Tungsten-based polymer composite, a new lead-free material for efficient shielding of coupled neutron-gamma radiation fields: A FLUKA simulation study

Metal-based polymer composites, a new category of advanced materials, are advantageous for effective protection of radiation field. Recent report of fabrication of tungsten (W)-Poly methyl methacrylate (PMMA) composite microcellular foams with enhanced mechanical strength properties opens up the possibility of its use in radiation attenuation. Objective of this theoretical study is to assess the efficacy of W-based polymer composite, a new lead-free shielding material for attenuating coupled neutron-gamma radiations. Current paper utilizes open-source Monte Carlo code FLUKA to evaluate shielding efficiency of PMMA composites reinforced with varying concentration W particles. Study shows that, adding even 20 vol% of W particles can significantly improve radiation shielding ability of PMMA. Performance of analogous composition Pb-based polymer composite is also examined to demonstrate its inadequacy in radiation protection compared to W-based composite. Study reveals an interesting fact that for any shield dimension, total radiation dose follows an initial descending trend with increase in heavy metal (W/Pb) proportion up to certain optimum value where dose becomes minimum, beyond that dose increases. Optimum heavy metal concentrations are found to be 70 vol% and 30 vol% for W and Pb respectively, with minimum dose for Pb shield being two orders of higher magnitude. Study is further extended to investigate shielding efficiency of conventional double-layer laminates employing W and PMMA in both high-Z/low-Z and low-Z/high-Z configurations as well as optimum concentration of W-PMMA composite and PMMA. It is shown that among all the potential designs, newly introduced composite-based double-layer shield performs best in terms of volumetric dose while single-layer optimized composite shield offers least specific dose.


