INTRODUCTION
SKYSHINE HAS been and still is the primary contributor to prompt radiation doses off-site at high-energy accelerator facilities. A general definition of skyshine is radiation particles that are emitted toward the sky and descend back to the ground due to scattering from air molecules. These radiation particles traditionally consist of both photons and neutrons but are dominated by neutrons at accelerator facilities. At electron accelerators , these neutrons are generated from GeV-range electron beam losses on accelerator components and structures during normal accelerator operations throughout the year, and they belong primarily to the giant resonance with energies less than 20 MeV and also high-energy neutrons with energies greater than 100 MeV (^{Rindi and Thomas 1973} ^{; } ^{Vylet and Liu 2001} ^{; } ^{Rokni et al. 2008} ).

Within the coming year, SLAC National Accelerator Laboratory will complete installation of a 4 GeV superconducting electron accelerator for its Linac Coherent Light Source II (LCLS-II) with first light expected in calendar year 2020. One significant upgrade of LCLS-II is increasing the beam’s repetition rate from 120 Hz to 1 MHz, which translates to a much higher beam power. An increase in beam losses on accelerator components and structures is expected during normal LCLS-II accelerator operations (6,000 h y^{−1} ), which will lead to an increase in neutron generation (and neutron skyshine). Such beam losses that occur within the Beam Transport Hall (BTH) tunnel section of the accelerator are of special interest because this section is located above ground. Both the sides and roof of the BTH tunnel are shielded with concrete, but neutrons generated from beam losses inside can contribute neutron skyshine dose to the public off-site beyond SLAC grounds. One of the shielding design requirements at SLAC is that the annual dose to a member of the public (dominated by skyshine neutrons ) is no more than 0.05 mSv y^{−1} .

Traditionally, the estimation of skyshine dose is performed with semiempirical formulae and analytical codes that estimate the neutron fluence at a certain distance. The neutron fluence then can be multiplied by a fluence-to-dose conversion factor to obtain the estimated dose at that distance. The key parameter in all the semiempirical formulae is the effective neutron attenuation length in air λ , which is based on the neutron energy spectrum of the skyshine (^{Cossairt 2016} ). For example, the reported values of λ in literature can range from 250 m to 850 m (^{Rindi and Thomas 1975} ) and from 300 m to 1,000 m (^{Liu et al. 1999} ). The general practice is that a smaller value of λ is appropriate when lower-energy neutrons in the 0.1 MeV to 20 MeV range (giant resonance neutrons ) dominate the neutron spectrum. On the other hand, a higher value is more appropriate when the neutron spectrum is instead dominated by high-energy neutrons with energies above 100 MeV, resulting from high-energy photons above the photopion production threshold (^{Vylet and Liu 2001} ).

Fig. 1 plots the estimated annual dose equivalent per watt of beam loss as a function of distance, which is based on calculations with several of these formulae for 6,000 h of 4 GeV LCLS-II operation in 1 y. Eqns (1), (2), and (3) provide the semiempirical formulae as given by ^{Patterson and Thomas (1973)} ^{, } ^{Rindi and Thomas (1975)} , and ^{Stevenson and Thomas (1984)} , respectively. The variables in the equations are as follows. H is the annual dose equivalent (in mSv y^{−1} ); r is the radial distance from the source (in m); and P _{n} is the neutron-fluence-to-dose-equivalent conversion coefficients (in mSv m^{−2} ), which in this study are from ^{Pelliccioni (2000)} . The parameter a is the buildup factor: 7 for the plotted ^{Rindi and Thomas (1975)} curve and 2.8 for the ^{Patterson and Thomas (1973)} curve, with a corresponding buildup relaxation length μ of 56 m. Q is the annual neutron source strength emitted from the shielding surface (in neutrons y^{−1} ).

Fig. 1: Different methods from semiempirical formulae and a code for estimating neutron skyshine dose as a function of radial distance from the beam loss. The effective neutron attenuation length in air λ is in units of meters and indicated in the legend.

