In recent years, laser-driven particle sources, such as electrons^[1^], ions^[2^] and neutrons^[3^], have been greatly developed due to their promising applications in high-energy density physics, nuclear physics, and cancer therapy treatment. Based on laser-accelerated electrons, gamma-ray radiations are also gaining increasing interest due to their ultra-high peak brilliance, short pulse duration and small beam size^[4^–7^]. Such compact gamma-ray sources could pave the way for nuclear photonics, producing ultra-short neutron sources and medical isotopes^[8^], and radiography. In particular, the small beam size and large peak flux of the laser-generated gamma-ray sources can greatly improve the contrast and spatial resolution for nondestructive radiography compared to other approaches^[9^]. In strong-field quantum-electrodynamics, a promising approach to observe the Breit–Wheeler electron–positron pair production^[10^] in the linear or nonlinear regime is to collide laser-driven gamma photons with superintense lasers^[11^], X-ray radiations^[12^] or with each other. This requires the gamma beams to be collimated, guaranteeing high photon density in the collision region.

There are three main mechanisms to generate gamma-ray beams based on laser-driven energetic electrons in experiments: betatron radiation^[13^], inverse Compton scattering (ICS)^[14^,15^] and bremsstrahlung radiation^[4^,5^,16^,17^]. In general, betatron radiation produces gamma rays with photon energies from hundreds of keV to MeV when electrons oscillate in the laser-driven plasma bubble field. In ICS, the number of photons obtained by laser photons scattered by high-energy electrons is usually at the ${10}^7$ level^[18^], with photon energies up to several tens of MeV and good beam collimation. On the other hand, copious gamma photons can be produced when energetic electrons collide with high atomic-number nuclei through bremsstrahlung radiation. In this case, the maximum energy of the gamma photon is comparable to the maximum electron energy. It is advantageous for producing large photon numbers, up to $3.2\times {10}^{10}$ , with a femtosecond laser^[17^] .

A key to increase the photon yield in bremsstrahlung radiation is enhancing the number of relativistic electrons in laser–plasma accelerations. For instance^[16^], using picosecond laser pulses of relatively high pulse energy, plasma wakefield acceleration in the self-modulated regime produces $7.5\;\mathrm{nC}$ electrons, hence inducing a photon number of ${10}^9$ photons ${\mathrm{keV}}^{-1}\;\mathrm{S}{\mathrm{r}}^{-1}$ . However, the divergence of bremsstrahlung gamma-ray beams is usually quite large (~several tens of degrees)^[17^] because of the scattering by the nucleus coulomb field.

In this work, to obtain high-yield low-divergence gamma sources, we first produce a collimated high-charge electron beam through picosecond laser-driven self-modulated wakefield acceleration (SM-LWFA). Then it is sent to a high-Z target. The bremsstrahlung gamma-ray photons are measured with a high-resolution Compton-scattering spectrometer (CSS). The latter contains a gradual magnetic field to improve the energy resolution. The measured spectra are reproduced with GEANT4 simulations, suggesting a total photon number of $2.2\times {10}^{11}$ gamma photons (> $0.3\;\mathrm{MeV}$ ) within a divergence angle of $7.73{}^{\circ}$ . Such gamma photons are advantageous in radiography, exploring nuclear photonics, strong-field quantum electrodynamics (QED) physics, etc.