Introduction
Dual radiation fields comprising of neutrons (n) and gamma rays (γ) are very common in various nuclear installations, such as, fission nuclear reactors, transportation and storage of nuclear materials, medical instruments (radiation therapy or diagnostics), etc. Physics design of mixed radiation shield is of great significance for these above mentioned utilities as well as for advanced special-purpose nuclear reactors, like, nuclear marine propulsion systems, space reactors, small modular reactors (SMRs) and upcoming fusion reactors.Primary objective of shield design is to efficiently attenuate n and γ radiations so that the effective dose out of the shield remains within a prescribed limit.With this purpose, shields need to be constructed by appropriate combination of materials that are most suitable for attenuating individual radiation components i.e., n, γ etc.In addition to excellent shielding performance, these materials should be lightweight and lowvolume in support of increasing demand for miniaturization and should have good mechanical strength, durability leading to long service life, minimum radiation damage effect, low toxicity and finally cost-effective.
Traditionally lead (Pb), an element with high mass attenuation coefficient, was used for protecting from x-rays and γ radiations in various applications.Recently, long-term health risk to medical personnel due to exposure of hazardous element Pb has been of a great concern [1].Development of the new lead-free, lightweight, safe, robust and reliable radiation shielding materials for both industrial and space applications has made tremendous impetus [2,3].
While constructing shield for dual radiation, it is to be noted that mid to high-Z elements like, Fe, Bi, Pb, W, etc are relatively good absorber of γ rays but less effective against elastic scattering of neutrons.Whereas, materials like concrete, polyethylene, and others containing low-Z elements like H, Be, B, C are effective for attenuating neutrons through elastic scattering and/or absorption but not adequate for attenuating γ energy.Major shortcoming of these materials is that they cannot shield the secondary γ produced in the process of neutron interaction with shield material [4].Homogeneous mixtures (composites) or multi-layer laminates (stratified) of light and heavy nuclei are preferable for shielding both n and γ radiations [5,6].
Polymer, is advantageous due to its low density, chemical stability and good neutron slowing performance.Due to good process ability and flexibility, Polymers are ideal for advanced manufacturing technologies.So, polymeric composites are promising substitutes for traditional shielding materials and have attracted recent attention.Only disadvantage is their inferior thermo-mechanical properties that further degrade on exposure to ionizing radiations for extended period of time [7].However, blending polymers with inorganic fillers, mainly, metal-powders with good gamma shielding characteristics, have shown to improve the radiation resistance and mechanical properties.Demand for polymeric composites in radiation shielding application is rapidly increasing [8][9][10].
Polymers that are commonly used as matrix for fabrication of metal-reinforced composite include: polyethylene, polymethyl siliconate, PMMA, carbon fibre, polystyrene, neoprene, resin, nylon, polyvinyl chloride (PVC), teflon, epoxy, rubber, and many others.Gamma shielding characteristics of a plethora of different polymers are reported [11].A comprehensive review of different inorganic compounds and polymers used for this purpose can be found in [12].It is worth mentioning here that, radiation attenuation properties of polymeric composites are greatly enhanced by use of nanomaterials in place of bulk fillers, due to increase in surface to volume ratio [13].
Composite shields made out of thermoplastics have shown great potential for radiation shielding and possess the added advantage of flexibility to combine with variety of different fillers.PMMA (C 5 H 8 O 2 ) is a transparent thermoplastic with good tensile strength.Preparation of W-PMMA composite microcellular foam, with different W concentration, using melt-mixing and supercritical carbon dioxide foaming methods has been reported [14] with remarkably increased mechanical strength than those of pure PMMA.A recent work evaluated the gamma attenuation performance of Bi 2 O 3 metal particles dispersed in PMMA matrix [15].Present authors have evaluated gamma build-up factor of double-layer shield (DLS) involving iron and PMMA [16].It was also shown that PMMA performs better than water or low-density polyethylene (LDPE) [17].
Among different high-Z elements, Pb and W are obvious choice for gamma shielding.A recent study reported comparable values of gamma shielding parameters, namely, linear and mass attenuation coefficients for Pb, W and tungsten carbide (WC).Study revealed that although mass attenuation coefficient of W is slightly lower than Pb [33], but high density of W makes it a potential alternative to Pb.Moreover, fast neutron removal cross-section of W is much higher than Pb.Tungsten containing polymer composites are attracting special interest due to their low toxicity, malleability and ability to effectively attenuate both neutron and gamma radiations.Effect of size and proportion of W particles on shielding properties of LDPE has been investigated [34].In addition to metallic W, its oxides, carbides and bromides are also blended with polymers for shielding ionizing radiations [12].Epoxy-based composite materials with Ta, WC and W metal particles have been explored for the application as dual radiation shields [22,35].
So far, shielding properties of various metal-reinforced polymer composites have been studied extensively for mono-energetic neutron and γ sources, but the same for broader spectrum of energy interval, so called multigroup energy, as produced in a nuclear reactor, has not been explored to that extent.Designing shield for coupled n-γ sources, involving combination of high-Z and low-Z materials in composite or laminar form, is a complex problem as, it requires optimization of metal-particle content (composite) or layer thicknesses (laminar).
The aim of the current paper is to introduce a lead-free composite shield comprising of W and PMMA [14] and investigate its shielding properties in respect to n-γ mixed radiation fields.Characterization of radiation protection capability of different composition W-PMMA homogeneous mixtures is made by exhaustive Monte Carlo particle transport simulation using general purpose open-source code, FLUKA (https://fluka.cern/).
Our theoretical study reveals that for any radius of spherical composite shield, both neutron and secondary γ doses initially decreases with the increase in concentration of W particles in PMMA and then increases.Study brings out an interesting fact that there exists an optimum concentration of W particles for which neutron, secondary γ and total doses become independently minimum.Superiority of the proposed W-PMMA composite shield over Pb-PMMA composite is also demonstrated.
Further, effectiveness of W-PMMA composite shield in comparison with equivalent DLS involving W and PMMA has also been investigated.In doing so, following our recent work on iron/PMMA based DLS [16,17], both the combinations of high-Z followed by low-Z and vice versa have been considered.Study clearly indicates the superiority of the single-layer W-PMMA composite over double-layer laminates for shielding wide-energy coupled n-γ radiation.Additionally, composite based DLS with one layer as composite and other one of PMMA, a new concept, is introduced that exhibited least volumetric dose.Finally, efficiency of all potential shield designs is compared by introducing specific dose, which takes into account the mass of the shield.

