Design of Radiation Shielding for Terawatt-level High-power Laser Facility

Abstract

A wide range of particle species, including neutrons, electrons, and photons, will be generated in a terawatt-level (TW) high-power laser facility, which poses considerable challenges for the development of effective radiation shielding solutions. The safety of both facility personnel and the public requires specified design considerations for these shielding systems. The Monte-Carlo code JMCT was employed to simulate and design the shielding structure for the TW facility. We calculated the radiation dose distribution throughout the entire facility for both single-shot and multi-shot operational modes. Our findings indicate that the strategic use of locally thickened shielding walls and mobile shielding measures can effectively mitigate radiation risks in TW-level laser facilities, ensuring that radiation doses within the personnel working area remain within regulatory limits. The results demonstrate that with these shielding strategies in place, the occupational exposure dose in the control room and the clean room can be confined to below 3 mSv y⁻¹, while the public dose remains below 0.1 mSv y⁻¹, considering an experimental frequency of 5 × 10⁶ shots per year for overdense plasma experiments and 1 × 10⁴ shots per year for underdense plasma experiments. The radiation shielding design method and results presented in this paper can serve as a reference for similar devices.

INTRODUCTION

With the invention of the chirped pulse amplification technology during the last two decades, the modern laser system can generate ionizing radiation of significantly high energies by focusing ultrashort, intense pulses onto targets (Strickland and Mourou 1985; Courant et al. 1985). In this way, the intense accelerating gradients above 10 GV m⁻¹ are produced and have been used to create high-energy beams of electrons and ions by focusing a laser pulse on some target materials with the power density above 10¹⁸ W cm⁻². By manipulating laser parameters and selecting diverse targets, the characteristics of the particles can be meticulously adjusted to conform to an optimal range. Such modifications facilitate the generation of laser-accelerated electron and ion bunches, which may be used effectively for radiation therapy in the treatment of cancer, as well as for a variety of imaging applications, through the exploration of novel radiation generation mechanisms (Richter et al. 2016; Ledingham et al. 2014; Orimo et al. 2007).

In the forthcoming phase of our research, we propose the development of a laser acceleration application facility, which will be equipped with a high-intensity laser system rated at 45 TW (terawatts). The facility is designed to incorporate two distinct laser beam lines, each tailored for specific experimental regimes. Specifically, the single-shot regime is predominantly used for high-resolution x-ray imaging applications, leveraging underdense target materials. Conversely, the multi-shot regime, employed for computed tomography (CT) scans, operates within dedicated acceleration rooms using overdense target materials. The electrons and ions generated within underdense and overdense plasmas, via diverse acceleration mechanisms, serve as the primary sources of ionizing radiation within the 45 TW facility (Esarey et al. 2009; Schreiber et al. 2016). Consequently, a meticulously designed safety protocol is essential to mitigate radiation risks to both scientific personnel and the general populace. In the TW facility, the energy distribution and angular characteristics of the radiation source are highly contingent upon the experimental conditions. For instance, in experiments using underdense targets, the electrons will be accelerated to energies exceeding 100 MeV, leading to the generation of secondary gamma photons and neutrons (Olsovcova et al. 2014). Additionally, the differences in the position, energy, and other characteristics of the accelerated electrons generated by the two laser beamlines during operation result in variations in the key regions that need to be addressed in the radiation shielding design. The intricate and mutable nature of the radiation source terms presents significant challenges in the radiation protection design for the TW facility, thereby complicating the development of effective radiation protection measures.

In this paper, Monte Carlo simulation of electron, photon and neutron transporting has been performed to determine the dose map. Upon conducting a comprehensive analysis of the dose rate levels, an optimized radiation shielding design was developed to mitigate exposure, thereby ensuring the maintenance of both occupational and population annual dose limits within acceptable regulatory thresholds.

