Chapter 5. Quench Protection for Superconducting Magnets
where the ri,j is the radius. Figure 5.5 shows the calculated coil total inductance. The difference between the maximum and minimum of total inductance in each coil is within 1.3 mH, and the peak of total inductance is about 3.3 mH located in CS1 coil.
1.02 1.00 0.98 0.96 0.94 0.92 0.90 0.88 Z [m]
0.68 0.70 0.72 0.74 0.76 0.78 0.80 0.82
R [m]
1.65
1.80 1.95
2.10 2.25
1.51 1.601.69 1.78 1.87 1.96 2.05 2.14 2.23 2.32
Inductance [mH]
0.6 0.4 0.2 0.0 0.2 0.4
Z [m]
0.68 0.70 0.72 0.74 0.76 0.78 0.80 0.82
R [m]
2.25 2.50
2.50 2.75
3.00 3.25
2.055 2.190 2.325 2.460 2.595 2.730 2.865 3.000 3.135 3.270
Inductance [mH]
0.8 1.0 1.2 1.4 1.6 1.8 2.0
Z [m]
0.68 0.69 0.70 0.71 0.72 0.73 0.74 0.75
R [m]
1.80 1.95
2.10 2.25 2.40
1.72 1.80 1.88 1.96 2.04 2.12 2.20 2.28 2.36 2.44
Inductance [mH]
2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9
Z [m]
0.68 0.70 0.72 0.74 0.76 0.78
R [m]
1.40 1.80 1.60 2.00
1.25 1.35 1.45 1.55 1.65 1.75 1.85 1.95 2.05 2.15
Inductance [mH]
Figure 5.5: Estimated total inductance in CS0 (upper left), CS1 (upper right), MS1 (lower left) and MS2 (lower right).
0 500 1000 1500 2000 2500 3000
Current [A]
CS0 CS1 MS1 MS2 TS1a
0.00 0.05 0.10 0.15 0.20
Coil Resistance [
Ω
]0 20 40 60 80 100 120 140 160 Time [sec]
0 20 40 60 80 100
Hot Spot Temperature [K]
0 20 40 60 80 100 120 140 160 Time [sec]
0 50 100 150 200
Coil Voltage [V]
Figure 5.6: The quench characteristics during the current discharge for the CS0 (blue), CS1 (red), MS1 (green), MS2 (black) and TS1a (orange) coil in the PCS.
Table 5.2: Maximum temperature at hot spot and MIITs for each coil at non-irradiated condition.
CS0 CS1 MS1 MS2 TS1a TS1b TS1c
Thot [K] 96 76 74 81 66 93 92
M IIT s [MA2·sec] 233 179 211 217 263 258 258 TS1d TS1e TS1f
Thot [K] 89 93 85
M IIT s [MA2·sec] 259 259 243
quench is low enough that quench is difficult to detect, and the detection time contributes to the extra M IIT s. In principle, the coil with a small size has a low coil resistance, and the maximum temperature should close to the MIITs calculation, however, the one layer coil, TS1a, has the lowest among the all coils. It is found that the heat is absorbed significantly by the support shell located at outer layer of coil during a process of quench, which will be mentioned in Sec. 5.3.1 later.
Additionally, the effect of a dump resistor is also studied as a worst case that quench is occurred in CS0 coil1. Figure 5.7 shows the quench characteristics with various resistance of dump resistor. Even the pure aluminum strips are inserted between each layer of coil,
1In principle, a small coil gives an elevated temperature such as TS1 coils, however, the aluminum strips are attached on the innermost layer through the all TS1 coils so that the fast normal zone propagation through the each coil is expected. Thus the CS0 coil is considered as a worst case.
