Experimental realization of near-critical-density laser wakefield acceleration: Efficient pointing 100-keV-class electron beam generation by microcapillary targets

Laser wakefield acceleration (LWFA), which was first proposed by Tajima and Dawson in 1979,¹ has been intensively studied as a downsizing method for particle accelerators. Experimental studies of LWFA have markedly progressed^2–14 with the invention of the chirped-pulse amplification (CPA) technique proposed by Strickland and Mourou in 1985.¹⁵ LWFA experiments have been conducted in wide energy ranges, from keV to GeV. Applications of laser-driven energetic electrons are also being studied. High-energy electrons of ∼GeV order generated by LWFA are especially expected to be used in compact x-ray free electron lasers (XFELs).¹⁶ Laser-driven MeV-order electrons are used in x-ray imaging using an x-ray converter^17–20 or ultrafast pulse radiolysis.²¹ More applications of keV electrons are expected. The application research of electron diffraction using keV-order electrons driven by femtosecond lasers has markedly progressed, enabling high-time-resolution and low-jitter pump-probe experiments.^22,23 Potentially, laser-driven low-energy electrons may be relevant to various applications, such as advanced electron beam lithography²⁴ or the efficient generation of high densities of electrons that may be converted into x rays (through the Auger effect, for example), which in turn can be used to generate nuclear transmutation for compact radioisotope (RI) products and nuclear incineration.²⁵ From the viewpoint of medical applications, e.g., radiotherapy, there is also a strong demand for compact and highly efficient low-energy accelerators. Recent research shows that using sources of electrons with energies of 10–100 keV and doped with high-Z nanoparticles can effectively kill cancer cells irradiated with these electrons.²⁶ This finding indicates that the realization of a compact electron accelerator inside the body could markedly expand the possibilities of radiotherapy, and a treatment scheme based on LWFA using an optical fiber has been proposed.²⁷ On the other hand, relatively high-energy electron beam generation of a few MeV order by using a gaseous target has already been performed.^2,10–12,14 In particular, 1-MeV-order electron beam generation has been performed at high plasma densities.¹¹ Laser pulses of $<$10 mJ energy and 40 fs duration were used in such experiments. 1 pC charges and a beam divergence of ∼200 mrad were observed at a plasma density of n_e/n_c = 0.7, where n_e and n_c are the plasma density and the critical plasma density, respectively. Regarding keV-order electron beam generation, previous studies have shown that LWFA at a near critical density (n_e/n_c ∼ 1) can generate such electrons with high conversion efficiency.^28–30 At solid targets, Lei et al. proposed a foam cone-in-shell solid target design aiming at optimum hot electron production for laser fusion.³¹ They demonstrated that a high-Z low-density novel foam cone-in-shell target enhances laser conversion into hot electrons without increasing the electron temperature (T_e = 1.5 MeV) and beam divergence. In addition, Nicks et al. suggested the use of carbon nanotubes (CNTs) to generate a near-critical plasma density.³⁰ This scheme has an advantage in terms of the controllability and uniformity of the near-critical-electron-density region. However, it is necessary to predetermine the CNT density that satisfies the optimum condition for generating keV-order electrons. An alternative approach is the use of ablation plasma from a solid surface. This method can control the plasma density, but this requires another laser pulse to initiate the ablation. Very recently, high-yield and high-energy ion generation by using thin foil targets with evenly spaced holes was performed.³² In such an experiment, a 3D printer was used to place thin foils with holes at equal intervals on the surface of a solid plane target. They observed that the conversion efficiency from the laser beam to energetic electrons (E_e > 100 keV) enhanced to more than 50% at a laser intensity of 4 × 10²⁰ W/cm² by using such a target. The yield of energetic protons accelerated by the sheath acceleration field created by the energetic electrons increased to approximately eight-fold at energies above 10 MeV. This result indicates that solid targets with structures are useful for improving the feature of generated energetic particles. On the other hand, plasma near the critical density formed by the microcapillary target can efficiently couple with intense laser light and contribute to the generation of keV-class electron beams. A small diameter capillary (microcapillary) can expect to form and maintain dense plasma conditions with lower diffusion in free space compared with a plane target. Therefore, it is expected that a high-density state can be formed and kept even without another intense laser beam for plasma formation and efficiently couple between an intense laser beam and a near-critical density plasma. This is considered useful for the proof of principle of our theoretical studies.^29,30 Furthermore, the capillary has the capability to guide the particle beam such as electrons, and it can contribute toward suppressing the beam divergence and stabilizing the beam direction. In this work, we experimentally demonstrated a low-divergence electron beam from the microcapillary hole with an energy of 100 keV order generated at sub-relativistic laser intensities. In the case of using the lowest intensity (1 × 10¹⁶ W/cm², a duration of 1 ps), we still observed hot electrons around 50 keV. Our experimental results tended to be qualitatively in good agreement with the simulation results, which also indicates the optimum conditions for the electron beam generation by this scheme.

