With the rapid development of ultra-short ultra-intense laser technology, more and more petawatt (PW) laser facilities are coming online. The Extreme Light Infrastructure (ELI) delivered femtosecond laser pulses with 10 PW peak power in 2022.1 The Apollon laser in France, with the long-term goal of generating 10 PW pulses, has recently finished its commissioning in the 1 PW mode.2 By focusing the PW laser beams, an unprecedented intensity of 10²³ W/cm² has been achieved.3 Laser–foil interaction at such high intensity can lead to the generation of high-energy protons up to hundreds of MeV,4–6 which are highly desirable for tumor therapy,7–10 inertial fusion,11 neutron radiography,12,13 and other applications. For many of these applications, Hz-level or even higher repetition rates are required. The increasing power and repetition rates of these lasers, however, bring new challenges with regard to radiation safety.14–19

To evaluate radiation safety and ensure efficient operation, dosimetric assessment is necessary. Some work on prompt radiation and residual radiation has been reported. Prompt radiation induced by ions and electrons from laser–plasma interaction at the LION PW laser facility was studied by Tisi et al.20 through Geant4 Monte Carlo simulations. Their research showed that the secondary radiation environment was initially dominated by photons if the energies of the particles were low. However, when sources with higher-energy particles were introduced, neutrons dominated the radiation field. A characterization of the prompt radiation field at the ELI Beamlines facility together with a corresponding shielding strategy were presented by Ferrari et al.21 They demonstrated that the dose rate can be decreased to an acceptable level of 250 μSv/year by using a three-material dump composed of a low-Z neutron absorber, a low-Z moderator, and a high-Z degrader. To study the residual radiation doses at the Center for Advanced Laser Technologies (CETAL), monoenergetic proton beams with an energy of 100 MeV and electron beams with an energy of 300 MeV driven by a 1 Hz/1 PW laser were simulated by Florescu et al.22 The results of their simulations showed that the activation dose rate in the experimental hall can drop to the natural outdoor background level within several minutes of shooting in a daily laser campaign owing to the short lifetimes of the radionuclides produced.

Previous studies have focused mainly on the evaluation of the radiation dose produced by laser-driven high-energy particles. A complete radiation safety assessment, however, should also include other factors, such as the shot number, repetition rate, radiation shielding measure, and radiation cooling time. In this paper, we simulate the prompt and residual radiation produced in laser proton acceleration experiments at the Compact Laser Plasma Accelerator–Therapy (CLAPA-T) facility7 by employing the Geant4 and FLUKA Monte Carlo codes. The residual doses from both single and continuous shooting are assessed in detail, enabling us to give an integrated radiation dose assessment for a typical PW laser facility, and reasonable radiation safety strategies are proposed for different experiments.

CLAPA-T is a newly built PW-laser-driven proton accelerator facility at Peking University, based on research experience with the Compact Laser Plasma Accelerator (CLAPA).7 It is able to repeatedly deliver 60 J, 30 fs (2 PW) laser pulses at 1 Hz repetition rate. By utilizing the PW laser and advanced targets, proton beams with maximum energy up to 200 MeV are expected to be produced and applied to tumor therapy.

Radiation shielding has been considered in the design of the laser experimental hall of CLAPA-T, shown in Fig. 1. This hall is located at ground floor level and its internal dimensions are length L = 20 m, width W = 30 m, and height H = 4.2 m. The walls are made of concrete with a density of 2.4 g/cm³ and a thickness of 1.5 m. The thickness of the ceiling slab is 1 m. The access door has a maze design to reduce radiation leakage. The layout of the experimental setup is also shown in Fig. 1. The laser beam is 1.5 m above the ground. It propagates through a double-plasma-mirror system and a deformable mirror system, then enters the target chamber placed at the center of the experimental hall. The on-target energy will be around 30 J after energy loss during transmission and in the dual-plasma-mirror system. Focused by an off-axis parabolic mirror (F/3), the on-target intensity is expected to be higher than 10²¹ W/cm², which can trigger intense laser–plasma interaction and produce abundant ionizing radiation in the form of ions, electrons, and X rays. During the laser–target interaction, all personnel leave the experimental hall to avoid exposure to the prompt radiation.

The FLUKA 4.2.1 Monte Carlo code23–25 is utilized in this work, along with the standard PRECISIO and PHOTONUC physics model packages introduced in the input files. These models incorporate the common physics processes relevant to radiation protection applications, such as hadronic interactions, ionization, Coulomb scattering, photonuclear interactions, and bremsstrahlung. The models also include processes related to low-energy neutrons, such as transportation, scattering, and activation. Some of the simulations are also conducted with Geant426 to cross-verify the results. The physical process list used is a pre-constructed Bertini intranuclear cascade model with high-precision neutron data (QGSP_BERT_HP), which takes into account hadronic physics, electromagnetic showers, and synchrotron radiation.

