High Dose‐Rate MeV Electron Beam from a Tightly‐Focused Femtosecond IR Laser in Ambient Air

Ultrashort electron beams with femtosecond to picosecond bunch durations offer unique opportunities to explore active research areas ranging from ultrafast structural dynamics to ultra‐high dose‐rate radiobiological studies. It presents a straightforward method to generate relativistic electron beams in ambient air via the tight focusing of a few‐cycle, mJ‐class femtosecond infrared laser. It demonstrates experimentally that electrons can reach up to 1.4 MeV at a dose‐rate of 0.15 Gy/s, providing enough dose rate for radiation therapy applications. 3D Particle‐In‐Cell simulations confirm that the acceleration mechanism is based on the relativistic ponderomotive force and show theoretical agreement with the measured electron energies and divergence. Relativistic peak intensities up to 1019 Wcm−2 are reached in ambient air due to a very low B‐integral accumulation during focusing, which prevents intensity clamping. Furthermore, it discusses the scalability of this method with the continuing development of mJ‐class high average power lasers, and providing a promising approach for FLASH radiation therapy.


Introduction
Since Tajima and Dawson [1] theoretically proposed the ponderomotive force to generate strong accelerating fields in plasmas, the field of electron acceleration driven by high intensity lasers has rapidly progressed.The advent of Chirped Pulse Amplification (CPA) [2] gave rise to laser wakefield acceleration (LWFA), [3,4] which is now capable of generating GeV electrons with PW-class lasers [5,6] on significantly smaller length scale (in the centimeter range) compared to conventional particle accelerators.Recent advances have enabled LWFA to operate with mJ-class systems in the mid-IR, [7] also at kHz repetition rates, [8][9][10] producing a high particle flux of MeV electrons that can be very useful for radiobiological studies. [11]Despite great progresses, these sources of high-energy, laser-driven electrons require complex and bulky setups contained within a vacuum chamber, limiting close access to the beam.
In this work, we report on the generation of a high dose-rate (up to 0.15 Gy/s), MeV-ranged electron beam by tightly focusing a mJ-class infrared (IR) femtosecond laser in ambient air.Relativistic laser intensities up to 1 × 10 19 Wcm −2 are reached at atmospheric pressure despite the expectation of significant wavefront distortion due to nonlinear propagation effects.The generated electron beam was measured to have a maximum energy up to 1.4 MeV, closely matching the estimated 1.3 MeV from the cycleaveraged relativistic ponderomotive energy at 1 × 10 19 Wcm −2 .We show how the tight focusing, long wavelength and few-cycle pulse duration combine to limit the effect of the B-integral on the focused laser beam.The high density of air molecules in the focal volume available for ionization was sufficient to form a nearcritical density plasma, which provided a high conversion efficiency from the laser to the electrons, as shown by 3D Particle-In-Cell (PIC) simulations supporting the experimental conclusions.
The strength of this electron source stems from its simplicity.A single focusing optic in ambient air produces an electron beam capable of delivering a yearly radiation dose in less than one second to a person standing one meter away.The lack of a complex setup or vacuum chamber improves its usefulness in many irradiation applications, reducing the requirements for producing ultrafast MeV electron sources.Hard X-ray sources produced focusing parabola is on-axis, the last turning mirror blocks the radiation emitted for conical angles  < 4°with respect to the optical axis.OSLD1 is placed 0.7 m above (i.e.,  =  = 90°) the focusing optic, whereas OSLD2 is positioned 2 m away from the interaction point at about  = 45°in the incidence plane ( = 0°) of the laser.
using copper in ambient air and operated at kHz repetition rates have also been demonstrated, [12,13] however the produced dose rates were orders of magnitude lower.[16] Moreover, the rapid pace of laser source development to increase the available pulse energy and repetition rate will benefit the scaling of this technique to higher electron energies and larger dose rates, provided the air volume in the vicinity of the focus has time to replace between the pulse.In Section 2, we present the experimental results, supported by calculations and simulations.Section 3 provides a discussion on the acceleration mechanism, the optimization and scalability of the method, as well as an overview of electron-based FLASH-RT sources.

