3.3.1 Thermal Stability during the Beam Operation
The maximum temperature for CS and MS coils during the beam operation is shown in Fig. 3.19 as a function of continuous beam operation time. The coils of TS1a-f are considered to be thermally stable during the beam operation owing to their small size and low radiation environment. At the beginning of beam operation corresponding to the 0-day operation, the thermal path is not degraded by radiation, thereby, the peak temperature is kept below 5 K for each coil, which is warmed by the nuclear heating.
However, owing to the accumulated neutron flux, the coil starts to degrades, and the peak of coil temperature is increased continuously as the beam operation time increases.
4.5 K 4.5 K 4.5 K 4.5 K 4.5 K 4.5 K
4.5 K 4.5 K
Max.: 4.8 K Max.: 5.2 K Max.: 6.2 K Max.: 5.1 K
MS2 MS1 CS1 CS0
Figure 3.18: The temperature distribution for the CS and MS coils in a Z-R view at the 90 day beam operation, in which the temperature distribution at the angle from 135◦ to 225◦ corresponding to the peak of temperature along the azimuth is plotted here.
Figure 3.18 shows the temperature distribution in each coil from 135◦ to 225◦ at the 90 day beam operation. Among these coils, the temperature rise of CS1 coil is a worst case because of the large size, strong magnetic field and severe irradiation environment3, and the temperature margin is vanished for a 90-day beam operation. After the few month of
3The peak of magnetic field, neutron flux, and nuclear heating are located in CS1 coil.
Beam Operation Time [days]
0 50 100 150 200 250
Peak Temperature [K]
4.5 5 5.5 6 6.5 7 7.5
CS0 CS1
MS1 MS2
Figure 3.19: Maximum temperature for each coil after the varied beam operation time. Black (blue, green and red) line indicates the maximum temperature rises as a function of beam
operation duration for CS0 (CS1, MS1 and MS2) (copyright: IEEE [37]).
beam operation, the magnet quench caused by radiation could be occurred, and a thermal cycle up to room temperature must be preformed to recover the radiation damage.
3.3.2 Investigation of Parameters
In practice, the assumed parameters could induce the uncertainties of the thermal analysis. For instance, it is difficult to control the thickness of the insulation since the coil is impregnated with epoxy resin and reformed by the heat treatment after the coil winding, which could increase the coil temperature in analysis significantly. Thereby, to handle the uncertainties that affects the coil temperature in thermal analysis, the sensitivity of parameter is investigated for the worst coil, CS1, with the possible variation as listed in Table 3.18, in which the uncertainties of the radiation damage and nuclear heating will be discussed later.
Table 3.18: Possible variation for the parameters in thermal analysis.
Parameters Value in simulation Possible variation
Ground insulation 0.25 mm 0.25 ∼ 0.40 mm
Turn-to-turn insulation 0.20 mm 0.20 ∼ 0.30 mm
Resin 3 mm 3 ∼5 mm
Thermal conductivity of insulation 0.01 W·m−1·K−1 0.005 ∼ 0.02 W·m−1·K−1
Insulation The insulation is considered as the main parameters that could affect the thermal analysis because an innovative insulation is employed in the PCS and the thermal conductivity as well as the radiation tolerance on thermal conductivity has not been
Chapter 3. Thermal Stability during the Beam Operation
studied yet. The effect of the thermal conductivity and thickness of the insulation tape are given in Fig. 3.20. The change of thickness in turn-to-turn insulation with 0.05 mm could increase the peak temperature by 0.1 K at 90 day operation. On the other hand, the change of coil temperature is found to be 0.4 K for 90-day beam operation in the range of the thermal conductivity from 0.005 to 0.02 W·m−1·K−1.
The thickness of resin between the support shell and coil, and the thickness of ground insulation has the influence on peak temperature of 0.1 K at maximum since the heat transfer between the coil and thermal path is dominated in coil temperature. Therefore, the thermal conductance is found to be a very important parameter affecting the coil temperature, and the thermal conductivity of insulation tape is measured and will be presented in chapter 4.