MATERIALS AND METHODS

Setup of the TW Facility

The 45 TW laser application facility is a new research infrastructure in the field of laser-plasma acceleration, primarily dedicated to investigating applications in x-ray imaging and CT scanning. The key component of the research facility is an ultrashort pulsed laser system, equipped with two distinct beam lines, capable of generating laser pulses with a maximum energy of 1.5 J at a repetition rate of 10 Hz. The main laser line will be used for CT scan experiments with a multi-shot regime by focusing the 25-fs laser pulses onto the solid targets. The second beam line will be used for x-ray production experiments with a single-shot regime by focusing the 30-fs laser pulse onto the gas targets. The parameters of the laser system are shown in Table 1.

Table 1.

Parameters of the 45 TW laser facility.

Experiment regime	Pulse energy	Pulse duration	Repetition rate	Shot per year	Targets
Multi-shot regime	1.5 J	25 fs	10 Hz	5 × 106	Solid
Single-shot regime	1.5 J	30 fs	< 1 Hz	1 × 104	Gas

The structural layout of the 45 TW laser application facility is depicted in Fig. 1. As shown in Fig. 1, the building is longitudinally subdivided into two sections. The southern compartment is designated as a contamination-controlled environment, specifically tailored for housing the laser system, associated chillers, and power supply units. The overall architectural footprint is designed to fit within a 24 m × 12 m rectangular space with a vertical clearance of 6.3 m. This encompassing space includes both an acceleration area and an experimental control room, demarcated by a pair of labyrinthine walls for enhanced safety and isolation. The acceleration area is purposed for conducting laser acceleration experiments and is equipped with a pair of laser acceleration experimental setups. The laser beam is channeled from the laser system room in the southern section through a dedicated laser aperture into the acceleration area. Upon traversing the compression chamber, the beam is bifurcated into two distinct beam lines, each directed into an x-ray imaging system and a CT scanning experimental setup, respectively. Adjacent to the acceleration area, the control room serves as the central hub for the manipulation of experimental systems and the collection of data, facilitating a comprehensive interface for real-time monitoring and analysis.

Fig. 1.

Structural and laser accelerating system distribution of the 45TW facility.

In the preparatory phase of experimental protocols, personnel are tasked with conducting functional tests on the equipment situated within both the control room and the acceleration chamber. During the execution of CT scanning experiments, operators will retreat to the control room to manipulate the system and to gather experimental data systematically. To optimize the operational continuity of the CT imaging system, it is imperative that staff members are capable of maintaining continuous operation around the system during x-ray imaging experiments. Considering these operational requirements, the CT scanning system is strategically positioned at the center of the accelerating room, with the laser beam aligned along the eastern axis. Concurrently, the x-ray imaging zone is established on the eastern flank, with the laser beam directed towards the northern axis. This configuration is designed to minimize radiation exposure levels within the control room during experimental procedures, while also facilitating the development of shielding structures. These structures are intended to maintain radiation dose levels in the vicinity of the CT imaging system at the lowest feasible levels during x-ray imaging experiments, thereby ensuring both safety and efficiency in the experimental setup.

Radiation sources

Due to the variation in target materials and the differential densities between the two laser beams, the underlying mechanisms governing the laser-material interaction that result in the generation of radiation source terms exhibit distinct characteristics. In the x-ray experiments, the interaction of high-intensity laser pulses with a gas target can produce an underdense plasma. With the Laser Wakefield Acceleration (LWFA) mechanism, the electrons will be accelerated to high energies in short distances and produce a quasi-monoenergetic electron beam, which is the most important source for radioprotection. The energy distribution and yield of accelerated electrons depend on the laser power and target density. The energy gain ∆E of electrons in MeV can be modeled as eqn (1) (Lu et al. 2007):

$$\Delta E~1700{\left(\frac{P}{100}\right)}^{1/3}{\left(\frac{{10}^{18}}{n_t}\right)}^{2/3}{\left(\frac{0.8}{{\lambda }_0}\right)}^{4/3},$$ (1)

where P is the laser power in units of TW, n_t the density of the gas target in cm⁻³, and λ₀ the wavelength of the laser in microns. And the number of accelerated electrons N_e can be expressed as eqn (2) (Lu et al. 2007):

$$N_e~2.5\times {10}^9\frac{{\lambda }_0}{0.8}\sqrt{\frac{P}{100}.}$$ (2)