The experimental setup is shown in Fig. 1(a). The experiment was performed using a 4 TW, 40 fs Ti:sapphire laser, JLITE-X, at the National Institutes for Quantum Science and Technology (QST). The center wavelength (λ₀) of the laser was 0.81 μm. The terawatt p-polarized laser pulse was focused onto a microcapillary target by an f/22 off-axis parabolic mirror with a focal length of 646 mm. The focal spot diameter was 30 μm at e⁻² of the peak intensity. The maximum peak intensity I₀ was 1 × 10¹⁸ W/cm², corresponding to a dimensionless amplitude of the laser field, a₀ = 8.5 × 10⁻¹⁰λ₀(μm) $I0(W/cm2)$ = 0.7. We used a glass capillary array plate as a microcapillary target. The glass capillary array plate has a two-dimensional array of microcapillaries with an effective diameter of 27 mm attached to a 30-mm-diameter glass plate [Figs. 1(b) and 1(c)]. The diameter and pitch of a microcapillary hole at the plate were 10 and 12.5 μm, respectively. The thickness of the target or the capillary length was 400 or 410 μm, which is 60% of the Rayleigh length of the drive laser. The laser beam axis was set parallel to the microcapillary hole. To prevent damage to the laser system by the light reflected back from the target, the direction of the capillary hole was tilted at 12° with respect to the normal of the plate.

Figures 2(a) and 2(b) show the energy spectra of the generated electrons in the laser propagation direction, parallel to the microcapillary tube, at various laser intensities and pulse durations. The spectra were taken by multiple exposures of more than five shots. To measure these spectra, we used an electron spectrometer consisting of a slit, an electromagnet, and an imaging plate (IP)^33–35 (Fujifilm BAS-TR). As shown in Fig. 2(a), the pump laser intensity was varied from 4 × 10¹⁶ to 1 × 10¹⁸ W/cm² by changing the pump laser pulse duration from 1 to 40 fs at a fixed laser energy of 160 mJ. Here, the effective laser energy coupled to a single capillary was determined to be 27 mJ by considering the geometrical configuration. The electron yield and the slope of the spectra below 100 keV showed a weak dependence on the pump laser pulse duration except at a pump laser pulse duration of 1 ps. The electron yield markedly decreased at the pump pulse duration of 1 ps. The hot tail profile that contained a small humped structure at around 200–400 keV significantly changed with the increasing laser intensity. Below 2.5 × 10¹⁷ W/cm², the hot tail above 200 keV showed a Maxwell–Boltzmann (M–B)-like profile. It became a humped structure with peaks at around 300 keV at the highest intensity of 1 × 10¹⁸ W/cm². Next, the energy of the pump laser was reduced from 160 mJ (effective input energy: 27 mJ) to 40 mJ (effective input energy: 6.8 mJ), and the electron energy distribution as a function of pump laser intensity was also measured. Figure 2(b) shows the energy distribution of energetic electrons at a pump energy of 40 mJ or an effective input energy of 6.8 mJ. M–B-like energy spectra with a weak hot tail were also observed at intensities of 4 × 10¹⁶ and 2.5 × 10¹⁷ W/cm². In particular, we still observed energetic electrons up to 50 keV at the lowest intensity of 1 × 10¹⁶ W/cm².

