Ultrarelativistic electron beams accelerated by terawatt scalable kHz laser

Electron accelerators are a cornerstone technology of modern society. In their variations, they are daily used as strategic tools at the disposal of the healthcare system for medical imaging and cancer treatment. As an example, medical linear accelerators already use electron beams with energies up to $20 MeV$ for cancer radiotherapy.¹ Radio-frequency acceleration is the backbone of the technology driving these machines; after its first demonstration in 1928,² it is now generally acknowledged as an extremely reliable technology. Nevertheless, the fundamental limitation of radio-frequency acceleration technology is its maximum achievable accelerating gradient (⁠ $≈ 100 MV / m$⁠).

As of today, various proven technologies with the potential to overcome these limitations (by withstanding accelerating gradients exceeding $100 MV / mm$ and drastically reducing the accelerator footprint) exist, such as laser-driven wakefield acceleration (LWFA),^3,4 particle-driven (or plasma) wakefield acceleration (PWFA),^5,6 structure-based wakefield acceleration,^7,8 or a combination of these.^9,10 In recent years, the huge wakefield acceleration potential motivated an extensive effort by numerous groups worldwide, leading to remarkable achievements, ranging from the demonstration of the first GeV laser-driven electron beams^11–13 to the acceleration of multi-GeV electrons via plasma guiding^14,15 and the demonstration of free electron lasing.¹⁶ 

The desire to translate these exceptional results into working machines resulted in the demonstration of stable electron beam operation over more than 24 h¹⁷ and the acceleration of quasi-monoenergetic electron beams at $1 kHz$ repetition rate.^18,19 With the typical charge per pulse of the order of pC,^20–23 the resulting average current of a kHz LWFA is of the order of nA, which (provided the electron beam energy is $> 40 MeV$⁠) would be enough to enable several medical applications.^24,25 These groundbreaking achievements were obtained by exploiting nonlinearities through gas-filled hollow core fiber compression down to single-cycle laser pulses in order to reach the relativistic intensity on the target required to drive the wake wave in the plasma, where the injected electrons can be accelerated up to $15 MeV$⁠.¹⁹ Despite producing very stable electron beams, this technique is limited both by the maximum laser power available and by the maximum coupling efficiency into the hollow core fiber, setting a limit to the maximum electron energy attainable. Moreover, LWFA driven by single-cycle lasers is also sensitive to carrier-envelope phase effects,^26,27 posing an additional limit on the achievable electron beam energy and quality.

In this Letter, we show, for the first time, the production of quasi-monoenergetic (25% energy spread), collimated (2 mrad divergence) electron beams with energy up to $E ≈ 50 MeV$ with multi-cycle (⁠ $15 fs$⁠) laser pulses at $1 kHz$ repetition rate, overcoming the requirement of single-cycle compression and proving the energy scalability of the technology. This breakthrough was achieved by ELI Beamlines' in-house development of the L1-Allegra multi-TW $1 kHz$ laser,²⁸ based on the optical parametric chirped pulse amplification (OPCPA) technology.

Some first demonstrations of relativistic electrons accelerated with short-pulsed OPCPA systems^29,30 showed the potential of this laser technology, even if at a much lower repetition rate of $10 Hz$⁠. The L1-Allegra laser's key features for LWFA are its multi-stage power scalable design (final output expected $>100 mJ$⁠), the inherently excellent nanosecond contrast being pumped by $3 ps$ Yb:YAG thin-disk lasers, and its power and pointing stability (few % level) over many hours of continuous operation. Having a high contrast prevents unwanted detrimental effects due to pre-pulse-induced plasma profile modifications.

The L1-Allegra laser has six amplification stages [as shown in Fig. 1(a)], achieving a pulse energy of $26 mJ$⁠, measured inside the interaction chamber. Optimal compression of the output pulses was achieved through a combination of chirped mirrors and initial stretching by a programmable acousto-optic modulator (Dazzler). Ahead of the interaction chamber, the laser pulses were characterized by measuring the near-field profile [Fig. 1(b)] (where the elliptical profile is mainly due to the use of spherical mirrors in the laser telescopes and the little amount of residual spatial chirp from the amplifiers), the time duration [Fig. 1(c)], and the spectrum [Fig. 1(d)]. These were performed by a second harmonic generation frequency-resolved optical gating (SHG FROG) device, resulting in a pulse duration of $15 fs$ FWHM (with the transform-limited duration being $14.7 fs$⁠) and a central wavelength of $λ 0 = 820 nm$⁠.

