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Literature Review

Supports: Paper 1 Research Plan

Related evidence: Systematic Evidence Review · Annotated Bibliography

Executive summary

This review assesses the published basis for using a machine-learning surrogate to reduce the computation time required for PHITS shielding calculations for 5–7.5 MeV industrial X-ray LINAC facilities.

The literature establishes the relevant source and shielding physics. Published studies cover converter design, bremsstrahlung spectra and angular distributions, concrete attenuation, facility shielding, maze scattering, photonuclear reactions, and PHITS benchmark calculations [3–5,29–37,40,41]. Other studies establish machine-learning surrogates for neutron shielding, photon shielding, and spatial radiation fields [18–26,38,39]. No study located in this review combines a conventional industrial LINAC, electron-to-bremsstrahlung conversion, 5–7.5 MeV facility shielding, PHITS reference calculations, and prediction for complete shielding configurations excluded from the training data.

The proposed contribution is therefore a surrogate model applicable to one predefined industrial radiation-processing source archetype and a specified range of electron energies, shielding configurations, and calculation locations. Following the owner's 2026-09-10 representativeness amendment, the production source is a broad planar converter illuminated by a declared one-dimensional scanned-beam distribution. The earlier compact circular Petwal model remains a component benchmark, not the production archetype. PHITS remains the reference method for confirmation of final shielding designs and for professional shielding assessment.

IAEA SSG-8 states that neutron generation and propagation should be considered for X-ray irradiation facilities operating at 5 MeV and above [1]. The study must therefore calculate photon and neutron contributions separately or demonstrate, for the selected converter and shielding configurations, that the neutron contribution is below a specified reporting level. This conclusion cannot be based on nominal electron energy alone. A PHITS–MCNP6–TRIPOLI-4 benchmark found that photoneutron results depend on transport code, nuclear data, target material, energy, and scored quantity [37].

Scope of review and terminology

The title contains four technical commitments that should remain explicit throughout the paper.

Incident-electron energy

An industrial converted-X-ray source does not emit monoenergetic 5 MeV or 7.5 MeV photons. Electrons with those incident energies strike a converter and produce a continuous bremsstrahlung spectrum extending from low energies to an endpoint no greater than the electron energy. Converter self-absorption, backing and cooling layers, residual-electron absorption, beam footprint, and emission angle reshape that spectrum before it reaches the product or shield [3,4].

If the paper claims the full interval from 5 to 7.5 MeV, endpoint simulations alone are insufficient. Training and evaluation must contain justified intermediate energies, including at least one energy withheld as a complete test condition. Otherwise the accurate title would describe a comparison at 5 and 7.5 MeV rather than prediction from 5 to 7.5 MeV.

Converted-X-ray mode

The paper concerns electrons deliberately incident on a converter to create a useful photon field. It does not concern direct-electron-beam irradiation with incidental bremsstrahlung. The distinction matters because SSG-8 treats the converter as a known, predictable source of more intense X-rays; consequently, the forward primary barrier and the secondary barriers and maze paths require stronger attention than in direct-electron-beam operation [1]. Direct-electron-beam literature may support transport checks, but it is outside the paper’s prediction range.

Dose quantity

Absorbed dose in product, air kerma, effective dose, ambient dose equivalent, and ambient dose are not interchangeable. Peri and Orion reported photon absorbed dose/kerma under their stated charged-particle-equilibrium approximation [3]. Radiation-protection surveys and facility decisions commonly use operational quantities. ICRU Report 95 defines the newer ambient dose quantity, (H^), while many instruments and current regulatory systems still use ambient dose equivalent, (H^(10)) [17].

The paper must specify the predicted quantity, units, conversion coefficients, particle contributions, and normalization. Until the quantity is selected, “shielding dose” is the appropriate general term for this review. Product absorbed dose remains outside the scope.

IAEA guidance does not replace national regulatory requirements. For a facility in Malaysia, the Atomic Energy Licensing Act, applicable radiation-protection regulations, licence conditions, and current Department of Atomic Energy requirements remain controlling [27].

Computation time

Rapid prediction is meaningful only by comparison with the PHITS reference calculation. The paper should report PHITS computation time, hardware, number of histories, statistical uncertainties, variance-reduction methods, surrogate inference time, data-processing time, and speedup. Training-data generation time should be reported separately from inference time.

Literature search method

This narrative literature review was last updated on 2026-09-03. The companion Systematic Evidence Review contains the prospective protocol, search log, screening records, quality assessment, and accessible-source scope decision. The project owner approved that evidence-supported boundary as D1 on 2026-09-04. Unavailable institutional searches and unresolved full text remain reported coverage limitations, not evidence of zero relevant studies.

Industrial X-ray irradiation

Converted X-rays provide greater penetration than direct electrons and can treat thicker or denser products. The tradeoff is poorer electrical-to-photon conversion efficiency and a more demanding shielding problem. Petwal et al. described a 10 kW facility at the Raja Ramanna Centre for Advanced Technology (RRCAT) intended to operate at 10 MeV in electron mode and at 5 MeV or 7.5 MeV in X-ray mode for food processing and medical-product sterilization [4]. Zimek’s economic assessment likewise treats high-intensity X-ray processing as an industrial technology whose feasibility depends on throughput, conversion efficiency, facility cost, and utilization [7].

The 5–7.5 MeV interval also has a specific historical processing context. A 2004 United States Food and Drug Administration (FDA) rule permitted machine-generated X-rays up to 7.5 MeV for specified food uses when tantalum or gold is used as the target material [6]. That decision helped motivate engineering comparisons between 5 MeV and 7.5 MeV facilities. It is not a universal accelerator-energy authorization, a Malaysian shielding requirement, or evidence that all target materials have equivalent activation behaviour.