To consider possible acceleration mechanisms, experimental results were compared with computer simulation results. The one-dimensional (1D) particle-in-cell (PIC) simulation code EPOCH³⁶ was used. Using this simulation, the grid resolution based on the Debye length of electrons was dx = λ_D ∼ 5.9 × 10⁻¹⁰ m, grid size was 100 μm, and Courant number was cΔt/Δx → 0.95. All results were obtained before the high energy particles left the simulation. When a laser pulse is incident into the microcapillary tube, the laser ablates the cylindrical surface of the capillary material and generates an acceleration field. It thus appears that the plasma density is highest at the surface of the capillary wall and that it decreases toward the center of the cylindrical capillary as a function of the radius. The electron density is thus a function of the radius: n_e(r). In our simulation, we wish to study at which radius (or actual density at a given radial position) the laser interacts most strongly with the ionized plasma in the microcapillary. To increase the number of runs and make the operation as simple as possible, we performed a 1D PIC simulation in which the x axis is the direction of the laser propagation, and the wakefield propagation over various runs at the plasma density n_e has a particular value for each run, from which we compare the laser coupling to the plasma at different electron densities (i.e., at different radial positions). We performed this calculation under the following conditions: a pulse width of 40 fs at a₀ = 0.8 (I₀ = 1.4 × 10¹⁸ W/cm²) and a₀ = 0.4 (I₀ = 3.5 × 10¹⁷ W/cm²) close to the maximum laser intensity at effective laser pump energy E_eff values of 27 and 6.8 mJ [Figs. 2(c) and 2(d)]. The simulation results show the production of a humped structure similar to that in the experimental results shown in Figs. 2(a) and 2(b). At a high laser intensity of a₀ = 0.8, the interaction occurring near n_c/4 (the growth rate of laser–plasma instability such as stimulated Raman scattering and/or two plasmon decay³⁷ is maximized at n_c/4) is stronger than that occurring near n_c (n_e = 0.9 n_c) and is dominant in the generation of energetic electrons [see in Fig. 2(a)]. In contrast, at a lower laser intensity of a₀ = 0.4, the interaction is greatly decreased, and the interaction at 0.9 n_c is dominant in the generation of energetic electrons [see in Fig. 2(b)]. Figure 2(e) shows the peak electron energies of the higher energy humps observed in the experimental [plot A in Fig. 2(a) and plot A′ in Fig. 2(b)] and simulation [Figs. 2(c) and 2(d)] results. These peak electron energies of the higher energy hump in our simulation are in good agreement with the experimental results, and these tendencies are also consistent with those in previous studies.^29,30 We have already discussed the behavior of electron trapping at near critical plasma density under resonance ultra-short laser pulse irradiation³⁰ (t_p = λ_p/c). We defined the specific entropy index D (darkness). Three trapping conditions were found, i.e., n_e $<nc$/4 and D/D₀ ≪ 1 region as the “blue tsunami” region, $ne>nc$/4 and D/D₀ → 1 region as the “black tsunami” region, and a region between the “black tsunami” and “blue tsunami” regions, termed the “gray tsunami” region [see in Fig. 3)]. In Fig. 4, we see three separate behaviors depending on the electron density. Here, the laser intensity was a₀ = 1.0, and the pulse duration was 40 fs. These values are similar to our laser condition in the experiment. First, when the electron density is sufficiently higher than the critical density (to the top of Fig. 4), as expected, the laser is unable to penetrate deep enough to make sufficient acceleration because of the cutoff effect. Second, when the electron density is close enough to the critical density (in the middle of Fig. 4), we see strong laser interaction, which causes large amplitude wake-field oscillations, and because of the low phase velocity of the wakefields in this regime, the trapping of electrons into the wakefield happens and electrons are accelerated in a massive fraction of the bulk electrons. This regime is similar to that of the tsunami wave approaching the sea shore with less phase velocity and increased amplitude of the tsunami (due to the decreased phase velocity with the total momentum of tsunami wave approximately conserved). The regime was similar to the “black tsunami” regime of the high-density wakefield. Third, when the density of the electrons is sufficiently low compared with the critical density (in the bottom of Fig. 4), the phase velocity of the wakefield is sufficiently large so that the trapping only happens with its few tail distribution (and if the density is farther lowered, unless there is an injection externally, no or little electron trapping would happen). This small trapping was referred to as the “gray tsunami” regime of wakefield acceleration. However, at a more low-density regime, as in our former understanding, when there is no or little trapping of electrons happening without injection,³⁰ that was called the “blue tsunami” regime of wakefield acceleration. In the experiment, we use longer laser pulses, and this results in increased growth of the intense laser and low-density plasma interactions, such as stimulated Raman scattering, which is a typical generation mechanism for high-energy electron generation. Figure 5 shows the dynamics of acceleration under low plasma density conditions (i.e., n_e = 0.1 and n_e = 0.2) for two different laser intensities (a₀ = 0.4 and a₀ = 0.8). By increasing the laser intensity [a₀ = 0.4 (Fig. 5(a)) to 0.8 (Fig. 5(b))], there is a rapid growth in the acceleration field. Significant trapping of electrons by a strong accelerating electric field was also induced. Our new experimental and simulation results indicate that this contribution is not negligible for long laser pulse duration and higher laser intensity conditions. In addition, to suppress high-energy electrons exceeding several hundred keV, which would be harmful in practical low-energy electron applications, it is important to suppress the injection in the “blue tsunami” region, which is the origin of the high-energy electrons, under sufficiently low laser intensity conditions. By the way, the acceleration field contributing to the high-energy electrons generated near the critical plasma density of n_c by the laser–plasma interaction is very short. Figure 6 shows the typical time evolution of the laser propagation and acceleration field near n_c. In this result, the strong laser acceleration field was generated at a scale of about 10 μm after starting propagation, and energetic electrons were generated in the range of a few micrometers. Here, the energy gain in the wakefield is given by the expression^1,28 Δϵ_w(n_e) $∼CeE0La02$ (n_c/n_e), where e is the elementary charge, E₀ is the wave-breaking (or the Tajima–Dawson) field,¹  L is the acceleration length, and C is a dimensionless number of the order unity. When n_e approaches n_c (with the radius of the microcapillary r ∼ r_c where the electron density reaches the critical value), the energy gain may be approximately given as $Δϵw(nc)∼Ca02$ MeV (a conservative minimal L of micrometer order is assumed here). Since the strongest coupling occurs when n_e ∼ n_c, one may expect that this energy gain is approximately the maximum energy arising from the laser irradiating the microcapillary. In particular, this is in qualitative agreement with the experimentally obtained maximum energy under the condition that the humped structure by the contribution of the “blue tsunami” is weak [i.e., curve A′ in Fig. 2(b)]. In the above-mentioned discussions, the microcapillary has an inner diameter of only 10 μm in the experiment, which means that the plasma formed by such laser ablation is dense. Therefore, the laser beam will be strongly absorbed at $<$100 μm from the entrance of the microcapillary. Indeed, the transmittance of the laser beam after the capillary plate was less than 5% in our experiment, and strong absorption by the above-mentioned mechanism was considered to occur.