The laser power for underdense plasma experiments is limited to 5 TW, which constrains the maximum energy and number of accelerated electrons achievable in this regime. As for the target density of 1.5 × 1019 cm⁻³, the number of electrons per shot is about 1 × 10⁹, and the source term mean energy is about 100 MeV. While the value for the gas target density is reduced to 5 × 1018 cm⁻³, the energy of the accelerated electron distribution center will be 230 MeV. The primary constituent of the electron beam traverses in alignment with the laser beam, which exhibits a divergence angle of 5 mra, thereby conforming to the trajectory of the incident laser beam. This configuration is strategically designed to mitigate the photon dose within the confines of the laser system room by channeling the beam through the designated laser aperture. An anticipated maximum regime of 1 × 10⁴ shots a year will be employed for the single-shot configuration.

In the context of CT scan experimentation, the interaction between the laser pre-pulse and a solid target elicits the formation of an overdense plasma. Subsequently, the main ultra-intense laser pulse, impinging proximity to the target surface, facilitates the acceleration of electrons to high energies, which serve as the principal source of ionizing radiation. Empirical evidence and extant scholarly research indicate that the resultant accelerated electrons exhibit a broad energy spectrum, conforming to a Maxwellian distribution (Benlliure et al. 2019). Moreover, their angular distribution can be approximated as Gaussian in nature, with the electron propagation vector aligned with the laser beam axis. The parameters characterizing the accelerated electrons within the overdense plasma, encompassing the electron count, temperature, and angular divergence, are all intrinsically modulated by the laser power density. It has been observed that an elevated laser power density correlates with a higher fraction of laser energy being channeled into the kinetic energy of the electrons. Consequently, this results in an incremented electron temperature and a diminished angular divergence, highlighting the direct influence of laser power density on the electron acceleration dynamics. Based on the ponderomotive model (Wilks 1993), the relationship between the electron temperature T_h and the laser irradiance Iλ² is expressed as eqn (3):

$$T_h=\left[{\left(1+\frac{I{\lambda }^2}{1.4\times {10}^{18}}\right)}^{\frac{1}{2}}-1\right]\times 0.511\text{MeV,}$$ (3)

where I is the laser intensity in W cm⁻² and λ is the laser wavelength in μm.

The total number of accelerated electrons per laser shot, N₀, is calculated using eqn (4):

$$N_{0}T=\eta E_L,$$ (4)

where T = 1.5T_h is the mean electron energy, η is the absorption coefficient and E_L is the initial energy in the incoming laser pulse. According to Benlliure et al. (2019), the absorption coefficient exhibits a clear dependence on laser pulse intensity. Accordingly, the value of η used in this study was selected according to the laser power density and corresponding experimental data reported in Benlliure et al. (2019).

An aluminum target with dimensions of 10 × 10 × 1 μm³ was used in the overdense experiments. The spot size of the normal operation regime has a radius of 5 μm with an energy intensity of about 5.7 × 10¹⁹ W cm⁻², which can accelerate electrons to 2 MeV. In this regime, about 20% of the incident laser energy is converted into electron energy, and the number of acceleration electrons is 6 × 10¹¹ per shot with a divergence of 700 mrad (FWHM of the Gaussian distribution). With the radius being optimized to 2.5 μm, the electron temperature will be up to 5 MeV. At the same time, the number of electrons will be up to 7.5 × 10¹¹ with an absorption coefficient of 60% in aluminum target. The electron angle emission also concentrates in the forward direction of the laser incidence, making the angular divergence go down to 100 mrad, which is in agreement with averaged measured values in earlier experiments (Benlliure et al. 2019).