The laser pulses were focused by a $76.2−mm$ focal length off-axis parabola (nominal $f / 1$⁠) down to a measured focal spot [Fig. 1(e)] with FHWM of 4.2 and 3.1 μm along the horizontal and vertical axes, respectively. This corresponds to an effective beam waist of 3.1 ± 0.3 μm and to a Rayleigh range of $≈$ 37 μm. The resulting peak intensity in the focus was $I 0 ≈ 4.8 × 10 18 W / cm 2$ (corresponding to a normalized vector potential $a 0 ≈ 1.5$⁠). Considering the optimal electron density for this work of $n e ≈ 5.7 × 10 19 cm − 3$ (which corresponds to a fraction of the critical plasma density $n e / n c ≈ 0.034$⁠), the available laser power was well above the self-focusing threshold $≈ 0.52 TW$⁠. This allows for self-guiding⁴ inside the plasma, as is visible in the Thomson scattering diagnostic [Fig. 1(f)].

The pulses were focused in the first half of the in-house designed and characterized^31,32 300 μm diameter flat-top gas jet, 150 μm above the nozzle exhaust [Figs. 1(g) and 1(f)]. The gas target position was optimized in three dimensions with accuracy at the level of the plasma wavelength λ_p  $≈ 4.5$μm, leading to an optimal focusing position inside the plasma profile. The repeatability and stability of the acceleration process was assured by the laser contrast higher than 10¹⁰ at the ps-level (measured by the Sequoia cross-correlator), below detection limit beyond several picoseconds from the main pulse, as well as by the laser pointing stability on the target of 3.6 ± 0.3 μrad (averaged root mean square).

The accelerated electron beams were characterized by a calibrated electron spectrometer [Fig. 1(h)] consisting of a motorized 5-mm collimator aluminum slit, a motorized $39-mm$ long $0.1-T$ permanent magnetic dipole, and a LANEX Fast Back scintillator screen captured by using a 12-bit CMOS global shutter camera [Fig. 1(i)]. The electron beam spectra were retrieved by simulating the particle tracking in the measured three-dimensional (3D) field. The measured beam energy is conservative, as it is measured by the deflection from the furthermost slit edge.

Due to the limited energy output available from kHz laser systems, it is usually necessary to operate targets at relatively high plasma densities in order to enable relativistic self-focusing.¹⁹ This in turn shortens λ_p to a few micrometers and ultimately results in the need of a comparable resolution in the laser–plasma interaction diagnostics.³³ The laser–plasma interaction was first optimized at a reduced laser power of $0.8 TW$⁠, by carefully tuning the focus position inside the gas target profile monitored with a $5 ×$ magnification optical side-view and a $2 ×$ achromatic Thomson scattering spectrally filtered (550-nm longpass) top-view diagnostics, both with a resolution smaller than λ_p. The gas pressure was then tuned by an electronic valve in order to achieve simultaneously relativistic self-focusing and electron injection in the plasma wave.

The laser pulses were delivered on target at $1 kHz$ repetition rate for the whole duration of the experiment, in order to reach thermal equilibrium in all the components of the system. The gas jet opening time (synchronized with the arrival of the driving pulse by a trigger) was set, depending on the regime of operation, as either pulsed or continuous. In fact, it must be noted that the radiation level achieved by a kHz LWFA machine is well above the typical values for laser facilities. The possibility of running continuous gas flow was enabled by a double differential pumping system, on target and before the compressor, which kept the laser-driven acceleration process unaffected throughout several hours of continuous operation. Typical density profiles for the specific gas jet, along with the relevant gas types and backing pressures used, were computed using the ANSYS Fluent software and are depicted in Fig. 1(j).

After obtaining quasi-monoenergetic beams with $0.8 TW$⁠, we gradually ramped the laser energy up to $26 mJ$ (⁠ $1.7 TW$⁠), iteratively optimizing the gas density and the focusing position inside the target density profile. In addition, the second order spectral phase was optimized using an acousto-optic programmable dispersive filter [Dazzler in Fig. 1(a)] to compensate for the plasma medium dispersion and to extend the acceleration.