Beam Operation Time [days]
0 10 20 30 40 50 60 70 80 90
Peak Temperature [K]
4.8 5 5.2 5.4 5.6 5.8 6 6.2
6.4 0.005 W/m/K
0.010 W/m/K 0.020 W/m/K
Beam Operation Time [days]
30 40 50 60 70 80 90
Peak Temperature [K]
5.4 5.6 5.8 6 6.2 6.4
0.20 mm 0.25 mm 0.30 mm
Figure 3.20: The change of peak temperature against the beam operation time with the assumed thermal conductivity of insulation (left) and the thickness of turn-to-turn insulation (right).
Effect of the Cooling Pipe In this simulation, the outer surface of support shell (aluminum A5083) is assumed to be capable of cooling down to 4.5 K. However, the cooling pipe is welded on support shell, and the contact area between the support shell and cooling pipe is limited so that the coil temperature may be increased. To investigate the effect of cooling pipe, we examine two configuration of the cooling pipe alignment:
A). only both edges are fixed to 4.5 K,
B). both edges and middle of shell are fixed to 4.5 K,
in which the elements at the boundary are anchored to be 4.5 K has the length of 14 mm (along z-axis).
With an assumption of 90-day beam operation, the temperature distributions for each case in CS1 coil are plotted in Fig. 3.21. Compared with the assumption that all outer surface is fixed to 4.5 K, the temperature of support shell is elevated up to about 6.2 K as same as the peak temperature in coil for case A), then, the temperature of support shell is reduced by increasing the cooling pipe as the case B). However, the maximum coil
0 500 1000 1500 Z [mm]
700 750 800 850 900 950
R [mm]
Max. temperature = 6.28 [K]
4.6 4.8 5.0 5.2 5.4 5.6 5.8 6.0 6.2
Temperature [K]
0 500 1000 1500
Z [mm]
700 750 800 850 900 950
R [mm]
Max. temperature = 6.25 [K]
4.6 4.8 5.0 5.2 5.4 5.6 5.8 6.0 6.2
Temperature [K]
Figure 3.21: Temperature distribution in the CS1 coil simulated with different boundary conditions by assuming a beam operation time is 90 days. Left: the boundary of element at edge of shell are fixed to 4.5 K. Right: an additional element at center of shell is fixed to 4.5 K.
temperature for both cases is only increased by 0.1 K at maximum since the coil is cooled with the aluminum strips inserted between coil layer. Thus the peak temperature in coil is not affected by the position of cooling pipe.
3.3.3 Safety Factor
As discussed in chapter 2, the main uncertainty is considered from the damage rate correlated the neutron flux with electrical resistivity since the depleted zone of vacancy can be produced by the cascade of high energy neutron interactions in metals at cryogenic temperature. The damage rate could be changed in the irradiation of high energy neutron irradiation as the experimental data listed in Table 3.19. In a 14 MeV neutron irradiation, a damage rate of 4.18 Ω·m3 for aluminum is measured by M. Guinan et al.[70], which is higher than the damage rate used in simulation about factor 2. Also, the nuclear heating can be increased by replacing to a large production target as a study described in Sec. 2.3.2.
Although the PHITS simulation provides a good prediction and the conservative values for the estimation are used, from an aspect of safe design, the safety factors multiplied on the damage factor and nuclear heating are introduced here to investigate the lifetime of magnet in one operation cycle.
Table 3.19: The damage rate measured with the neutron irradiation for aluminum in the past.