Beyond electrons, the overdense plasmas also yield other accelerated light ions, including protons. These accelerated protons exhibit an energy spectrum characterized by an exponential-like distribution, culminating in a maximum cutoff energy of 20 MeV. The number of the accelerated proton is 7.5 × 10¹⁰ per shot with a coefficient of 6%, while the proton temperature is 5 MeV. In comparison to the accelerated electrons, the radiological hazard posed by the proton source is insignificant, with its quantity and coefficient being approximately tenfold less than those of photons. An anticipated maximum regime of 5 × 10⁶ shots a year will be employed for the multi-shot configuration with a maximum shot frequency of 10 Hz.

Design of radiation shielding structure

For both x-ray imaging and CT scan experiments, the angle at which the ionizing radiation is emitted by the laser-focused target is dictated by the laser’s directionality. Consequently, the radiation dose is concentrated along the direction of laser incidence, necessitating significantly greater shielding in this region compared to elsewhere. If the radiation protection requirements are met solely by reinforcing the building walls, the thickness of the walls along the laser beam path will significantly increase, consequently reducing the available space within the experimental area. Furthermore, changes in the laser beam direction or the nature of the target experiment could render the existing shielding walls insufficient. To address this challenge, a modular shielding system with adjustable configurations has been designed to ensure compliance with the radiological protection requirements across diverse experimental setups.

The structural walls, roof, and the access labyrinth walls collectively form the primary shielding barrier, delineating the radiation-controlled zone. This barrier is designed to arrest particles emitted in the forward direction relative to the laser incidence, as well as any scattered particles. All walls and roofs will be made of standard concrete with a density is 2.26 g cm⁻³. The concrete elements composition including 23 kinds of elements used in the simulation is measured by a 1 dm³ concrete sample made of cement, coarse aggregate, and fine aggregate in the locality. The wall thickness between the acceleration area and the laser area is 35 cm. In contrast, the surrounding walls of the acceleration area are constructed with an 80 cm thickness. Additionally, the roof is engineered to be 30 cm thick, aiming to mitigate the sky-shine dose rate extern to the facility. Access to the acceleration area is safeguarded by labyrinth walls that exhibit variable thicknesses: those in proximity to the control room measure 80 cm in thickness, whereas those adjacent to the laser system’s clean room are 50 cm thick. Entry of the optical laser pulses into the acceleration area is facilitated through a 20 cm radius aperture formed by a straight hole in two walls that lie between the laser system area and the acceleration zone.

The second barrier consists of two movable lead walls shown in Fig. 1, primarily designed to attenuate particles emitted along the laser incident direction, thereby reducing radiation doses in the personnel activity area and the area outside the facility during the experiment. It is positioned as close to the target as possible to maximize the shielding of the primary particle flux with minimized mass.

Monte Carlo simulations

All radiation protection calculations presented in this study were performed with the Monte Carlo particle transport code JMCT (Li et al. 2013), which is developed by the IAPCM and CAEP-SCNS. It is designed to simulate neutrons, photons, electrons, protons, light radiation, atmosphere, and molecule transport. The nuclear data that JMCT used was from the ENDF/B-VII and CENDL-3.2 evaluation libraries. The cross-section parameters were generated by using the NJOY code. The energy ranges are 10⁻¹¹ MeV ~ 20 MeV for neutrons, 1 keV ~ 100 GeV for photons, and 1 keV ~ 1 GeV for electrons. The simulations in this study were conducted using JMCT Version 2.2.

A detailed geometry model of the 45 TW facility was implemented by JLAMT, a three-dimensional visualization modeling tool based on Siemens NX. A horizontal cross-section of the detailed geometry model is shown in Fig. 1 at 1.2 m height where the two targets are placed. The primary source particles for radiation transport calculations were accelerated electrons generated at the target position, approximated as a point source, with their energy and angular distributions determined by analytical mathematical formulations. In the case of overdense acceleration targets, Maxwellian functions were used to parametrize the energy distribution of electrons. And for underdense targets, calculations were performed for an electron beam of monoenergetic energy. The angular distributions were all parameterized using a Gaussian distribution with different divergences.

