In this thesis, feasibility study on the stable operation of the conduction-cooled superconducting magnet for high intense muon beam line (COMET-PCS) regarding the coil temperature and the quench protection is performed by using a novel design method with a consideration of energy deposition in the magnet and degradation of the material properties due to the radiation. As shown in Fig. 1.8, the thermal design depends on the radiation level on superconducting magnet for the special case of the PCS. In order to take the radiation effect into account, the radiation analysis is newly included into the design flow to determine the three-dimensional profile of electrical resistivity and thermal
Chapter 1. Introduction
conductivity. Additionally, to determine the radiation damage on the thermal conductivity of a new insulation tape in thermal design, its thermal conductivity is measured and examined by gamma ray irradiation with total 5 MGy at maximum. The details of each chapter is given as follows.
Electromagnetic analysis
Radiation Analysis
Shielding design Thermal analysis
Tcoil < Tc ? False
Ture
Thermal propertyThermal conductivityThermal property
Quench protection circuit design Quench analysis
Tcoil < Tallow False
Ture Quench designQuench designQuench designNext step
Thermal propertyElectrical resistivityThermal property
Beam Operation TimeBeam Operation Time Magnetic field map
Operation current Coil alignment
Coil temperature map
optimization
Coil temperature map
Heat Generation
2]
>0.1MeV) [n/m Neutron Fluence (En 1016 1017 1018 1019 1020 1021 1022 1023 1024 1025
Residual Resistivity Ratio
2 10−
1 10−
1 10 102 103
Conductor (RRR=400) Cooling Path (RRR=2000)
Thermal conductivity [a. u.]
Thermal propertyThermal conductivityThermal property Joule Heating
Electrical Resistivity [a. u.]
Neutron Fluence [n/m2]
Figure 1.8: The schematic flow diagram of a novel method with the consideration of radiation influence. The conventional thermal design follows the black flows, and the red flows shows the novel method to take the radiation effects into account in this study.
Chapter 1 gives a motivation of this study. The coil structure of PCS and the radiation degradation effects on the materials utilized in the magnet are introduced.
In chapter 2, the neutron flux and the energy deposition in PCS is estimated by performing a Monte Carlo simulation for the studies in chapter 3, 4 and 5. A detailed geometry of PCS and a magnetic field map calculated by a finite element method are implemented into the simulation. Eventually, the total heat load and the peak of the neutron flux in the coil are estimated to be more than 200 W and 1.2×1014 n/m2/sec, respectively. Spatial distributions of the neutron flux and heat load are found to be asymmetrical in the coil due to the tilted incident proton beam, thus the three-dimensional
thermal and quench analysis are essential for the studies in chapter 3 and 5.
In chapter 3, a three-dimensional thermal analysis is performed to investigate the coil temperature rise during the beam operation. Firstly, spatial distribution of thermal conductivity in the coil degraded by the neutrons is estimated. Then, the coil temperature is calculated with the heat load profile due to the radiation. It is found that COMET-PCS can be operated for three months at most in view of the temperature margin decrease during the beam operation.
In chapter 4, radiation tolerance on thermal conductivity of a newly developed in-sulation tape is experimentally determined. A new inin-sulation, bismaleimide-triazine prepreg tape, is employed to enhance the radiation resistance for PCS. To investigate the irradiation effect on the thermal conductivity, a measurement system is developed with a Gifford-McMahon cryocooler. The thermal conductivity is measured before and after the gamma ray irradiation. A heat-scan method is utilized to improve the measurement accuracy. With a detailed data analysis, no significant degradation on the thermal con-ductivity of the insulation tape is observed after the gamma-ray irradiation with a total dose up to 5 MGy.
In chapter 5, influence of the radiation on the magnet quench is analyzed. Firstly, a quench protection circuit is designed with a by-pass dump resistor to extract the stored energy. Then, a three-dimensional quench analysis implementing the radiation degradation of the thermal conductivity of the cooling paths as well as the electrical conductivity of aluminum stabilizer is performed. It is found that the magnet is capable of being protected even after a long-term operation. Additionally, it is shown that the novel method to insert the thermal path between the coil layers for enhancing the cooling performance also helps to reduce the coil temperature by accelerating the normal zone propagation.
In chapter 6, a conceptual design of a compact coil using a high temperature supercon-ductor (HTS) is proposed as the first step for future high intense muon beam line. The conduction-cooled HTS coil is designed for operating at the same radiation environment as the COMET-PCS magnet but the operation temperature will be set around 20 K where very large thermal conductivity and heat capacity can be expected. It is shown that the HTS coil has a good thermal stability at operation temperature of 20 K and can be applied to the PCS in future high intense muon beam line with the large temperature margin.
Chapter 7 gives a conclusion of the thesis.
