Chapter 6. Prospect for Future Muon Beam Line
B [Tesla] Br [Tesla] Bz [Tesla]
340 mm 25 mm
Figure 6.2: Magnetic field calculated with an asymmetrical model. The coil has a length l of 340 mm, inner diameter of 340 mm and a thicknesstof 25 mm. The current density is calculated to 139 A/mm2 from the equation ofJ =nturn×nlayer×Iop/(t×l). The total magnetic field, that ofr component and that of z component are shown on left, middle and right.
pion yield by around 10%, while the secondary particles and effect of the irradiation have asymmetric distributions in the pion capture solenoid.
Table 6.1: Design parameters for the HTS coil.
Item Value
Conductor ReBCO coated HTS tape
Cu : Others = 4:6 Cable dimension 0.1 mm× 4 mm
(0.1 + 0.025) mm× (4 + 0.025) mm (with insulation) Magnet dimension length: 340 mm, inner diameter: 340 mm
Number of coils 34 double pancake coils Operation current 105 A (20% of Ic)
Operation temperature 20 K (conduction-cooling with pulse tube cryocooler) Thermal path pure aluminum sheets, RRR = 2000, thickness: 1.9 mm Magnetic field 3 Tesla on target
Coil layers 68
Coil turns 166
operation point Load line
Figure 6.3: Critical current (B //c-axis) of ReBCO coated conductor (SuperPower, SCS4050) with a operation point.
energy deposition, particle flux and DPA are calculated conservatively without the applied magnetic field by using the Monte Carlo simulation code, PHITS. The simulation is preformed with JAM and INCL4.6 hadronic cascade model, and the nuclear library of JENDL4.0 is also included for the neutron interaction below 20 MeV. The cut off energy of all particles are set below 0.1 MeV.
As for a simulation model, the superconducting coils are considered as a stainless steel cylinder with an inner diameter of 340 mm and with a thickness of 25 mm, which is divided into 4 pieces along the solenoid axis. The aluminum sheets with a thickness of 2 mm are inserted between each cylinder and attached to the both ends. The 8 GeV proton beam is settled on the surface at the center of production target. As shown in
Chapter 6. Prospect for Future Muon Beam Line
File = GeoXZPhaseI.dat COMET phase-I new scenario Date = 07:43 18-Jun-201
plotted by ANGEL 4.35 calculated by PHITS 2.7
−20 0 20
−20 0 20
z [cm]
x [cm]
no. = 1, y = 0.0000E+00
void Aluminium Stainless Tungsten Graphite
Energy [MeV]
0 100 200 300 400 500 600 700 800 900 1000 /sec]2Flux [n/cm
105
106
107
108
109
1010
neutron proton photon electron positron muon+
muon-pion+
Energy [MeV]
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 /sec]2 Flux [n/cm
105
106
107
108
E < 1 MeV
particle of hits for HTS
HTS coil Thermal path
Radiation shielding
K𝞪1 (W)
Annihilation
v
proton
Figure 6.4: Estimated flux of each particle (right) with a simulation model of pion capture solenoid (left).
Fig. 6.4, except from the neutron, the charged particles with high energy such as the proton and electron contribute to the radiation damage.
The HTS coil is divided into 4 segments along the azimuth, in which the distribution of energy distribution in each azimuthal segment are plotted in Fig. 6.5. The origin of the azimuthal angle is defined at the coil location close to the exiting proton beam, where the irradiation is most severe in the coil. The peak energy deposition is estimated about 0.43 W/kg and the overall energy deposition to the coil is about 7 W. The maximum DPA in aluminum sheet is predicted to be about 1.3×10−11 DPA/sec. To take the charged particles into account, the DPA is utilized to calculate the degradation of thermal conductivity. According to the experimental measurement [26], an increase of electrical resistivity is proportional to DPA that is about 0.07 nΩ·m for 10−5 DPA. For 5000-hour operation, the integrated DPA is 2.3×10−5 that results in degradation of RRR from 2000 to about 130.