The neutron and photon spectrum and fluence have been scored by a three-dimensional visual mesh tally with a voxel size of 30 cm × 30 cm × 30 cm. And to evaluate the dosimetric field generated, the effective dose conversion coefficients (AP) of ICRP NO.74 Publication have been used (ICRP 1997). For each radiation source simulation, over 1 × 10⁸ events were run to keep all the statistical uncertainties below 10%.

Radiation limits

The annual dose serves as the fundamental standard for radiation protection design at the 45 TW facility. From a radiation protection perspective, the facility is categorized into three areas, as illustrated in Fig. 2: the controlled area, the supervised area, and the unclassified area.

Fig. 2.

Zoning of the 45TW facility.

The external area surrounding the facility is consistently designated as an unclassified area, regardless of the experimental conditions. In this area, public access is permitted during laser operation without the need for protective measures. To ensure compliance with radiation safety standards, the annual radiation dose in this area must remain below 0.2 mSv y⁻¹ to meet the requirement of 0.1 mSv y⁻¹ limitation for public, assuming an occupancy factor of 0.5.

The supervised area is a zone where professional personnel can enter to perform operations, maintenance, and other tasks without wearing additional protective measures during the experimental process. The annual dose in these areas should be below 3 mSv y⁻¹ according to the regulation rule in the institute. The control room and laser area are categorized as supervised areas because personnel need to enter for operation and maintenance during the experimental process.

The acceleration area is categorized as controlled area. Based on the operational regimes of the laser beam lines, the control measures for the entry of different parts varied. The x-ray imaging experimental area is a prohibited entry area, where entry is strictly prohibited for all personnel during all experiments. The CT scanning experimental area is a restricted entry area; personnel are only allowed to enter during underdense plasma experiments, to accommodate the frequent operational and maintenance needs of the CT scanning system. The annual dose in CT scanning experimental area should be below 3 mSv y⁻¹.

RESULTS

Single-shot regime

For the strong dependence of the energy and number of accelerated electrons with the target density of underdense targets, two cases have been used for the design of the radiation shielding installed at the facility; with different target densities, the electron source defined of 100 MeV and 230 MeV mean energy and 1 × 10⁹ electrons per shot. Besides the electrons and photons, the neutrons produced by (γ, n) reactions by the photons above 8 MeV were also included. The prompt annual dose distribution for the single-shot regime is shown in Fig. 3, Fig. 4, and Fig. 5.

Fig. 3.

Photon dose distribution in the single-shot regime at an electron energy of (a) 100 MeV and (b) 230 MeV.

Fig. 4.

Electron dose distribution in the single-shot regime at an electron energy of (a) 100 MeV and (b) 230 MeV.

Fig. 5.

Neutron dose distribution in the single-shot regime at an electron energy of (a) 100 MeV and (b) 230 MeV.

As expected, the prompt dose generated by photon concentrates in the forward direction concerning the laser incidence, which is above 700 mSv y⁻¹ at a distance of 30 cm from the underdense target and about 3.74 mSv y⁻¹ outside the facility without movable lead walls for the 100 MeV electron source. After incorporating a mobile lead wall with a maximum thickness of 6 cm, the photon dose in the unclassified areas was reduced to 0.17 mSv y⁻¹, with the contribution predominantly from photons. If the electron energy increases to 230 MeV, the annual photon dose would exceed 0.28 mSv y⁻¹. Assuming an occupancy factor of 0.5, the resulting public dose in this area would be 0.14 mSv y⁻¹, which exceeds the radiation management limit of 0.1 mSv y⁻¹. However, since this area is a roadway where the public does not remain for extended periods, the dose level would still fall within acceptable limits if the occupancy factor is reasonably reduced to one-third or lower. In a perpendicular direction to the acceleration zones, the radiation dose remains below 50 μSv y⁻¹, even when accounting for the presence of a 230 MeV monoenergetic electron source. Furthermore, due to the reduced backward emission from the electron source, the radiation dose passing through the laser hole in the wall is below 1 μSv y⁻¹.