Theoretical background
The principle of coupled n-γ shielding is to attenuate the components of radiation fields generated from source neutron, primary gamma and secondary gamma generated by neutron interaction (largely by thermal neutron capture) with elements of the shield.In the fast energy region (MeV), inelastic scattering of neutrons dominates producing scattered gamma rays, whereas in the thermal energy region (eV) neutron capture and activation reactions are the dominant mechanisms for generating secondary gamma rays.Challenge is to understand the role of shield in reducing the intensity of all these radiation components simultaneously, each dictated by their own interaction processes.
Radiation shielding in W-PMMA composite functions on the basis of four interconnecting processes: i) thermalization of neutrons in hydrogenous materials, PMMA, ii) absorption of neutrons in hydrogen and other elements, iii) capture of thermal neutrons to produce secondary gamma, and iv) attenuation of gamma photons in W. Hydrogenous materials also captures neutron, but the outcome of 2.2 MeV gamma (produced when H 1 absorbs a neutron) remains within the system.Thus pure polymer does not serve the purpose.Use of high-Z gamma attenuator in hydrogenous material is beneficial in this regard.Gammas are also produced in the neutron shield by neutron (radiative) capture, inelastic scattering, and the decay of activation products.High-Z materials also help in slowing down fast neutrons mainly through in-elastic scattering.
According to International Commission on Radiological Protection (ICRP) the absorbed dose serves as the fundamental dosimetric quantity in radiation protection.Radiation equivalent dose is defined as the product of absorbed dose and radiation weighting factors.Here, we are concerned with ambient dose-equivalent H, of dual radiation field.Utilizing the energy dependent weighting factors of each radiation components as listed in ICRP tabulated data [36], we have calculated dose-equivalent to neutrons, H n ; primary gamma, Hγ; and secondary gamma, H n, γ separately.Total dose-equivalent H T is sum of the contribution from each sources, i.e., = + + We express dose-equivalent in pico-Sievert (pSv) per source particle unit.

Simulation system
In the present simulation study, we have investigated the efficiency of PMMA composite reinforced with different concentration tungsten powder additives.Simulations are also performed for both the pure materials, i.e., 100% PMMA and 100% natural W with isotopic composition W 180 (0.13%), W 182 (26.3%),W 183 (14.30%),W 184 (30.67%) and W 186 (28.6%).Analogous composite shield with Pb additives has also been analysed.In this context, normally the components are mixed with their mass fractions, but in case of making homogeneous mixture of two or more materials with large difference in their densities (one order in the present case), it is convenient to measure concentrations in terms of their volume fractions.In this case, the density of the composite (r comp ) has been calculated using equation (2).Here, f v and r metal are the volume fraction and density of heavy metal (W/Pb) respectively and r polym denotes density of PMMA.3) represents a straight line with r polym as intercept and density difference as slope; and implies linear variation of composite density with volume fraction of metal.Thus a uniform distribution of composite density can be achieved by mixing the two components according to their volume fraction, as displayed in figure 1.
On the other hand, if the components are mixed according to their mass fractions then specific volume of the composite can be determined from relation Thus density of composite is largely controlled by density of polymer.In table 1 we have illustrated this two mixing approaches in respect to W and Pb based polymer composites.It can be noticed that in the case of massmixing, r comp changes maximum when metal concentration is beyond 90% by mass.As discussed in subsequent sections that optimum concentration for minimum dose is 70 vol% of W and 30 vol% Pb, which is equivalent to 97% and 80% of W and Pb by mass.Henceforth, W/Pb concentrations in PMMA will be referred by vol%.
We have also evaluated the performance of equivalent DLSs with constituent layers made up of W and PMMA.Following [16], both the cases of layer material ordering, i.e., high-Z (W) surrounded by low-Z (PMMA) and low-Z (PMMA) surrounded by high-Z (W) have been considered.
We have chosen spherical geometry for both composite and DLSs with point isotropic radiation source (n and γ) placed at the centre.Spherical geometry has been chosen as it mimics many realistic applications, can achieve better calculation accuracy [37] with fewer particles and provides the conservative estimates for doses.Radius of the sphere is varied from 10 cm to 1 m in a systematic manner.Simulation geometries for homogeneous composite shield (a) and representative double-layer configuration (b) are shown in schematic diagram of figure 2.