Dose Measurements
The experiment was performed at the Advanced Laser Light Source (ALLS) facility (Varennes, Canada) that provided the 12 fs, IR ( 0 = 1.8 μm), 100 Hz beamline based on a high-energy Optical Parametric Amplification (OPA) technique. [17,18]Laser pulse energies up to 2.8 mJ were incident on a tight-focusing on-axis parabola with a Numerical Aperture (NA) of about one (i.e., halfsphere focusing).The same system was used for Longitudinal Electron Acceleration (LEA) with radially polarized beams [19,20] in a low pressure environment (10 −4 atm).A schematic of the experimental setup is shown in Figure 1.Three independently calibrated radiation detectors with absolute dose calibrations were used in order to separately confirm the data.The first one is an Exradin A12 ionization chamber (IC) used for high dose-rate measurements (called IC1), the second one is a Fluke 451B ionization chamber for low dose-rate measurements (called IC2) and the third is a pair of Optically-Stimulated Luminescence Devices (OSLD) from Health Canada [21] used as passive area dosimeters (called OSLD1 and OSLD2).Dose was measured over eight orders of magnitude at distances up to 6 m away from the laser focus, as well as for different angles at a fixed distance in order to verify the angular dose profile.Further details about the setup are provided in Methods.
Figure 2a displays the measured radiation dose in mGy/min (1 Gy = 1 Jkg −1 ) as a function of the distance r from the source with detectors IC1 and IC2, for five different laser pulse energies.The dose follows an Inverse-Square Law (ISL), i.e., D ∝ 1∕r 2 fitting with a determination coefficient of R 2 > 0.99, as expected for a diverging particle beam emerging from a point-like source.The lowest average dose rates ̇D reported are on the order of a few μGy/min when measured far from the source (5-6 m) at 1.2 mJ, whereas the highest measured dose rate at 0.1 m and 2.8 mJ reaches ̇D = 8.9 Gy/min (0.15 Gy/s).The radiation dose scaling is shown in Figure 2b and plotted as a function of laser pulse energy.A power law of the form D = a n L was fitted in the log-log domain (i.e., linear fits) for all cases.We observed that the dose D scales with  6 L when measured close to the source (i.e., electrons and X-rays contributing), and slightly decreases to  4 L at 6 m (i.e., only X-ray photons contributing).[24][25] The scaling of the dose will depend not only on the laser energy but on parameters such as the incident wavelength, pulse duration, as well as the gas type and pressure.
The angular dose profile measurement of the source is shown on Figure 2c shows a highly peaked distribution (i.e., anisotropic emission) with an estimated half-cone divergence angle of  HWHM = 17°.As the data at  = 0°was inaccessible due to view obstruction from the last turning mirror, a more realistic estimation would be  HWHM ≤ 17°.In addition, electrons scattering in air, enroute to the detector, is a source of increased divergence.After correcting for dose decrease due to beam divergence (i.e., converting to an equivalent collimated electron beam using the ISL), the shape of the highest energy (2.8 mJ) dose-distance curve from Figure 2d is similar to a typical electron beam Percent Depth-Dose (PDD) curve that describes the dose deposition profile in a medium as a function of depth, which is specific for a particular particle type and its energy.The "electron-like" shape of the curve is characterized by a slight increase at low depths, up to a range of maximum dose of R 100 = 0.3 m here, and then a rather steep decrease exhibiting a half-dose range of R 50 = 1.7 m and practical range of R p = 2.5 m.Beyond r = 3 m, the dose is characterized by a slowly decreasing tail consisting of Bremsstrahlung X-ray photons, as expected for an electron PDD consisting of both electrons and X-rays.Using this depth-dose profile, we can estimate that the maximum electron range R max is at least 2.5 m from the source and before 6 m in the Bremsstrahlung tail.Using the CSDA (Continuous Slowing Down Approximation) electron range tables in air from the NIST-ESTAR database, [26] this leads to an estimated maximum electron energy in the range of 0.8 ≤  max e ≤ 1.4 MeV.Half-Value Layer (HVL) measurements in the Bremsstrahlung tail at 5 m from the source showed effective photon energies in the range of 18-25 keV (see Supporting Information).Nevertheless, the presence of photons with energies up to the maximum electron energy  max e is expected due to the broadband nature of Bremsstrahlung emissions.
