Particle production and energy deposition studies for the Neutrino Factory target station

We present FLUKA and MARS simulation studies of the pion production and energy deposition in the Neutrino Factory baseline target station, which consists of a 4 MW proton beam interacting with a liquid mercury jet target within a 20 T solenoidal magnetic field. We show that a substantial increase in the shielding is needed to protect the superconducting coils from too much energy deposition. Investigations reveal that it is possible to reduce the magnetic field in the solenoid capture system without adversely affecting the pion production efficiency. We show estimates of the amount of concrete shielding that will be required to protect the environment from the high radiation doses generated by the target station facility. We also present yield and energy deposition results for alternative targets: gallium liquid jet, tungsten powder jet and solid tungsten bars.


I. INTRODUCTION
The current baseline option for the Neutrino Factory [1] is to use a 4 MW proton beam interacting with a free-flowing mercury jet to create an intense muon beam [2]. The MERIT experiment has shown a proofof-principle demonstration of a high intensity liquid mercury jet target [3]. The interaction of the bunched proton beam (rms bunch length equal to 3 ns) with the mercury jet creates low-energy pions that are captured by the high field (∼ 20 T) solenoid and transported through a decay channel. Muons resulting from the decay of these pions pass through a cooling section and circulate around a storage ring until they decay to neutrinos.
In this paper, we present a series of simulation studies, using the FLUKA [4] and MARS [5] computer packages, on particle production and energy deposition (radiation dose) calculations. We first show the simulation results for the so-called Study 2 geometry configuration, and then describe how the geometry needs to be modified to address various safety issues. We also compare useful muon yields and energy deposition doses for different target material alternatives. Finally, we present a study on the concrete shielding requirements that will be necessary to protect the environment from the high radiation doses emanating from the target station. * J.J.Back@warwick.ac.uk

II. SIMULATION PARAMETERS
As a starting point, the Neutrino Factory mercury jet target station geometry is based on the Study 2 configuration [6], as shown in Fig. 1, with the appropriate 20 T field map based on the dimensions and currents in the normal-conducting copper (∼ 6 T) and superconducting (∼ 14 T) coils. Variations to the geometry are made to reduce the energy deposition in the superconducting magnets, as well as incorporating more engineering considerations to the overall target station design. In all simulations, the proton beam has a transverse Gaussian profile with a root mean square radius of 1.2 mm. The kinetic energy of the proton beam is nominally set to 8 GeV, but is varied when finding the optimal number of useful muons from the target. The mercury jet is modeled as a simple cylinder with a radius of 4 mm, tilted at approximately 100 mrad to the magnetic z axis. We also investigate the yields and energy deposition for alternative targets, also tilted at 100 mrad to the z axis: liquid gallium jet, powder tungsten jet (50% density), and solid tungsten bars. The first two alternatives are also modeled as cylinders with a radius of 4 mm, while the solid target is modeled as a 20 cm long, 2 cm diameter cylinder with a density of 19.25 g/cc. The angle between the target and the proton beam at their intersection (z = −37.5 cm) varies between 20 and 30 mrad, depending on the initial kinetic energy, in order to optimize pion production [7].