The original FAO/IAEA/WHO consultation that motivated the 7.5 MeV option is more informative than the regulatory endpoint alone [29]. It compared 5 MeV and 7.5 MeV X-ray processing, estimated overall electron-power utilization of roughly 4% and 8%, respectively, and discussed converter-specific photonuclear thresholds. Its conclusion that food processing up to 7.5 MeV could avoid significant induced activity was conditional on converter design and energy control. It was an application and activation assessment, not a general personnel-shielding calculation, so its statement that only a few additional centimetres of concrete might be needed cannot be transferred to a new facility.

The broader source literature is also deeper than a single converter study. Seltzer, Farrell and Silverman established the high-power electron-accelerator bremsstrahlung framework for radiation processing [30]. Meissner et al. evaluated X-ray treatment at 5 MeV and above [31], and Cleland and Stichelbaut later reviewed the source characteristics, penetration, facility implications, and industrial applications of high-energy X-rays [32]. Some of that evidence comes from Rhodotron systems and therefore supports the physical and industrial context but not the Paper 1 LINAC applicability claim.

Commercial maturity and adoption

The literature supports industrial X-ray irradiation as a commercially established but still emerging modality; it does not support calling it the most common industrial irradiation device. A 2021 National Academies assessment reported that X-ray systems were commercially available but accounted for less than 1% of medical-device sterilization volume at that time, behind cobalt-60 gamma irradiation and direct electron beam [28]. It identified an operating 700 kW accelerator-driven X-ray facility in Däniken and announced investments in additional X-ray facilities, including one in Malaysia. The same assessment expected several more X-ray irradiators but not a complete transition away from established modalities [28].

The industrial justification is therefore based on capability and growth rather than present prevalence. High-energy X-rays offer penetration comparable to gamma rays, allowing dense products and complete pallets to be processed, while accelerator sources provide electrical on/off control and avoid a large continuously radioactive cobalt-60 inventory [28]. Direct-electron-beam irradiation provides higher efficiency and dose rate but lower penetration. X-ray adoption has been constrained by inefficient electron-to-photon conversion and the need for dependable high-power accelerators; improvements in accelerator power and pressure to diversify beyond cobalt-60 have increased commercial interest [28].

The evidence does not establish that conventional LINACs dominate industrial X-ray processing; commercial systems also include recirculating accelerators such as the Rhodotron [28]. Paper 1 is limited to conventional LINACs so that the accelerator architecture and beam-delivery conditions remain consistent in the initial simulation dataset. Results must not be generalized to other accelerator types without separate verification and validation.

Industrial source conditions differ from medical megavoltage X-ray systems. Peri and Orion emphasized that industrial accelerators operate at much higher dose rates and often lack the heavily shielded, tightly collimated treatment head used in radiotherapy [3]. Radiation may therefore be important over a broad angular range rather than only in a forward treatment field. They concluded that medical primary- and secondary-barrier data cannot simply be transferred to industrial facilities because source energies, target construction, collimation, workload, and angular emission differ.

The computational scale is severe. The IAEA modelling guide describes process-chamber dose rates of several kilogray per second and required attenuation of roughly ten to twelve orders of magnitude between the irradiation region and accessible areas [2]. Deep penetration creates the central runtime problem: an unbiased Monte Carlo calculation spends most histories far from the exterior tally, while the few histories reaching it control the estimate. Increasing histories reduces statistical uncertainty only in proportion to approximately (1/\sqrt{N}), so halving uncertainty requires about four times as many histories [2]. Repeated calculations across energies, barrier dimensions, materials, and source positions therefore provide a legitimate target for surrogate acceleration.

Bremsstrahlung converter and source characteristics

Converter material and construction

Bremsstrahlung yield rises with incident-electron energy and target atomic number, but useful industrial converter design is not a single-material slab problem. It must balance photon yield, forward transmission, self-absorption, residual electrons, heat deposition, cooling, mechanical construction, activation, and maintainability.

Petwal et al. studied a cylindrical composite converter containing tantalum, cooling water, and stainless steel [4]. Their MCNP model varied tantalum thickness for 5 MeV and 7.5 MeV electrons and examined the transmitted field in a water phantom. For their optimized designs, they reported useful transmitted energy fractions of 9.3% at 5 MeV and 14.2% at 7.5 MeV, with mean photon energies reported as approximately 0.84 MeV and 1.2 MeV. Their paper contains a minor inconsistency between 1.14 and 1.24 MeV for the latter value, so only the approximate value should be reused. The result is specific to their beam and converter construction, not a universal conversion coefficient.

Converter behaviour has also been checked with measurements outside the tantalum design used by Petwal et al. Tuan and Tao compared MCNP-4C2 calculations with film-dosimeter measurements for a titanium–water–lead converter at 5, 7.5, and 10 MeV [35]. Their reported conversion efficiencies differed materially from the Petwal tantalum assembly. Together, the studies show that converter material, cooling structure, backing, optimization criterion, and measurement definition must be included in the source specification.

Peri and Orion considered iron, aluminium, gold, tantalum, and tungsten for angular dose calculations and gold, tantalum, and tungsten for spectral calculations [3]. Tantalum and tungsten produced similar results under several examined conditions because of their nearby atomic numbers, while gold gave only a modest backward-angle increase. This does not make converter material irrelevant. Target thickness, density, radial extent, cooling and backing layers, finite-edge leakage, and photonuclear thresholds remain part of the source definition.

The initial study should use one verified converter design. If converter material or layer dimensions are predictor variables, the training and test data must sample them as independent physical parameters. Results for different converter designs must not be treated as interchangeable.

Photon spectrum and angular distribution

The source field is strongly anisotropic. Peri and Orion divided the full angular range from 0° to 180° and calculated dose rate at one metre, bremsstrahlung spectra at selected angles, and attenuation through concrete [3]. Forward spectra were harder and more intense than backward spectra. They reported forward-to-backward dose-rate differences approaching two orders of magnitude and increasingly large spectral differences at high photon energies.