The electron dose contribution is primarily confined to the x-ray imaging experimental area and the adjacent unclassified area to its north. With 6 cm of lead shielding, the maximum electron dose in the northern unclassified area reaches approximately 0.03 mSv y⁻¹, accounting for 15% of the total dose, at an electron source energy of 100 MeV. As the electron energy increases to 230 MeV, the dose in this area rises to approximately 0.08 mSv y⁻¹, representing about 20% of the total dose.

Compared to photons and electrons, the neutron dose contribution in the unclassified area north of the x-ray imaging experimental region is less than 1% and can therefore be considered negligible. In contrast, in the CT scanning experimental area, the radiation dose is predominantly attributed to neutrons. In the vicinity of the CT scanning experimental system, for a 100 MeV electron source, the total radiation dose is approximately 170 μSv y⁻¹ after penetrating a lead wall with a maximum thickness of 14 cm with both electron and photon dose levels remaining below 3 μSv y⁻¹. As the electron energy increases to 230 MeV, the total radiation dose at the same location rises to approximately 470 μSv y⁻¹, while both electron and photon dose levels remain below 8 μSv y⁻¹. This indicates that the design of the movable wall offers substantial shielding capacity for photons, ensuring that the radiation dose within the CT scan area is confined to levels equivalent to those in supervised areas under single-shot operational conditions. In addition, neutrons resulting from (γ, n) reactions emerge as a significant radiation hazard in the vicinity of the CT scanning experimental system during underdense plasma experiments. Should the single-shot regime be operated at a higher frequency, additional layers of polyethylene would be necessary to block secondary neutrons effectively.

Multi-shot regime

Using the source terms outlined in preceding sections, this study employs two distinct scenarios as the radiation sources for multi-shot regime calculations. The first scenario involves a lower-energy electron source characterized by T = 2 MeV and a divergence of 700 mrad, while the second scenario consists of a higher-energy electron source with T = 5 MeV and a divergence of 100 mrad. These two cases are used to assess the efficacy of radiation shielding. When the average energy of the accelerated electrons is significantly lower than that of electrons originating from underdense plasmas, the resulting neutron dose is approximately three orders of magnitude less than the photon dose, rendering it negligible.

The annual dose distribution of the multi-shot regime is shown in Fig. 6. In this context, photons serve as the principal source of radiation, with the maximum dose rate recorded near the vacuum chamber reaching 3.53 Sv y⁻¹, corresponding to an electron temperature of 2 MeV. When accounting for the angular distribution, it is observed that the dose levels across all regions escalate as the electron temperature increases to 5 MeV. Specifically, the dose rate at the entrance to the labyrinth of the control room and the laser system room stands at 2.83 mSv y⁻¹. This figure represents approximately 90% of the supervised area’s annual dose limit. Moreover, when the laser system operates continuously at a 10 Hz repetition rate, the dose rate can reach as high as 20.3 μSv h⁻¹, exceeding the established limit of 1.5 μSv h⁻¹. This higher rate threatens to surpass the acceptable accumulated dose of 3 mSv y⁻¹, based on a 2,000-h annual occupancy, thus restricting facility staff from engaging in additional radioactive work activities.

Fig. 6.

Photon dose distribution in the multi-shot regime at an electron temperature of (a) 2 MeV and (b) 5 MeV.

The maximum annual dose outside the facility exceeds 609 mSv y⁻¹ in the direction of the radiation source when no mobile wall shielding is in place. In all other directions, the dose levels outside the facility remain below 0.19 mSv y⁻¹ for both radiation sources. Specifically, at the northern section, the facility’s exterior dosage can rise above 1 mSv y⁻¹ when the electron temperature reaches 5 MeV. This indicates that the primary shielding barrier of the building’s structure possesses sufficient shielding efficacy against scattered particles and those not emitted from the primary direction of the source, considering experimental conditions of fewer than 3 × 10⁵ shots per year at an electron temperature of 5 MeV. The installation of a lead wall with a maximum thickness of 14 cm between the two acceleration rooms will reduce the dose level outside the facility to 0.19 mSv y⁻¹. Furthermore, approximately 70 m² of the roof area exhibit dose levels surpassing 3 mSv y⁻¹, with a peak dose exceeding 46 mSv y⁻¹, necessitating the designation of this roof section as an exclusion zone. The sky-shine dose contribution at the ground level has been assessed and found to be less than 0.02 mSv y⁻¹, which is considered negligible.