Concerning OSLD passive area dosimeters, OSLD1 reported a dose 2330× higher than the ALARA (As Low As Reasonably  Measured radiation doses integrated for 1 min (≈20°from the optical axis) for the two detectors, IC1 (triangles) and IC2 (dots), as a function of A) distance from the source for different laser pulse energies ranging from 1.2 mJ up to 2.8 mJ.B) Radiation dose also shown as a function of laser pulse energy, for four distances from the source.Data points were fitted with a Power Law of the form D = a n L using a linear regression in the log-log domain, fitting with a determination coefficient of R 2 = 0.98, 0.98, 0.97, and 0.95 for 0.1 m, 1 m, 3 m, and 6 m, respectively.C) Relative angular dose distribution at highest pulse energy ( L = 2.8 mJ) with respect to the optical axis and measured 0.4 m from the source (blue dashed line shown for better visualization of the data).D) Relative dose distribution as a function of distance from the source in air, corrected for the Inverse-Square Law.Electron ranges of R 100 = 0.3 m (range of maximum dose) and R 50 = 1.7 m (half-dose range) are obtained using a shape-preserving spline interpolation (full red line).The practical range R p = 2.5 m is extracted from the tangent line passing through R 50 , as for electron PDD curves.From this value, the maximum range of the electrons, R max , is estimated between 2.5 and 6 m, corresponding to a maximum kinetic energy of 0.8 ≤  max e ≤ 1.4 MeV.
Achievable) public dose limit of 0.1 mGy/year, whereas OSLD2 was 12380× higher, during just one single experimental campaign (about 100 acquisitions of 1 min).This demonstrates the high degree of danger of such an experimental configuration.We emphasize the use of proper radiation safety precautions in this context (see Supporting Information for a discussion on radiation safety and dose characterization).

Numerical Modeling
In order to verify the validity of the upper bound for the maximum electron energy, we simulated the tightly-focused electromagnetic (EM) fields of the laser using an in-house code that calculates the Stratton-Chu integral formulation of EM fields. [27]he code takes as input the parameters of the incident laser field and the focusing parabola (see Supporting Information for more information).The simulation considers an ideal linearly-polarized beam (i.e., no aberrations) and the propagation of the fields in vacuum, and does not account for any possible nonlinear effects or plasma generation during focusing.A spot size of 1.0 μm at FWHM was obtained, yielding a peak intensity of The interaction dynamics was further investigated with 3D PIC simulations using the SMILEI code. [28]Figure 3a shows a snapshot of the electron kinetic energy density at the peak of the interaction.The electron micro-bunches, larger than the laser beam itself and trailing slightly behind it, stem from the Laser Photonics Rev. 2024, 18, 2300078 Figure 3. 3D PIC simulation using the SMILEI code [28] to model the high-intensity (I 0 = 1 × 10 19 Wcm −2 ) interaction with air.A) Snapshot of the electron kinetic energy density at the peak of the interaction at t = 180 fs.Large conical electron micro-bunches trailing behind the laser pulse are observed, induced from the laser's ponderomotive kick.B) Angular energy spectrum d 2 N dd of the forward-traveling electrons at t = 180 fs.Electrons are forming a cone of a few tens of degrees wide and centered at 0°, also exhibiting decreasing divergence with increasing electron energy.C) Total energy (black), EM energy (blue), and electron energy (red) contained in the simulation box as a function of time.All the curves are normalized to the maximum of the EM energy (blue line).Electrons are absorbing as high as 49% of the laser energy during the initial high-intensity interaction.D) Electron spectra at t = 180 fs for both the high (red) and low (blue) intensities, also for forward (full line, FWD) and backward (dashed line, BWD) traveling electrons.