In this study, the value of Q was obtained from FLUKA Monte Carlo (^{Ferrari et al. 2005} ^{; } ^{Böhlen et al. 2014} ) calculations for 1 W loss of 4 GeV electrons inside the concrete BTH tunnel. For eqns (1) and (2), the Q values at different neutron energies were multiplied by P _{n} conversion coefficients from ^{Pelliccioni (2000)} . For eqns (3) and (4), the neutron energy spectrum emitted from the tunnel roof was integrated over all energies to obtain a Q value of 1.56 × 10^{13} neutrons y^{−1} . The FLUKA calculation was normalized to an annual electron loss rate of 3.37 × 10^{16} electrons y^{−1} (1 W of 4 GeV electrons and 6,000 operation h y^{−1} ). Further details of the FLUKA calculation are described in a later section. Finally, λ is the effective neutron attenuation length in air (in m), which is indicated in Fig. 1 for each curve:

A more recent study by ^{Stapleton et al. (1994)} sought to improve the dose calculations at distances less than 100 m from the work by ^{Stevenson and Thomas (1984)} . Eqn 4 provides the resulting formula, where b is 40 m and λ is the neutron attenuation length in air (in m) associated with the upper neutron cut-off energy E _{c} assuming a typical 1/E neutron spectrum. The plotted curve uses a λ of about 620 m from an E _{c} of 4 GeV (^{Stapleton et al. 1994} ):

In addition, the estimated dose from the SKYSHINE code (^{Jenkins 1974, 1989} ) is also plotted in Fig. 1 . SKYSHINE is an analytical code that combines source and shielding algorithms from SHIELD11 (^{Nelson and Jenkins 2005} ) to estimate the yearly dose from neutron skyshine. The different estimation methods yield rough agreement within about 1.5 orders of magnitude over all radial distances shown. Furthermore, another source of uncertainty lies with the effective attenuation length λ that was chosen for the formulae, which can cause a variation up to a factor of 10.

Therefore, in this study, the Monte Carlo code FLUKA (^{Ferrari et al. 2005} ^{; } ^{Böhlen et al. 2014} ) was used to simulate 4 GeV LCLS-II beam losses within a generalized section of the BTH concrete tunnel. From the neutrons that escape the roof and side walls of the tunnel, FLUKA calculates the fluence and effective dose of neutron skyshine as a function of both distance from the tunnel wall and angle relative to the beam direction.

Separation of neutron transport pathways
The methodology for calculating skyshine dose using Monte Carlo simulations was adapted from the study by ^{Oh et al. (2016)} . A key principle in Oh’s study is that skyshine dose to the public off-site of an accelerator facility is the summation of several neutron transport pathways. The end of each pathway is a person off-site, for example. Fig. 2 is a diagram that visualizes the different transport pathways that neutrons would take to reach a location at a certain distance away from the accelerator tunnel:

Fig. 2: Transport pathways for neutrons that escape the accelerator tunnel: (1) skyshine, (2) direct, (3) groundshine, and (4) multishine. Method adapted from study by ^{Oh et al. (2016)} .

The skyshine term (1) consists of radiation particles, dominated by neutrons , that escape the accelerator tunnel and are emitted skyward and descend back towards the ground by scattering from air molecules in the atmosphere.
The direct term (2) consists of those that escape the accelerator tunnel laterally and do not scatter off the sky or ground.
The groundshine term (3) are particles that escape laterally with a downwards trajectory and are scattered by the ground back up.
The multishine term (4) consists of particles that scatter off both the ground and sky multiple times before ultimately reaching the off-site location.
Attenuation from any nearby buildings or hills mainly affect the direct, groundshine, and multishine terms. Furthermore, each pathway contributes differently to the total dose at the location of interest, and their relative contributions will be characterized using neutron fluence and effective dose as the primary metrics. Because neutrons scatter more than photons with air molecules and contribute much more to the total dose off-site than photons, only neutron dose is considered in this study. The different transport pathways for neutrons escaping the accelerator tunnel can be separated from each other by replacing the air or ground in the Monte Carlo simulation with vacuum, which results in no interactions in that medium. Fig. 3 demonstrates the different cases of FLUKA calculations for separating the neutron transport pathways.

Fig. 3: Separation of neutron transport pathways into four cases by replacing air or ground with vacuum (no neutron interactions). Method adapted from study by ^{Oh et al. (2016)} .

As seen in Fig. 3 , case 1 includes all the pathways from Fig. 2 and has no vacuum medium. By replacing the sky with vacuum, case 2 isolates only the neutrons reaching an off-site location from the direct term (2) and groundshine term (3). Case 3 isolates the direct term (2) by replacing both the ground and sky with vacuum, so neutrons in those mediums stream through without interaction or scattering. Lastly, case 4 has only the skyshine term (1) and the direct term (2) by replacing the ground with vacuum. The neutron fluence and effective dose calculated with the different cases can be logically subtracted or added to isolate each individual transport pathway. For example, the skyshine term (1) is obtained from case 4 − case 3. Similarly, the groundshine term (3) is obtained from case 2 − case 3.