The change from 5 MeV to 7.5 MeV is therefore not a scalar multiplication. For the tantalum, tungsten, and gold cases studied, the 7.5 MeV dose rate was about 2.6 times the 5 MeV value in the forward direction and about 1.5 times the value in the backward direction [3]. The harder 7.5 MeV field was also attenuated less effectively by thick concrete. Energy, direction, and shielding thickness interact.

These results support a surrogate that includes incident-electron energy and geometry among its predictor variables. A single photon spectrum cannot be scaled by beam power and applied at every direction and energy. A PHITS calculation may record a converter phase-space source for reuse in facility transport, but the phase-space data must preserve the verified energy, position, direction, particle type, and normalization. A coupled source-to-shield calculation remains the reference model.

Beam power and normalization

Radiation transport is linear in source strength while the material state and geometry remain unchanged. The reference calculation should therefore retain a result per primary electron launched at the D3 source plane and apply beam current, duty factor, workload, and time and distance units through documented normalization. The surrogate does not need to learn the linear dependence on beam current.

D3 historically fixed the compact computational source as a declared monoenergetic 5–7.5 MeV electron, centred normally on a fixed finite tantalum-water-stainless converter with a published Gaussian footprint. The 2026-09-10 D3/D5 amendment instead requires a broad plate and a verified normalized scan-position distribution. A future validation machine requires comparison with its measured energy and spatial distributions.

The revised source representation has methodological precedent, but the level of equivalence must be stated precisely. Ziaie and Tahami used EGS4 for an industrial Rhodotron with a 100 cm scanned electron beam and a layered tantalum-water-stainless converter; their dynamic calculation integrated stationary spatial dose distributions [42]. Ma et al. represented a scanned electron accelerator using spatial and multiple-source Monte Carlo beam models and reported close agreement with full phase-space dose calculations [43]. In Paper 1, RAMAL-EBX applies the same linear-superposition principle through PHITS's native weighted multi-source facility [8]: translated s-type = 13 Gaussian sources approximate the normalized time-integrated scan density. This is not evidence that either cited study used PHITS or our exact quadrature. Consequently, normalization, scan-node convergence, and converter-edge effects must be demonstrated before D5 acceptance.

Shielding of industrial X-ray facilities

Primary and secondary barriers

For X-ray irradiation facilities, SSG-8 states that the primary barrier directly in front of the beam should be substantially greater than for an electron-only facility and that scattered X-rays strengthen secondary-barrier and maze requirements [1]. Concrete is generally preferred for these high-energy irradiation rooms for economic reasons and to limit activation concerns. Penetrations for personnel, products, ventilation, services, and conveyors must avoid direct leakage paths and may require mazes, plugs, curved paths, or local shielding.

Peri and Orion provide the closest published numerical comparator for the proposed energy range [3]. They transported the source through spherical ordinary-concrete shields from 10 to 180 cm thick at selected emission angles. Above 80 cm, they used geometry splitting to improve statistics. They found that concrete attenuated the 5 MeV field more effectively than the 7.5 MeV field, with differences approaching an order of magnitude for thick shields. Backward radiation was softer and more readily attenuated than forward radiation.

Their worked upgrade example is useful but must remain an example: for a 120 cm concrete shield evaluated at 90°, their model predicted roughly a sixfold dose-rate increase when changing from 5 to 7.5 MeV, or about 22 cm of additional concrete to recover the previous result [3]. That number depends on their tantalum target, source geometry, concrete, angle, beam conditions, and quantity. It is not a generally safe wall increment.

Barkova, Kiselev and Chudaev provide an earlier facility-scale check at 5 MeV [33]. For pre-commissioning of the ILU-10 radio-frequency accelerator, they combined Monte Carlo angle–energy source calculations with analytical concrete attenuation and evaluated control points outside an existing shield. They found the aluminium-dump configuration acceptable under their operating assumptions, but warned that replacing it with a tantalum or tungsten target could raise radiation levels by roughly 50–100 without additional shielding or operating restrictions. The numerical factor is installation-specific; the general result is that intentional high-(Z) conversion changes the source term enough that shielding designed for direct-electron-beam operation cannot be assumed adequate.

Cleland, Galloway and Brown address X-ray scattering through industrial-irradiator mazes and openings [34]. Their method follows energy and dose-rate reduction over successive wall scatterings. It provides an independent calculation for a fixed maze, but it does not replace full transport calculations when reflection areas, opening dimensions, penetrations, or source orientation vary. Paper 1 must either model a specified range of opening configurations or limit the initial study to closed-room barrier calculations.

Facility geometry and as-built concrete

The Peri–Orion geometry isolates source angle and spherical-shield attenuation. Real facilities add floor and roof boundaries, corners, finite wall extent, doors, mazes, conveyor openings, ducts, penetrations, beam stops, product and equipment scattering, and external evaluation volumes. A rapid predictor trained only on slabs or concentric shields can claim barrier attenuation, not arbitrary facility prediction.

The RRCAT facility work provides a complementary engineering example [5]. Its 10 kW accelerator was designed for photon operation at 5 MeV and 7.5 MeV, and its shielding study addressed dose in accessible areas around an irradiation vault. The project cast concrete test blocks up to 3.25 m thick and assessed radiological and mechanical properties. The authors stressed that site-specific construction variables can make actual concrete properties differ from design assumptions. A surrogate can reproduce PHITS results accurately while both remain incorrect for an as-built wall whose composition, density, reinforcement, voids, or joints were modelled incorrectly.

The initial simulation dataset therefore requires a specified range of shielding geometries. It may begin with closed rooms and vary barrier dimensions, source location, and calculation locations. Openings dominated by radiation streaming must either be represented explicitly in the training and test data or excluded from the range of applicability.