The experiment was carried out on the SG-II UP picosecond experimental platform^[19^] at the Shanghai Institute of Optics and Fine Mechanics (SIOM). A schematic diagram of the experiment is shown in Figure 1. A linearly polarized laser pulse with a pulse duration of ${\tau}_{\mathrm{p}}=1\;\mathrm{ps}$ , a center wavelength of 1053 nm and an energy of $120\kern0.24em \mathrm{J}$ was focused $600\;\unicode{x3bc} \mathrm{m}$ above a pulsed nozzle that is employed to produce a high-density argon gas jet by an $f/2.8$ off-axis parabolic mirror. The focal spot has a full width at half maximum (FWHM) of $35\;\unicode{x3bc} \mathrm{m}$ , reaching peak intensity of $3.1\times {10}^{18}\;\mathrm{W}/\mathrm{c}{\mathrm{m}}^2$ . The on-target laser field corresponds to a normalized laser amplitude $a\approx 2.3$ , where $a= eE/ m\omega c$ , $e$ and $m$ are the electron charge and mass, $E$ is the electric field, $\omega$ is the laser frequency and $c$ is the speed of light in vacuum. The back pressure of the argon gas target in the experiment was 17–30 bar, and the optical interferometry of the laser–gas jet interaction indicated that the electron density reached a near-critical density region of ( $2\hbox{--} 4) \times {10}^{20}\;\mathrm{c}{\mathrm{m}}^{-3}$ , corresponding to a plasma wavelength of ${\lambda}_{\mathrm{p}}\approx 1.9\;\unicode{x3bc} \mathrm{m}$ . A $2\;\mathrm{mm}$ thick lead target was placed $2\;\mathrm{mm}$ behind the gas jet. When the laser-accelerated energetic electrons pass through the solid target, they are scattered by the nuclei and emit photons through bremsstrahlung radiation. Electron–positron pair creation through the Bethe–Heitler process^[20^] also occurs during the interaction process when the emitted photons further interact with nuclei. An electron–positron spectrometer (EPS) with the magnetic field of $B=0.8\;\mathrm{T}$ was added $220\;\mathrm{mm}$ behind the lead target to deflect the positrons and electrons and measure their energy spectra, which had an acceptance divergence angle of $2.86{}^{\circ}$ . We chose Fuji BAS-SR (or BAS-TR) image plates (IPs) as the recording detector. The IPs were scanned using a GE Typhoon 7000 flatbed IP scanner^[21^].

One key aspect of our experiments is the measurement of the gamma-ray spectrum. Gamma-ray beams driven by laser-accelerated electrons are of short pulse duration, comparable to that of the laser pulse (~1 ps here). Conventional scintillation and semiconductor detectors are not applicable to resolve the energy spectrum of the gamma-ray flash since all photons reach the detector in a short instance, resulting in the integrated photon energy being the sum of all received gamma-ray beam energy. Therefore, methods such as Compton scattering^[22^,23^], photonuclear activation^[24^,25^] and differential filtering^[26^,27^] are employed to detect ultra-short gamma-ray flashes. The neutron separation thresholds relevant to the photonuclear activation cover a wide energy range^[25^], while the attenuation coefficients are not so sensitive to gamma energy above 2 MeV in differential filtering^[28^]. Thus, their spectrum resolutions are limited, especially in the high-energy region.

In this experiment, we chose a differential filtering detector (DFD) and a CSS together to detect these photons. A typical CSS usually uses a uniform magnetic field profile^[22^] or a stepped magnetic field profile^[23^] to deflect the photon-induced electron–positron pairs. The latter employs a curved surface plate to improve the energy resolution. Instead, we apply a gradual magnetic field for CSS, which increases linearly along the laser direction and fills the whole spectrometer. Thus, it is capable of gathering the converted electrons with the same energy but different emitting angles together and enhances the energy resolution of the gamma-ray beam, as shown in Figure 1(b). There is the electron–positron pair effect in the MeV gamma-ray range. The influence of the electron–positron pair effect can be largely eliminated through their mutual cancellation by the adoption of a symmetrical design for the spectrometer such that the positron and electron spectra are measured simultaneously. Then the energy spectrum of gamma beams can be obtained from the corrected converted electron energy spectrum. The DFD is placed behind the CSS, which consists of 13 pieces of lead filters with dimensions of $2.5\;\mathrm{cm}\times 2.5\;\mathrm{cm}$ and different thicknesses in the range of 3–10 mm, placed one by one in the beam path, as shown in Figure 1(a). The gamma-ray beam spectrum is calculated using the gamma-ray signal in each IP, considering the lead filter thickness and the attenuation coefficients of these 13 energy groups. We use equation ${D}_i={\Sigma}_j^n{R}_{ij}{\Phi}_j,i=1,2,\cdots, 13$ to calculate the gamma-ray beam spectrum, where ${D}_i$ represents the energy deposition on the ith channel detector, ${\Phi}_j$ is the photon number in the jth energy interval, n is the number of filters and ${R}_{ij}$ is the energy deposition coefficient of photons in the jth energy interval on the ith filter. The CSS and DFD are added $500\;\mathrm{mm}$ behind the lead target, which has an acceptance divergence angle of $1.1{}^{\circ}$ . In addition, the CSS and DFD are shielded by lead boxes with thicknesses of 1 and $2\;\mathrm{cm}$ to avoid the background radiation. Thus, the spectrometers measure the gamma-ray photon signal with low noise.