Chapter 5. Quench Protection for Superconducting Magnets
0 500 1000 1500 2000 2500 3000
Current [A]
0.0 Ω 0.1 Ω 0.2 Ω 0.3 Ω
0.00 0.050.10 0.150.20 0.250.30 0.35 0.400.45
Coil Resistance [
Ω
]0 20 40 60 80 100 120 140 160 Time [sec]
0 50 100 150 200 250 300
Hot Spot Temperature [K]
0 20 40 60 80 100 120 140 160 Time [sec]
0 100 200 300 400 500 600
Coil Voltage [V]
Figure 5.7: The evolution of discharge (upper left), hot spot temperature (lower left), coil resistance (upper right) and voltage (lower right) with various resistance of dump resistor. Blue line indicates the by-pass resistor is not employed, and red (green, black) line shows the quench characteristics when the coil is protected with a 0.1 (0.2, 0.3) Ω dump resistor.
the hot spot temperature rises up to 300 K without the protection of a by-pass dump resistor. The maximum temperature can be reduced to about 60 K when a 0.3 Ω dump resistor is employed, while the inductive voltage drops to lower than -600 V at beginning of quench. Thereby, a by-pass dump resistor is essential to protect the PCS, furthermore, even with a lower resistance of dump resistor such as 0.1 Ω, the hot spot temperature can also be suppressed below 200 K, and much lower peak of voltage in by-pass circuit can be achieved.
Although the possibility of magnet quench occurred in the middle of innermost layer is very high because the peak of magnetic field, mechanical strength and radiation are concentrated, the magnet quench could be occurred in the other place, for instance the quench could be occurred in the bus bar that connects the magnet and magnet. As shown in Fig. 5.8, the location of hot spot is examined with two cases for a CS1 coil:
1). Quench simulation is performed with a uniform magnetic field of 5 Tesla, 2). Quench simulation is performed with a magnetic field map.
By eliminating the effect of magnetic field, the worst case that a highest temperature after quench is estimated by the change of hot spot position is located at corner of the magnet. However, the maximum temperature after quench is found to be sensitive with a magnetic field map, in which the difference of maximum temperature is about 27 K by comparing the case when hot spot is assumed at the middle of inner layer and outer
72 K 71 K
64 K 63 K
69 K
71 K
case 1) Uniform field of 5 Tesla case 2) Magnetic field map
76 K 65 K
54 K 49 K
62 K
76 K
Hot spot
Figure 5.8: Maximum temperature after quench when the hot spot is set in the different place at CS1 coil. The symbol of ×and the temperature indicate the maximum temperature after quench when the hot spot position is changed.
layer. Since the aluminum strip contributes to the normal propagation significantly, the maximum temperature difference is small even by changing the hot spot along the horizontal direction. Hence, assuming the hot spot located at middle of inner layer gives a conservative result for the quench study.
All the peak of coil voltage and temperature is suppressed below the allowable value, thus the design of the quench protection system is capable of protecting the magnets at non-irradiated condition.
Investigation of Parameters
The parameters used in the quench simulation could have some uncertainties for PCS.
Here, the parameters are studied with the known uncertainties and some assumptions to investigate the impact of parameters on the result of this simulation. The possible variation of each parameters are listed in Table 5.3.
n-Value In this simulation, then-value in the expression of voltage-current (V-I) charac-teristic of superconductor is assumed to be 40. As for the low temperature superconductor, the n-value is from 30 to 80 given in Ref. [94]. Thus, the effect of n-value is examined from 20 to 80. Figure 5.9 presents the behavior of current sharing in the aluminum-stabilized conductor. The superconductor with higher n-value shares its current with the aluminum-stabilizer and copper matrix quickly at the beginning of quench, however, the final temperature after the shut-down is only changed within 1 K. Therefore, the n-value is not significant parameter in this simulation.
Chapter 5. Quench Protection for Superconducting Magnets
Table 5.3: The assumed parameters and possible variation of each parameters in quench analysis.
Parameter Value in simulation Possible variation
n-value 40 20∼ 60
Ratio of cross-sectional area 7.3:0.9:1 (7.3±0.5):(0.9±0.1):1
Epoxy resin 3 mm 3∼ 5 mm
Thermal conductivity of insulation polyimide factor 2
RRR of conductor 400 300 ∼ 700
0 500 1000 1500 2000 2500 3000
I
Al[ A ]
0 500 1000 1500 2000 2500 3000
I
sc[ A ]
130 135 140 145 150 155 160 165 Time [msec]
200 4060 10080 120140 160180
I
Cu[ A ]
130 135 140 145 150 155 160 165 Time [msec]
6.5 7.0 7.5 8.0 8.5 9.0
Temperature [K]
n = 20 n = 30 n = 40
n = 50 n = 60
Figure 5.9: The flowing current in aluminum stabilizer (upper left), superconductor (upper right) and copper matrix (lower left), and temperature (lower right) at beginning of quench.
