The potential of the ILC beam dump for high-intensity and large-area irradiation field with atmospheric-like neutrons and muons

It is possible to provide irradiation spaces at a location perpendicular to the beam axis or downstream of the beam dump. We perform simulations in the following three geometries to examine the neutron and muon fluxes:

1. Geometry-1

   Uniform concrete shield around beam dump;

2. Geometry-2

   Concrete shield of thickness $T_{\rm shield}^{(x)}$ perpendicular to beam axis, and irradiation space placed behind it;

3. Geometry-3

   Concrete shield of thickness $T_{\rm shield}^{(z)}$ downstream of beam dump, and irradiation space placed behind it.

The three geometries are described in Fig. 1.

Calculations using Geometry-1 provide an overall characterization of the neutron and muon fluxes around the dump and their attenuation. This will help to determine the optimum location of the irradiation field. For simplicity, the shield is uniformly made of concrete. Although, in reality, iron shields are likely made of different parts, their length can be converted into an equivalent length of concrete. For muons, the stopping power of steel is about 3.2 times higher than that of concrete, which results in a shorter attenuation distance. For neutrons, iron has an interaction length approximately 2.5 times shorter than that of concrete and therefore has a shorter attenuation distance.²²2The density of the concrete used in the calculations is 2.3 g/cm³, and the composition is standard [20].

Geometry-2 and -3 have a space with a width of 3 m, assuming irradiation of large volumes such as cars. The results can be inferred to some extent from the results of Geometry-1. However, the flux spread and energy spectrum are slightly different in the concrete and the space. For this reason, calculations are also carried out for Geometry-2 and -3, which are close to the expected shape of the irradiation field.

The PHITS code [21] is used in this study. Electromagnetic showers make use of EGS5 [22], which is implemented in PHITS. Neutrons are mainly produced by photons in electromagnetic showers or secondary hadrons interacting with nuclei or nucleons. In PHITS, they are calculated based on JAM [23], JQMD [24], and GEM [25] models modified for photonuclear reactions. INCL4.6 [26] is used for the transport of hadrons such as neutrons. These models have been validated with various experimental results [27, 28]. For the interaction of neutrons with nuclei below 200 MeV, an Evaluated Nuclear Data Library, JENDL4.0/HE [29, 30], is used. It is one of the best ways for neutron transport in that energy range.

The intensity of neutrons produced in the electron beam dump and their attenuation in the shield has been comprehensively studied at SLAC [31]. This study and PHITS are widely used in the shielding design of operational electron accelerator facilities, and their consistency has been confirmed in the operation of accelerator facilities.

Muons are mainly produced by pair production from a real photon in electromagnetic showers, pair production from a positron above 43.7 GeV, and $\pi^{\pm}/K^{\pm}$ decay. The differential cross section obtained by QED’s perturbation theory is implemented in PHITS for the former two. The calculation accuracy of the muon pair production from a real photon, which is the dominant process, has been verified with high accuracy [32] by the data of the muon shielding experiment at SLAC [33, 34].

For neutron and muon production, the direct electron production due to virtual photons is negligible in thick targets, such as beam dumps.

Figure 2 shows the density distribution of the fluxes in Geometry-1. The beam axis is assigned to the $z$-axis, and its perpendicular direction to the $x$-, $y$-axis. The $x$ and $y$ coordinates of the beam axis are zero.

Neutrons are emitted almost isotropically from the beam dump. It can be seen from the left panel of Figure 2 that the core of neutron production is in the region between 2 - 4 m in the beam direction from the beam injection point. Since the radiation length of water is 36 cm, that region corresponds to a length of 6 - 11 radiation length, where the photons in the evolved electromagnetic shower produce neutrons through photonuclear reactions. We, therefore, see that the high-intensity neutrons can be obtained close to the neutron emission region on the side of the beam dump.

As shown in the right panel of Figure 2, muons tend to be scattered in the beam direction. These forward muons are mainly produced by pair production from the bremsstrahlung. This shows the potential for a high-intensity muon irradiation field downstream of the beam dump on the beam axis.

We quantify the production and attenuation of neutrons and muons. In Figure 3, the $z$ distribution of the flux at each $x$-range is shown. The $y$-direction is integrated in the region $-50~{}{\rm cm}<y<50~{}{\rm cm}$. The right $y$-axis of the plots shows the flux ratio to the secondary cosmic ray at sea level in Tokyo. Fluxes in the beam dump area that cannot be used for irradiation are represented by dotted lines. In the initial phase of the ILC, it can be seen that the beam dump can deliver neutrons $\sim 10^{11}$ times the secondary cosmic ray on the region perpendicular to the beam axis and muons $\sim 10^{8}$ times downstream of the beam dumps.

We perform calculations using Geometry-2 to investigate the flux and energy distribution of neutrons and muons in the irradiation space placed perpendicular to the beam axis. Figure 4 shows the $z$-dependence of the flux in that space. The $x$-direction is integrated over the whole space, and the $y$-direction over the region $-50~{}{\rm cm}<y<50~{}{\rm cm}$. The thickness of the concrete shield is chosen for $T_{\rm shield}^{(x)}=0,0.5,$ and 1 m. The flux is found to be maximum at $z=3\text{ - }4$ m. The variation of neutron flux intensity is within an order of magnitude over 10 m length, which enables uniform large-area neutron irradiation.