Calculation of neutron skyshine with FLUKA
The Monte Carlo code FLUKA 2011 version 2c.6 (^{Ferrari et al. 2005} ^{; } ^{Böhlen et al. 2014} ) was used to simulate electron beam losses in the BTH and to characterize the skyshine generated from the loss scenario. For the beam loss scenario, electron primaries were emitted as a pencil beam with an energy of 4 GeV and normally incident on the face of cylindrical pure copper (8.96 g cm^{−3} ) target. The copper target has a radius of 3.136 cm (2 Molière radii) and a thickness of 28.72 cm (20 radiation lengths). The target was located inside the BTH tunnel at beam height of 113 cm from the concrete floor of the tunnel.

Fig. 4 shows a top view of the BTH tunnel in FLUKA as plotted using the flair tool (^{Vlachoudis 2009} ). A generalized section of the accelerator tunnel was simulated with a lateral Portland concrete^{2} (2.3 g cm^{−3} ) wall thickness of 180 cm. The concrete floor and roof both have thicknesses of 120 cm, and the length of the tunnel section was 8 m. The tunnel rests on 50 cm of soil^{3} (1.5 g cm^{−3} ), and the maximum altitude of the sky (dry air;^{4} 1.205 × 10^{−3} g cm^{−3} ) was set at 2 km above the soil level. This sky height is sufficient for multiple interactions of the neutrons with the air because the neutron attenuation length in air is on the order of 250 m to 850 m (^{Rindi and Thomas 1975} ).

Fig. 4: FLUKA model of a section of the BTH accelerator tunnel and detector rings for scoring neutron fluence and effective at increasing distances from the tunnel wall up to 1 km. The detector rings are further subdivided into 15° bins.

FLUKA detector rings for scoring neutron fluence and effective dose (USRBIN and EWTMP fluence-to-dose conversion coefficients in FLUKA) were located at 5, 10, 50, 100, 150, 200, 300, 350, and 400 m radially from the tunnel wall. Additional detector rings were located at 100 m increments from 400 m to 1 km. The detector rings in Fig. 4 had a height of 5.4 m above the soil and were modified to characterize the neutron fluence and effective dose with respect to the beam direction by dividing the detector rings into 15° polar angle bins (from 0° to 360°). To improve statistics of the FLUKA results, the detector ring had a radial thickness that scaled as 10% of its distance from the accelerator tunnel. For example, the detector ring at a distance of 10 m had a radial thickness of 1 m, 50 m had a thickness of 5 m, and so forth.

For the FLUKA calculations, neutron production was activated with PHOTONUC set for all energies, and the neutron energy transport cutoff was set at 1 eV using PART-THR. Electron and photon transport and production cutoffs were both set at 1 MeV using EMFCUT. Region importance BIASING was implemented by dividing the concrete tunnel into layers and was activated for all particles.

The operation plan of LCLS-II assumes 35 W of 4 GeV electron beam losses on average inside the concrete-shielded accelerator tunnel in 6,000 operation h y^{−1} (^{Santana and Mao 2013} ). In this paper, the FLUKA-calculated neutron fluence and effective dose will be normalized to 1 W of beam loss. This provides ease of scaling for the results in this paper and can be applied to similar electron accelerator facilities elsewhere besides SLAC. The normalization factor for FLUKA results is 3.3704 × 10^{16} electrons lost in 1 y, which corresponds to an average 1 W of 4 GeV beam loss over 6,000 h of operation.

Neutron source from electron beam loss
Fig. 5 shows an elevation view of the annual effective dose of neutrons near the BTH accelerator tunnel. The electron beam direction is from left-to-right at a height of X = 113 cm. A perfectly absorbing medium (a black hole in FLUKA) was implemented in the upstream and downstream tunnel directions. This technique removed the neutrons (generated from 4 GeV electron beam loss on the copper target) that were streaming inside the accelerator tunnel from reaching the scoring detectors outside the tunnel. Thus, only the neutrons escaping the tunnel’s roof and side walls remained in the simulation.

Fig. 5: Elevation view of the annual effective dose of neutrons near the BTH accelerator tunnel.