15
Chapter 2
Radiation Estimation for Pion Capture Solenoid
The PCS is the main part of COMET muon beam for the pion production, in which a primary proton beam with high intensity of 56 kW bombards a massive target to produce the secondary particles so that the one of secondary particle, pion, can be collected efficiently. In the high intense proton bombardment on a production target, most of charged particles such as electron or proton are trapped in a magnetic field, however, the uncharged particles and charged particle with a high transverse momentum are possible to reach the coil and cause the energy deposition resulting in the heat generation, and radiation damage in the superconducting magnet.
To study and design a superconducting magnet in high irradiated environment for the further studies on coil temperature and magnet quench, first of all, the radiation in superconducting magnets is investigated in this chapter. A Monte Carlo simulation model is described in Sec. 2.1, in which an algorithm is developed for the transportation of charged particles in magnetic field map. Then, in Sec. 2.2, the simulation result is presented to validate the radiation level for the PCS and estimate the spatial radiation distribution for the thermal and quench analysis presented in chapter 3. In final, a discussion is given to show the simulation reliability of the estimation on energy deposition, and a feasibility to enlarge the length of production target in Sec. 2.3.
2.1 Simulation
In past study reported in Ref. [32], we designed a hybrid radiation shielding, which consists of copper, stainless steel and tungsten alloy, to reduce the total mass of magnet system. In consequence, in use of the hybrid shielding, the coil temperature is substantially increased up to the temperature limitation by the nuclear heating even for a 30-day beam operation. To improve the magnet lifetime in a cycle of beam operation, a tungsten alloy shielding is adopted, and its radiation estimation is presented here.
2.1.1 Monte Carlo Code
The Monte Carlo simulation code: PHITS [33], FLUKA [34], MARS [35] and GEANT4 [36] are usually utilized to handle the transportation of particles. They have been widely used for various applications such as radiation shielding design, medical therapy, estimation of radiation exposure in space, high energy physics and so on. To estimate the radiation level for the PCS magnets, the PHITS code1 is utilized in this study.
In PHITS code, the nuclear data libraries are used for simulating the neutron, photon and electron interactions below 20 MeV. From 20 MeV to 3 GeV, the particle interactions are calculated with the intra-nuclear cascade models combined with evaporation model, in which the INCL4.6 combined with GEM is a default model. The hadronic cascade model, JAM combined with GEM, is applied in the energy region higher than 3 GeV. Various quantities can be estimated from the PHITS simulation such as production yield, track length and energy deposition.
2.1.2 Simulation Model
As shown in Fig. 2.1, a detailed geometrical model for PCS magnet system is con-structed in simulation because the energy deposition can be doubled by the implementation of iron yoke and the other components surrounding the coils.
The PCS system consists of 10 superconducting coils (CS0, CS1, MS1, MS2 and TS1a-f), cryostat, radiation shielding and iron yoke. A production target (length: 160 mm, radius: 3 mm) made of pure tungsten (density: 19.2 g/cm3) is set on the center of the radiation shielding with an angle of 10 degree with respect to the magnet axis. The superconducting coil compounded with copper, NbTi and aluminum are supported by an aluminum support shell. A 10 mm thick thermal shield made of aluminum is surrounding the CS and MS coils, while the thermal shield for the TS1 coils is neglected in this simulation since it is far from the production target. The cryostat made of stainless steel has a thickness of 10 mm at inner wall, and 30 mm at outer wall. The cryostat for CS and MS coils are divided with the one for TS1a-f coil in the cold mass. Radiation shielding is separated to two parts, a tungsten alloy part and a copper part covered the CS coils and the MS coils respectively, in which tungsten alloy shielding is implemented with a realistic polygonal shape. The tungsten alloy is made of the composition of material provided by manufacture as given in Table 2.1. The cryostat is enclosed in a rectangle-shaped iron yoke which has a length of 6.4 m and a width of 0.6 m.
Table 2.1: The composition of tungsten alloyAN-1800. Density [g/cm3] Composition [wt.%]
Nickle Copper Tungsten 18.0±0.2 3.0±0.25 2.0±0.25 95.0±0.5
1PHITS: Particle and Heavy Ion Transport Code System. In this study, version 2.88 is used.
Chapter 2. Radiation Estimation for Pion Capture Solenoid
File = Geo_All3d.dat [t-3dshow] Date = 16:27 18-Oct-201
plotted by ANGEL 4.35 calculated by PHITS 2.8
0 100 200 300 400
0 100 200 300
Iron Stainless TungstenAlloy ThermalShield Aluminium Magnet Kapton Tungsten Copper
x y
z
(cm)
(c m )
File = Geo_All3d.dat [t-3dshow] Date = 16:27 18-Oct-201
plotted by ANGEL 4.35 calculated by PHITS 2.8
0 100 200 300 400
0 100 200 300
Iron Stainless TungstenAlloy ThermalShield Aluminium Magnet Kapton Tungsten Copper
x y
z
CS0 CS1
MS1 MS2 TS1a-f
6.4 m
primarsoley protonnoid axi beams
Cryostat Thermal Shield
Radiation Shielding
Iron Yoke R θ Z
0 π/2
π 3π/2
Production Target
1.7 m
Figure 2.1: The geometry of Pion Capture Solenoid System implemented in PHITS simulation.