In addition, the microcapillary may have improved the collimation of the high-energy component of accelerated electrons. We measured the spatial distribution of electrons using an IP (Fujifilm BAS-SR) with an Al 12 μm filter. In the measurement, the slit and the electromagnet were removed. Figure 7(a) shows the divergence of the generated electrons with energies above 40 keV as a function of pump laser intensity at an effective pump energy of 27 mJ. This result was taken with a single shot. In the measurement, we observed a beam divergence of ∼30 mrad at half-angle in the form of a weak background electron energy of a few tens of keV. The beam divergence shows a very weak dependence on the pump laser intensity (29 mrad in half-maximum at 1 × 10¹⁸ W/cm² and 35 mrad at 4 × 10¹⁶ W/cm²) and is close to the field of view angle at the capillary tube (α ∼ 24.5 mrad, where α is the half-angle). In a previous study,^38,39 collimated x-ray beam generation for two-dimensional imaging x-ray spectrography from an x-ray tube using a capillary array plate was demonstrated. They used a thick microcapillary plate (thickness: 2 mm) consisting of a diameter and pitch of a microcapillary hole at the plate of 12 and 15 μm, respectively. The beam divergence of x rays transmitted through the microcapillary plate was measured to be 5.6 mrad in the half angle for TiKα, which agrees with the field of view angle at the capillary tube (α = 6 mrad). A similar mechanism is considered to occur in our experiment. Here, collimation properties in microcapillary plates are determined by the length-to-diameter ratio (l/d), where l is the capillary length, d is the diameter of the capillary, and (l/d) was 166.7 in their experiment. In our experiment, a low l/d ratio (l/d = 40.9) microcapillary was used, whereas a higher collimated electron beam would be generated by using such higher (l/d) ratio microcapillaries. Moreover, the pointing stability is very high. In the experiment, shot-to-shot pointing fluctuations in root-mean-square deviation (RMSD) were 1.7 mrad in horizontal and 1.9 mrad in vertical directions for ten shots at the maximum laser intensity (I₀ = 1 × 10¹⁸ W/cm²). These values were more than ten times smaller than the beam divergence. Thus, microcapillaries are also expected to contribute to beam stabilization. Here, the yield of energetic electrons at $>$40 keV was 10⁶ order or sub-pC electron charge, as determined from the electron energy distributions and beam divergence measurements [Fig. 7(b)]. This value is estimated to be of 1% order of the number of electrons contained in the volume by the product of the microcapillary diameter and the acceleration length when the average density is assumed to be the critical density.

In conclusion, we have carried out the first definitive near-critical-density LWFA experiment using a microcapillary target that shows a strong coupling of the laser to electrons through the low phase velocity of the wakefield. A pointing stable low-divergence 100-keV-class electron beam was generated by using a 400 μm thick microcapillary target. We discussed the appearance of the hump structure of the energy of the electron beam generated under higher laser intensity conditions in our experiment using the simulation results. Some early supportive theoretical evidence emerged, which qualitatively agrees with the properties of this near-critical-density LWFA obtained in the experiment. This new regime of LWFA may be very suitable for future extremely compact keV electron accelerators such as endoscopic radiotherapy equipment.

This research was partially supported by the JST-Mirai Program (Grant No. JPMJMI17A1) and by the Japanese Ministry of Education, Culture, Sports, Science and Technology (MEXT) through the JSPS KAKENHI Program (Grant Nos. 20K12505 and 23K11716). One of our coauthors (Ernesto Barraza-Valdez) participated in the experiment at KPSI under the auspices of the Department of Research Planning and Promotion of QST.