Fig. 6 plots the isolethargic neutron spectrum dφ /d(lnE ) (units of cm^{−2} s^{−1} W^{−1} ) exiting 1.2 m of concrete roof as a function of neutron energy (MeV). Note that the normalization for the neutron fluence is per second (does not factor in 6,000 h of operation time) and per watt of 4 GeV beam loss. Such a plot of the neutron fluence provides an easier visual understanding of the neutron fluence magnitude at each energy region. Uncertainties in the neutron fluence from the FLUKA calculation are not plotted in Fig. 6 because they are less than 1%. The neutron spectrum has two clear peaks around 2 MeV (evaporation neutrons from interactions of high-energy hadrons in the concrete shielding) and around 80 MeV (high-energy neutrons ). For the two peaks, 66% of the neutrons have energies above 10 MeV, and 21% of the neutrons have energies between 0.5 and 10 MeV. This is the typical equilibrium neutron spectrum because the spectral shape does not change with thicker shielding (a concrete roof in this case), but only the magnitude of the fluence is reduced.

Fig. 6: Isolethargic neutron spectrum dφ /d(lnE ) (units of cm^{−2} s^{−1} W^{−1} ) exiting the 1.2 m concrete roof of the BTH accelerator tunnel.

Dependence of neutron energy spectra with radial distance
In a similar manner as Fig. 6 from the previous section, Fig. 7 plots the neutron fluence spectrum at increasing distances from the accelerator tunnel as a function of neutron energy. These neutron energy spectra were calculated by averaging over all angles within a detector ring in FLUKA. Each plot corresponds to one of the four cases detailed earlier in Fig. 3 . Note that the normalization is now per year (6,000 h operation time). Also, the y-axis in Fig. 7 has a logarithmic scale to allow comparison of the neutron energy spectra, which are scored in the detector rings at increasing radial distances from the accelerator tunnel wall out to 1 km. As expected, the neutron energy spectra for the four cases are similar to the equilibrium spectrum exiting the 1.2 m concrete roof in Fig. 6 (peaks at around 2 MeV and 80 MeV). With the technique from ^{Oh et al. (2016)} , the different cases can be logically separated from each other to isolate the neutron transport pathways to obtain:

Fig. 7: Isolethargic neutron spectrum dφ /d(lnE ) (units of cm^{−2} y^{−1} W^{−1} ) at increasing distances from the accelerator tunnel. Each plot corresponds to one of the four cases used to separate the transport pathways of neutrons escaping the accelerator tunnel.

Skyshine (pathway 1) = case 4 − case 3.
Direct (pathway 2) = case 3.
Groundshine (pathway 3) = case 2 − case 3.
Multishine (pathway 4) = case 1 − case 2 + case 3 − case 4.
As an example, Fig. 8 plots the isolethargic neutron spectrum, which has been calculated to obtain purely the skyshine transport pathway. Uncertainties in the neutron fluence are not plotted to avoid visual clutter but are less than about 10% for MeV range neutrons , which dominate the spectrum. The skyshine transport pathway is dominated by neutrons within the few MeV range (evaporation neutrons ), but the pronounced peak at 80 MeV (high-energy neutrons ) in Fig. 8 is no longer as dominant a component of the neutron spectrum as compared with the equilibrium spectrum exiting the concrete roof in Fig. 6 . Recall in Fig. 6 that 66% of the neutrons have energies above 10 MeV, and 21% of the neutrons have energies between 0.5 and 10 MeV. Now in Fig. 8 for the neutron spectrum at a distance of 500 m, 29% of the neutrons have energies above 10 MeV, and 44% of the neutrons have energies between 0.5 and 10 MeV. This occurs because higher-energy neutrons have a larger effective attenuation length λ in air, and thus, they scatter less with air molecules in the atmosphere back down to the ground, especially compared with the neutrons around a few MeV.

Fig. 8: Isolethargic neutron spectrum dφ /d(lnE ) (units of cm^{−2} y^{−1} W^{−1} ) for the purely skyshine transport pathway, which was isolated with case 4 − case 3.

Typical neutron detectors used for measuring skyshine are capable of measuring neutrons with energies around 2 MeV but are completely blind to neutrons with energies above 80 MeV. Traditionally, neutron skyshine dose measurements were multiplied by a factor of 2 to account for the high-energy neutron component. The skyshine neutron spectrum in Fig. 8 demonstrates that this practice is not necessary because neutron skyshine is dominated by neutrons around a few MeV in energy, which are readily detectable.