The most energetic and collimated electron beams were obtained by firing the laser on a gas mixture of helium (98%) and nitrogen (2%), which allowed acceleration at an electron density at the target profile plateau as low as $n e / n c ≈ 0.034$⁠. In this configuration, record-high energy (up to $50 MeV$⁠) electron beams were obtained [Fig. 2(a)]. By averaging over thousands of laser shots, we observed the high-energy quasi-monoenergetic distribution to have an average peak of $32 ± 5 MeV$⁠, with an average energy spread of $≈ 8 MeV$ (25%) FWHM and a beam divergence of $2.1 ± 0.8 mrad$ FWHM.

The experimental measurements are in agreement with theoretically estimated values (supplementary material). Considering the “best” focusing scenario, where all the available laser energy is concentrated within the focal spot, the anticipated maximum electron energy is $≈ 55 MeV$⁠. However, taking into account the “average” experimental focusing performance [Fig. 1(e)], the maximum energy drops to $≈ 33 MeV$⁠.

We observed that small changes in certain laser and plasma parameters can significantly alter the LWFA process away from its optimal configuration. For example, a change in the plasma density from $n e / n c ≈ 0.034$ to $≈ 0.038$ (13%) results in a significant reduction of the beam energy and in the loss of the quasi-monoenergetic feature [shown as example in Fig. 2(b)]. This transition is readily discernible from the average one-dimensional (1D) electron spectra depicted in Fig. 2(c) for both density profiles.

We investigated the electron acceleration for the “average” experimental laser and plasma parameters also with 3D particle-in-cell (PIC) simulations using the EPOCH³⁴ code. The simulations, which used the mixture of a neutral gas obtained from a hydrodynamic simulation of the gas jet and incorporated the effect of field ionization, showed a negligible contribution from the electrons injected via the ionization mechanism. Therefore, the laser pulse was set to propagate in a cold and collisionless plasma consisting of $5 ×$ ionized nitrogen and fully ionized helium [Fig. 1(j)]. The simulations were evolved over the time interval of $2.2 ps$ and utilized the technique of moving window with dimensions of $70 λ 0 × 80 λ 0 × 100 λ 0$⁠. The underlying Cartesian grid was uniform with the resolution of 30 and 15 cells per $λ 0$ along the laser propagation direction and the transverse directions, respectively. Closer details regarding the setup of simulations can be found in supplementary material.

In the $n e / n c = 0.034$ case, the laser pulse self-focuses within the plasma and its peak amplitude attains a value $≈ 1.7 ×$ higher than a₀. The electron self-injection occurs within the focus at several periods of the wake wave except the first one [Fig. 3(a)]. A second self-injection occurs when the laser enters the region of the electron density down-ramp, corresponding to the mechanism described in Ref. 35. Consequently, two distinct electron populations can be observed in the energy spectrum [Fig. 3(b)]. The electrons with energies in the ranges $≈ 5 – 15$ and $≈ 20 – 30 MeV$ originate from the second and first injection processes, respectively. The electrons originating from the first injection process begin to dephase after $≈$ 48 μm of propagation within the accelerating phase of the wakefield. The wakefield structure, however, starts to slip back (with respect to the electron beam motion) due to the nonlinear evolution of the driving laser pulse such that the electrons can traverse into the accelerating phase of the preceding wakefield period. Herein, they undergo an additional energy boost, resulting in an increase of $≈ 5 MeV$ compared to their energy after the initial acceleration phase (supplementary material). At the end of the simulation, the energy spectra of both electron beams are quasi-monoenergetic. The cutoff energies of the beams are $≈ 16.4$ and $≈ 31.2 MeV$⁠, whereas the energy spread of the higher energy beam is $≈ 1.2 MeV$ (5%) in FWHM. The charge and the FWHM divergence of electrons with kinetic energy $≥ 20 MeV$ are $≈ 4 pC$ and $≈ 20 mrad$⁠, respectively.