FLUKA simulation details
FLUKA [38,39] is a general-purpose open-source Monte Carlo particle transport package to simulate interactions between different types of sub-atomic particles and matters capable of handling wide energy (TeV) range.Applications of FLUKA has widened from original high energy physics to currently shielding study, detector design, cosmic ray studies, dosimetry, medical physics and radiobiology.
Calculations in FLUKA, version 4-2.2, are based on updated data libraries, e.g., ENDF/B-VI.R8, ENDF/B-VII.R0-1, JEFF-3.2 and JENDL-3.3.Neutrons with energies below 20 MeV are classified as low-energy neutrons and their transport uses a multi-group approach wherein energy range is divided into 260 discrete groups with A point isotropic radiation source consisting of both neutron and gamma with their respective energy spectrum is placed at the center of the sphere.Source spectrum for our problem has been generated by writing a source file, source.f.This file is compiled along with FLUKA code for transport simulation.About 10 7 particles are simulated with importance biasing technique for variance reduction.This enabled handling 100 cm radius of W-PMMA composite shield.Neutron and gamma interaction with shield material and subsequent transport in spherical shield geometry are simulated with surface detector tally.
In FLUKA, fluence-to-dose conversion has been properly accounted by using AUXSCORE card along with USRBDX surface fluence estimator card in respect to neutron, primary gamma and secondary gamma, to estimate dose-equivalent (hereafter termed as 'dose' only) in pSv.In AUXSCORE card ICRP-74 data has been used for radiation weighting factors.Residual nuclei produced in neutron interaction with shield material are determined using RESNUCLEi card.
Estimation of gamma dose has been carried out invoking detailed physics approach that takes into account of bound electron coherent scattering (Rayleigh), bound electron incoherent (Compton) scattering, photoelectric edge treatment, fluorescence emission, annihilation gamma photons and bremsstrahlung due to secondary electrons.Ignoring bound electron contributions has been found to cause significant difference for high-Z materials particularly gamma energies exceeding 3 MeV [16].In order to validate FLUKA simulation in respect to neutron transport, we have determined macroscopic removal cross-section, the universal parameter that measures the neutron shielding performance.It is basically a pseudo cross-section indicating the probability of fission neutrons to be removed from the fast energy group by colliding with the atoms of the target material and is defined as Σ R = −1/j (dj/Dr) (cm −1 ), where j is the neutron fluence.Prior to this, quite a few reports of employing FLUKA for estimate effective removal cross sections (Σ R ) of materials existed [22,23].Following Ref. [41], we consider a spherical shield of radius r 1 made up of materials of interest (i.e., W, Pb and PMMA).It is surrounded by light water of thickness r 2 (r 2 > 50 cm) making outer radius of (r 1 + r 2 ).The spherical shell geometry is analogous to double-layer configuration as illustrated in figure 2(b) with M 1 as the material whose Σ R is to be determined and M 2 as water.Detector response (dose) at r 2 due to water alone (r 1 = 0), i.e., R 1 (r 2 ) and at (r 1 + r 2 ), i.e., R 2 (r 1 + r 2 ) are related by the expression given below A point neutron source having fission spectrum (equation ( 8)) is placed at the centre.
While measuring Σ R , the radius of W, Pb and PMMA are chosen to be 11, 20, and 25 cm respectively.About 5 × 10 6 particles are simulated that resulted in less than 5% standard deviation for estimated response.Cumulative thermal fluence for E n < 1 eV (last 36 groups) has been estimated using USRBDX card.
In table 2 we have compared the values of Σ R for W, Pb and PMMA estimated by FLUKA with those obtained by MCNP [41].Σ R of PMMA in that reference has been calculated by using weight fraction of carbon (C), hydrogen (H) and oxygen (O) as in the molecular formula C 5 O 2 H 8 .It can be seen that the relative deviation Δ, of FLUKA results are within 10% of the MCNP generated data.Where, Δ is defined as The observed minor difference seen is the artefact of neutron cross-section libraries used in these codes and multi-group treatment of FLUKA.Observed good agreement with MCNP-based published data validates FLUKA code.
Next, we validate FLUKA for estimation of dose-equivalent due to neutron and secondary gamma through a high-Z shield, W. To that end, following Cai et al [42] we consider a spherical shell assembly with inner air (radius 10 cm), followed by W shell of outer radius varying from 20 cm to 1 m and an outer air-layer of radius 5 m.Point isotropic 14 MeV neutron source is placed at the centre.In figure 3 we show FLUKA calculated neutron and secondary gamma doses at 5 m and compare them with MCNP results.Very good agreement between the two validates FLUKA based simulation and provides confidence in proceeding further.

Performance analysis of W-PMMA composite shield
Next we turn on to evaluate the dose-equivalent at outer surface of single-layer spherical composite shield made up of different concentration W particles embedded in PMMA matrix.