Angular dependence of skyshine dose
Skyshine calculations in literature (Fig. 1 ) traditionally stop after characterizing the dose as a function of distance. The neutron energy spectra in the previous section would be folded with fluence-to-dose conversion coefficients, and the effective dose due to skyshine neutrons would be simply estimated as a function of distance. This study took an extra step and characterized the angular dependence of skyshine in addition to its dependence on radial distance by subdividing the detector rings in Fig. 4 into 15° bins for each of the four cases in Fig. 3 .

Fig. 9 plots the annual effective dose of neutrons from all transport pathways (case 1) as a function of the polar angle of the scoring detector. The x-axis is reversed to give a more intuitive plot of the angular dose profile, where the electron beam direction travels from left to right along the x-axis towards 0°. The effective dose is normalized to 1 W of 4 GeV electron beam loss inside the accelerator tunnel and 6,000 h of accelerator operation time in 1 y.

Fig. 9: Annual effective dose of neutrons from all transport pathways (case 1) as a function of the polar angle of the scoring detector. The distance of the scoring detector from the tunnel wall is indicated in the legend. w.r.t.: with respect to.

It can be observed for the neutron dose values around 90° compared with neutron doses at 0° and 180°. This ratio is at least an order or magnitude and decreases with increasing distances from the accelerator tunnel to about a factor of 3 at 1 km. However, this strong angular dependence is primarily due to the direct (pathway 2) term due to the geometry of the BTH tunnel in the FLUKA simulation. Fig. 10 plots the skyshine (pathway 1) and multishine (pathway 4) neutron doses as a function of angle with the same y-axis scale as Fig. 9 for comparison. The dose curves in Fig. 9 for distances close to the tunnel (such as 5, 10, 50, and 100 m) have flattened out. At distances of hundreds of meters and greater, the angular dependence of the neutron dose in Fig. 10 has also decreased compared with Fig. 9 , but a factor of 2–3 is still observable. Previous methods of calculating skyshine dose do not account for the angular dependence of skyshine, unlike the new methodology presented in this paper.

Fig. 10: Annual effective dose of neutrons from the skyshine and multishine pathways (case 1 − case 2) as a function of the polar angle of the scoring detector. w.r.t.: with respect to.

Fig. 11 replots the annual effective dose of neutrons from Fig. 9 but now as a function of distance from the accelerator tunnel wall. To avoid visual clutter, only the dose results from five angles are plotted. However, it may not be realistic for all accelerator facilities to account for every neutron transport pathway. It was demonstrated with Figs. 9 and 10 that the direct transport pathway has a significant effect on the angular dependence of the neutron dose at distances close to the loss location.

Fig. 11: Annual effective dose of neutrons as a function of distance with each curve’s corresponding angle indicated in the legend.

The following is an example of how the new methodology presented in this paper was applied for evaluating neutron skyshine at SLAC. If one accounts for geographical conditions at SLAC, the groundshine and direct pathways can be excluded from Fig. 11 because the BTH accelerator tunnel at SLAC is located within a basin and surrounded by hills. Therefore, only the skyshine and multishine pathways contribute to the annual dose off-site SLAC. Fig. 12 plots the annual effective dose of neutrons from the skyshine and multishine pathways as a function of distance from the tunnel wall. Results are normalized to 1 W of 4 GeV electron beam loss and 6,000 h of accelerator operation in 1 y. For reference, SLAC’s shielding design limit to the public is 0.05 mSv y^{−1} from skyshine radiation. It is expected that LCLS-II operations will generate 35 W of annual beam losses in the BTH tunnel. Therefore, the shielding design limit of 0.05 mSv y^{−1} per 35 W of annual losses is 1.4 × 10^{−3} mSv y^{−1} W^{−1} , which is also plotted.

Fig. 12: Annual effective dose of neutrons from the skyshine and multishine pathways as a function of distance. This represents the geographical scenario of the BTH accelerator tunnel at SLAC. SLAC’s shielding design limit of 1.4 × 10^{−3} mSv y^{−1} W^{−1} to a member of the public is plotted for reference. The neutron skyshine dose calculated from the SKYSHINE code (^{Jenkins 1989} ) and from the formula by ^{Stapleton et al. (1994)} are also plotted for comparison.