The production target is set in the center of the radiation shielding which has 10 degree with solenoid axis. Blue and Red arrow indicate the axis of the primary proton beam and solenoid (copyright: IEEE [37]).
The 8 GeV proton beam is set and perpendicular to the surface of production target with a gaussian spatial distribution fitted as the diameter of production target. (σx = σy
= 1.5 mm). Because the charged particles can be trapped in a magnetic field so that the energy deposition could be overestimated, the magnetic field calculated by using the finite element method (FEM) simulation is also implemented in PHITS simulation as shown in Fig. 2.22. The transport of charged particles in an external magnetic field map is newly implemented into the simulation code with a standalone algorithm as follows:
1). When a charged particle comes into the magnetic field region, the magnetic field are interpolated from the field map by a given location of the particle, (x, y, z), with three-dimensional linear interpolation method.
2). The angle between the vector of magnetic field andy-axis3 is calculated firstly, then
2Magnetic field is calculated with a three-dimensional model by a commercial Finite Element Analysis (FEA) software,Opera.
3In the PHITS simulation, to track the charged particles in a uniform magnetic field, the direction of
Z [cm]
−800 −700 −600 −500 −400 −300 −200 −100 0 100
X [cm]
−300
−250
−200
−150
−100
−50 0 50
Magnetic Field [Tesla]
0 1 2 3 4 5
Figure 2.2: Magnetic field map implemented to transport the secondary particles in PHITS simulation.
the momentum vector and position of particle are forced to be rotated with this angle.
3). The information of the modified momentum and position is passed to the subroutine in PHITS code to calculate the transport in magnetic field.
4). After finished the tracking, the momentum and position are rotated back to the original position.
5). It is repeated every tracking step until the particle leaves to the magnetic field region.
Figure 2.3 gives an illustration that negative-pion and negative-muon are transported in a gradient magnetic field shown in Fig. 2.2 with the above-mentioned algorithm.
2.1.3 Parameters
To simulate the radiation in a right way, the major physics model suggested in the benchmark studies for PHITS code [38] is utilized with the event generator. As for the hadronic interaction, the cascade model INCL4.6 and JAM combined with the evaporation model GEM is applied in this simulation from 20 MeV until 8 GeV. Below 20 MeV, the nuclear data library, JENDL-4.0 is used in the calculation of neutron transport. The EGS5 code is utilized for the calculation of electron and photon transport. The other physics models such as the processes of photon nucleus interaction, muon capture, etc.
are also switched on.
The energy cutoff is applied on neutron to 10−3 meV since the photon emitted from the neutron capture will affect the energy deposition in magnet, while, the energy cutoff for the
magnetic field must point to they-axis.
Chapter 2. Radiation Estimation for Pion Capture Solenoid
File = ParticleDistributionXZ.dat
Neutron distribution (x-z) [COMET Phase I]
Date = 18:07 10-Dec-201plotted by ANGEL 4.35 calculated by PHITS 2.8
1000 500 0 500
400 200 0 200
z [cm]
x [cm]
no. = 2, ie = 1, iy = 1
100 101 102 103 104 105 106 107 108 109 1010 1011 1012
Particle flux [n/cm2/sec]
emin = 0.0000E+00 [MeV]
emax = 8.0000E+03 [MeV]
ymin = -2.0000E+01 [cm]
ymax = 2.0000E+01 [cm]
part. =
pion-File = ParticleDistributionXZ.dat
Neutron distribution (x-z) [COMET Phase I]
Date = 18:07 10-Dec-201plotted by ANGEL 4.35 calculated by PHITS 2.8
1000 500 0 500
400 200 0 200
z [cm]
x [cm]
no. = 3, ie = 1, iy = 1
100 101 102 103 104 105 106 107 108 109 1010 1011 1012
Particle flux [n/cm2/sec]
emin = 0.0000E+00 [MeV]
emax = 8.0000E+03 [MeV]
ymin = -2.0000E+01 [cm]
ymax = 2.0000E+01 [cm]
part. =
muon-negative-pion
negative-muon
11
Figure 2.3: The negative-pion (upper) and negative-muon (lower) transported in the magnetic field in PHITS simulation. The magnetic field applied on target is 5 Tesla, and the magnetic field from TS1a to end of TS2 coils is about 3 Tesla as given in Fig. 2.2.
other particles is set to the order of keV to reduce the computation time. In this simulation, the results are normalized with a proton intensity of 4.4×1013 pps corresponding to the beam power of 56 kW to calculate the neutron flux and dose rate, and the required total protons of 1021 proton on target (pot) until the experiment finished to calculate the neutron fluence and total dose [39], which corresponds to about 280 days.