ponderomotively-driven electrons that were accelerated by the intense laser pulse at each half-cycle, from the 2 forward push of the Lorentz force, as the pulse propagated in the plasma.Given these results and due to the present experimental conditions, it is clear that the electron acceleration is caused by the relativistic ponderomotive force and not by LWFA. [3,7,8]Figure 3b shows the angular spectral distribution d 2 N dd of the forward-traveling electrons.The conical distribution centered around the longitudinal axis at 0°agrees with the measured angular dose profile.Figure 3c shows the total (black), EM (blue), and electron (red) energies contained within the simulation box.We observe a high laser energy coupling to the electrons, absorbing as high as 49% of the incident EM energy due to their nearcritical density (n e ≈ n c ).This strong absorption efficiency led to high electron numbers in the beam and therefore to the observed high radiation doses.This is enabled by the long wavelength, which has a relatively low critical plasma density, and the high intensity reached at the focus, which produces a plasma density near the critical density as deep states of air molecules are ionized.Figure 3D shows electron spectra at 20 • (same angle as experimental measurement) for two intensities (1 × 10 19 Wcm −2 in red and 4 × 10 18 Wcm −2 in blue), for both forward (full lines, FWD), and backward (dashed lines, BWD) traveling electrons.All spectra follow a typical Maxwell-Boltzmann distribution, where dN d ≈ e − K ∕k B T e up to a maximum cut-off energy, with the electron temperature T e determined from ponderomotive energy.The simulated maximum electron energies in the forward direction are of  PIC max (a 0 = 4.86) = 2.6 MeV and  PIC max (a 0 = 3.08) = 1.9 MeV.In order to test the ponderomotive scaling, we compare the maximum electron energy ratios from PIC simulations and the peak ponderomotive energies at the two aforementioned intensity bounds as: The good agreement with the ponderomotive energy scaling further shows that the ponderomotive force is the dominant acceleration mechanism in this configuration.In absolute terms, the maximum electron energy at the highest intensity in the PIC simulation is of 2.6 MeV, only 28% higher than the peak ponderomotive energy of 2.0 MeV.The difference is due enhanced electric fields in the plasma and to lack of an appropriate tight-focusing field model in the PIC code.As previously mentioned, the measured upper bound on the electron energy of 1.4 MeV is in good agreement with the cycle-averaged ponderomotive energy of 1.3 MeV, but is slightly lower than the expected peak ponderomotive energy of 2.0 MeV, and this is because the highest energy electrons in the Maxwellian spectrum are below the detection threshold of our detector.Full 3D PIC simulations that include a tightly-focused EM field model will further improve the model but is beyond the scope of the current study.
Finally, regarding the backward accelerated electrons, we observe lower maximum energies and fewer energetic electrons.The forward-traveling electrons are pushed by both the leading edge of the pulse through the ponderomotive force F pond ∝ −(|E| 2 ) and the v × B forward the Lorentz force, whereas the backward-traveling feel only the ponderomotive force from the trailing edge of the laser pulse.It is important to note that it is the relativistic ponderomotive force that enables the formation of a directional, forward-oriented conical beam of electrons, as observed in this experiment.This regime is reached for intensities above I 0 = 4 × 10 17 Wcm −2 for  0 = 1.8 μm.

Acceleration Mechanism and Source Optimization
Diffraction-limited focal spots are typically not achieved when focusing a mJ-class, ultrashort laser in ambient air due to both wavefront distortions from the strong Kerr effect and plasma generation that destroy the integrity of the focused laser beam.The B-integral quantifying the non-linear phase shift is expressed as: where n 2 is the non-linear refractive index and I(z) is the laser intensity along the propagation axis z.The B-integral needs to be minimized in order to produce a near diffraction-limited focus and the accompanying higher peak intensity.From Equation (2), the wavelength as well as the non-linear refractive index of the medium are critical to determine the amount of phase shift in the laser beam.In gases, the non-linear refractive index n 2 typically decreases with increasing wavelength, [29,30] and dramatically decreases for higher ionization states.This further limits the Bintegral accumulation during focusing [31] after the first ionization level.Assuming negligible phase shift before the focusing optic, integrating Equation ( 2) up to the first ionization intensity gives the following analytical expression: where P 0 is the peak power, Ω is the focusing solid angle, R ion is the radius of the first ionization sphere and f is the focal length of the parabola (see Supporting Information for more details).Using the Ammosov-Delone-Krainov (ADK) model for tunnel ionization, [32,33] the first ionization of air molecules (N 2 and O 2 ) was estimated to occur around 2 × 10 14 Wcm −2 , only 163 μm before geometrical focus.Here, the B-integral was calculated to reach 8.8 mrad, much less than 628 mrad ( 0 ∕711 ≪  0 ∕10) where the accumulated phase shift becomes significant.The relatively long wavelength, the few-cycle pulse duration (where only the electronic component of non-linear refractive index n 2 is involved [34] ), and the tight-focusing geometry with a large solid angle combine to reduce the B-integral to a negligible value.The aberrations are insignificant and the intensity clamping limit is increased, permitting higher laser intensities to be reached in ambient air.At the calculated peak intensity of 1 × 10 19 Wcm −2 , the ADK model estimated the maximum ionization state for atomic nitrogen and oxygen to be 5+ and 6+, respectively.This leads to a calculated electron density of n e = 2.65 × 10 20 cm −3 within the plasma, which is only 23% below the critical density (n e = 0.77n c ) of n c =  0 m e  2 0 ∕e 2 = 3.44 × 10 20 cm −3 at  0 = 1.8 μm.The plasma is underdense and therefore transmissive to the laser.The contribution of plasma defocusing has to be minor according to the agreement between the measured, calculated and simulated maximum electron energies.This is due to the short travel length through the plasma (≈ 163 μm) before the geometrical focus.Investigations on plasma defocusing in tightly-focused configurations will be the subject of further work.