Energy spectrum of source particles
For the present academic study, we have considered analytical form of neutron energy spectrum adapted from published literature of [43].It corresponds to energy spectrum of pool type MTR reactor RP-10 of Peru.Following that work, neutron fluence rate per unit energy (cm −2 s −1 eV −1 ) in three different energy ranges are expressed as Here A, B and C are three normalization constant having values 2.86 × 10 15 , 1.26 × 10 10 and 2.12 × 10 5 respectively.Following Schaeffer [44], source gamma spectrum considered here corresponds to prompt gamma spectrum of U 235 fission and is expressed by the empirical formula given below:

Shielding parameters of polymer composites
Shielding parameters, namely, neutron removal cross-section (spectrum averaged value) and linear attenuation coefficient (LAC) for 1 MeV gamma for varying concentration W or Pb particles in PMMA are shown in figure 5.
Effective mass removal cross-section for composites are calculated from the weighted sum of mass removal cross-section (Σ R /ρ) pertaining to individual components Here w i is the weight fraction of the ith component in the mixture.Removal cross-section is obtained by multiplying Σ R /ρ mix with density of the mixture.
LAC, which describes the gamma shielding capability of a shield material, has been calculated by use of Lambert-Beer law (equation ( 12)) [16].

I I e 12
x 0 t ( ) LAC (μ t ) of W, Pb and PMMA have been calculated by considering a beam of 5 × 10 5 gamma-photons impinging on a simple cylindrical geometry made up of different shield materials.μ t can be calculated by the transmission ratio for each material thickness and energy using USRBDX score card in FLUKA.In case of 1 MeV gamma, LAC values for W, Pb and PMMA obtained from FLUKA are 1.26997, 0.80021 and 0.08084 cm −1 respectively.Whereas, values evaluated from XCOM [45] for these same materials are 1.27727, 0.80537 and 0.08107 cm −1 respectively.The deviation is within 0.7% than that of XCOM database.LAC values for composites are calculated by the mixture rule given in equation (11) with Σ R being replaced by μ t .

Estimation of individual and total doses for different shield thicknesses
At first, we analyse the contribution of individual doses due to neutron, primary and secondary gamma as a function of W concentration in composite shield.Here 0 and 100% refer to pure PMMA and pure tungsten respectively.Results are generated for different shield radii, i.e., 10, 25, 50, 75, and 100 cm.For illustration, in figure 6 we show the individual and total doses for four different thicknesses of single-layer composite shields.It can be noticed that for low shield radii of 10 and 25 cm, neutron dose (red curves) are largely insensitive to W concentration, even though it performs better than pure PMMA.At larger radii, neutron dose slowly decreases and reaches minimum at some higher concentration of W, before finally increasing.The decrease is noticeable for 50 cm and 75 cm where minimum dose is achieved for 70% and 80% W respectively.Inelastic scattering of high energy neutrons in presence of high-Z element like W is the primary reason for reducing dose with increasing W content.The excess energy of the inelastic process is departed into the target nucleus as excitation energy, which de-excites by emitting one or more gamma photons.Thus, in raising W content from zero to 80%, almost two order reduction in neutron dose can be achieved with 75 cm composite shield.
Secondary gamma dose shown by blue curves of figure 6 exhibit similar trend.For all shield dimensions below about 25% W concentration, secondary gamma dose is higher than corresponding neutron dose, beyond which the former reduces at a faster rate and attains minimum value at around 70%-80% W (except for 10 cm radius).Two orders magnitude difference between neutron and secondary gamma dose can be observed for 100% PMMA and 100% W.
Primary gamma dose (green curves) decreases steadily as fraction of W increases in the shield material.It can be easily noticed that dose due to primary gamma has dropped to significantly low value even with 35% W for   50 cm shield radius.Hence for still larger radii, primary gamma dose becomes too low to contribute in total dose.
From figure 6 it is clear that for a particular concentration of W, all three doses decrease with distance.Nevertheless, the decrease is not uniform for all concentrations.For example, in case of pure W, neutron and secondary gamma dose drops by five and three orders respectively.Irrespective of thickness, even with 25% W in PMMA, secondary gamma dose becomes comparable to neutron dose (point of crossing the respective dose curves).This is the artefact of two phenomena i) capture reaction is most likely with thermal neutrons, thermalization of neutrons in PMMA matrix and ii) increasing W content in smaller volumes enables onsite attenuation of gamma.In the same manner, only about 15% of W in composite shield is adequate to reduce the primary gamma dose comparable to that of neutron dose.Embedding 80% W in PMMA matrix causes neutron and secondary gamma dose to reduce by seven and eight orders of magnitude in extending shield radius from 10 cm to 75 cm.
Figure 6 also conveys that there exists an optimum W concentration for W-PMMA composite for which minimum dose for neutron and secondary gamma is realized.Optimum W concentration for minimum neutron dose is found to be within 70%-80%, except for 10 cm radius where it is 20% W. Similarly, optimum W concentration for minimum secondary gamma dose is about 70%.This is an important finding of this work and perhaps first report of observation of optimum concentration of metal particles in polymer composite to generate least dose at certain distance from source.
Total dose comprising of neutron, secondary gamma and primary gamma for varying W content are estimated at the surface of different radii spheres.The variation of total dose for four representative radii are displayed by black curves of figure 6.It is evident that for low W concentrations (<40%), dominant contribution to total dose comes from primary and secondary gamma.But the trend reverses beyond 40% W where total dose is controlled by neutron fluence only.Consequently, total dose versus W content curve passes through minimum thereby indicating the existence of optimum W concentration for total dose as well.
Consolidated results of total dose at outer surface of different-radii W-PMMA composite shield as a function of W content are shown in 3D bar diagram of figure 7. Results for five different radii composite shields, namely, 10 cm (purple), 25 cm (red), 50 cm (green), 75 cm (cyan) and 100 cm (blue) are presented.Presence of optimum concentration of W for maximum attenuation of total radiation dose is evident for all radii (marked with arrow in figure 7).Optimum concentration (∼70%) does not vary significantly with shield dimension.To be precise, optimum W concentrations that correspond to minimum total dose at 10, 25, 50, 75 and 100 cm radii are 70%, 60%, 70% and 80% (last two) respectively, nearly coinciding with neutron dose, except for 10 cm radius.Numerical values of total dose for five different radii shields are given in table 3. Statistical uncertainty in all the cases lies within 5%.