Neutron fluxes decrease by one order of magnitude for a concrete shield of 1 m, while muons 0.5 m. The muons in the perpendicular space are mainly due to the decay of charged pions produced in photonuclear reactions. Charged pions emitted with a wide production angle have low energy due to kinematics and energy loss in materials. As a consequence, muons have low energy and penetration power. Therefore, the number of muons can be adjusted by the thickness of the shield without reducing neutrons.

We found that the neutrons in the perpendicular space have a spectrum quite similar to the secondary cosmic neutrons. Figure 5 shows the energy distribution of neutrons and muons at $z=6\text{ - }7$ m, where the dashed curves are the secondary cosmic rays at sea level multiplied by $3\times 10^{10}$, calculated with the EXPACS code [36, 37, 38]. We can obtain the neutron spectra that perfectly agree with the secondary cosmic neutrons spectrum up to 2 GeV in the perpendicular space. Higher energy neutrons can also be obtained, although the spectra are different. These characteristics of the ILC cannot be obtained with other neutron irradiation facilities using low-energy protons. The behavior of the high-energy tail of the neutron spectra depends slightly on the $z$-range of the irradiation space. We found that the ILC spectra are particularly consistent with that of cosmic-ray neutrons at $z=6\text{ - }7$ m. This $z$-range is located at about 30 degrees to the beam axis from the region of maximum neutron production³³3$z=2\text{ - }3$ m on the beam axis. in the beam dump. It can be seen that the spectra do not change significantly when the thickness of the shielding is changed. Spectra at different $z$-ranges are shown in Appendix A. From these findings, this perpendicular space is suitable for studying the soft errors induced by cosmic ray neutrons.

For the distributions of muons, the peak of the spectrum results from the combined effect of absorption at low energies and production spectrum at high energies. The peak position is of the order of total energy loss in the beam dump and the shield, which is a few 100 MeV in the perpendicular space. Therefore, it differs from the peak position of the secondary cosmic ray muons. However, the discrepancy can be improved in the region downstream of the beam dump, as described in the next section.

This agreement of the neutron spectra is qualitatively understandable. Secondary cosmic neutrons are induced by the primary cosmic protons. In contrast, in the case of electron incidence on beam dumps, neutrons are induced by bremsstrahlung photons. The energy dependence of the primary cosmic proton spectrum is $d\phi/dE\propto 1/E^{p}$, with $p$ ranging from 1 to 2.7 above 1 GeV, close to 2. On the other hand, the spectrum of bremsstrahlung in thick targets is $1/E^{2}$, and they show a similar distribution. Spectra of secondary hadrons produced by the interaction of the photons, protons and also other hadrons with matter typically have an energy dependence of $\sim 1/E$. Although the high energy proton emits high energy neutrons forward and breaks the $1/E$ structure, this is a minor effect in the perpendicular region. Moreover, secondary hadrons produce additional neutrons in the atmosphere or the water beam dump, which further average the neutron spectra. Thereby the difference in the produced neutron spectra due to the difference of the initial particles is lessened.

As in section 4.2, we perform the calculations using Geometry-3. The number of high-energy muons downstream of the beam dump differs between the electron and positron beams. In this section, we show the results for the electron beam dump. Details of the differences are given in Sec. 4.5.

Figure 6 shows the $x$-dependence of the flux in that irradiation space, where $T_{\rm shield}^{(z)}=1,5,$ and 10 m are chosen for the thickness of the concrete shield. The flux is integrated over the width for $z$ and in the region $-50~{}{\rm cm}<y<50~{}{\rm cm}$. Especially, we can utilize high-intensity muon flux on the beam axis. The forward muons are more penetrating than neutrons, so the ratio between the fluxes of muons and neutrons can be optimized by changing the shielding thickness. The variation of muon flux intensity is within an order of magnitude in a region within 1 m² centered on the beam axis, enabling large-area muon irradiation. If an irradiation sample larger than 1 m is preferred to be uniformly irradiated with muons, it may be necessary to rotate the target or vibrate it in the $x$ direction.

As can be seen from Figures 6 (and 3), the neutron attenuation per distance becomes more gradual in the region where the shielding thickness exceeds 5 m. This is because the neutrons in this region are induced by muon interaction with the nucleus.

We found that the muons and neutrons in this space have a spectrum quite similar to secondary cosmic rays. Figure 7 shows the energy distribution at $|x|=0\text{ - }0.5$ m in the space, where the dashed curves are the secondary cosmic ray at sea level in Tokyo, scaled by $10^{8}$. The neutron spectrum of the ILC is perfectly consistent with the secondary cosmic ray spectrum up to 400 MeV. Sufficient quantities of neutrons up to 40 GeV are available. Also, the high energy beam of the ILC provides sufficient high energy muons. The peak positions of the ILC muon spectra are close to that of the secondary cosmic ray muons. This is because the amount of material in the water beam dump is comparable to the amount of material in the atmosphere piled up on the ground. The energy at this peak position is close to the total energy that muons lose in the material. Therefore, this space is suitable for studying the effects of soft errors due to cosmic ray muons and neutrons. We want to emphasize that the ILC beam dump has the potential to be the only irradiation facility capable of providing high intensity, large area, and atmospheric-like muon flux.