Dose quantity, particle contributions, and statistical reporting

PHITS should retain energy-dependent fluence and separate photon and neutron contributions to the selected dose quantity. This allows the conversion coefficients and particle contributions to be assessed independently.

Deep-shield tallies can have high relative statistical uncertainties or no contributing histories. A tally with no scored events is not a zero-dose result. The training data must retain statistical uncertainties and identify unresolved tallies rather than replace them with zeros. Relative error is unstable near zero, so evaluation should also include absolute error in the selected units and separate analysis of the largest dose underestimations.

Photoneutron production and activation

SSG-8 states that neutron generation in the X-ray target and neutron propagation should be considered for X-ray irradiation facilities at 5 MeV and above; the neutron source can influence shield and maze design even if product activation is not significant [1]. It also states that neutron monitoring may be required above 5 MeV [1].

The practical magnitude is target-dependent. Petwal et al. noted photonuclear thresholds near this range for tantalum isotopes and discussed activation products for 7.5 MeV operation [4]. The 2004 FDA authorization limited its 7.5 MeV provision to tantalum or gold partly because target material affects induced activity and neutron production [6]. These application-specific findings do not justify deleting neutrons from a general industrial shielding model.

The 1995 FAO/IAEA/WHO consultation gives the isotope-level reason that a nominal 7.5 MeV limit is not equivalent to a universal zero-neutron assumption [29]. It reported low photonuclear thresholds for some tungsten isotopes, a very low-abundance tantalum isotope near 6.6 MeV, the dominant tantalum isotope near 7.6 MeV, and gold near 8.1 MeV. Yield depends on isotopic abundance, the true electron-energy distribution, the bremsstrahlung tail, and the complete converter assembly. Endpoint calibration and energy spread therefore belong in the source evidence.

Grégoire et al. supplied theoretical and experimental evidence for food irradiated using approximately 7.3–7.5 MeV X-rays from a tantalum converter [36]. Measured induced activities were low relative to natural food radioactivity under their conditions. This supports the processing-safety history behind 7.5 MeV; it does not prove that prompt neutron dose in shielding, a maze, or a maintenance location is negligible.

Sari's 2023 critical review documents the broader difficulty of characterizing photoneutron fluxes from 4–20 MeV electron accelerators with Monte Carlo codes [40]. The subsequent Sari et al. benchmark directly compared PHITS, MCNP6, and TRIPOLI-4 for electron-accelerator cases across that range; its tantalum and tungsten electron-target cases covered 7–20 MeV [37]. Differences from a few percent to more than a factor of three depended on code, evaluated data or reaction model, target, energy, and observable.

Garnaud et al. expanded the nuclear-data comparison in 2026 by comparing the same three codes with ENDF/B-VIII.1 and JENDL-5 for monoenergetic photon-induced neutron production in 49 elemental targets from threshold to 30 MeV [41]. That compendium isolates photonuclear data and model behaviour rather than the upstream electron-to-bremsstrahlung calculation. Together, these studies require Paper 1 to specify the photonuclear data library and reaction model, perform sensitivity calculations, and verify neutron results before using them as training data.

D6 selects JENDL-5 as the conditional photonuclear reference and compares ENDF/B-VIII.1 and PHITS built-in models. This is a study-design choice, not a claim of universally superior data. Installation, isotope coverage, and component verification remain prerequisites.

Photon and neutron contributions remain separately reportable throughout the interval, and neutron dose is retained in the D2 combined target without a small-fraction omission rule. Neutron spectra, moderation, and capture photons require separate statistical assessment. Unscored neutrons are not zero; poor convergence cannot justify replacing the combined target with photons only.

Activation and post-shutdown dose are related but distinct quantities. The present study covers prompt radiation during operation, not radionuclide inventories or dose after shutdown.

Existing shielding calculation methods

Analytical and empirical methods

Inverse-square scaling, attenuation coefficients, tenth-value layers, buildup factors, source-term tables, and empirical barrier formulae remain useful for preliminary estimates and independent checks. Their advantages are speed and transparency. Their weakness is restricted applicability: the IAEA modelling guide warns that empirical results may fail when extrapolated beyond the geometry and conditions in which they were verified [2].

For the proposed study, simple calculations remain essential reference methods. A machine-learning model has little research value if interpolation, a fitted attenuation curve, or a conventional regression model provides equal accuracy over the same variables.

Deterministic and point-kernel methods

Deterministic solvers and point-kernel methods can be much faster than general Monte Carlo and are established alternatives for shielding analysis. The recent POKER-X system combines a graphics processing unit (GPU) point-kernel calculation with a machine-learning prediction of the transmitted photon spectrum [21]. Its reported dose-rate differences from Monte Carlo references were approximately 16–30%, with more than 200× speedup over the authors’ central processing unit (CPU) implementation.

POKER-X uses an incident photon field, whereas Paper 1 includes electron-to-bremsstrahlung conversion and industrial 5–7.5 MeV shielding in its PHITS reference calculations. Paper 1 should not claim that rapid machine-learning-assisted photon shielding is unprecedented. A point-kernel or attenuation model should be included as a reference method where applicable.

Monte Carlo reference calculations

Monte Carlo transport handles coupled electron, photon, and neutron physics in complex materials and geometries without reducing the field to one attenuation law. Peri and Orion used MCNP; other relevant industrial and shielding work uses EGS, Geant4, and PHITS [2,3,8–13]. Monte Carlo is therefore the appropriate reference method, but a code name alone does not establish correctness.

The IAEA identifies four broad uncertainty sources: geometry input, the simulation engine and settings, the physics model and cross-sections, and downstream data handling [2]. Statistical uncertainty is only one component. A low tally error cannot reveal an incorrect converter thickness, wrong material density, omitted penetration, inappropriate photonuclear option, or normalization mistake.