The current in copper matrix decays due to the current redistribution in aluminum-stabilizer.
Copper and Aluminum Ratio In practice, the aluminum and copper ratio in aluminum-stabilizer given by the manufacture with the uncertainties is (7.3±0.5):(0.9±0.1):1 for Al:Cu:NbTi. Thus the influence of the copper and aluminum ratio on the maximum temperature is assessed with the case of CS0 coil. The fluctuation of both the copper and aluminum ratio only affects the maximum temperature after quench by ±0.5 K.
Epoxy Resin Between the support shell and last layer of coil, the gap is filled by epoxy resin. The thickness of epoxy resin contributes the thermal resistance between the support shell and coil which could affect the heat transfer between the coil and support shell.
Thus the thickness is investigated by assuming the thickness is 10 mm at maximum. As a result, the maximum temperature in CS0 coil after the quench is only changed within 1 K.
Thermal Conductivity of Insulation The thermal conductivity of insulation is assumed to be polyimide (Kapton) in this simulation, however, in accordance with the
measurement of thermal conductivity, the insulation employed in PCS has a better thermal conductivity. By assuming the thermal conductivity is higher than the one of polyimide by factor 2 through the whole range of temperature, the maximum temperature in CS0 coil is changed by 1 K.
RRR of Conductor As for the magnet design, the RRR of aluminum-stabilizer is required to be 400, however, the RRR of aluminum-stabilizer has been measured to be 700 at maximum given by the manufacture. Additionally, the degradation of RRR could be occurred by the strain [105], thus the RRR of aluminum-stabilizer may has a distribution along the conductor, For these reasons, we assess the influence on the RRR of aluminum-stabilizer by assuming the possible change of RRR from 300 to 700. As given in Table 5.4, the degradation of the RRR will cause the increasing of the maximum temperature after quench.
Table 5.4: Impact of the conductor RRR on the maximum temperature after quench. Rcoil indicates the reached coil resistance when the current is discharged until 0 A.
RRR Thot [K] M IIT s [MA2·sec] Rcoil [Ω]
300 99 231 0.063
400 96 233 0.060
700 88 243 0.043
Support Shell As mentioned in previous section, the impact of support shell on the peak temperature is significant in TS1a coil due to the increasing of the heat capacity and thermal conductivity in support shell. Whereas, the support shell does not affect the maximum temperature for the other coils since the hot spot is far away from the support shell. Figure 5.10 shows the evolution of temperature at the hot spot and center of the support shell. The temperature at hot spot rises to the peak then decreases at 60 sec after coil quench, meanwhile, the temperature at support shell keeps growing up until the current decays to zero. The maximum temperature is also a function of the thickness of support shell, without the support shell, the maximum temperature of TS1a coil is expected to be 95 K.
5.3.2 Irradiation Effect on Magnet Quench
Similar to the study in chapter 3, the irradiation effect is investigated with CS0, CS1, MS1 and MS2 coil by assuming the magnet quench is occurred after an elapsed time of beam operation. The profile of the neutron flux is utilized to calculate the RRR to take into account the possible degradation in aluminum strips and also in aluminum stabilizer.
In addition, the profile of temperature estimated in chapter 3 is treated as the initial coil temperature after irradiation.
Figure 5.11 shows the predicted current discharge, coil resistance, temperature at hot spot and the coil voltage. Obviously, the temperature at hot spot is increased as the degradation on the RRR of aluminum stabilizer since the heat generation becomes higher
Chapter 5. Quench Protection for Superconducting Magnets
Shell Thickness [mm]
0 10 20 30 40 50 60 70 80 90
Maximum Temperature [K]
55 60 65 70 75 80 85 90 95
0 20 40 60 80 100 120 140 160
Time [sec]
0 500 1000 1500 2000 2500 3000
Current [A]
0 10 20 30 40 50 60
Temperature [K]
Hot spot Center of shell
Figure 5.10: Effect of support shell on maximum temperature after quench for a single layer coil, TS1a (left). The evolution of temperature in hot spot (red line) and center of support shell (green line) is plotted on right.
than the non-irradiated case. At the beginning of quench, the resistance of dump resistor is dominated in the discharge, while the current decay becomes faster after few ten seconds due to the increase of coil resistance. The degradation of RRR also affects the coil voltage, however, both of inductive and resistive voltage are suppressed below an acceptable value.