Most air ionization events occur during the leading edge of the laser pulse when the intensity climbs above 10 14 Wcm −2 .Free electrons are then driven by the relativistic ponderomotive force when the peak laser intensity reaches I 0 > 4 × 10 17 Wcm −2 , which is the relativistic intensity threshold (a 0 = 1) calculated for  0 = 1.8 μm.For intensities above this threshold, electrons at rest start oscillating mostly along the E-field polarization at velocities near the speed of light and then feel a strong v × B longitudinal push from the Lorentz force.This accelerates the electrons in the forward direction, explaining the high directionality of the electron beam seen in the experiment.This acceleration mechanism is further validated by 3D PIC simulations that show the conically-shaped electron beam, the proper range of observed electron energies and the absence of an accelerating plasma wave for LWFA.The strong laser-matter interaction stems from the near-critical density plasma that enables high laser energy absorption by the electrons.This efficient coupling explains the high flux of energetic electrons and the resulting large dose rates generated with only a few mJ of input laser energy.
Further optimization of the source is planned to increase both the electron energy and the dose rate.Higher pulse energies will increase the number of accelerated electrons from a larger ionization volume and increase the ponderomotive energy associated with higher laser intensities, as observed with the non-linear dose-energy scaling.The use of longer central wavelengths in the mid-IR will reduce the effect of optical beam aberrations as well as further limit the B-integral contribution of non-linear effects in air.Increasing the wavelength will decrease the peak intensity as I 0 ∝ 1∕ 2 0 but will keep the ponderomotive energy the same since  pond e ≈ I 0  2 0 .The net effect will be an increased ionization volume (V focal ∝  3 0 in tight focusing) and consequentially a much higher measured dose.The influence of a longer wavelength at  0 = 3.9 μm on the ponderomotive scaling was also shown in the work by Weisshaupt et al., [35] providing a 25× higher X-ray flux using a K  -based source with solid targets, compared to a central wavelength of  0 = 800 nm at the same laser intensity I 0 .An upper limit is foreseen in air around  c = (2c∕e) √  0 m e ∕n e ≈ 2.1 μm when the critical density decreases to a level similar to the plasma density (i.e., n c ≈ n e ) and hinders the propagation of the pulse closer to the focus.This limitation can vary if the gas type and pressure are properly chosen in order to reduce the plasma density.Moreover, the onset of the Relativistic Self-Induced Transparency (RSIT), [36][37][38] for which n e → n e ∕ at relativistic laser intensities (a 0 > 1), can loosen the constraint on the critical density and further enable the use of longer wavelengths at high intensities for radiation generation.The mechanism is rather complex but a simple estimation with a 0 = 5 (i.e., I 0 ≈ 1.1 × 10 19 Wcm −2 ) would bring the 2.1 μm limit in air to The presented experimental implementation is much simpler than other laser-based electron beam sources such as LWFA since there is no requirement for a vacuum setup or gas jets to obtain increased gas density.Our technique can scale to higher repetition rates and increased pulse energies to enhance both the rate of electron production (i.e., dose) and the electron energy.Provided that the air volume in the vicinity of the focus has time to replace between the pulses (otherwise gas flows may be required), the repetition rate can be increased by up to three orders of magnitude with the next generation of Ytterbium-pumped Optical Parametric CPA (OPCPA) [39] or Thulium-doped fiber lasers. [40,41]his will rapidly escalate the observed dose rates as well as the radiation exposure risks for laboratory personnel.Through further optimization, it is foreseen that in-air, laser-based high doserate sources of this type will provide a critical platform for ionizing radiation applications.We emphasize the potential of this technique for studying the FLASH effect in radiobiology (see section 3.2) due to its ease of implementation and ability to provide not only a high instantaneous dose rate but also a very high average dose rate.Future work will also investigate the measurement of the radiation pulse duration in order to characterize the instantaneous dose rate.