PHITS verification and validation evidence

PHITS capabilities

PHITS is a general-purpose particle-transport system used in accelerator technology and shielding [8,9]. Its EGS5 mode transports electrons, positrons, and photons; its current manual documents photon-induced reaction models, material definitions, three-dimensional geometry, spatial and angular sources, particle-fluence and surface-current tallies, deposited energy, dose-conversion multipliers, statistical errors, and variance-reduction tools [8]. These capabilities cover the physical chain required by the proposed paper:

[ e^- \rightarrow \text{converter transport} \rightarrow \gamma\text{ bremsstrahlung} \rightarrow \text{facility transport} \rightarrow \text{shielding dose}, ]

with neutron production and transport included when required by the verified model.

PHITS benchmark publications provide broad evidence for the code across electron and photon transport and accelerator-shielding cases [9–11]. Shikaze compared PHITS and Geant4 calculations of bremsstrahlung dose generated by energetic beta particles [12]. These publications support the selection of PHITS as the reference transport code, but they do not verify or validate the converter, incident-electron energies, shielding geometries, tallies, or physics settings selected for Paper 1.

The 2017 PHITS benchmark is more directly relevant than a generic code citation suggests [10]. Its EGS5 cases compared calculated thick-target bremsstrahlung spectra with measurements for 1 MeV electrons on several materials and 15 MeV electrons on aluminium and lead. Agreement was generally useful, but low-energy discrepancies for high-(Z) targets were attributed partly to attenuation and omitted experimental surroundings. Those cases bracket rather than reproduce the Paper 1 energy range. They support verification of electron and photon transport while reinforcing the need to validate the selected 5–7.5 MeV converter model against applicable measurements.

Verification and validation requirements

Before generating the training data, the PHITS model should undergo the following checks:

  1. Electron transport checks. Compare stopping power and range for converter and backing materials with NIST ESTAR [15].
  2. Photon interaction checks. Compare attenuation behavior and material definitions with NIST XCOM [16].
  3. Converter checks. Compare photon yield, residual-electron transmission, angular distribution, and spectra with Petwal et al., Peri–Orion, and the measurement-to-MCNP comparison of Tuan and Tao under closely reproduced conditions [3,4,35].
  4. Independent spectrum evidence. Use measured 6 MeV lead and tantalum spectra from Deshmukh and Bhoraskar if their original geometry, detector response, and uncertainties can be reconstructed adequately [14].
  5. Concrete and maze checks. Reproduce selected Peri–Orion 5 MeV and 7.5 MeV attenuation cases, the Barkova 5 MeV source-angle cases, and a Cleland maze case where the published geometry is sufficiently specified [3,33,34].
  6. Photonuclear sensitivity. Compare applicable PHITS nuclear-data libraries and reaction models, guided by the critical review, electron-accelerator benchmark, and elemental photonuclear compendium, and report the resulting variation near threshold [37,40,41].
  7. Inter-code comparison. Compare selected source and barrier cases with a separately configured code where practical; Shikaze supplies methodological precedent but not the exact benchmark [12].
  8. Facility or component measurements. Use independent measurements if a suitable 5–7.5 MeV installation becomes available. Comparisons with published calculations support verification; validation of the selected model requires relevant measurements.

Mohd Zin et al. demonstrated a PHITS-to-measurement bunker workflow [13], but their source was Ir-192. Their work supports geometry construction, tally comparison, and measurement practice; it does not validate a bremsstrahlung converter model.

Reproducibility of reference calculations

Each PHITS result should record the code version, input file, nuclear and electromagnetic data, converter specification, material compositions and densities, source normalization, transported particles, physics options, energy cutoffs, variance reduction, numbers of histories and batches, tally definition, conversion coefficients, random seed, and statistical uncertainties. Version control is required because PHITS publications document continuing changes to models and corrections [8,9].

The training dataset should omit or mark results that do not meet a specified statistical-uncertainty criterion. A machine-learning model cannot recover physical information absent from its training data. Training on poorly converged deep-shield results without their uncertainties causes the model to reproduce Monte Carlo statistical fluctuations.

Machine-learning surrogates for radiation transport

Accelerator-shielding applications

Pal Chowdhury and colleagues provide the closest methodological precedent [18,19]. Their 2024 study used PHITS 3.29 to transport quasi-monoenergetic neutrons from 1 to 250 MeV through concrete. Approximately 250 PHITS response calculations were combined linearly to create 10,000 spectral examples. A one-dimensional convolutional neural network (CNN) predicted transmitted neutron spectra; for a Facility for Rare Isotope Beams test spectrum through 50 cm of concrete, the effective-dose result was within approximately 10% of PHITS and inference took milliseconds rather than hours [18].

The later journal study extended this surrogate approach toward shielding-material and thickness optimization [19]. Zamora et al. then used a related CNN in Bayesian inference to quantify uncertainty against experimental concrete-shield data [20]. Together, these studies establish three relevant points:

  • PHITS-generated transport data can train a useful shielding surrogate;
  • predicting spectra before dose conversion improves inspectability; and
  • fast surrogates can make optimization or repeated uncertainty inference practical.

Their physical problem remains different. It is neutron transmission through simplified shielding, not electron conversion, anisotropic bremsstrahlung, and full industrial X-ray facility transport. Linear combinations of source spectra are physically justified by transport linearity; arbitrary combinations of geometries are not. Their reported accuracy cannot be transferred to RAMAL-EBX.

Photon-shielding and three-dimensional applications

POKER-X is an important hybrid rapid photon-shielding comparator [21]. It predicts a transmitted multigroup photon spectrum for a point-kernel calculation rather than directly calculating one dosimetric quantity. This supports retaining energy spectra and particle-specific results where practical, followed by calculation of the specified dose quantity using documented conversion coefficients.