When a high-intensity $a>1$ laser pulse with pulse duration ${\tau}_{\mathrm{p}}$ larger than the plasma period ${\lambda}_{\mathrm{p}}/ c$ propagates through an underdense plasma ${n}_{\mathrm{e}}<{n}_{\mathrm{c}}$ , it undergoes self-focusing and drives plasma waves through the Raman forward scattering (RFS) and self-modulation instabilities^[16^]. The gas target is ionized simultaneously and a significant number of electrons are injected and accelerated. In our case, an argon cluster target with high density is employed to enhance the beam charge of energetic electrons from laser-driven electron acceleration^[29^]. The raw-data recorded by the EPS in Figure 2(a) show that the electron bunch has a broad energy spectrum with a cut-off energy of $80\;\mathrm{MeV}$ . After the deconvolution^[30^], the electron spectrum is plotted as shown in Figure 2(b). The electrons are first accelerated by the longitudinal field, while the transverse field leads to betatron-like oscillations of the off-axis electrons. This transverse electric field of the laser, when in near resonance with the betatron motion of the electrons, will in turn increase the transverse momentum of the electrons, which can be converted into longitudinal momentum via the v×B force. This process is analogous to the direct laser acceleration (DLA)^[31^]. The black line in Figure 2 represents the geometric mean value of the data. It is noted that the electrons accelerated in the plasma wave also undergo betatron oscillations about the laser axis due to the restoring force of the ion column that forms behind the drive laser^[16^]. However, most of the radiation from betatron oscillations cannot pass through the thick lead target in the experiment.

Removing the lead target and spectrometers, a spatial high-energy electron beam analyzer (SHEEBA)^[32^] composed of Al plates and IPs is located $500\;\mathrm{mm}$ behind the argon target to detect the spatial distribution of the electrons. Figure 3(a) shows a spatial profile of the electrons with energy of more than $2.2\;\mathrm{MeV}$ , blocked by a 5-mm-thick Al plate in front. It has a Gaussian-type distribution with horizontal divergence of $1.51{}^{\circ}$ and vertical divergence of $2.59{}^{\circ}$ for shot 4. The spatial distribution of the electrons seems to be elliptic, almost the same direction as laser polarization, which could be attributed to the residual transverse momentum^[16^,33^] that the electrons gain at the moment of ionization and/or to DLA^[34^,35^]. The divergence angle of the electron beam increases while the energy increases from $E>9.2\;\mathrm{MeV}$ to $E>15\;\mathrm{MeV}$ , as shown in Figures 3(b) and 3(c). Electron beam divergence angles of four continuous shots show good stability in Figure 3(d), where the blue and red lines indicate the horizontal and vertical divergence angles, respectively. An electron beam charge of $26\;\mathrm{nC}$ is measured here, which is beneficial to the subsequent applications. Detailed analysis of the generated electron beams will appear elsewhere. Such high-charge electron beams have also been obtained by a picosecond-scale^[31^] kilojoule-class laser, where the total charge in the electron beams exceeds $700\;\mathrm{nC}$ and scales approximately linearly with the laser intensity.

