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A method for interplay analysis between quench protection and quench characteristics of close-wound superconducting magnet
Physica C: Superconductivity and its applications 566 (2019) 1353523
Contents lists available at ScienceDirect
Physica C: Superconductivity and its applications journal homepage: www.elsevier.com/locate/physc
A method for interplay analysis between quench protection and quench characteristics of close-wound superconducting magnet
T
Li Minga,b, Zheng Jinxinga, , Song Yuntaoa,b, Zeng Xianhua,b, Wang Minga,b ⁎
a b
Institute of Plasma Physics, Hefei Institutes of Physical Science, Chinese Academy of Sciences, Hefei, Anhui 230031, China University of Science and Technology of China, China
ARTICLE INFO
ABSTRACT
Index Terms: Interplay analysis Quench protection Quench characteristic
The quench protection of the close-wound superconducting magnet is a key factor during the design process, especially when used on the particle therapy gantry system. Therefore, the interplay between quench protection and coil quench needs to be considered from the earliest stage of the design. For this purpose, a method using Cryosoft code is presented in this paper. Based on the quench protection electric circuit, the current and voltage evolution of the quench protection circuit and the temperature and normal zone evolution of the superconducting coil all can be obtained with this method. By studying the allowable action time for the quench protection associated with the operating current, the quench voltage threshold and the resistance of the dump resistor are determined, which is 0.4 V and 0.3 Ω. The differences of the voltage evolutions obtained with different kinds of dump resistor connections are also studied. The results show that it is better to have the dump resistor directly connected to the coil than with a switch. The advantage of this method is its integration and comprehensiveness and can be used in the design procedure of different kinds of magnets.
1. Introduction The utilization of a close-wound superconducting (SC) magnet on the proton therapy gantry system can significantly reduce the weight of the gantry and cut the costs [1]. The first SC gantry is finished by the National Institute of Radiological Science (NIRS) in Chiba, Japan. It is designed for carbon ion therapy [2]. The SC coil of the dipole magnet developed by NIRS is wound on the surface of the cylindrical mandrel with a certain angle of inclination. It adopts the conduction cooling method and its operation needs to be very careful because of the small temperature margin. As to the design process of the SC dipole magnet, the quench protection system is the key issue. It needs to consider the energy dissipation and its impact on the quench propagation. Most of the quench protection design only focus on the energy dissipation [3–5] and determine the key parameters according to the experimental data. Salmi et al. has accounted for the quench protection system in the process of developing dipole magnet [6]. They describe the usage of the quench protection in the magnet design. Dixon et al. describes the impact of the quench voltage threshold on the quench propagation [7]. However, the other parameters of the quench protection system have not been analyzed in detail. Bermudez gives detailed introduction on the quench protection of the dipole magnet for the LHC upgrade [8]. ⁎
For better knowing the quench protection system and considering the interplay between the quench protection and coil quench, we need a comprehensive analysis of the quench protection system. This paper introduces an analysis method [9], which can analyze the interplay between quench protection system and the stability characteristics. The method performs quench propagation analysis while considering the quench protection electric circuit. 2. Simulation model description 2.1. The close-wound SC magnet The 90-degree dipole magnet with saddle-shaped superconducting coil, which is shown in Fig. 1, is aiming for the upgrading of the SC200 proton therapy gantry system [10]. The radius of the magnet centerline is 1.1 m and the target maximum magnetic field in the bore region is 2 T. The SC coil is designed to be saddle-shaped in order to avoid reversing field at both ends, which makes the coil winding very difficult. The coil is hand-wound using a specially-made mold. The NbTi conductor with rectangular cross-section is selected for easier compression during the winding process. The stronger fields of the gantry magnets located near the patient also lead to more extended and stronger stray fields. In general, the magnetic field should not exceed 0.5 mT at the
Corresponding author. E-mail address: [email protected] (J. Zheng).
https://doi.org/10.1016/j.physc.2019.1353523 Received 12 March 2019; Received in revised form 18 August 2019; Accepted 31 August 2019 Available online 06 September 2019 0921-4534/ © 2019 Elsevier B.V. All rights reserved.
Physica C: Superconductivity and its applications 566 (2019) 1353523
M. Li, et al.
Fig. 1. The 90-degree superconducting magnet with saddle-shaped coil. Table 1 The specifications of the NbTi conductor and the coils.