III. STUDY 2 GEOMETRY
A. Muon yields One important figure of merit concerning the performance of the target is the total number of muons that pass through the Neutrino Factory cooling channel. This is calculated by first counting the number of pions, kaons, and muons that are directly produced by the mercury jetproton beam interaction. These secondary particles are then tracked through the solenoidal target decay channel up to z = 50 m. The ICOOL simulation package [8] is used to find what fraction of these secondary particles end up as muons within the accelerator acceptance (30 mm transversely and 150 mm longitudinally, with zmomenta between 100 and 300 MeV/c). Figure 2 shows the expected muon yields for the Study 2 (ST2) and Study 2a (ST2a) target configurations, as a function of the kinetic energy of the incoming proton beam. These yields are normalized to the number of protons on target as well as the proton beam kinetic energy. In general, the results are in agreement with the model-independent conclusions of Ref. [9] that "the dependence of the muon yield on proton beam energy at constant beam power is relatively flat, and any energy between 4 and 11 GeV has a yield that is within 10% of the maximum at 7 GeV." There is some variation in the calculated muon yield, depending on what version of the simulation codes are used, as well as on the assumptions made about the proton beam bunch spacing (0 or 3 ns). For the former, this can only be improved by updates to the simulation codes.  Figure 3 shows the distribution of energy deposition in the Study 2 target station using the FLUKA simulation code, which agrees rather well with those results obtained using MARS [10]. Also shown is the total power dissipated in the first few superconducting coils. The values in SC1-SC3 are unacceptably high and certainly have to be reduced by increasing the shielding thickness [11]. Previous studies have shown that the forces between the superconducting coils are very high [12], and in the present geometry there is no space for support structures between individual coils, which needs to be addressed. Another issue is that the normal conducting magnets also experience very high levels of power dissipation (142 and 90 kW). This problem is avoided by removing them completely and replacing the volume with more shielding. This means that the magnetic field in the beam-jet interaction region is decreased from 20 T down to 15 T. Also note that the power deposition in the mercury pool is quite low (13 kW). This means that the volume of the pool reservoir needs to be increased in order for it to act as an effective beam dump for protons that do not interact with the mercury jet. In the next section we explore what effect these necessary geometry changes have on both the distribution of the energy deposition and on the accepted muon yield efficiencies.  Figure 4 shows the new target station geometry configuration that has increased shielding (approximately doubled in thickness laterally) to protect the superconducting (SC) coils, with the normal conducting magnets removed, as well as a larger mercury pool reservoir (88 cm < z < 367 cm, y < −15 cm, r < 45 cm). Table I provides the geometrical and current density parameters of the SC coils. The SC coils are arranged in triplets, each corresponding to one cryostat module. Gaps are introduced between neighbouring coils to provide space for the cryostat modules and supporting structures to hold them in place (the cooling components and their internal shielding are not included in the simulation). Each cryostat is protected by large shielding volumes, made from tungsten beads (60%) with an assumed low-grade density of 15.8 g/cc, and fast-flowing helium gas (40%), which replaces water as the cooling agent. This change is motivated by the concern that any creation of bubbles in the water will affect its circulation, giving nonuniform cooling of the tungsten beads, as well as the problem of corrosion in a high radiation environment [13]. Each shielding section, separated by 20 cm gaps, is surrounded by stainless steel container vessels (each with a thickness between 2 and 10 cm) that must support the ∼200 tonne weight while limiting stresses and deformations to acceptable values [14].

IV. IMPROVED SHIELDING CONFIGURATION
The beam pipe is modeled as a 2 cm-thick stainless steel tapered volume, which defines the inner bore of the decay vacuum region. The beam pipe section just above the mercury pool surface is removed between z = 88 and 200 cm to allow the mercury jet (and noninteracting protons) to enter the pool unhindered. The beryllium window, which separates the jet-beam interaction region  Fig. 4: z0 is the initial z position, ∆z specifies the length along z, r1 is the inner radius, ∆r is the radial thickness, while I is the average current density. The last column specifies the coil materials used in the FLUKA simulation, where SCon is the compound Cu (54%), Nb (24%), Ti (12%), and kapton (10%). The mass densities for Nb3Sn and SCon are 6.8 g/cc and 7.0 g/cc, respectively.
−240.5 355.0 120.0 75. 8  from the rest of the decay channel vacuum, is moved further upstream to coincide with the edge of the first cryostat module. It consists of a 0.5 cm gap containing rapidly flowing He gas for cooling sandwiched between two 0.5 cm Be layers. The iron yoke plug has been removed to allow for space for the mercury jet nozzle injection and return flow system (which is ignored in the simulation). The mercury jet is still modeled as a simple cylinder of radius 4 mm, tilted at approximately 100 mrad with respect to the magnetic z axis.

