Chapter 2. Radiation Estimation for Pion Capture Solenoid
File = Det_DepositAll_xz.dat energy deposit distribution Date = 10:12 15-Sep-201
plotted by ANGEL 4.35 calculated by PHITS 2.8
−400 −200 0
−100 0 100
z [cm]
x [cm]
no. = 1, iy = 1
10−3 10−2 10−1 100 101 102 103
Energy Deposition [Gy/sec]
ymin = -3.0000E+00 [cm]
ymax = 3.0000E+00 [cm]
part. = all
File = Det_FluxAll_xz.dat particle flux distribution Date = 10:03 15-Sep-201
plotted by ANGEL 4.35 calculated by PHITS 2.8
400 200 0
100 0 100
z [cm]
x [cm]
no. = 1, ie = 1, iy = 1
107 108 109 1010 1011 1012 1013
Flux [n/cm2/sec]
emin = 1.0000E-03 [MeV]
emax = 8.0000E+03 [MeV]
ymin = -8.0000E+00 [cm]
ymax = 8.0000E+00 [cm]
part. = neutron
File = Det_DpaAll_xz.dat DPA distribution for CS and MS Date = 10:07 15-Sep-201
plotted by ANGEL 4.35 calculated by PHITS 2.8
−400 −200 0
−100 0 100
z [cm]
x [cm]
no. = 1, iy = 1, tot DPA
10−13 10−12 10−11 10−10 10−9 10−8
DPA [DPA/sec]
particle = all ymin = -3.0000E+00 [cm]
ymax = 3.0000E+00 [cm]
File = Det_FluxAll_xz.dat particle flux distribution Date = 10:03 15-Sep-201
plotted by ANGEL 4.35 calculated by PHITS 2.8
400 200 0
100 0 100
z [cm]
x [cm]
no. = 1, ie = 1, iy = 1
107 108 109 1010 1011 1012 1013
Flux [n/cm2/sec]
emin = 1.0000E-03 [MeV]
emax = 8.0000E+03 [MeV]
ymin = -8.0000E+00 [cm]
ymax = 8.0000E+00 [cm]
part. = neutron
File = Det_DpaAll_xz.dat DPA distribution for CS and MS Date = 10:07 15-Sep-201
plotted by ANGEL 4.35 calculated by PHITS 2.8
−400 −200 0
−100 0 100
z [cm]
x [cm]
no. = 1, iy = 1, tot DPA
10−13 10−12 10−11 10−10 10−9 10−8
DPA [DPA/sec]
particle = all ymin = -3.0000E+00 [cm] ymax = 3.0000E+00 [cm]
Figure 2.7: Distribution of energy deposition (left) and DPA rate (right) in PCS from a view of z-x plane.
2.2.3 Heat Loads
In the COMET muon beam line, the superconducting coils in PCS and MTS are cooled by the two-phase forced helium flow with one cryogenic system [31]. To determine the cooling capacity of liquefier in cryogenic system, the heat loads in PCS, comprising the coils, thermal shield and support shell, are estimated as listed in Table 2.3. The total heat load is predicted to be about 240 W, in which the CS and MS coils contribute over 150 W in the PCS, over 50 W of heat load is generated in support shell and thermal shield. For these reasons, a liquefier with the cooling capacity over 600 W at 4.5 K will be adopted in COMET experiment.
Table 2.3: The predicted total nuclear heat load from the PHITS simulation.
Item Heat load [W] Volume [m3] Comments
Pion Capture Solenoid 166.2 Coil from CS0 to TS1f
CS0 10.3 1.2×10−1
CS1 93.4 9.0×10−1
MS1 41.1 5.0×10−1
MS2 13.9 3.5×10−1
TS1a 1.9 5.2×10−3
TS1b 2.3 2.0×10−2
TS1c 1.2 2.3×10−2
TS1d 1.1 3.6×10−2
TS1e 0.3 1.7×10−2
TS1f 0.7 9.7×10−2
Support shell 39.6 Support shell in PCS
CS 20.0 7.1×10−1
MS1 9.6 5.1×10−1
MS2 3.1 4.0×10−1
TS1a-e 6.6 2.0×10−1
TS1f 0.3 7.1×10−2
Thermal Shield 14.5 4.9×10−1 for the coils of CS and MS
Muon Transport Solenoid 15.5 Coil from TS2a to TS3
TS2a 0.6 6.1×10−3
TS2-1 0.2 4.5×10−3
TS2-2 0.4 1.1×10−2
TS2-3 0.8 1.1×10−2
TS2-4 1.2 1.1×10−2
TS2-5 1.0 1.1×10−2
TS2-6 0.8 1.1×10−2
TS2-7 1.2 1.1×10−2
TS2-8 1.0 1.1×10−2
TS2-9 1.1 1.1×10−2
TS2-10 1.3 1.1×10−2
TS2-11 1.0 1.1×10−2
TS2-12 1.0 1.1×10−2
TS2-13 1.1 1.1×10−2
TS2-14 0.7 1.1×10−2
TS2-15 0.5 1.1×10−2
TS2-16 0.7 8.9×10−3
TS3 0.9 2.9×10−3
Total 236
and length of 30 mm are embedded in two copper cylindrical absorbers: inner absorber and outer absorber, and the nuclear heat load is measured with a heater calibration
Chapter 2. Radiation Estimation for Pion Capture Solenoid
system. Compared with the experimental data, the energy deposition is well reproduced by PHITS as well as FLUKA simulation for a case of a high energy proton bombardment.