Conductor parameters
Coil parameters
Parameter
Unit
Value
Conductor type Bare nominal dimension Insulated nominal dimension Superconductor cross section Copper cross section Copper residual resistivity ratio Critical current @ 3 T, 4.2 K Number of layers Number of turns in each layer Inductance of single coil Mutual inductance of the two coils
– mm mm mm2 mm2 – A – – H H
WIC NbTi 2.286 × 1.524 2.553 × 1.765 0.401 3.083 200 1977 12 10 0.128 0.05
Fig. 3. Schematic representation of the electrical network used for the simulation.
an optical isolation circuit and then sent to the quench trigger circuit. For safe operation, the dump resistor is always connected in the quench protection circuit. Under normal operation, the resistance of the dump resistor is always greater than the superconducting coil and the switch S1 keeps closed. When the quench voltage exceeds the quench voltage threshold, the energy of the two coils can be dissipated with the dump resistor as soon as possible and the current supply will be cut off. 2.3. Simulation model
patient position [11]. Two warm iron yokes are used to generate the desired magnetic field with acceptable field uniformity and shield the stray fields around the magnet. The critical current density is parameterized with the equation proposed in [12] and the fitting parameters are also listed in Table. 1. When the operating current is 800 A/ turn, the maximum magnetic field density within the conductor is about 3 T and the maximum magnetic field in the bore region is 2.4 T. The GM Cryocoolers can only be installed at both ends of all the coils. The total heat leakage of the all coils and coil supports is about 3 W. The practical heat leakage may be greater. The practical cooling capacity of the four GM cryocoolers is only 4.8 W (rated power is 6 W @ 4.2 K). Due to the restriction of the conduction cooling system, the heat cannot dissipate immediately. Therefore, the operating environment is simplified to an adiabatic environment.
For realizing the integrated analysis of the quench protection, an integrated simulation model is established. The model is based on the quench protection circuit, which is shown in Fig. 3. We can see that RQ1 and RQ2 indicate the normal zone resistance of coil #1 and coil #2 separately. RD is the dump resistor and the resistance value is Rdump. The whole model is established with THEA code [13] and POWER code [14]. The THEA code is used for thermal analysis and the POWER is used for the electrical circuit calculation. The total cable current used for simulation by THEA can be obtained by a simulation of an electric network with POWER. The normal zone resistance (RQ1 and RQ2) used for the electric circuit calculation is obtained from THEA code, similarly, the operating current used in THEA code is obtained from POWER code. The communication between THEA and POWER code is governed by SUPERMAGNET (Multitask Code Manager) [15]. The THEA code is usually used for the analysis of cable-in-conduit cable (CICC) [16,17]. In order to use THEA software for tightly wound magnets operated under adiabatic environment, the transverse heat conductions between turns and layers needed to be taken into consideration. The heat which is expressed with (1), in which the heat capacity of the insulation is omitted because it is very thin compared to the conductor.
2.2. Quench protection circuit A schematic of the passive quench protection circuit is shown in Fig. 2. For clarity, the signal processing circuit and the quench detection circuit is not shown. The two coils are connected in series and driven by a 1000A regulated DC power supply. The voltage signal is processed by
Pconductor = (k ins/ th ins) d (Tconductor
Tx )
(1)
Where, Tx indicates the temperature at position x. Tconductor indicates the temperature of the adjacent conductor. Pconductor is the turn to turn (layer to layer) heat conduction. kinsand thins is the thermal conductivity and thickness of the insulation separately. d is the nominal dimension of the NbTi conductor, which is shown in Table 1. The transverse heat conduction is defined in the user-routine (UserSHeating) [14] in the THEA code. For simulating practical quench protection process, the resistance value of the dump resistor (Rdump) is also defined in the user-routine (UserBranchResistance) [15].
