radiation reaction and $\zeta_{p^+}<0$ with radiation reaction. Regions corresponding to the interaction classes discussed in section \ref{['sec:resultsclasses']} are shaded and labeled with text bubbles. The black line in all panels represents Eq. (\ref{['eq:thresh4']}) with $C=100$. The horizontal gray line corresponds to $v_{ZMF}=1/2$. The pink line in panels (b) and (c) represents Eq. (\ref{['eq:rc1']}).