A separate pair of newer works narrows the photon-surrogate gap further. Chen et al. published the Photon Shielding Spectra Dataset, generated with the RMC Monte Carlo code for 92 elements, 22 incident photon energies, and thicknesses up to 40 mean free paths [38]. A follow-on study trained a conditional generative adversarial network with a U-Net generator to predict multigroup spectra and derive buildup factors [39]. These are direct precedents for machine-learning prediction of photon spectra in shielding materials.

They still leave the Paper 1 research gap open. Their reference geometry is an isotropic monoenergetic photon source in a homogeneous spherical medium parameterized by mean free path. It does not model bremsstrahlung production from a LINAC electron beam, a finite converter, the angular distribution of the industrial X-ray source, facility rooms or penetrations, or a PHITS-based surrogate for a specified dose quantity. Their reported accuracy cannot be applied to an industrial facility without separate verification and validation.

Medical-dose studies demonstrate that learned models can reproduce complex spatial transport under defined conditions. Keal et al. trained a small neural network on Monte Carlo calculations in randomly generated heterogeneous media and reported a mean 3%/3 mm gamma pass rate of 94.7% and average error of 1.45% of peak dose for megavoltage photon dose [23]. Sarrut et al. reviewed broader artificial-intelligence and Monte Carlo methods in medical physics [22]. These studies support the feasibility of spatial prediction but do not validate industrial shielding calculations.

RadField3D provides an open Geant4-based generator and machine-readable format for three-dimensional radiation-field machine-learning research [24]. Hao et al. published Monte Carlo radiation-field datasets for simplified nuclear-facility scenarios [25], and Hu et al. used a neural operator with basis-function-generated data to predict radiation distributions [26]. These studies demonstrate geometry-dependent radiation-field prediction in related applications, but not industrial X-ray shielding.

Limitations of the machine-learning evidence

The literature supports using a surrogate within specified parameter ranges to reduce the time required for repeated transport calculations. It does not establish that one model can extrapolate reliably to arbitrary rooms, untested penetration arrangements, converter designs absent from the training data, or poorly converged low-dose results. Nor does it identify one universally superior machine-learning method.

Model choice should follow output structure:

  • scalar exterior-dose values or barrier responses: interpolation, Gaussian processes, tree ensembles, or small multilayer perceptrons;
  • one-dimensional spectra or depth profiles: one-dimensional convolutional models;
  • fixed-grid spatial fields: CNN or U-Net variants;
  • geometry-to-field mappings across grids: neural operators only if simpler models fail and the data volume justifies them.

The study should compare the machine-learning surrogate with interpolation and conventional regression before considering a more complex model.

Implications for training and test data

Predictor variables

Predictor variables should include only physical parameters varied in the simulation data. Revised D3–D5 will fix the converter, local beam footprint, scan-position density, source placement and orientation, concrete, and air. Candidate predictors are:

  • incident-electron energy within 5–7.5 MeV;
  • interior room width, length, and height;
  • forward primary-wall thickness; and
  • shared secondary-barrier thickness.

Beam current and workload remain analytical scaling factors rather than predictors. Every simulation must still record all fixed source, material, and geometry conditions.

Separation of training and test data

Randomly assigning tally points or voxels from one PHITS calculation to both training and test sets transfers source and geometry information between the sets. The test data should therefore contain complete shielding configurations excluded from training. More demanding tests may exclude:

  • complete barrier-thickness combinations;
  • one or more intermediate electron energies; and
  • room-dimension combinations near the approved domain boundaries.

Predictions should be limited to the specified parameter ranges. Results outside those ranges should be identified as extrapolations and should require a PHITS calculation.

Model evaluation

Mean error alone can conceal important dose underestimations and overestimations. The evaluation should include:

  • signed, absolute, and relative error in the specified dose quantity;
  • frequency, distribution, and maximum magnitude of dose underestimation and overestimation;
  • performance by energy, barrier role, distance, and particle type;
  • incorrect classification relative to any predefined design dose criterion;
  • calibration or empirical coverage for any uncertainty interval;
  • comparison with PHITS statistical uncertainty; and
  • wall-clock time and speedup.

Both error directions must be reported. Underestimation of transmitted dose is non-conservative and requires separate scrutiny; overestimation is conservative but can result in unnecessary shielding, cost, and space requirements.

Statistical uncertainty

PHITS outputs are stochastic estimates, not exact values. Training and evaluation should retain their statistical uncertainties. Calculations with a poor figure of merit should receive more histories or improved variance reduction, especially when the result is relevant to a predefined design dose criterion. Independent PHITS calculations with different random seeds can help distinguish surrogate error from Monte Carlo statistical variation.

Uncertainty must include more than Monte Carlo variance. Geometry, concrete composition and density, source definition, converter construction, physics models, cross-sections, cutoffs, and measurement response are distinct uncertainty sources [2,5,20]. A surrogate uncertainty interval calibrated only against PHITS labels represents emulator uncertainty within the PHITS model, not total facility uncertainty.