These electrons with nC of charge and low divergence then collide with the 2-mm-thick lead target to generate gamma-ray photons through bremsstrahlung radiation. The EPS serves to remove the secondary electrons and positrons leaving the converting target here. The raw-data recorded by the DFD are shown in Figure 4(a) within the acceptance angle $1.1{}^{\circ}$ . The spectrum of the gamma-ray beam shows a two-temperature structure ( $0.6$ and $4.4\;\mathrm{MeV}$ ). It should also be noticed that the gamma-ray signal on the sixth IP is still clear enough after penetrating a 3.8-cm-thick lead-layer. With a 3-mm-thick lead layer in front of the first IP in Figure 4(a) to block gamma-ray beams with energy lower than $0.3\;\mathrm{MeV}$ , a high total photon number of $2.2\times {10}^9$ is detected by the DFD. The raw-data of positrons and electrons recorded by the CSS are shown in Figures 4(b) and 4(c). The continuous gamma-ray beam spectrum of the geometric mean is shown in Figure 4(d) by a black line, which is in good agreement with the result from the DFD and has a higher energy resolution.

To model the gamma-ray generation process, a series of test particle simulations are carried out with the Monte Carlo code GEANT4^[36^]. The simulation includes several physical processes, such as bremsstrahlung, scattering, ionization, pair production, photoelectric effect and Compton scattering. A total of ${10}^7$ electrons with the same energy and spatial distributions as the experimental measurement in Figures 2 and 3 impact a 2-mm-thick lead target. The electron source is considered to be point-like. The simulated gamma-ray beam spectrum is shown by the blue line in Figure 4(d), and it is in good agreement with the experimental result, especially in the energy range above $2.5\;\mathrm{MeV}$ . The simulated temperatures of the gamma-ray beam within $1.1{}^{\circ}$ are found to be $0.9\;\mathrm{MeV}$ for the low-energy part and $2.7\;\mathrm{MeV}$ for the high-energy part. The slight difference for the low-energy part from the experimental result has not been clarified, and further work is needed. Simulations also indicate that the produced gamma-ray source has an FWHM size of $433\;\unicode{x3bc} \mathrm{m}$ at the emergent surface of the lead converter.

The simulated angular divergences of gamma-ray beams with different energies are summarized in Figure 5(a). It can be seen that the FWHM divergence of the gamma-ray beam of more than $0.3\;\mathrm{MeV}$ is only $7.73{}^{\circ}$ , which is lower than the recent experimental results under commensurate laser conditions^[16^]. Considering that the gamma-ray beam has a 2D Gaussian distribution, the acceptance angle of $1.1{}^{\circ}$ in the experiment means that only $1\%$ of the photons are measured. Therefore, the total photon number generated in the experiment is estimated to be $2.2\times {10}^{11}$ among the highest yield comparing to previous results^[16^,17^,37^] driven by laser-accelerated electrons. It is noted that the gamma-ray photon number could be further increased by raising the picosecond-scale laser energy^[31^]. The divergence of the gamma-ray beam decreases with the increase of energy, as shown in Figure 5(a). Overall, the gamma-ray beam with high yield and low divergence produced in our experiment could be a promising source for electron–positron production, radiography measurements in high energy density physics (HEDP) and inertial confinement fusion (ICF), and nuclear photonics.

The influence of thicknesses and the FWHM have also been studied by simulation, as shown in Figure 5(b). At the target thickness, the generated gamma-ray photon number increases due to continuous interaction between the electrons and the target. However, the energetic photons will be attenuated as the target thickness further increases. When these two processes reach a balance, the largest yield of gamma photons is obtained with the lead target thickness of $4\;\mathrm{mm}$ . The divergence angle of the gamma beams is basically unchanged while the target thickness increases.

In conclusion, we use a picosecond laser to generate electron beams with large charge and low divergence, and subsequently to generate gamma-ray beams with high yield and low divergence through bremsstrahlung radiation. A typical DFD and a specially designed high detection resolution CSS with a gradual magnetic field are used at the same time to detect the generated gamma-ray beams precisely. The gamma-ray beams have a total photon number of $2.2\times {10}^{11}$ , size of 433 μm and divergence of $7.73{}^{\circ}$ , which make them promising sources for photonuclear reaction and clinical applications. Future improvements on these sources can be done by using higher laser energies.