Several operations with different beam energies are planned at the ILC, as summarised in Table 1. Neutron and muon fluxes for different beam energies are reported in this sub-section.

As the beam energy increases, the peak position of the flux slightly shifts downstream. Figure 8 is the $z$ distribution of the flux in the irradiation space of Geometry-2, as in Figure 4. The results are normalised to 2.6 MW beam power, and a concrete thickness of $T_{\rm shield}^{(x)}=0$ m is chosen. The peak position of the shower profiles in the beam direction is shifted by $X_{0}\log(E_{\rm beam,2}/E_{\rm beam,1})$ for different beam energies $E_{\rm beam,1}$ and $E_{\rm beam,2}$ [39], where $X_{0}$ is the water radiation length.

The energy distribution of the flux in the perpendicular space is almost independent of the beam energy when normalised by beam power. Figure 9 shows the energy distribution for each beam energy in Geometry-2 at $z=6\text{ - }7$ m. Photons induce neutrons and muons in the perpendicular region with energies sufficiently lower than the beam energy. The number of low-energy photons is simply proportional to the beam power, so only the beam power is an important parameter.

Figure 10 shows the energy distribution of the flux for each beam energy in the irradiation field of Geometry-3. All the results are normalised by 2.6 MW beam power. Downstream of the beam dump, it can be seen that the spectra of produced particles are similar to those of secondary cosmic rays for any ILC beam energy. The higher the beam energy, the higher the neutron flux, even when the beam power is normalised. This is because the multiplicity of neutrons produced in photonuclear reactions is greater at higher photon energies. On the other hand, muons are induced by pair production, and the multiplicity of the muon is two. Therefore, the muon flux is approximately proportional to the beam power. We can also see that the high-energy tail of the muon spectrum extends up to the beam energy.

In this section, we compare muon fluxes downstream of the electron beam dump and the positron beam dump. The differences are essential in experiments for particle physics using the beam dumps. There are two main processes for producing muons from positron beams or electromagnetic showers:

1. (1)

   Muon pair production induced by real photons $(\gamma\,{\rm N}\to\mu^{+}\mu^{-}X)$;

2. (2)

   Muon pair production induced by positrons $(e^{+}e^{-}_{\rm atomic}\to\mu^{+}\mu^{-})$,

where N denotes the nucleus. Process-(2) is caused by the pair annihilation of positrons above 43.7 GeV with atomic electrons in matter, which needs to be considered when using high-energy positron beams.

The muon production cross section for one water molecule for each process is represented in Figure 11 (Left panel). The energies $E_{i}$ are those of the initial state photon and positron for processes (1) and (2). The corresponding cross sections per water molecule are given approximately by [40]

where $\hat{\sigma}_{\gamma\to\mu\mu}^{\rm(coherent)}$ is the coherent interaction between a real photon and a nucleus, neglecting the atomic number dependent term, and $Z_{\rm H}$ and $Z_{\rm O}$ are the atomic numbers of hydrogen and oxygen. From the above results, cross sections for any atom or molecule can be approximatively evaluated.

The energy distribution of the number of muons generated per injection into the beam dump is expressed by

$n_{\rm H_{2}O}$ is the number density of water mole, $dl/dE_{i}$ is the track length of particle $i$ in the beam dump. The track lengths of photons and positrons in the electron and positron beam dump [41] are given in Figure 11 (Right panel). Figure 12 shows the energy distribution of the calculated number of muons. The results are for beam energies of 45.6, 61.4, 125 and 500 GeV, where 61.4 GeV is the energy that gives the largest cross section for Process-(2). The black line represents the contribution from Process-(1), and the results are equal for electron or positron beam dumps. The red and blue lines represent the contribution from Process-(2) in the electron or positron beam dump. Process-(2) contributes significantly to the high energy region in the positron beam dump, especially when the beam energy is around 100 GeV.

We investigate the detailed energy distribution and spatial extent of the muons penetrating the downstream face of the beam dump cylinder $(z=11~{}{\rm m},r<0.9~{}{\rm m})$, where the spatial extent is expressed as the distance of the muon from the beam axis, $r=\sqrt{x^{2}+y^{2}}$. This information is essential for particle physics experiments. Figure 13 shows the kinetic energy distribution of the muon flux. It can be seen that Process-(2) is dominant at high energies in positron beam dumps. Figure 14 shows the muon radial distribution around the beam axis for different energy ranges. The muons are concentrated in the forward region over a wide energy range. In particular, muons produced in Process-(2) are more likely to be scattered forward than those in Process-(1).

We would like to thank Takashi Nakano, Masanori Hashimoto, Yoshihito Namito, and Hitoshi Murayama for helpful discussions and comments.