Reference [26] [70] [48] [27]
RRRAl 2286 74 1500 500
Neutron source reactor 14 MeV reactor reactor
Neutron fluence (E>0.1 MeV) [n/m2] 2×1022 1021 2.9×1021 6×1020
∆ρ/Φ [×10−31 Ω·m3] 1.9 4.1 3.3 3.0
Assuming a maximum safety factor of 4 on damage rate as well as that of 2 on the nuclear heating, the peak temperature in CS1 coil through an evolution of beam operation time is compared in Fig. 3.22. The heat load affects the peak temperature more significantly then that of damage rate. Even with a doubled heat generation, at least 1-month beam operation is capable for the PCS. Similarly, the coil temperature
Chapter 3. Thermal Stability during the Beam Operation
Beam Operation Time [days]
0 10 20 30 40 50 60 70 80 90
Peak Temperature [K]
4.5 5 5.5 6 6.5 7 7.5
factor 1
× ζ
factor 2
× ζ
factor 4
× ζ
Tcs
Beam Operation Time [days]
0 10 20 30 40 50 60 70 80 90
Peak Temperature [K]
5 5.5 6 6.5 7 7.5
factor 1
× Q
factor 2
× Q
Tcs
Figure 3.22: Comparison of the peak temperature in CS1 coil estimated with a safety factor multiplied on the term of damage rate (left) and heat generation (right).
can be suppressed below the temperature limitation for 1-month beam operation even multiplying a factor of 4 on damage rate.
3.3.4 Study of Aluminum Strips
In general, the installation of aluminum strips between the coil layer is a technical issue since the high pure aluminum strips are so soft that could be misaligned in coil, furthermore, the bending could cause the degradation of RRR during the coil winding.
From the view of magnet fabrication, the installation of aluminum strips between coil layer is not desirable if the coil can be cooled well. Here, the effect of aluminum strips is studied to search for the best way to install the aluminum strips efficiently.
Effect of Aluminum Strips The coil temperature at 90 day operation is analyzed with various of number of aluminum strip inserted between coil layer along the radius to investigate the effect of aluminum strips. Figure 3.23 shows the peak temperature in each coil when the aluminum strips are inserted from innermost layer to outermost layer. As no aluminum strips is applied, the coils are only conduction-cooled by the support shell against the nuclear heating. Thereby, the peak temperature in CS1 is heated up to 8 K, and even in a small coil, CS1, the temperature is increased to 6.5 K.
By inserting the aluminum strip between coil layer, the coil peak temperature is decreased significantly. In particular, the aluminum strips affects the coil temperature when they are installed in the inner layer of coil since the peak of heat generation and magnetic field is expected to be in the inner layer, and the temperature is reduced by increasing the thermal path. The peak temperature converges when the aluminum strips are filled to 90% of coil layer along the radius. Therefore, the aluminum strips have to be installed in all layers of coil for CS and MS coils for a long-term operation.
Extraction of Aluminum Strips As for each coil, the aluminum strips must be extracted from the coil and connected to the cooling pipe. To extract the aluminum
Number of Layers
0 1 2 3 4 5 6 7 8 9
Peak Temperature [K]
5 5.5 6 6.5 7 7.5 8
CS0 CS1
MS1 MS2
Figure 3.23: The peak temperature in each coil when the coil layers are filled with the aluminum strips. Black (blue, green and red) line is the peak temperature in CS0 (CS1, MS1 and MS2) coil.
strips, the spacers made of aluminum have to be installed to fix the position of aluminum strips at the end of coil. To investigate whether these aluminum strips are not needed to be extracted from coil, four configurations of extraction are considered and examined as follows4:
A). The strips are extracted from the coil end at downstream, and fixed to 4.5 K.
B). The strips are extracted from the coil end at upstream, and fixed to 4.5 K.
C). The strips at even number of coil layer are extracted from the coil end at upstream, vice versa, the one at odd number are extracted from the end at downstream. All the extracted aluminum strips are fixed to 4.5 K.
D). All strips are extracted from the coil both ends, and fixed to 4.5 K.
Figure 3.24 presents the temperature distribution in CS1 coil with a beam operation of 90 days for each configuration. As for the configuration A) and B), the configuration of A) has higher peak temperature and short high temperature region than that of B) owing to the distribution of heat generation as described in Sec. 2.2.2. Due to the less thermal paths for configuration A), B) and C), the peak temperature can be reduced by 1 K with the extraction of aluminum strips from both ends. Thereby, the aluminum strips have to be extracted from both ends.
Aluminum Strip at Innermost Layer In present design, the thickness of aluminum strip at innermost layer of coil is 1 mm, however, it can be optimized to enhance the
4Only the aluminum strips inserted between the coil layers are considered here.