Total dose and discussion

Based on the energy of accelerated electrons generated in the experiment, two cases were considered in this section’s calculations:

1. In case 1, the electron temperature in overdense plasma experiments and the electron energy in underdense plasma experiments is 2 MeV and 100 MeV, respectively. These values correspond to the current experimental capabilities of the facility.

2. In case 2, the electron temperature in overdense plasma experiments and the electron energy in underdense plasma experiments is considered to be 5 MeV and 230 MeV, respectively. These values exceed the facility’s current capabilities but represent potential future experimental parameters.

The electron source parameters for the two cases are summarized in Table 2. The total annual doses for both cases at the critical location were calculated considering an experimental frequency of 5 × 10⁶ shots per year for overdense plasma experiments and 1 × 10⁴ shots per year for underdense plasma experiments.

Table 2.

Electron source parameters for case 1 and case 2.

	Single-shot regime (underdense experiments)		Multi-shot regime (overdense experiments)
Case	Electron energy	Electrons per shot	Electron temperature	Electrons per shot
Case 1	100 MeV	1× 109	2 MeV	6 × 1011
Case 2	230 MeV	1× 109	5 MeV	7.5 × 1011

The annual dose calculation results are presented in Table 3 for case 1. It is observed that under the operating mode of case 1, the maximum annual doses in the control room and laser room are 0.27 mSv y⁻¹ and 0.37 mSv y⁻¹, respectively, which are well below the management target of 3 mSv y⁻¹. In the case where only underdense plasma experiments are conducted, the highest annual dose level in the CT scanning area is 0.17 mSv y⁻¹, also below the management target of 3 mSv y⁻¹. For the four publicly accessible areas outside the 45 TW facility, the maximum annual dose is 0.20 mSv y⁻¹, which does not exceed the radiation management target of 0.1 mSv y⁻¹, assuming an occupancy factor of 0.5. Therefore, under the currently achievable operating parameters of the facility, the radiation shielding design provides sufficient protective performance and meets the management target values for all designated areas.

Table 3.

Annual dose calculations of critical locations in the 45 TW facility for case 1.

	Max annual dose (mSv y−1)
	overdense plasma experiments			underdense plasma experiments			Total dose
Area	n	P	e	n	P	e	n	P	e	Total
Control room	<0.01	0.27	—	<0.01	<0.01	<0.01	<0.01	0.27	<0.01	0.27
Laser area	<0.01	0.37	—	<0.01	<0.01	<0.01	<0.01	0.37	<0.01	0.37
CT scanning area (only under-dense plasma experiments)	—	—	—	0.17	<0.01	<0.01	0.17	<0.01	<0.01	0.17
To the north of the under-dense target, outside the facility	<0.01	<0.01	—	<0.01	0.17	0.03	<0.01	0.17	0.03	0.20
To the north of the over-dense target, outside the facility	<0.01	0.19	—	<0.01	<0.01	<0.01	<0.01	0.19	<0.01	0.19
To the east of the facility	<0.01	0.01	—	<0.01	<0.01	<0.01	<0.01	0.01	<0.01	0.01
To the west of the facility	<0.01	<0.01	—	<0.01	<0.01	<0.01	<0.01	<0.01	<0.01	<0.01