By slightly reducing the electron density (⁠ $n e / n c = 0.03$⁠), the self-injection is suppressed, resulting in a negligible number of electrons being accelerated, which is in agreement with the experimental measurements. In the opposite case, corresponding to a density increase to $n e / n c = 0.038$⁠, the laser pulse peak amplitude in the focus is $≈ 1.8 ×$ higher than a₀. This case is characterized by fast laser energy depletion, which manifests itself in the carrier frequency downshift, and slowing down of the pulse front.³⁶ After passing the focus, the laser splits longitudinally into two distinct pulses, each propagating at a different velocity and consisting of only a few cycles. Due to the short duration of both pulses and the relatively dense plasma, the rapid evolution of their carrier-envelope phases causes oscillations of the wake wave cavities in the laser polarization direction as well as their longitudinal modulations, strongly affecting the parameters of self-injected electrons.²⁶ Furthermore, the electrons injected into the first period of the wake wave interact with the rear part of the laser pulse. The resulting electron energy spectrum has a thermal profile [Fig. 3(c)]. The cutoff energy is $≈ 39.2 MeV$⁠; the majority of electrons in the beam, however, have energy $< 20 MeV$⁠. The charge of electrons with $E ≥ 1$ and $≥ 20 MeV$⁠, respectively, is $≈ 65$ and 2 pC. The FWHM divergence of electrons with $E ≥ 1 MeV$ is $≈ 100 mrad$⁠.

By further increasing the plasma density, i.e., operating at $n e / n c = 0.042$⁠, the simulations indicate that the regime of laser–plasma interaction does not change substantially. Even though a larger fraction of electrons gets trapped, resulting in a higher beam charge, the pulse depletion is stronger, which reduces both the acceleration length and the maximum reachable electron energy. Overall, the PIC simulations clearly reproduce the transition from the quasi-monoenergetic to the broadband electron energy spectra with the increase in the plasma density over the same values observed experimentally (Fig. 2).

Since the medical applications mentioned above rely on high-current electron beams at relevant energies (⁠ $> 20 MeV$⁠), we optimize our LWFA source into two main modes of operation that are freely titled “high-energy mode” and “high-power mode.” The high-energy mode, described earlier and shown in Fig. 2(a), has the beam energy and collimation maximized by tweaking the laser–plasma interaction at the lowest possible plasma density (given the available laser power). In the high-power mode (supplementary material), the chosen approach is to optimize the electron beam power by working with pure nitrogen at a higher plasma density of $n e ≈ 8.4 × 10 19 cm − 3$ (equivalent to $n e / n c ≈ 0.05$⁠), partially sacrificing the average peak energy and collimation. The fact that higher beam charge can be obtained at lower electron beam energies is likewise observed in other experiments.¹⁴ The key parameters of the two modes of operation are summarized in Table I.

With our current setup in the high-power mode, we estimate a dose rate exceeding $1 Gy / s$ for beam sizes of few mm, which could lead to the first demonstration of laser-driven stereotactic radiosurgery in a similar setup to the one described in Ref. 25, showing that approximately 600 shots were necessary to deposit $1 Gy$ into $1 cm 3$ target volume. While medical devices for clinical use have more stringent requirements on beam stability and variability, other applications relying solely on the dose rate and repetition rate, such as space radiation hardness testing³⁷ and radiobiology,^38,39 are already possible.

In conclusion, we demonstrate the generation of quasi-monoenergetic electron beams at $1 kHz$ repetition rate with an unprecedented energy of tens of MeV (up to $50 MeV$⁠), which paves the way toward establishing LWFA technology as an innovative tool for the treatment of small tumors (e.g., brain metastasis) and for the generation of high-flux monoenergetic x-ray beams in the medical imaging range (⁠ $20 – 50 keV$⁠). The latter may represent a unique source for x-ray fluorescent imaging (XFI), phase contrast imaging (PCI), and micro-beam radiotherapy. Consistent work is ongoing to produce a stable and reliable high-energy (⁠ $> 100 MeV$⁠), high-flux electron beamline for innovative user experiments. Finally, we want to highlight that the all-reflection LWFA setup based on OPCPA technology, shown in this work, is fully scalable in laser power. This paves the way toward the realization of a future GeV-class kHz electron beamline.