Performance of Pb/PMMA composite shield
To establish the superiority of W based composite over Pb, we have calculated the total radiation dose due to different composition Pb-PMMA shield.The configuration is same as illustrated in figure 2(a) except that W is replaced by Pb.Comparison of total dose corresponding to 50 cm radius of Pb-PMMA and W-PMMA shields are presented in figure 8.As in W-PMMA composite, total dose for Pb-based composite too exhibits initial decrease, reaches minimum and then increases with further rise in Pb vol%.However, for same concentration, Pb-based shield delivers much higher dose than W-based one.Further, minimum dose is realized for only 30 vol% in Pb case as against 70 vol% for W doping, even though minimum dose in W reinforced polymer turns out to be almost two orders of magnitude less than the corresponding minimum for Pb-based shield.This proves the superior performance of W-based composites.It is worth mentioning that, this superiority is the direct consequence of the difference in removal cross-section between W (0.1673 cm −1 ) and Pb (0.0908 cm −1 ).Also, from figure 5 it is evident that, neutron removal cross-section for W-PMMA composite increases with W concentration, whereas, for Pb-PMMA composite it shows slightly decreasing trend.

Performance comparison of W-PMMA composite shield with equivalent double-layer shield
In the above section we have shown that for single-layer composite shield, the dominant contribution to total dose comes from neutrons for higher concentration of W, while primary and secondary gamma dominates for lower relative volume of W. This resulted in attaining minimum total dose by PMMA composite shield embedded with 70% W. Hence we feel prudent to explore the shielding efficiency of equivalent DLS involving W