The skyshine dose curve in Fig. 1 from the analytical SKYSHINE code (^{Jenkins 1989} ) is also plotted for comparison, and it has a very different slope than the FLUKA results. The SKYSHINE code overestimates the neutron dose up to an order of magnitude at distances less than 700 m. Additional comparison between SKYSHINE and FLUKA results showed that SKYSHINE also overestimates the neutron dose through the 1.2-m-thick concrete roof of the BTH tunnel by at least order of magnitude: 1,580 mSv y^{−1} W^{−1} (SKYSHINE code) vs. about 50 mSv y^{−1} W^{−1} (FLUKA calculation in Fig. 5 ). At distances greater than 700 m, SKYSHINE begins to underestimate the neutron skyshine dose, which is a similar observation as in Fig. 1 . For additional comparison, the curve from Fig. 1 that is calculated from the semiempirical formula by ^{Stapleton et al. (1994)} is also plotted in Fig. 12 . As can been observed, the semiempirical formula with a λ of 620 m gives results closer to FLUKA than compared with the SKYSHINE code.

In Fig. 12 , the annual skyshine dose exceeds the limit at distances less than about 50 m from the tunnel wall, but it is very unlikely for a member of the public to be that near the accelerator tunnel for extended periods of time. Instead, the location closest to SLAC where members of the public may be is the Stanford Guest House, which is marked in Fig. 12 . The Stanford Guest House is located about 350 m radially from the BTH tunnel where beam losses from LCLS-II operation are expected to occur and is at 80° relative to the LCLS-II beam direction. From Fig. 12 , the estimated annual effective dose to a member of the public at the Stanford Guest House is about 0.005 mSv over 6,000 h, which is factor of 10 below the shielding design limit for skyshine radiation.

For many accelerator facilities, including the one at SLAC, the realistic length of the accelerator tunnel is much longer than the 8 m used in FLUKA calculations (Figs. 4 and 5 ). Therefore, additional calculations were performed to evaluate the sensitivity of the skyshine neutron dose to the length of the tunnel. The same methodology as before was implemented but for 14- and 100-m-length tunnels. The beam loss target was centered halfway within the longer tunnels for both cases. Increasing the tunnel length from 8 to 14 m increases the skyshine and multishine neutron doses in Fig. 10 by 10% for angles between 75° and 180° and by 15–20% for the more forward-direction angles between 0° and 75°. Further increases to the tunnel length from 14 to 100 m increases the neutron doses by about 1–3% across all angles. Applying this to the earlier analysis in Fig. 12 , the annual effective dose to a member of the public at SLAC’s Stanford Guest House is still below the shielding design limit for skyshine. In the future, SLAC will upgrade LCLS-II to LCLS-II HE, which will increase the electron beam energy from 4 GeV to 8 GeV. Additional calculations were performed with the same methodology as the previous sections, and although the beam energy is doubled from 4 GeV to 8 GeV for LCLS-II HE, the annual effective dose per watt of beam loss increases by no more than 10%. This is because the magnitude of the equilibrium neutron spectrum penetrating through 1.2 m of concrete roof in Fig. 6 is about 10% higher for 8 GeV than 4 GeV, and the skyshine dose scales with neutron fluence (H = P _{n} × Φ ).

CONCLUSION
Older methods of calculating neutron skyshine provide estimates of the effective dose as a function of distance. However, they can overestimate or underestimate the dose because they often assume a single value for the effective absorption length λ of neutrons in air. Furthermore, they do not account for the angular dependence of skyshine. The new methodology presented in this paper uses FLUKA Monte Carlo code to characterize the neutron skyshine dose as both a function of distance from the accelerator tunnel and angle with respect to the beam direction. Furthermore, the slopes of the calculated neutron dose curves in this study are in good agreement with those given by semiempirical formulas in literature.

For future LCLS-II operations at 4 GeV, the annual effective dose due to neutron skyshine to a member of the public off-site at the Stanford Guest House will be below SLAC’s shielding design limit of 0.05 mSv y^{−1} from skyshine. Skyshine measurements will be conducted by the SLAC Radiation Protection Group around the BTH area when the LCLS linac beam resumes operation in 2020 and also when the high-power LCLS-II superconducting linac beam starts in 2021. These measurements will be used to validate and provide a benchmark for the calculations in this study.

This study’s characterization method is also applicable for evaluating the neutron skyshine dose from line losses along the length of an accelerator by simply integrating the dose at different distances and angles. The methodology and characterization of neutron skyshine in this study provides skyshine dose data for health physicists at electron accelerator facilities to evaluate dose limits and design shielding appropriately.

Acknowledgments
This material is based upon work supported by the US Department of Energy, Office of Science, Office of Basic Energy Sciences, under contract no. DE-AC02-76SF00515.

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