Waveform Control of Relativistic Electron Dynamics in Laser-Plasma Acceleration

The interaction of ultraintense laser pulses with an underdense plasma is used in laser-plasma acceleration to create compact sources of ultrashort pulses of relativistic electrons and x rays. The accelerating structure is a plasma wave, or wakefield, that is excited by the laser ponderomotive force, a force that is usually assumed to depend solely on the laser envelope and not on its exact waveform. Here, we use near-single-cycle laser pulses with a controlled carrier-envelope phase to show that the actual waveform of the laser field has a clear impact on the plasma response. The beam pointing of our relativistic electron beam oscillates in phase with the carrier-envelope phase of the laser, at an amplitude of 15 mrad, or 30% of the beam divergence. Numerical simulations explain this observation through asymmetries in the injection and acceleration of the electron beam, which are locked to the carrier-envelope phase. These results imply that we achieve waveform control of relativistic electron dynamics. Our results pave the way to high-precision, subcycle control of electron injection in plasma accelerators, enabling the production of attosecond relativistic electron bunches and x rays.

Popular Summary

In laser-wakefield acceleration, an extremely short and intense laser pulse creates a plasma wave in a gas jet that accelerates ultrashort electron pulses for applications in particle, solid-state, and medical physics. In our experiment, we can change the exact shape of the electric field of the laser pulse, and we observe that this changes the accelerated electron beam. This effect shows the shortcomings of the main model used by the community and can be used to gain an unprecedented level of control over the technique.

The main model used in laser-wakefield acceleration is the “ponderomotive approximation,” which assumes that the interaction between the laser and the plasma depends only on the intensity profile of the laser pulse and not on the exact waveform of the electric field. This approximation is predicted to break down for pulses that are almost as short as an optical cycle.

We observe this breakdown in our experiment, as the beam pointing of our electron beam changes when we vary the phase of the electric field of our near-single-cycle laser pulse, while keeping the intensity profile constant. Through simulations, we show that this effect is caused by an asymmetry in the plasma wave at the moment the electron beam starts to form. This asymmetry is coupled to the phase of the laser electric field. So by controlling this phase, we can control the initial conditions of the electron acceleration process.

We expect that this new capability will open novel ways to make compact sources of ultrashort and intense pulses of electrons and x rays.

Figure 1

Principle of the experiment. Upper: An intense, near-single-cycle laser pulse is focused into a gas jet, where it ionizes the gas and drives a plasma wake. Through laser wakefield acceleration, electrons are accelerated to relativistic energies. A phosphor screen is used to image the electron beam. The shape of the electric field of the laser pulse is controlled through the CEP. Varying the CEP in the experiment changes the pointing of the electron beam. Lower: 2D map of the gas density, retrieved from the phase map of an interferometry measurement (left). The height of the laser beam is indicated in red ($150\mu \mathrm{m}$ from the jet exit). A lineout at this position of the plasma density (assuming full ionization of nitrogen up to ${\mathrm{N}}^{+5}$) is shown on the right. The dotted black line indicates the laser focal position.

Figure 2

Experimental results showing changes in electron beam parameters as the CEP is varied over three cycles of $2\pi$. (a) The pointing of the electron beam in the plane of polarization ($y$, red) and in the perpendicular plane ($x$, blue). (b) Typical images of the electron beam (acquired in 200 ms, which corresponds to 200 shots) at a high (1), central (2), and low (3) beam pointing. The white circle indicates the part of the beam sampled by the pinhole of the electron spectrometer. (c) Evolution of the electron beam charge as a function of the CEP. (d) The normalized energy spectra of the electron beam as a function of the CEP. Each data point in (a) and (c) is the average of 20 acquisitions. The vertical error bars indicate the rms error of these acquisitions, yielding a sub-2-mrad pointing jitter (rms). The horizontal error bars indicate the rms error of the CEP stability, averaged over 200 shots (on the order of 40 mrad).

Figure 3

Results of PIC simulations. (a),(b) Snapshots of the wakefield, for an initial CEP of $\pi$, at two different times, showing the injection of two separate bunches. Electron density in the $z\text{−}y$ plane is shown in gray, and injected electrons are displayed in orange (blue) when their pointing is positive (negative) at the end of the simulation. The normalized laser electric field $E_l/E_0=E_l/(m_{e}c{\omega }_0/e)$ (red dashed line) and its envelope (blue solid line) are also shown. The arrows show the typical trajectories prior to injection for each case. (c) Simulated electron beam for an initial CEP of $\pi$ (single shot). (d) Wakefield oscillation in the polarization plane (red), peak wavelength of the laser normalized by the initial wavelength (black), and charge injection rate for the two electron populations shown in (a),(b) with corresponding colors, as a function of the simulation time for an initial CEP of $\pi$. The gray dashed lines highlight the three main injection events. (e) Electron beam pointing in the simulations in the directions parallel (red) and transverse (blue) to the laser polarization as a function of the initial CEP. The corresponding experimental data are shown in gray (the absolute value of the experimental CEP cannot be determined and is assumed so as to match the phase of the oscillations of the pointing in the simulations). (f) Simulated electron beams for initial CEP values of $-(\pi /2)$, 0, and $+(\pi /2)$, which produce a high, centered, and low beam, respectively. The experimental beam pointing jitter is simulated by averaging 200 simulated shots with randomly generated beam-pointing variations following a normal distribution with a 15-mrad standard deviation (shot to shot) in both $x$ and $y$.

Figure 4

Single-shot measurements (blue) and average over 200 shots (black) of the CEP during the first loop of the experimental CEP scan.

Figure 5

(a) Schematic drawing of the spectrometer used in the experiment. The source, pinhole, magnet, and detector remain fixed throughout the CEP scan. The laser polarization and the CEP-dependent pointing oscillation (red arrows) are in the $y$ direction. Dimensions are in millimeters. (b, upper) The electron energy spectra from Fig. 2, without normalization. (b, lower) The mean electron energy as a function of the CEP.

Figure 6

(a) Simulated spectra for initial CEP values of $-(\pi /2)$, $+(\pi /2)$, and $\pi$. (b) Mean electron energy in the simulations as a function of the initial CEP, considering the full beam (blue) and the beam sampled through an off-center 15-mrad pinhole (red) in order to simulate the experimental configuration.

Figure 7

The amplitude of the pointing oscillation $\delta \theta$, normalized to the beam divergence $\mathrm{\Delta }\theta$, for different plasma densities. The error bars are calculated as the propagation of the statistical errors on $\delta \theta$ and $\mathrm{\Delta }\theta$.