Comparison of energy dependent neutron and gamma fluence
Next we compare neutron and gamma fluence arising due to 50 cm radius of 70% W-PMMA composite shield and same radius DLSs.Herein we consider double-layer radii combinations that delivered minimum total dose, i.e., (i) 40 cm PMMA followed by 10 cm W and (ii) 42 cm W followed by 8 cm PMMA with overall W concentration equivalent to 50% and 60% by volume respectively.
Neutron fluence spectrum for all three different shields is compared in figure 10(a).It can be observed that for all energies neutron fluence is lowest for composite shield thereby indicating it to be the best in terms of neutron dose.Inelastic scattering of fast neutrons by inner W layer and subsequent slowing down in PMMA layer causes lower fluence in fast region as compared thermal region as visible in blue curve.The trend reverses for inner PMMA layer that helps in thermalization of neutrons (red curve).Moreover, it can be observed that thermal neutron fluence for both composite and PMMA/W DLSs are nearly same.This signifies that hydrogen atoms even in 30% volume of PMMA cause same thermalization effect as 100% PMMA.
Corresponding secondary gamma spectrum for 70%W-PMMA composite shield, PMMA/W and W/PMMA DLSs are shown by black, red and blue histograms of figure 10(b) respectively.Like neutron fluence, secondary gamma fluence for composite shield lies below both the double-layer cases in the entire energy range.Even though both composite and PMMA/W DLS generates same neutron fluence in thermal region, but the latter has produced more gamma in this energy range.This is a direct consequence of the fact that dominant contribution to (n-γ) reactions arise from isotopes of natural tungsten as well as hydrogen with less overall W (having high linear gamma attenuation factor) mass in PMMA/W compared to the composite.Using RESNUCLEi card in FLUKA, it has been found that the residual nuclei produced in (n, γ) reaction are H 2 , W 181 , W 185 and W 187 .Higher gamma fluence for W/PMMA DLS in thermal region is the artefact of appreciably higher neutron thermal fluence.

Effect of W-PMMA composite based double-layer shield
We have observed that 70 vol% of W in PMMA generates minimum radiation dose at 50 cm away from source.In order to further reduce the concentration of W in PMMA composite, we have explored design of DLS with inner layer made up of 70%W-PMMA composite and outer layer with pure PMMA.Optimization of layer thicknesses revealed that 45 cm composite layer followed by 5 cm PMMA leads to total volumetric dose lower than even optimum concentration W-PMMA composite shield as shown in figure 11.

Minimum dose versus mass
Before concluding, we present the consolidated picture of different shield materials studied in this work in respect to their minimum total dose.The shields considered in figure 11 are: single-layer pure materials (Pb, PMMA and W), single-layer composites (30%Pb-PMMA and 70%W-PMMA), double-layer combinations (PMMA/W, W/PMMA and 70%W-PMMA/PMMA).Total mass of each shield (50 cm outer radius) is also displayed.It is evident that W-PMMA composite based DLS provides the minimum dose proving it to be the best when same shield volume is considered.For comparing effectiveness of different shields, we take into account of their masses by introducing specific dose, defined as dose per unit tonne of shield material.It is clear from figure 11 that pure Pb, even though almost half the weight of pure W, produces two orders of magnitude higher dose.Thus Pb, apart from being hazardous material, is also not very efficient for attenuating coupled (n-γ) radiations in comparison to W. Specific dose for the shields (left to right) shown in figure 11 are: 2.69E-05, 1.37E-04, 4.51E-07, 6.96E-08, 6.79E-08, 3.18E-08, 5.48E-09 and 6.48E-09 pSv/tonne respectively.Specific dose of Pb is nearly three orders of magnitude greater than W. It is interesting to find that apparently low-Z material PMMA performs better than Pb, but specific dose offered by PMMA is five times that of Pb.Efficiency of all W-based shields is much better than Pb.Further, specific dose for W-based DLSs are about one order more than composite shields.Study thus establishes the important fact that W-based composite or DLSs have good potential to replace Pb-based shields.

Conclusions
The present theoretical study is devoted to characterize PMMA composite, reinforced with varying concentration of W particles, for shielding coupled neutron-gamma radiation fields.Open-source Monte Carlo code FLUKA has been utilized for this purpose.Results for single-layer composite shield with optimum W content are compared with analogous composite with Pb additives as well as with equivalent DLSs involving W and PMMA.Important conclusions are summarized below.
(i) In single-layer composite shield, for higher concentration of W particles in PMMA, the prevalent contribution to total radiation dose arises due to neutrons, while capture and primary gamma contributes for lower relative volume of W.
(ii) Significant improvement in radiation shielding ability of PMMA composites can be achieved by addition of even 20 vol% W particles, with enhancement being more for larger shield dimensions.Moreover, only 25% W is sufficient to reduce primary gamma dose to significantly low level.
(iii) For any shield radius, there exists an optimum concentration of W particles in PMMA composite that offers minimum radiation dose.
(iv) Radiation dose produced by Pb-based analogous composite is found to be much higher than W-based composite.
(v) Radiation dose of optimum concentration W-PMMA composite is compared with equivalent DLSs with W and PMMA as layer materials to show that composite performs better.
(vi) A new DLS with 70%W-PMMA composite and PMMA as layer materials has been introduced that delivers least volumetric dose among all designs studied here.
(vii) W-based composite, in any configuration has the potential to replace the hazardous Pb-based shields.
specific volumes of metal particles and polymer respectively; and f m is metal mass fraction.Equation (4) leads to the following relation for composite density r

Figure 1 .
Figure 1.Density of W and Pb based PMMA composites.