Application to FLASH-RT
The FLASH effect [14][15][16] is a radiobiological outcome observed when high radiation doses are delivered during short time frames (< 100 ms, i.e., at ultra-high dose rates) that, when compared to conventional radiation therapy (RT) treatments, promises to deliver fewer normal tissue complications for the same biological damage to malignant cells.This topic generated excitement in the RT community in 2014 after successful demonstrations in mice, [42,43] cats and mini-pigs. [44]These noticeable FLASH-RT ef-Table 1. Summary of dose rate characteristics for various electron beam sources.The value ̇D is the on-axis ( = 0 • ) average dose rate, f rep is the repetition rate, D pulse is the dose per pulse and Ḋ is the estimated instantaneous dose rate.mJ-class LWFA [ 11] 1.1 10 3 1.1 10 7 e − FLASH-RT [15,46] 10 1 − 10 6 10 1 − 10 6 10 2 − 10 4 10 3 − 10 10 a) The number in parentheses is at 0.4 m from the source and 3 mJ per laser pulse.As reference, conventional RT is typically performed around 0.1 Gy/s under continuous beam irradiation (i.e., ̇D = Ḋ).
fects were observed for average dose rates of ̇D = D pulse f rep ≳ 40 Gy/s and maximized above ∼100 Gy/s, where D pulse is the dose per pulse and f rep is the repetition rate.Table 1 shows a comparison of the dose rate characteristics of mJ-class laser-based electron beams relative to current electron FLASH-RT sources ranging from small mobile units to large-scale particle accelerator facilities.As reference, conventional RT is typically performed around 0.1 Gy/s under continuous beam irradiation (i.e., ̇D = Ḋ), nearly four times lower than the maximum dose rate of this experiment reported in Table 1.In this work, we estimate that the on-axis dose per pulse at 3 mJ and 0.4 m was 0.36 mGy which is 3× lower than the work of Cavallone et al. [11] at the same endpoint.This difference is explained by the high density supersonic gas jets used, [45] the longer focal length of their focusing optic (i.e., larger focal volume), and the shorter pulse duration used in the LWFA process.From our dose per pulse and the beam divergence of  HWHM = 17 also measured at r = 0.4 m, an estimation of our electron number per pulse gives: where S  is the mass stopping power and  is the particle fluence.We determined the effective mass stopping power in air S eff air  as the mass stopping power evaluated at the mean electron energy of the spectrum  e , with  e ≈  max e / 3 for Maxwellian spectra, giving  e = 0.8 MeV / 3 ≈ 250 keV.Note that this is a conservative estimate of the electron number as we used the lower maximum energy bound, which overestimates the effective mass stopping power and therefore leads to an underestimation.Nevertheless, this gives an order-of-magnitude calculation of the electron number generated by the present experimental configuration.It is important to mention, that the simplicity of our setup permits access to the radiation at much shorter distances from the source compared to LWFA.At 0.1 m, we estimate that the on-axis dose per pulse is of 3.8 mGy, which is 3.5× greater than measured in the work of Cavallone et al. [11] Considering the femtosecond nature of the laser-plasma interaction and the broadband electron spectrum generated, the electron bunch duration is estimated to be on the picosecond Laser Photonics Rev. 2024, 18, 2300078 scale a few millimeters away from the interaction volume as a result of debunching.This yields an instantaneous dose rate Ḋ = D pulse ∕ as high as 10 9 Gy/s, which is orders of magnitude above most Linac-based electron FLASH-RT sources.Largescale facilities typically have more electrons per pulse spread over much longer time scales. [46]As mentioned in the recent work of Vozenin et al., [47] the 40 Gy/s average dose rate definition of FLASH-RT has proven to be over simplistic.Accumulated evidence rather points toward the instantaneous dose rate and overall irradiation time as the critical parameters.This highlights ultrafast laser-based radiation as prominent sources to investigate the FLASH effect at ultra-high instantaneous dose rates.As noted in the work of Bourhis et al., [48] a logical first step toward the clinical translation of FLASH-RT is to use low-energy electrons of a few MeV in pre-clinical conditions as a proof of concept of the FLASH effect in human patients.Hence, a laser-based electron beam, as presented in our experimental configuration and used at higher repetition rates, is an ideal candidate in this matter.Due to the ultrafast nature of the laser-driven electron acceleration mechanism, the source demonstrated here is a very promising candidate for characterizing the potential of the FLASH effect for medical applications.