The architecture and the target chambers are precisely constructed with the simulation program for the dose calculation. The geometry and materials are modeled identically in the two simulation codes. The main structure of the experimental hall as shown in Fig. 1 is modeled in the geometry configurations of the codes, including the concrete walls, the pillars, the maze, and the ceiling. The target chamber (3.6 × 2.2 × 1.3 m³) is modeled in detail, including the stainless-steel frame, the aluminum plates (6060-T6 aluminum alloy), and the stainless-steel supporting legs. A Cartesian coordinate system is established, with its origin at the geometric center of the target chamber and with the +X, +Y, and +Z directions corresponding to the east, north, and upward directions, respectively. The primary particle source is positioned inside the chamber where the laser interacts with targets, at (−1.05, 0.92, 0 m), which is 1.5 m above the ground. The particle momenta are in the −X direction, with an angular divergence of 100 mrad [full width at half maximum, (FWHM)].

Two types of primary particles are considered in this study, namely, protons and electrons. For simplicity, heavy ions are not considered as primary particles, given that it is protons that are predominantly accelerated in the experiments. The input proton energy spectrum, depicted in Fig. 2, is derived from the results of previous experiments conducted by Ma et al.5,27 at the Center for Relativistic Laser Science (CoReLS), which has similar laser parameters. The spectrum is fitted with an exponential function with a temperature of 18.7 MeV and extrapolated to a higher energy limit of 200 MeV. To simplify the simulations, the electron temperature is also set to 18.7 MeV, with a low-energy limit of 1 MeV and an energy spread of 100%. The total number of electrons is set to 6.2 × 10¹¹ (100 nC), which is the same as the total number of protons. According to the energy spectrum and the divergence angle, the laser-to-proton efficiency is 6%, which is slightly higher than typical reported values.28

The radiation doses deposited in humans are assessed by examining the ambient dose equivalent H*(10), derived by converting the spatial particle fluence using the fluence-to-dose conversion coefficients AMB74.29

To assess the radiation intensity at critical locations, four scorers labeled Nos. 1–4 are placed around the target chamber (shown in Fig. 1) at the height of the laser, i.e., 1.5 m above the ground. Each scorer records energy deposition with linear energy bins ranging from 0.1 keV to 200 MeV. A comparison of simulated doses recorded by each scorer from the Fluka and Geant4 simulations is presented in Table I for crosschecking. The results represent an average of multiple runs conducted repeatedly to reduce statistical uncertainties, with the relative errors for both codes being less than 1.0%. The relative deviation data for electrons and protons indicate that there is good agreement between the two codes. Particle fluences and energy spectra are also compared to verify the agreement between the codes. The FLUKA simulation utilizes the RESNUCLEi card to assess induced radiation and record the isotopes produced during activation processes. The simulation also captures time evolution and residual doses resulting from the decay of the isotopes in a specific run.

Both prompt radiation and residual radiation are considered in the estimation of the total radiation dose. The prompt dose results are presented as ambient dose equivalent and normalized to one shot (6.2 × 10¹¹ prims), recorded in a 10-cm-bin-width scoring mesh. The residual dose is characterized by the ambient dose equivalent rate for a given time after the shooting ranging from 10 min to several hours.

The distributions of the prompt dose induced by protons and electrons are depicted in Figs. 3(a) and 3(b). It can be seen that the maximum values of H*(10) for protons and electrons, obtained near the surface of the target chamber along the beam direction (−X), are about 0.06 and 4 mSv/shot, respectively. Sectors on the reverse direction (+X) receive a relatively low dose. The 1.5-m-thick concrete wall reduces the prompt dose by three to four orders of magnitude. The overall dose in the west part of the experimental hall is several orders of magnitude higher than that in the east part. The dose distribution along the red dashed line in Figs. 3(a) and 3(b) (X = −5.5 m) is illustrated in Fig. 3(c). For both proton and electron cases, the maximum dose is identified as being locatted near the target point close to the west wall of the target chamber. It is notable that the dose distribution generated by protons is more collimated than that generated by electrons. During laser shooting, personnel are not allowed to be present in the experimental hall or in the area to the west next to the hall. The control room is far enough away to be safe from radiation. However, there is still a possibility that someone may pass along the north corridor around the experimental hall (see Fig. 1). Therefore, the dose received by the sector outside the maze door should be evaluated carefully. Figure 3(d) shows the dose distribution along the corridor [Y = 15 m, green dashed line in Figs. 3(a) and 3(b)]. Taking into account the total dose from electrons and protons, the highest H*(10) at the entrance of the maze is 1.2 × 10⁻⁶ mSv/shot. The radiation safety issues arising from prompt radiation will be analyzed in Sec. V.