6.2.2 Thermal Analysis
In order to investigate the influence of irradiation on the HTS coil, the thermal analysis is preformed by solving the 3D model with FDM. As shown in Fig. 6.6, a model is divided in each double pancake coil longitudinally that is thermally connected to the 1.9 mm thick aluminum thermal path through the insulation assumed as polyimide with a thickness of 25 µm. As introduced in Sec. 6.1, the HTS tape is almost compounded with the hastolly substate and copper stabilizer, thereby, the HTS tape is assumed to be copper and stainless steel (SUS304). Each pancake coil is divided into 6 cells radially and is assumed to have a thermal conductivity equivalent to a series of stainless steel, copper (RRR = 50) and polyimide with a cross-sectional ratio of 6:4:5. The thermal conductivity
HTS Length [cm]
0 5 10 15 20 25 30
Radius [mm]
17 17.5 18 18.5 19 19.5
Energy Deposition [Gy/sec]
0.05 0.1 0.15 0.2 0.25 0.3 0.35 < 90
φ 0 ≤
HTS Length [cm]
0 5 10 15 20 25 30
Radius [mm]
17 17.5 18 18.5 19 19.5
Energy Deposition [Gy/sec]
0.05 0.1 0.15 0.2 0.25 0.3 0.35 < 180
φ 90 ≤
HTS Length [cm]
0 5 10 15 20 25 30
Radius [mm]
17 17.5 18 18.5 19 19.5
Energy Deposition [Gy/sec]
0.05 0.1 0.15 0.2 0.25 0.3 0.35 < 270
φ
≤ 180
HTS Length [cm]
0 5 10 15 20 25 30
Radius [mm]
17 17.5 18 18.5 19 19.5
Energy Deposition [Gy/sec]
0.05 0.1 0.15 0.2 0.25 0.3 0.35 < 360
φ
≤ 270
[cm]
Coil Length Coil Length
Coil Length
[cm] [cm][cm]
Coil Length
Figure 6.5: Distribution of energy deposition in HTS coil in the unit of Gy/sec (=W/kg).
Horizontal axis indicates the axis of HTS solenoid, and vertical is the radius from the solenoid axis. (copyright: IOP science [111])
along the longitude and the azimuth are assumed to be stainless steel. The thermal conductivity is averaged as
kz = (dzins+dzCu)·(dzins kins
+ dzCu kCu
)−1 (6.2)
kθ = ηCu·kCu+ηSU S·kSU S +ηins·kins (6.3) kr = (drins+drCu+drSU S)·(dzins
kins +dzCu
kCu +dzins
kSU S)−1 (6.4) where ηCu (ηins, ηSU S) is the cross-sectional ratio of copper (insulation, stainless steel), and dr (dz) is the thickness of each component along the r(z)-axis, respectively.
To reduce the computation time, all the constant of thermal conductivity at 20 K is used. For the aluminum thermal path, the RRR of 40 is used in the thermal analysis to take in account the degradation by irradiation.
The distribution of energy deposition shown in Fig. 6.5 is used as the input of heat generation in each element. For the boundary condition, the outer shell of HTS coil is fixed to 20 K. The computation is constructed starting from the base temperature, 20 K, then the coil is heated by energy deposition until it becomes thermal equilibrium. The coil is expected to reach the thermal equilibrium after 5-minute beam operation, and a profile of coil temperature at the thermal equilibrium is plotted in Fig. 6.7. Owing to the contribution of thermal conduction at high temperature region, the maximum temperature is about 21.6 K, which is well below the HTS critical temperature.
Chapter 6. Prospect for Future Muon Beam Line
Conductor Insulation tape
Copper Stainless Steel
… … x 34 double pancake coils
20 K Pure aluminum sheets
340 mm
Figure 6.6: The simulation model for the thermal analysis.
Z [mm]
0 50 100 150 200 250 300
Radius [mm]
170 175 180 185 190 195
Temperature [K]
20 20.2 20.4 20.6 20.8 21 21.2 21.4 < 90
φ 0 <
Z [mm]
0 50 100 150 200 250 300
Radius [mm]
170 175 180 185 190 195
Temperature [K]
20 20.2 20.4 20.6 20.8 21 21.2 21.4 < 180
φ 90 <
Z [mm]
0 50 100 150 200 250 300
Radius [mm]
170 175 180 185 190 195
Temperature [K]
20 20.2 20.4 20.6 20.8 21 21.2 21.4 < 270
φ 180 <
Z [mm]
0 50 100 150 200 250 300
Radius [mm]
170 175 180 185 190 195
Temperature [K]
20 20.2 20.4 20.6 20.8 21 21.2 21.4 < 360
φ 270 <
Figure 6.7: Temperature distribution in the HTS coil during the beam operation, in which the only temperature distribution of double pancake coil is plotted here. The coil is divided to 4 part along the azimuth, and the peak of temperature is located from 90 to 180 degree due to the axis asymmetry of energy deposition. (copyright: IOP science [111])