0 500 1000 1500 2000 2500 3000
Current [A]
0 day operation 30 day operation 60 day operation 90 day operation
0.00 0.05 0.10 0.15 0.20 0.25 0.30
Coil Resistance [
Ω
]0 20 40 60 80 100 120 140 160 Time [sec]
0 1020 3040 5060 70 8090
Hot Spot Temperature [K]
0 20 40 60 80 100 120 140 160 Time [sec]
400 300 200 100 0 100 200 300
Coil Voltage [V]
Figure 5.11: The evolution of the current, coil resistance, hot spot temperature, coil inductive and resistive voltage in CS1 coil for various beam operation time.
The temperature at hot spot for each coil is plotted in Fig. 5.12. Even after the irradiation of 90 day beam operation, the hot spot temperature is expected to be 110 K in CS0 coil at maximum, and also those in the other coils are well below the criteria for
the quench protection. In MS2 coil, the change of peak temperature is not significant owing to the low radiation.
Elapsed Time of Beam Operation [days]
0 10 20 30 40 50 60 70 80 90
Peak Temperature [K]
75 80 85 90 95 100 105 110
CS0 CS1
MS1 MS2
Figure 5.12: The peak temperature after quench as a function of the elapsed time of beam operation.
5.3.3 Effect of Aluminum Strips
During a process of quench, the aluminum strips act as the quench propagator. The pure aluminum strips are applied to enhance the normal zone propagation in ATLAS central solenoid [106] and the detector solenoid for BELLE experiment [107]. However, both of the superconducting solenoid above are with a single layer, in which the aluminum strips are attached to the innermost layer of coil. In PCS, the aluminum strips are inserted between each coil layer. Of interest to the effect of aluminum strips in a multilayer solenoid, three cases are investigated with a largest coil, CS1, as follows:
A). A solenoid coil without the installation of aluminum strips.
B). Aluminum strips are only attached on the innermost layer of coil.
C). Aluminum strips are inserted into each layer of coil.
Figure 5.14 show the evolution of the normal zone propagation for the cases with and without the aluminum strips inserted between coil layer, and its quench characteristics are shown in Fig. 5.13. Obviously, the aluminum strips accelerate the normal zone propagation along the longitude significantly, in which all elements quenches after 7 sec for the case C), in contrast, the case A) costs about 29 sec when all elements become normal state. Due to the contribution of aluminum strips, the coil resistance grows faster and reaches to a higher resistance so that the current decay also becomes faster. The hot spot temperature is reduced by 15 K (Tmax: 92 K for case A and 76 K for case C). We also examine the multilayer coil only with a aluminum strip attached to the innermost layer of coil to
Chapter 5. Quench Protection for Superconducting Magnets
0 500 1000 1500 2000 2500 3000
Current [A]
With Al strips Without Al strips
0.00 0.05 0.10 0.15 0.20
Coil Resistance [
Ω
]0 20 40 60 80 100 120 140 160 Time [sec]
0 20 40 60 80 100
Hot Spot Temperature [K]
0 20 40 60 80 100 120 140 160 Time [sec]
0 50 100 150 200
Coil Voltage [V]
Figure 5.13: The quench characteristics for the cases with and without the aluminum strips inserted between coil layer.
validate whether the normal zone can be accelerated with less aluminum strips. The normal zone propagation is shown in Fig. 5.15, in which two cases with a hot spot located near and far from the aluminum strips are tested. The normal zone propagation can also be accelerated significantly, and the maximum temperature is estimated to be 78 K. Even the hot spot is far from the aluminum strips, the maximum temperature after quench is calculated to be about 75 K, and decreased a bit due to the low magnetic field. Of interest to the radiation influence on the aluminum strips, the effect of aluminum strips in an irradiated condition is also assessed. In comparison of the non-irradiated condition, the hot spot temperature after quench is reduced by 9 K for 90-day beam operation (Tmax: 93 K for case A, 88 K for case B, and 84 K for case C).
As a conclusion, the aluminum strips combined with a dump resistor may be useful to protect a multilayer magnet against the magnet quench. The degradation of thermal conductivity affects the contributions of aluminum strips, however, the impact is not significant.