When particle beams interact with the materials around the target, such as the steel frame and aluminum plates of the target chamber (as depicted in Fig. 1), the excited nuclei lead to residual radioactivity that may persist for a considerable time after the shooting. This induced activity arises from various nuclei with half-lives ranging from microseconds to years, resulting in a multicomponent decay pattern for the overall radioactivity profile.30 We construct the geometrical configuration of the experimental hall in the same way as in the prompt radiation simulations. Our results indicate that the primary particles will produce ²⁹Al, ²⁴Na, ²²F, and other nuclei from aluminum alloy, and⁵⁵Fe, ⁵⁴Mn, ⁵⁶Co, ⁵⁷Ni, and other nuclei from stainless steel. The radioactive nuclei from stainless steel generally have higher residual activities and need longer cooling times compared with those from aluminum alloy.31 The simulations also include the generation and transportation of secondary neutrons induced by protons and gamma rays, and the resulting dose is incorporated into the results.

For the single-shot mode (in which 6.2 × 10¹¹ protons and electrons, respectively, are generated), the residual dose rate distribution at t = 0 (immediately after the laser shot) is shown in Fig. 4(a). The highest dose rate is observed inside the target chamber. The dose rate is at a level of 10⁻²–10⁰ μSv/min outside the target chamber. After 30 min cooling (the typical chamber venting time), the dose rate in the experimental hall is reduced by 10⁴–10⁵ [as shown in Fig. 4(b)].

We simulate the residual dose equivalent rate (RDER) induced by protons and electrons at different positions as a function of cooling time up to 100 days and show the results in Fig. 5. The RDER from protons is two to three orders of magnitude higher than that from electrons, because protons are more likely to induce nuclear reactions through hadronic interactions. Therefore, we neglect the activation dose from the incident electrons in the discussion below. The RDER induced by protons decreases rapidly with time. The dose rate near the chamber surface is ∼200 μSv/min immediately after the shot, but drops rapidly below 0.01 μSv/min after 15 min. Residual doses induced by protons at distances 20 and 50 cm (along the X axis) from the west wall of the target chamber are also shown in Fig. 5. It is evident that the dose outside the chamber (X = −50 cm) is significantly lower than that inside the chamber.

For continuous shooting experiments, the residual radioactivity builds up with each laser shot as a result of the contribution from nuclei with medium to long half-lives. To estimate a more realistic dose that one person might receive, we calculate the long-term RDER as depicted in Fig. 6(a). We assume that t = 0 represents the moment at which the last laser shot is finished. All n shots are evenly performed in time before t = 0. Each shot generates an identical dose rate cooling curve R₀(t) as shown in Fig. 5, with a time delay of [(n − i)/(n − 1)]T for the ith shot. The total dose rate at delay time t can be written as$$R(t,n)=\sum _{i=1}^n{R}_0\left(\frac{n-i}{n-1}T+t\right).$$If a person enters the target chamber at t = t_c and works for a period of Δt, then the total residual dose that he or she will receive will be$$H(t_c,\mathrm{\Delta }t,n)={\int }_{t_c}^{t_c+\mathrm{\Delta }t}R\left(t,n\right)\mathrm{d}t.$$For a typical experimental scenario in CLAPA-T, the expected total number of shots per day is n = 600. Figure 6(b) shows the residual dose decay curves after the last shot, which are strongly dependent on the shooting mode. The dose rate is quite high when t = 0 for all the modes. In the single-shot mode, the dose rate decays below the natural radiation dosage32 [4.7 × 10⁻³ μSv/min, the red dashed line in Fig. 6(b)] in 1 min, which is similar to previous results (3 min) reported by Florescu et al.22 In the case of continuous shooting, however, we find that the residual doses are significantly higher than those in the single-shot mode. For example, if 600 shots are performed in 8 h (which is typical for a low-repetition proton acceleration experiment), the dose rate is an order of magnitude higher than the natural background at 30 min after the shooting, and more than 10 h are needed for the dose rate to drop to the natural background. For applications to tumor therapy, the required shooting rate is higher than that in scientific studies. Figure 6(b) shows that if 600 shots are performed in 10 min, the dose rate is ten times higher than in the case of 600 shots in 8 h at t = 0.5 h. For comparison, we also change the material of the target chamber wall from aluminum alloy to stainless steel in the FLUKA simulations. The results indicate that the RDER decays much more slowly than in the case of aluminum, and several tens of hours are needed for it to decay to the natural background after continuous shooting with 600 shots.

Therefore, radiation cooling becomes a critical issue for an experimental hall without a beam dump21 and a dedicated radiation shielding design. According to our simulations, the RDER may need tens of hours to drop to the natural radiation dosage background level after hundreds of shots. Nevertheless, this does not mean that people are unable to work in the experimental hall shortly after shooting. The effective dose can be controlled below the 1 mSv/year criteria by adopting an appropriate working strategy, as we discuss below.