Conclusion
This work reports on the generation of a high dose-rate MeV electron beam produced by direct laser acceleration in ambient air using a mJ-class femtosecond IR laser operated at 100 Hz repetition rate.The electron beam reaches the MeV-level of kinetic energy via the relativistic ponderomotive force from the laser, with the measured beam characteristics further supported by 3D PIC simulations.Relativistic peak intensities in ambient air are enabled by the low B-integral from the use of a 1.8 μm central wavelength, a few-cycle pulse duration and a tight focusing geometry, which altogether push further the intensity clamping limit.Further work will investigate the scaling of the dose, both numerically and experimentally, by varying a series of parameters including laser wavelength, gas, and pressure.This laser-based ionizing radiation source generated a maximum dose rate of 0.15 Gy/s (0.38 Gy/s estimated on-axis), which is several times higher than the conventional dose rates used in clinical radiotherapy for cancer treatments.Furthermore, the ultrafast nature of the electron beam with instantaneous dose rates up to 10 9 Gy/s (assuming picosecond electron bunch duration) makes it very promising to investigate the FLASH effect in radiobiology.Cellular and small animal studies are in preparation through collaborative work with medical physicists and oncologists.

Experimental Section
The ALLS Infrared Beamline: The high-energy OPA [17] delivers 7 mJ per pulse at 1.8 μm, which was coupled into a 1 mm-diameter, 4.35 mlong, stretched hollow-core fiber filled with a static pressure of 180 Torr of argon. [18]After the spectrally broadened output of the hollow-core fiber, dispersion compensation was achieved using fused silica windows. [49]he compressed pulses were characterized using SHG-FROG (Second Harmonic Generation -Frequency-Resolved Optical Gating) yielding two optical cycles with a 12 fs pulse duration at Full-Width-Half-Maximum (FWHM).A ND-filter wheel was used to vary the energy  L of the 10.5 mm diameter (FWHM) s-polarized laser beam on the focusing optic ( L = 1.2, 1.7, 2.3, 2.7 and 2.8 mJ).The laser repetition rate was 100 Hz with a pulse-to-pulse energy stability of 2.5% RMS.The tight focusing optic was an on-axis parabola with focal length of 6.35 mm and diameter of 2.54 cm giving NA ≈ 1.The focal spot was located in ambient air and the parabola alignment was ensured by maximizing the radiation dose rate.A metallic turning mirror oriented at 45°was located 50 cm from the parabola focus, which defined the optical axis, as shown in Figure 1.Note this mirror obstructed the view for  < 4°making radiation measurements in this range not possible.
Dosimetry: For high dose rate measurements close to the source, a classical Farmer-type air-filled Exradin A12 ionization chamber was used (called IC1).The calibration coefficients for this Exradin A12 ionization chamber were determined in a primary standards laboratory using a Su-perMax electrometer to collect the charge.This total collected charge was converted to the absolute dose using the AAPM TG-51 formalizm [50] corresponding to precision-level clinical dosimetry.For the lower dose measurements farther from the source, a calibrated Fluke 451B hand-held portable ionization chamber was used (called IC2) because IC1's active volume of 0.64 cm 3 was not sensitive enough.IC2 had a very sensitive pressurized volume of 349 cm 3 with a thin entrance window that could detect low energy electrons (≥ 100 keV) and photons (≥ 7 keV).Each measurement was made with the detector placed in an un-obstructed view of the focal spot at about  = 20°with respect to the optical axis.For the angular dose profile measurements the angle  was varied at a fixed distance of r = 0.4 m.Acquisitions were recorded for one minute at distances of r = 0.1, 0.15, 0.25, 0.5, 1, 2, 3, 4, 5, and 6 m between the source and the detector.Since detectors IC1 and IC2 exhibit different energy-dependent sensitivities, it performed a cross-calibration consisting of four identical measurements at the same endpoints (same laser pulse energy and position).The third detector type consisted of two identical Optically-Stimulated Luminescent Devices (OSLD1 and OSLD2) from Health Canada. [21]OSLD1 was placed 0.7 m above the focusing optic ( = = 90°), and OSLD2 was placed 2 m away from the focus at an angle of  = 45°in the laser's incidence plane ( = 0°).Further details are provided in the Supporting Information.