Chapter 3. Thermal Stability during the Beam Operation
0 500 1000 1500
Z [mm]
700 750 800 850 900 950
R [mm]
Max. temperature = 7.065 [K]
4.5 4.8 5.1 5.4 5.7 6.0 6.3 6.6 6.9
Temperature [K]
0 500 1000 1500
Z [mm]
700 750 800 850 900 950
R [mm]
Max. temperature = 6.941 [K]
4.5 4.8 5.1 5.4 5.7 6.0 6.3 6.6 6.9
Temperature [K]
0 500 1000 1500
Z [mm]
700 750 800 850 900 950
R [mm]
Max. temperature = 6.914 [K]
4.5 4.8 5.1 5.4 5.7 6.0 6.3 6.6 6.9
Temperature [K]
0 500 1000 1500
Z [mm]
700 750 800 850 900 950
R [mm]
Max. temperature = 6.19 [K]
4.5 4.8 5.1 5.4 5.7 6.0 6.3 6.6 6.9
Temperature [K]
Figure 3.24: The temperature distribution in CS1 at 90-day beam operation coil with four configurations of extraction of aluminum strips, A (upper left), B (upper right), C (down left) and D (down right). The maximum temperature for each configuration is 7.1, 6.9, 6.9 and 6.1 K (A, B, C and D).
cooling ability of coil. Realized the thick aluminum strip is difficult to be adhered with epoxy resin, we examine the thickness of innermost aluminum strip until 3 mm, while those in the other layer are kept in 1 mm. Compared with the temperature distribution as plotted in Fig. 3.25, since the peak temperature is located in the innermost layer owing the coincidence of peak of magnetic field and radiation, the peak temperature is removed by increasing the thickness of innermost aluminum strip. As given in Fig. 3.26, the peak temperature can be reduced by 0.3 K by increasing the thickness of innermost aluminum strip to 3 mm.
0 500 1000 1500
Z [mm]
700 750 800 850 900 950
R [mm]
Max. temperature = 6.19 [K]
4.8 5.0 5.2 5.4 5.6 5.8 6.0
Temperature [K]
0 500 1000 1500
Z [mm]
700 750 800 850 900 950
R [mm]
Max. temperature = 5.87 [K]
4.6 4.8 5.0 5.2 5.4 5.6 5.8 6.0
Temperature [K]
Figure 3.25: The temperature distribution in CS1 coil at 90-day beam operation for the cases with a 1 mm thick (left) and 3 mm (right) aluminum strip attached to the innermost layer of coil.
Aluminum Strips Filled along the Azimuth Totally 24 sheets of pure aluminum strips with a width of 150 mm are inserted between coil layers. The effect of aluminum strips filled along the azimuth is also investigated to validate the possibility of optimization.
Figure 3.26 shows the peak temperature as a function of beam operation time. The peak of coil temperature is sensitive with the filled aluminum strips along the azimuth, and
Beam Operation Time [days]
0 10 20 30 40 50 60 70 80 90
Peak Temperature [K]
4.5 5 5.5 6
6.5 1 mm
2 mm 3 mm
Beam Operation Time [days]
0 10 20 30 40 50 60 70 80 90
Peak Temperature [K]
4.5 5 5.5 6 6.5
7 15 sheets 20 sheets
24 sheets 25 sheets
Figure 3.26: Effect of the thickness of innermost layer aluminum strip (left) and the aluminum strip filled along the azimuth.
the aluminum strips must be filled between the coil layers along the azimuth as much as possible to reduce the peak temperature.
Summary As for a novel method, the effect of aluminum strips is studied to search for the best way to align the thermal path for removing the nuclear heating from the coils, and the optimized alignment is proposed as follows:
1). Inserting the aluminum strips between each layer of coils, in which the last layer may be eliminated since the impact is relatively inefficiently.
2). Extracting the aluminum strips from the both ends and connecting to the cooling pipe.
3). Increasing the thickness of aluminum strip at inner layer to 3 mm.
4). Increasing the number of aluminum strips along the azimuth.