A. Pion and muon yields
The removal of the normal conducting magnets implies that the peak magnetic field in the jet-beam interaction region is decreased from 20 to 15 T. To ensure that secondary pions from the target maintain their magnetic rigidity, the inner bore radius of the beam pipe at this location is increased from 7.5 to 10 cm. Figure 5 shows a comparison of the axial magnetic field profile between the original Study 2 geometry and the new increased shielding geometry. The latter has a much wider magnetic field profile, which helps to capture much more secondary charged particles from the target. This can be clearly seen in Fig. 6, which shows the improved charged averaged yield of useful pions and muons from the target, normalized to the total number of protons on target and the initial beam kinetic energy. Using the FLUKA simulation package, these yields are calculated by finding the number of pions and muons (of both signs) that pass a transverse plane 50 m downstream from the beam-jet interaction region, within the decay channel aperture that has a bore radius of 30 cm. To obtain a figure of merit for the muon yield for the Neutrino Factory, we require that these particles have kinetic energies between 40 and 180 MeV [7].
In addition to the baseline mercury jet case, the yields from alternative target materials are also shown in Fig. 6, using the simulation parameters outlined in Sec. II. Between 5 and 15 GeV, there is a two-peak structure in the normalised yield distributions, owing to the transition between different hadronic models used at low-and highenergies in the FLUKA simulation code. Above 5 GeV, the mercury jet provides the best yields, although the performance of the solid tungsten target matches this very closely. Note that we do not see a dramatic reduction in the yield for the tungsten powder jet, which is assumed to have an effective density of 50% of solid tungsten. The reason for this is that, even though less protons will interact with the powder target, the amount of reabsorption of secondary particles inside the target will also be lower, giving an overall figure of merit comparable to either the mercury jet or solid tungsten case. At low beam kinetic energy (below 5 GeV), there is an indication that the liquid gallium target gives the best yield compared to the other materials. Further analysis is required to optimize the yields for this improved shielding geometry.

B. Energy deposition
We have seen that the change to the target station geometry has had a positive effect to the useful muon yield. The situation regarding the energy deposition for the superconducting coils is also improved. Figure 7 shows the energy deposition in the new target station geometry, obtained using the FLUKA simulation code, which shows that the increase to the shielding has dramatically re- duced the power dissipation in the SC coils. Table II provides a detailed breakdown of the deposited power in various subregions of the new geometry, where the uncertainties are estimated by using different initial random number seeds for the simulation. The first SC coil experiences a total power of 0.4 kW, with the other coils experiencing much lower values, giving a total approximately equal to 0.6 kW. These correspond to energy densities below 0.1 mW/g, which permits at least a 10 year (of 2 × 10 7 s each) operational lifetime against radiation damage to their organic (MgO) insulators, assuming the maximum permitted radiation dose is 10 MGy [15]. About 2.4 MW is deposited in the combined shielding and beam pipe sections. Removing the heat load from these materials will prove quite challenging. The target and mercury pool receives a total power deposition approximately equal to 0.9 MW, which must be dis-  sipated in a heat exchanger in the mercury flow return loop. The downstream Be-He-Be window (1.5 cm thick) receives a large energy deposition of 9 kW. About 250 kW will continue into the downstream pion-muon transport system. This will contain scattered, high energy protons that must be removed by a chicane and absorber system in order to stop radiation damage to other accelerator components [16]. Table II also shows the deposited power in the various regions when alternative materials are used for the target. In general, most of the differences are seen in the energy deposition in the target itself, the shielding and the liquid/powder collection pool. Less protons interact with the liquid gallium jet target, going directly into the pool reservoir. This very slightly reduces the overall power deposited in the shielding and beam pipe sections. The reduced density in the tungsten powder jet also means that more energy is deposited in the powder collection reservoir (assumed to have the same geometry as the mercury pool), although not as much as was the case for the gallium target. In contrast, the solid tungsten target itself experiences a much larger energy deposition, corresponding to a quarter of the total beam power. Experimental work using fast, high current pulses passing through tungsten wires has demonstrated that a 20 cmlong, 2 cm diameter tungsten target will be able to withstand the peak stresses from such an energy deposition, allowing a target lifetime of at least three years [17]. The removal of the reservoir pool for the solid target means that about 5% more energy is deposited in the shielding, with a slight reduction in the radiation dose absorbed by the downstream beam pipe.