According to the International Commission on Radiological Protection (ICRP)33,34 and Chinese Regulation Standard GB18871-200223, the effective dose limits are 1 mSv/year for public exposure and 20 mSv/year for occupational exposure. In this section, we take 1 mSv/year as the criterion for human radiological safety assessment. The total dose received by someone working in the experimental hall can be expressed as H_total = H_prompt + H_residual, where H_prompt is the prompt dose and H_residual is the residual dose.

Regarding the prompt dose, there are several possible scenarios. In most cases, the experimental personnel stay in the remote control room during laser shooting. The prompt dose can therefore be neglected. Occasionally, a person may pass along the corridor for a short time. He or she may thus receive a prompt dose from several shots at the level of 10⁻⁵–10⁻³ μSv, which can also be neglected. If a person is standing in a corner of the experimental hall during the shooting, the prompt dose that they will receive is about 10⁻⁴–10⁻³ mSv/shot, which is nonnegligible and should be avoided. In extremely rare cases, which are unlikely to happen except as the result of an accident, someone might stand near the target chamber during laser shooting. The prompt dose that he or she would then receive can be up to 10 mSv/shot, according to Fig. 3, which is higher than the safety criterion (1 mSv/year). Therefore, the presence of personnel in the experimental hall should be strictly prohibited during laser shooting.

The residual dose after a continuous series of shots is shown in Fig. 6. If we exclude the contribution from long-lived radionuclides, the permitted working time near the chamber for a specific radiation cooling time of t_c in a specific shooting mode can be easily derived from Fig. 6. For example, for 600 shots during 8 h (in the low-repetition mode), H_residual = 2.7, 2.0, and 1.6 μSv/h, for t_c = 10, 20, and 30 min, respectively. As long as personnel wait longer than t_c before starting to work in the chamber, the permitted total working times per year will be longer than 370, 500, and 625 h, respectively. In comparison, for 600 shots during 10 min (in the high-repetition mode), H_residual = 24.2, 15.5, and 9.9 μSv/h, for t_c = 10, 20, and 30 min, respectively. The permitted total working times per year are then 41, 64, and 101 h, respectively. It is clear that continuous shooting in high-repetition mode requires much longer radiation cooling times than the low-repetition mode if long working times per year are to be achieved.

If we consider the contribution from long-lived radionuclides, then the assessment becomes more complicated. Here, we discuss one particular strategy as an example. We assume that a member of the experimental personnel works for one hour per day inside the target chamber after t_c. He or she may receive the dose contributed by long-lived radionuclides from previous shots. Our simulation shows that his or her remaining dose, initiated at μSv, will drop to nSv level after 30 days and become negligible. Thus, we only need to consider radionuclide contribution from shots in the last 30 days. The pursued working time inside the target chamber is one hour per day and 220 weekdays per year. By considering the accumulation of the dose over different days, the required cooling time t_c is found to be as shown in Fig. 7. In the low-repetition mode with 600 shots during 8 h before the person works inside the target chamber, the minimum cooling time is 11 min. In comparison, in the case of 600 shots during 10 min in the high-repetition mode, the minimum cooling time is 99 min, which is much longer than in the low-repetition mode. Figure 7 also indicates that the radiation cooling time rises rapidly for a larger number of shots. For example, if this number is increased to 800 in the low-repetition mode, a cooling time of 34 min is required.

We have simulated both prompt and residual radiation from laser-driven ion acceleration experiments that will be performed in the experimental hall of the PW laser facility CLAPA-T. We have found that the prompt radiation, produced by 100 nC protons and 100 nC electrons with exponential energy spectra up to 200 MeV, can be effectively shielded by the concrete walls of the experimental hall. The ambient dose equivalent outside the maze structure and shielding walls is attenuated to the level of 10⁻⁵–10⁻³ μSv per laser shot, which can be neglected. However, in extremely rare cases, personnel standing near the target chamber during laser shooting may receive up to 10 mSv/shot, which may lead to serious health problems and should be strictly prohibited. In addition, the residual radiation due to the activation of the target chamber needs to be seriously considered. After continuous shooting for hundreds of shots, the residual dose rate in the target chamber will exceed the natural background for a certain time, and so radiation cooling is mandatory. We have demonstrated that reasonable radiation safety strategies for 600 daily shots considering the shooting rate and radiation cooling time can be formulated on the basis of our simulation results. If a higher number of daily shots is pursued, then a dedicated beam dump and shielding will be needed.

Acknowledgment. This work was supported by the National Natural Science Foundation of China (Grant No. 12205008), the NSFC Innovation Group Project (Grant No. 11921006), and the National Grand Instrument Project (Grant Nos. 2019YFF01014402 and 2019YFF01014403). W. Ma acknowledges support from the National Science Fund for Distinguished Young Scholars (Grant No. 12225501).