Synthesis of the evidence

The literature can be organized into four bodies:

Evidence body What is established What remains unresolved for Paper 1
Industrial 5–7.5 MeV X-ray studies [3–6,29–36] High-power processing context, converter behaviour, angular spectra, concrete attenuation, maze scattering, facility-scale shielding requirements, and activation evidence Rapid PHITS-based prediction across a defined range of LINAC shielding configurations
PHITS and transport benchmarks [8–16,37,40,41] Coupled transport capabilities, measured bremsstrahlung benchmarks, verification methods, and photonuclear data and model sensitivity Verification of the selected converter, electron-energy distribution, geometry, tallies, photonuclear treatment, and data-processing sequence; validation against applicable measurements
Accelerator-shielding machine learning [18–20] PHITS-based surrogates can reduce computation time for neutron attenuation and optimization calculations Converted-X-ray source generation, photon-dominated facility fields, and dependence on incident-electron energy from 5 to 7.5 MeV
Photon and spatial machine learning [21–26,38,39] Rapid photon-shielding, spectral, and spatial-dose prediction is feasible in related problems Industrial LINAC source physics, deep concrete shielding, particle-specific results, and facility-specific validation

Research gap

Existing work provides high-power source studies, Monte Carlo converter calculations, angular spectra, barrier attenuation, maze-scattering methods, and activation evidence for 5 MeV and 7.5 MeV industrial converted-X-ray systems [3–6,29–36]. Separate work provides PHITS-based neutron-shielding surrogates and Monte Carlo-based photon-shielding surrogates [18–21,38,39]. The unresolved issue is the absence, in the accessible literature, of one study that combines the following five components:

  1. Complete source-to-shield calculation: a conventional LINAC electron beam, electron transport in a verified converter model, bremsstrahlung production, transport through the facility shielding, and calculation of a specified radiation-protection quantity.
  2. Application and energy range: industrial X-ray LINAC shielding over a specified range of incident-electron energies from 5 to 7.5 MeV, including the energy dependence of the spectrum, angular distribution, and attenuation.
  3. Radiation-protection output: prediction of a specified dose quantity used for shielding assessment rather than only a photon spectrum, neutron spectrum, buildup factor, or product absorbed dose.
  4. Independent test configurations: evaluation using complete shielding configurations excluded from the training data rather than tally points or voxels randomly divided from the same PHITS calculation.
  5. Photoneutron assessment: separate photon and neutron contributions and sensitivity to the photonuclear data library and reaction model, particularly near 7.5 MeV [1,29,37,40,41].

This is an intersection of established topics, not a claim that converter modelling, industrial X-ray shielding, photon-spectrum prediction, or machine learning for accelerator shielding is individually new. The conclusion is limited to the accessible literature and should be reconsidered if additional studies emerge during peer review.

Requirements for evaluating the contribution

The following are not additional literature gaps. They are requirements for determining whether Paper 1 addresses the combined gap credibly:

  1. Quality of the PHITS reference data: verification against applicable benchmark calculations, validation against relevant measurements where available, and retention of Monte Carlo statistical uncertainties.
  2. Prediction error and applicability: separate assessment of dose underestimation, dose overestimation, incorrect classification relative to any predefined design dose criterion, and predictions outside the specified parameter ranges.
  3. Computational performance: comparison with interpolation and conventional regression, separate reporting of PHITS runtime, training-data generation, model training, and inference time, and PHITS confirmation of selected predictions.

Limitations of the review

Subscription database access and some document delivery are unavailable. The companion evidence review supports the focused research gap, and D1 fixes its scope, but inaccessible, proprietary, or poorly indexed studies cannot be excluded. Absolute priority claims must be avoided, and the research-gap statement must be updated if additional literature changes the combined contribution.

Conclusion

The title is supported by an industrial shielding problem and a focused literature gap. The 5–7.5 MeV range is supported by published converter and shielding studies. Increasing the incident-electron energy from 5 MeV to 7.5 MeV changes source strength, photon spectrum, angular distribution, concrete attenuation, and photonuclear sensitivity.

PHITS has the required transport and tally capabilities, but calculations used as training data must be checked against measured bremsstrahlung data, published converter and source results, attenuation and maze calculations, photonuclear sensitivity studies, independent transport calculations, and measurements where available. Machine learning is justified by the cost of repeated calculations, not by novelty alone. Final shielding designs require PHITS confirmation, professional assessment, regulatory review, and commissioning measurements.