V. FAILURE MODES
It is important to know how the 4 MW total beam power will be distributed within the new target station geometry for specific (baseline) failure modes: when the magnetic field fails, when the mercury jet stops flowing, and when both happen together. Table III shows comparisons of the average power deposition in various regions of the target station between normal and failuremode operating scenarios.
Under normal conditions, noninteracting protons from the beam have a trajectory that enters the mercury pool reservoir. This is illustrated by the case when there is no mercury jet target, in which more than half of the total beam power (2.6 MW) is deposited in the pool. This will produce significant agitation of the pool surface with splashes of radial velocities expected to approach 50 m s −1 [18]. In contrast, when there is no magnetic field present to steer the proton beam (and any secondary charged particles), the energy deposition for the combined mercury jet and pool system decreases by roughly a factor of 3. The proton beam almost completely misses the mercury jet target and hits only part of the mercury pool, instead dramatically increasing the energy deposition in the surrounding shielding (1.6 to 2.3 MW) and the nearby beam pipe section (from 0.4 to 1 MW). For the scenario when there is no mercury jet and no magnetic field, the results are essentially identical to the case when only the magnetic field is turned off, owing to the fact that the proton beam will miss the target in both cases.

VI. RADIATION SAFETY
Any construction of the target station must take into account the safety requirements of the surrounding environment to prevent radiation contamination of the soil (and ground water). The entire target station must be enclosed within a concrete shielding structure of adequate thickness to stop radiation from escaping; the effective total radiation dose must not exceed 1 mSv per year [19], which is equivalent to a continual residual dose of 0.1 µSv/hr. Figure 8 shows the estimated total radiation ambient dose equivalent from the 4 MW target station after a total irradiation time of 2 × 10 7 s (1 year), using the FLUKA simulation code and AMB74 conversion factors [20]. The target station is surrounded by a concrete shielding structure (tunnel) that is modeled as three connecting cylindrical sections, extending from z = −8 m up to z = 30 m, with an outer radius of 6 m. This tunnel creates a barrier between the surrounding rock, assumed to be molasse soil based at the CERN site, and the radiation generated by the target system. The chemical composition (with mass fractions in parenthesis) assumed for the concrete is O (51.1%), Si (35.8%), Ca (8.6%), Al (2.0%), Fe (1.2%), H (0.6%), C (0.4%) and Na (0.3%), while the composition of the molasse soil is taken to be O (49.2%), Si (19.8%), Ca (9.3%), Al (6.4%), C (4.9%), Fe (4.1%), Mg (3.5%), K (1.9%), Na (0.6%), Mn (0.2%) and Ti (0.1%) [21]. The densities assumed for the concrete and molasse are 2.35 g/cc and 2.4 g/cc, respectively. For a range of cooling decay times, it can be seen that no radiation escapes the concrete shielding, which means that there will be minimal activation of the surrounding soil and ground water. We can also infer that remote handling will be mandatory for maintaining the target system; even at a radial distance of 2 m from the interaction region, the residual dose rate after 1 year of cooling is of the order of 10 mSv/hr, which greatly exceeds the safety limit for radiation workers (20 mSv/yr) [19].

VII. SUMMARY
We have presented FLUKA and MARS simulation studies of the pion production and energy deposition in the Neutrino Factory target station. Compared to the original Study 2 geometry, a doubling of the lateral shielding thickness is needed to protect the superconducting coils from radiation. In addition, a reduction in the focusing magnetic field from 20 T down to 15 T does not affect the pion production efficiency, provided the inner bore radius is increased. Alternative target materials were also investigated, such as liquid gallium, and powdered and solid tungsten. Each of these offer comparable muon yields, with some differences observed in the power deposited in the target, collection pool, and surrounding shielding. We have investigated what effect various operational failure modes have on the deposited power in the target station. Finally, we have provided estimates of the amount of concrete shielding that will be needed to protect the environment from the high radiation generated by the target station, with remote handling mandatory for any maintenance work.