The annual dose calculation results are presented in Table 4 for case 2. It is observed that under the operating mode of case 2, the maximum annual doses in the control room and laser room are 2.85 mSv y⁻¹ and 2.61 mSv y⁻¹, respectively, which are still below the management target of 3 mSv y⁻¹. In the case where only underdense plasma experiments are conducted, the highest annual dose level in the CT scanning area is 0.47 mSv y⁻¹, also below the management target of 3 mSv y⁻¹. The maximum dose to the east of the facility is 0.19 mSv y⁻¹, which is below the design target of 0.2 mSv y⁻¹. The dose level in the westward direction of the facility is negligible. To the north of the facility, near the overdense target, the maximum dose reaches 1.86 mSv y⁻¹, significantly exceeding the design target of 0.2 mSv y⁻¹. The dose in this area primarily originates from scattered photons generated during overdense plasma experiments that are not shielded by the lead wall. Therefore, if the facility operates at the higher parameters of case 2 in the future, measures such as limiting the frequency of overdense plasma experiments and implementing additional lead shielding structures will be necessary to reduce the dose and ensure the ionizing radiation safety of the public.

Table 4.

Annual dose calculations of critical locations in the 45 TW facility for case 2.

	Max annual dose (mSv y−1)
	overdense plasma experiments			underdense plasma experiments			Total dose
Area	n	P	e	n	P	e	n	P	e	Total
Control room	<0.01	2.83	—	0.02	<0.01	<0.01	0.02	2.83	<0.01	2.85
Laser area	<0.01	2.59	—	0.02	<0.01	<0.01	0.02	2.59	<0.01	2.61
CT scanning area (only under-dense plasma experiments)	—	—	—	0.47	<0.01	<0.01	0.47	<0.01	<0.01	0.47
To the north of the under-dense target, outside the facility	<0.01	0.03	—	0.03	0.28	0.08	0.03	0.31	0.08	0.41
To the north of the overdense target, outside the facility	<0.01	1.86	—	<0.01	<0.01	<0.01	<0.01	1.86	<0.01	1.86
To the east of the facility	<0.01	0.19	—	<0.01	<0.01	<0.01	<0.01	0.19	<0.01	0.19
To the west of the facility	<0.01	<0.01	—	<0.01	<0.01	<0.01	<0.01	<0.01	<0.01	<0.01

Overall, since the annual number of overdense plasma experiments is 500 times that of underdense plasma experiments, the annual dose in most areas outside the facility is primarily contributed by overdense plasma experiments, with x-ray photons being the dominant source. In contrast, the dose in the CT area mainly originates from secondary neutrons generated during underdense plasma experiments. If the operation frequency of underdense plasma experiments increases in the future, the movable wall should be optimized to add materials such as polyethylene to enhance the shielding performance and reduce the neutron-contributed occupational dose levels in the CT experimental area.

CONCLUSION

The Monte Carlo simulations program JMCT has been used to design the radiation shielding structure of the 45 TW facility operated at different experimental conditions. By accurately modeling the electron source terms from both overdense and underdense plasmas, we have characterized the principal radiation contributions and their directional dependencies. The simulation results indicate that for overdense plasma electrons, the forward-directed photon-induced dose is predominant, warranting the addition of a local shielding structure, especially when electron temperatures exceed 5 MeV. Conversely, for electrons from underdense plasmas, the neutrons resulting from (γ, n) reactions emerge as a significant radiation hazard, necessitating potential redesigns of the shielding in response to increased operational times in this regime. While light ions were not included in the calculations post-radiation source simulation, the designed shielding barriers incorporating mobile lead walls, concrete walls, and the facility roof offer robust protection for the control room, laser system clean room, and surrounding areas. Importantly, our calculations confirm that the radiation shielding design for the 45 TW facility maintains the dose level within the working areas below the threshold of 3 mSv y⁻¹, ensuring the safety of personnel in and around the facility during both single-shot and multi-shot acceleration operations. This comprehensive radiation shielding design thus not only meets the safety standards required for high-power laser facilities but also paves the way for the safe execution of future experiments at the 45 TW facility.

Acknowledgments

This work was supported by Institute of Nuclear Physics and Chemistry, China Academy of Engineering Physics.