References

  1. IAEA (2010). Radiation Safety of Gamma, Electron and X Ray Irradiation Facilities, Specific Safety Guide SSG-8.
  2. IAEA (2010). Use of Mathematical Modelling in Electron Beam Processing: A Guidebook, Radiation Technology Series No. 1.
  3. Peri, E. and Orion, I. (2017). Shielding calculations for industrial 5/7.5 MeV electron accelerators using the MCNP Monte Carlo Code. EPJ Web of Conferences, 153, 03011.
  4. Petwal, V.C., Bapna, S.C., Sandha, R.S., Kotaiah, S. and Subbaiah, K.V. (2007). Bremsstrahlung converter for high power EB radiation processing facility. APAC 2007, THPMA088.
  5. Petwal, V.C., Kumar, P., Suresh, N., Parchani, G., Dwivedi, J. and Thakurta, A.C. (2011). Biological shielding design and qualification of concreting process for construction of electron beam irradiation facility. Conference on Accelerator Radiation Safety, p. 76.
  6. U.S. Food and Drug Administration (2004). Irradiation in the Production, Processing and Handling of Food, 69 FR 76844.
  7. Zimek, Z. (2020). Economical evaluation of radiation processing with high-intensity X-rays. Nukleonika, 65(4).
  8. PHITS Development Team. PHITS User’s Manual.
  9. Sato, T. et al. (2024). Recent improvements of the Particle and Heavy Ion Transport code System—PHITS version 3.33. Journal of Nuclear Science and Technology, 61(1), 127–135.
  10. Iwamoto, Y. et al. (2017). Benchmark study of the recent version of the PHITS code. Journal of Nuclear Science and Technology, 54(5), 617–635.
  11. Iwamoto, Y. et al. (2022). Benchmark study of particle and heavy-ion transport code system using shielding integral benchmark archive and database for accelerator-shielding experiments. Journal of Nuclear Science and Technology, 59(5), 665–675.
  12. Shikaze, Y. (2024). Evaluation of radiation dose caused by bremsstrahlung photons generated by high-energy beta rays using the PHITS and Geant4 simulation codes. Journal of Nuclear Science and Technology.
  13. Mohd Zin, M.R. et al. (2019). Monte Carlo studies for the radiation shielding in the bunker of the electron beam accelerator using PHITS. IOP Conference Series: Materials Science and Engineering, 555, 012020.
  14. Deshmukh, V.S. and Bhoraskar, V.N. (1986). Bremsstrahlung spectra from lead and tantalum at 6 MeV electron energy. Journal of Radioanalytical and Nuclear Chemistry Letters.
  15. NIST. ESTAR: Stopping-Power and Range Tables for Electrons.
  16. NIST. XCOM: Photon Cross Sections Database.
  17. ICRU (2020). Operational Quantities for External Radiation Exposure, Report 95.
  18. Pal Chowdhury, R., Zamora, J., Ginter, T. and Bollen, G. (2024). Machine Learning in Accelerator Shielding: Application Using Convolutional Neural Networks. RPSD 2024, pp. 128–130, DOI 10.13182/T131-45920.
  19. Pal Chowdhury, R., Zamora, J.C., Bollen, G. and Ginter, T. (2025). Surrogate modeling of Monte Carlo radiation transport with convolutional neural networks for shielding optimization. Nuclear Instruments and Methods in Physics Research B, 570, 165909.
  20. Zamora, J.C., Bollen, G., Ginter, T. and Pal Chowdhury, R. (2025). Uncertainty Quantification for Neutron Shield Using Convolutional Neural Networks. Nuclear Technology.
  21. Chen, J. et al. (2026). POKER-X: An AI-enhanced and GPU-accelerated platform for rapid radiation shielding analysis. Nuclear Engineering and Technology, 58(6), 104189.
  22. Sarrut, D. et al. (2021). Artificial Intelligence for Monte Carlo Simulation in Medical Physics. Frontiers in Physics, 9, 738112.
  23. Keal, J., Santos, A., Penfold, S. and Douglass, M. (2021). Radiation dose calculation in 3D heterogeneous media using artificial neural networks. Medical Physics, 48(5), 2637–2645.
  24. Lehner, F. et al. (2025). RadField3D: a data generator and data format for deep learning in radiation-protection dosimetry for medical applications. Journal of Radiological Protection, 45(2).
  25. Hao, Y. et al. (2024). A Monte Carlo Simulation Dataset of Radiation Field Parameters for a Simple Nuclear Facility Scenario. Scientific Data, 11, 1008.
  26. Hu, A., Li, K., Qiu, R. and Li, J. (2025). Predicting radiation distribution via neural operator trained on basis function-generated data. Computer Physics Communications, 315, 109710.
  27. Department of Atomic Energy Malaysia. Legal materials under the Atomic Energy Licensing Act and radiation-protection regulations.
  28. National Academies of Sciences, Engineering, and Medicine (2021). Radioactive Sources and Alternative Technologies in Sterilization, Chapter 5. National Academies Press.
  29. FAO/IAEA/WHO International Consultative Group on Food Irradiation (1995). The Development of X-Ray Machines for Food Irradiation: Proceedings of a Consultants’ Meeting.
  30. Seltzer, S.M., Farrell, J.P. and Silverman, J. (1983). Bremsstrahlung beams from high-power electron accelerators for use in radiation processing. IEEE Transactions on Nuclear Science, 30(2), 1629–1633.
  31. Meissner, J. et al. (2000). X-ray treatment at 5 MeV and above. Radiation Physics and Chemistry, 57(3–6), 647–651.
  32. Cleland, M.R. and Stichelbaut, F. (2013). Radiation processing with high-energy X-rays. Radiation Physics and Chemistry, 84, 91–99.
  33. Barkova, V.G., Kiselev, A.V. and Chudaev, V.Ya. (2006). Evaluation of efficiency of concrete shielding against bremsstrahlung of 5 MeV electrons at pre-commissioning of the accelerator ILU-10. RuPAC 2006, MOKP01, 339–341.
  34. Cleland, M.R., Galloway, R.A. and Brown, D.F. (2017). X-ray scattering in the shielding of industrial irradiation facilities. Physics Procedia, 90, 151–156.
  35. Tuan, N.A. and Tao, C.V. (2020). Assessment of X-ray converter for electron beam radiation processing facility. Science and Technology Development Journal – Natural Sciences, 4(4), 737–743.
  36. Grégoire, O. et al. (2003). Radiological safety of food irradiation with high energy X-rays: theoretical expectations and experimental evidence. Radiation Physics and Chemistry, 67(2), 169–183.
  37. Sari, A. et al. (2025). A benchmark for Monte Carlo simulation of photoneutron fields from electron accelerators. Nuclear Instruments and Methods in Physics Research A, 1072, 170168.
  38. Chen, J. et al. (2025). A simulated comprehensive photon flux shielding spectra dataset for advanced radiation safety assessment. Scientific Data, 12, 1498.
  39. Chen, J. et al. (2026). A unified surrogate model for enhanced photon shielding through an all-natural-element multi-group flux dataset. Annals of Nuclear Energy, 226, 111887.
  40. Sari, A. (2023). Characterization of photoneutron fluxes emitted by electron accelerators in the 4–20 MeV range using Monte Carlo codes: a critical review. Applied Radiation and Isotopes, 191, 110506.
  41. Garnaud, L. et al. (2026). Compendium on Monte Carlo simulation of photoneutrons in the Giant Dipole Resonance energy range. EPJ Nuclear Sciences & Technologies, 12.
  42. Ziaie, F. and Tahami, S.M.R. (2005). Mass throughput rate calculation for X-ray facilities. Nukleonika, 50(3), 121–124.
  43. Ma, C.-M., Faddegon, B.A., Rogers, D.W.O. and Mackie, T.R. (1997). Accurate characterization of Monte Carlo calculated electron beams for radiotherapy. Medical Physics, 24(3), 401–416.