File = geometry.out Check geometry using [T-gshow] tally Date = 17:26 09-Dec-201
plotted by ANGEL 4.35 calculated by PHITS 2.8
−20 −10 0 10 20
−20
−10 0 10 20
z [cm]
x [cm]
no. = 1, y = 0.0000E+00
void Absorber Target 90
11 10 1
10
11 Absorber
Target 20 mm
50 mm
240 mm
30 mm 30 mm
Target position [mm]
−80 −60 −40 −20 0 20 40 60 80 protons]11 Energy deposition [J/10
0.4 0.6 0.8 1 1.2 1.4 1.6
1.8 Measurement
PHITS FLUKA
Figure 2.8: Comparison of the Monte Carlo calculation to the measurement data (right) with a simulation model shown on left. Three points of energy deposition are measured by shifting the target along thez-axis with±80 mm.
Although the Monte Carlo simulation provides a good agreement with experimental data, the main uncertainty is derived from the damage rate, which could affect the thermal analysis described later. For the COMET experiment, a lot of high energy neutrons are predicted as plotted in Fig. 2.4, in which the mechanism of radiation damage is different with a low energy neutron irradiation. According to the explanation in Ref. [42], the depleted zone of vacancy can be created in the center of cascade so that the cluster of vacancy could affect the electrical resistivity significantly at the high energy region. From an aspect of magnet design, the uses of damage rate with a safety factor of 2 is also discussed in the thermal analysis described in chapter 3.
2.3.2 Radiation Estimation for Larger Target
In the conceptual design of the COMET muon beam line, the nominal radius and length of a tungsten production target are determined to be 3 mm and 160 mm. However, as reported in Ref. [43], the production target can still be optimized to has a radius of 10 mm and a length of 320 mm to achieve the peak of muon and pion yield. Also, a larger target is easy to be supported as well as be targeted by a proton beam. To validate the effect of the change of target on superconducting magnets, the radiation level is estimated with same simulation model as described in Sec. 2.1.2 besides the size of target.
Table 2.4 lists the peak of neutron flux, DPA rate, dose rate and total nuclear heat loads. Compared with the configuration of use of original target, the peak of total dose, neutron fluence and DPA are 1.3 MGy, 4×1021 n/m2 and 4.3×10−4 DPA by assuming the required beam time is 280 day. The peak of neutron flux and total dose are same with the original configuration, however, the nuclear heat load are increased to about 280 W (Shell support: 52 W, TS1a-f: 7 W). Secondly, the DPA rate and heat density for tungsten target
is increased to about 7×10−8 DPA/sec and 4 kW/kg, which are doubled in comparison of the original configuration. Since the design cooling capacity of 600 W at 4.5 K, the heat loads is capable of being removed with two-phase helium flow by using a optimized target.
As the coil temperature analyzed in chapter 3, the coil temperature is capable of being kept below a magnet quenching temperature for 1-month operation at minimum even the heat generation is doubled. However, more severe thermal or mechanical problem on production target could be encountered for a long-term beam operation.
Even using a larger production target, the neutron flux and nuclear heating are only increased by about 30%, the superconducting magnet is capable of being operated for more than one month. Thus estimated radiation with a nominal size of production is utilized in the following analysis.
Table 2.4: The peak of neutron flux, DPA rate, dose rate and total nuclear heat load in each coil for the use of a production with a length of 320 mm and a radius of 3 mm.
Coil Neutron flux Displacement per atom Dose rate Heat load
[n/m2/sec] [DPA/sec] [Gy/sec] [W]
CS0 (1.13±0.01)×1014 (1.24±0.02)×10−11 (4.0±0.3)×10−2 12.8 CS1 (1.65±0.01)×1014 (1.77±0.02)×10−11 (5.4±0.2)×10−2 128.2 MS1 (1.08±0.01)×1014 (1.05±0.01)×10−11 (2.9±0.1)×10−2 60.1 MS2 (3.54±0.03)×1013 (3.48±0.05)×10−12 (1.6±0.1)×10−2 19.3