Particle-In-Cell Simulations: Three dimensional Particle-In-Cell (PIC) simulations were performed using the SMILEI code. [28]The beam model used a linearly-polarized 3D Gaussian laser beam at a central wavelength of  0 = 1.8 μm, a pulse duration of  FWHM = 12 fs and focused down to a Gaussian focal spot size of w FWHM = 1 μm.It simulated two laser intensities of 1 × 10 19 Wcm −2 (a 0 = 4.86) and 4 × 10 18 Wcm −2 (a 0 = 3.08), where a 0 is the normalized amplitude of the vector potential.The simulation grid uses Δx = Δy = Δz = 100 nm, Δt = 0.99Δx∕(c √ 3) = 0.19 fs (applying CFL-condition) and runs over 400 fs.The box size is of 864 × 864 × 648 cells, assuming the propagation of the beam along the z-axis and its polarization along the y-axis, corresponding to box dimensions of 86.4 × 86.4 × 64.8 μm 3 (48 0 × 48 0 × 36 0 ).Atomic nitrogen ion species were initiated at the 2+ ionization level, with tunnel ionization enabled.This ensures the starting ionization level was one charge state below the highest possible state at the laser entrance plane (5 × 10 15 Wcm −2 is 3+) as there was no recombination module in SMILEI.It was also a way to mimic the pre-plasma produced by the temporal lobes that were absent from the Gaussian pulse and reduces computation time.To provide smooth entry of the beam into the plasma, for spatial distribution of the plasma density in the z-direction, it used super-Gaussian distribution of order eight with a standard deviation of 27 μm (15 0 ) and initial maximum density of n e,0 = 0.31n c , where n c is the critical density at  0 = 1.8 μm.It used 20 macroparticles per cell for electrons and ten for nitrogen ions a total of over 14.5 × 10 9 macroparticles.Each simulation runs for 10 h on 2560 cores.

Figure 1 .
Figure 1.Top view sketch of the experimental setup for the in-air, laserbased radiation generation.As the high Numerical Aperture (NA ≈ 1)focusing parabola is on-axis, the last turning mirror blocks the radiation emitted for conical angles  < 4°with respect to the optical axis.OSLD1 is placed 0.7 m above (i.e.,  =  = 90°) the focusing optic, whereas OSLD2 is positioned 2 m away from the interaction point at about  = 45°in the incidence plane ( = 0°) of the laser.

Figure 2 .
Figure 2.Measured radiation doses integrated for 1 min (≈20°from the optical axis) for the two detectors, IC1 (triangles) and IC2 (dots), as a function of A) distance from the source for different laser pulse energies ranging from 1.2 mJ up to 2.8 mJ.B) Radiation dose also shown as a function of laser pulse energy, for four distances from the source.Data points were fitted with a Power Law of the form D = a n L using a linear regression in the log-log domain, fitting with a determination coefficient of R 2 = 0.98, 0.98, 0.97, and 0.95 for 0.1 m, 1 m, 3 m, and 6 m, respectively.C) Relative angular dose distribution at highest pulse energy ( L = 2.8 mJ) with respect to the optical axis and measured 0.4 m from the source (blue dashed line shown for better visualization of the data).D) Relative dose distribution as a function of distance from the source in air, corrected for the Inverse-Square Law.Electron ranges of R 100 = 0.3 m (range of maximum dose) and R 50 = 1.7 m (half-dose range) are obtained using a shape-preserving spline interpolation (full red line).The practical range R p = 2.5 m is extracted from the tangent line passing through R 50 , as for electron PDD curves.From this value, the maximum range of the electrons, R max , is estimated between 2.5 and 6 m, corresponding to a maximum kinetic energy of 0.8 ≤  max