Figure 2 .
Figure 2. Schematic diagram of spherical simulation system (a) W-PMMA composite shield of variable radius r, (b) representative double-layer shield involving materials M 1 and M 2 with respective radii of r 1 and r 2. Two cases studied here are: (i) M 1 : W and M 2 : PMMA and (ii) M 1 : PMMA and M 2 : W.
Source particle energy spectrum, i.e., neutron (a) and gamma (b) as reproduced in FLUKA are shown in figure 4.

Figure 4 .
Figure 4. Energy spectrum of (a) source neutron and (b) primary gamma as reproduced in FLUKA and used for simulation.

Figure 5 .
Figure 5. Linear attenuation coefficient and neutron removal cross-section as a function of heavy metal (W/Pb) concentration in PMMA.

Figure 6 .
Figure 6.Variation of total dose with W concentration in W-PMMA composite shield.Neutron (red), secondary gamma(blue), primary gamma (green) contributions in total dose (black) are shown for different spherical shield radius of 10 cm (a), 25 cm (b), 50 cm (c) and 75 cm (d).

Figure 7 .
Figure 7.Total dose as a function of W content in polymer composite with optimum concentration for each thickness marked with arrow.Results shown refer to shield radius 10 cm (purple), 25 cm (red), 50 cm (green), 75 cm (cyan) and 100 cm (blue).

Figure 8 .
Figure 8.Comparison of total doses obtained with 50 cm W-PMMA and Pb-PMMA composite shields.

Figure 9 .
Figure 9. Variation of individual doses with concentration of W: (a) neutron dose, (b) secondary gamma dose and (c) the total dose.In all the figures black bars represent composite shield, red and blue bars refer to PMMA/W and W/PMMA double-layer shields.Outer radius for all the cases is fixed at 50 cm.

Figure 10 .
Figure 10.Energy dependent fluence spectrum of neutron (a) and secondary gamma (b) radiations for 50 cm shield radius.Black histogram refers to 70%W-PMMA composite shield.Red and blue represent PMMA/W and W/PMMA combinations respectively.

Table 1 .
Densities of W-PMMA and Pb-PMMA composites for different volume percent and mass percent of heavy metals (W or Pb).In each case remaining quantity refers to PMMA.

Table 2 .
Comparison of neutron removal crosssection obtained by FLUKA and MCNP.

Table 3 .
Estimates of total dose due to different composition W-PMMA composite shields of five different radii.PMMA as individual layers and compare them with optimum concentration composite shield.Both the combinations of layer-ordering, i.e., high-Z followed by low-Z (W/PMMA) and low-Z followed by high-Z (PMMA/W) as illustrated in figure 2(b) are considered.4.4.1.Comparison of dosesIn figure9we compare individual doses pertaining to neutron (a) and secondary gamma (b) at outer surface of 50 cm spherical shields.The distinct scenario considered are (i) single-layer W-PMMA composite shield with concentration of W same as in previous section, (ii) W/PMMA DLS, and (iii) PMMA/W DLS.The last two cases have been simulated with the aim of determining optimum two-layer interface position and hence effective volume fraction of W in DLS that delivers minimum total dose.Observations made from figure 9 are the following: (i) neutron dose for PMMA/W combination does not show appreciable variation with volume fraction of W; (ii) for W/PMMA shield neutron dose increases with rise in W vol%, nevertheless, it is lower than PMMA/W shield; iii) for very low W content, neutron dose is minimum for W/PMMA case; iv) secondary gamma dose for both DLSs are comparable and much higher than composite shield; (iv) unlike composite shield, total dose [figure9(c)] for PMMA/W DLS does not follow any pattern, W/PMMA exhibits a trivial dip in total dose indicating presence of optimum W concentration at 60% (with 42 cm radius of inner W layer).Further, among two types of DLSs, W/PMMA provides lower dose.However, global minimum for total dose is attained in case of composite shield.Consolidated results for composite and two cases of DLSs are listed in table 4. and

Table 4 .
Comparison of minimum total dose for 50 cm composite shield and double-layer combinations.