5.3.4 Eddy Current Effect
In this quench model, the heat generation of eddy current and coupling loss are not included. In general, these losses induced by time-varying magnetic field can increase the heat generation in coil so that the hot spot temperature may be changed if the current is discharged quickly. Here, the effect of eddy current and coupling loss are examined by assuming the quench is occurred in a biggest coil, CS1.
T im e [a .u.]
without aluminum strips with aluminum strips
Figure 5.14: Comparison of the quench propagation for a coil with (left) and without (right) aluminum inserted between each layer. All elements quenched at more than 20 sec for a case without aluminum strips, and about 7 sec for the case with inserted aluminum strips.
Eddy Current in Conductor
A solution of current loss in a metallic strip with an infinite length is given in Ref. [94], in which a time-varying magnetic field is assumed to be perpendicular to a metallic strip (x-y plane) with a thickness ofa and width of b as shown in Fig. 5.16.
Because the system is independent of x-axis, according to the Faraday law, the
Chapter 5. Quench Protection for Superconducting Magnets
T im e [a .u.]
hot spot at center of coil hot spot at inner layer
Figure 5.15: Comparison of the quench propagation when the hot spot is located in the center (left) and inner layer (right) of coil for a coil only with a innermost aluminum strip. All elements quenched at about 10 sec for a case when the hot spot is far from the aluminum strips, and about 8 sec for the case when the hot spot is near to the aluminum strip.
correlation can be written as
∂Ex
∂y = ∂Bz
∂t (5.30)
where E is the electrical field. The solution is given by Ex =y∂Bz
∂t . (5.31)
z x y Bz
b a
Figure 5.16: A metallic strip model with a time-varying magnetic field perpendicular to the x-y plane for the investigation of the effect of eddy current for quench propagation.
Thus, the eddy-current loss per unit length P in the unit of W/m can be calculated by P =
Z a 0
dz Z b/2
−b/2
Ex2
ρ dy = ab3 12ρ(∂Bz
∂t )2 (5.32)
where ρis the resistivity of conductor. The heat generation of eddy current loss Qe per unit volume can be written as
Qe= b2 12ρ(∂Bz
∂t )2 (5.33)
in which b is the conductor width of 15 mm, ρ is treated as the resistivity of aluminum stabilizer, and Bz is assumed as the total magnetic field in simulation. This eddy-current loss is linearly added into the heat generation term in thermal model.
Coupling loss
In a twisted superconducting cable, an eddy current opposite to the direction magnetic field will be induced in the loop between copper matrix and filament. As described in Wilson’s textbook [102], an approximation of the inter-filament coupling loss Qc per unit volume is given by
Qc= ηCu ρef f(ps
2π)2(∂B
∂t )2 (5.34)
where ρef f is the effective transverse resistivity, ηCu is the fraction of copper matrix in a aluminum-stabilized conductor, and ps is the twist pitch, respectively. In this calculation, the effective transverse resistivity is assumed to hasρef f ≈ρtrans. Since there is a contact resistance at the interface between the filament and copper matrix, W. Carr gives an expression to calculate the transverse resistivity as [108]
ρtrans=ρCu1 +λ
1−λ (5.35)
where λ is the fraction of superconductor in the cross section of Rutherford cable. The twist pitch is assumed to be 18 mm for the superconducting cable applied in the PCS.
Chapter 5. Quench Protection for Superconducting Magnets
0 50 100 150 200 250 300 350 400 450
Heat Generation [W/m3]
0 20 40 60 80 100 120 140 160
Time [sec]
0 500 1000 1500 2000 2500 3000
Current [A]
Figure 5.17: The heat generation from the eddy current effects (top) during the current discharge (bottom) in the CS1 coil.
Figure 5.17 shows the calculated heat generation from the eddy current effects including the coupling loss and eddy current in conductor. As a conclusion, the hot spot temperature is only increased by 1 K when the both of the eddy current in conductor and the inter-filament coupling loss are implemented, in which the eddy current in conductor is dominated. Compared with the maximum heat generation from the eddy current effects of 400 W/m3, the heat generation from the ohmic heating is more than 200 kW/m3 at beginning of the discharge, therefore, the current eddy does not affect the maximum temperature after quench owing the slow current decay.