Fig. 2. The schematic of the quench protection. 2
Physica C: Superconductivity and its applications 566 (2019) 1353523
M. Li, et al.
3. Results
difference is calculated with the temperature data of the point A1 (A2) and point B1 (B2). The longitudinal-inner temperature difference is calculated with the temperature data of point A1 (A2) and A3. The longitudinal-outer temperature difference is calculated with the temperature data of the point B1 (B2) and point B3. The definitions of the points are shown in Fig. 5. The cross section #1 is the position where the perturbation is applied. The cross section #2 is 1 m away from cross section #1. The cross section #3 is the farthest section from cross section #1. We can see that the temperature difference in the cross section increases very quickly when the perturbation is applied and then decays to nearly 0 in very short time. It means that the temperature in the cross section reach equilibrium very quickly. Due to the fast quench propagation velocity, the temperature difference between cross section #1 and cross section #3 in the longitudinal direction starts to decay at 0.25 s. The temperature difference between the cross section #2 and cross section #3 appears at 0.15 s, which means that the longitudinal quench propagation velocity is about 10.75 m/s. In the Fig. 4, the T50K indicates the time when the temperature of the magnet reaches 50 K and the Tthr indicates the time when the terminal voltage of the magnet reaches quench voltage threshold. We can see from Fig. 7 that the T50K – Tthr is strongly dependent on the operating current. The T50K – Tthr is less than 300 ms when the operating current is greater than 900 A and the voltage threshold is greater than 0.5 V. However, the total time (tdelay + tv) for the quench detection and quench protection action is 305 ms. So, for safe operation, the operating current of the 90-degree dipole magnet should be less than 900 A, which is 45% of the critical current. Due to the existence of the delay time for the action of quench protection system, the T50K – Tthr is much larger than Tthr and the impact of the quench voltage threshold on the quench protection system is weakened. In comprehensive consideration of the sensitivity of quench detection, the quench voltage threshold is set to be 0.4 V.
3.1. Analysis of quench protection As to the quench protection, the quench voltage threshold (Vthr) is a key parameter and needs to be confirmed by the user. The quench detection time (td) depends on the sensitivity and thresholds of quench detection system. The validation time (tv) is typically defined by the hardware. Typically, for LTS (Low Temperature SC) magnets (td + tv) is 7–15 ms. So, we take 5 ms for tv in our calculation. When the quench voltage exceeds Vthr for the given tv, the SC coil is considered to be quenched. When the quench is validated, there is a time delay (tdelay) between the validation of quench and the cutting off of the current supply. The delay is included for the physical opening of the circuit breaker and avoiding the voltage spikes, which is assumed to be 300 ms in the computations. So, as to the quench protection system, when the coil terminal voltage exceeds the quench voltage threshold, it takes tv + tdelay for the current supply to be cut off. With different operating currents, the ramp rate of the coil terminal voltage and temperature is different. The given Vthr needs to be able to meet different operating conditions. Different Vthr of the quench protection will result in different maximum temperature in the coil. According to Iwasa [18], the quench protection should be able to limit the stresses and strains in the coils by limiting the maximum temperature within the coils to be under 200 K (considered safe). Because the SC dipole introduced in this paper is used on the gantry, the safe operation is in the dominated position. So, the temperature limit for cutting off the current supply is set to be 50 K from the engineering point of view. The coil terminal voltage and temperature evolution are analyzed under different operating currents. The thermal conductivity of insulation (kins) is 0.05 Wm−1 K−1 in this case. The quench of coil #1 is triggered with minimum quench energy and there is no perturbation in coil #2. The duration of the perturbation is 0.1 s and the perturbation length is 0.1 m in the central position of the coil. The evolution of current in copper, normal zone length, temperature and terminal voltage is shown in Fig. 4. We can see that the current in the perturbation position shares to the copper region immediately. The normal zone propagates very quickly and the whole superconducting coil turns to normal state at about 0.23 s. The temperature difference in the transverse direction and longitudinal direction is shown in Fig. 6. The transverse temperature
3.2. Interplay analysis For better analyzing the interplay between the quench protection system and the quench characteristics, the stability analysis of coil #1 is conducted in detail. The quench is triggered with the 110% of the minimum quench energy (MQE) in the coil #1. The quench voltage threshold is set to be 0.4 V and the tdelay + tv is set to be 0.305 s. The operating current is 900 A. When the terminal voltage exceeds the
Fig. 4. The evolution of temperature, terminal voltage, Cu current and normal zone length during quench triggered by minimum quench energy, Iop = 600 A. 3
Physica C: Superconductivity and its applications 566 (2019) 1353523
M. Li, et al.
Fig. 5. The schematic view of the temperature difference calculation.
quench voltage threshold, the current supply is cut off after tdelay + tv. The energy stored in the coil is dissipated in the dump resistor. The analysis is based on two kinds of quench protection connections. Case #1 is shown in Fig. 2. Case #2 is similar to the first one and the difference is that the dump resistor is connected with a switch. In the simulation, the dump resistance value is set to be 0.1 Ω, 0.3 Ω, 0.5 Ω in case#1. In the case#2, the dump resistance value is the piecewise function of time and changes from infinity to 0.1 Ω (0.3 Ω, 0.5 Ω) when the quench protection is triggered. The dump resistance value is set to be infinity to indicate that the dump resistor is connected with a switch and the switch is open. When the resistance value changes to 0.1 Ω (0.3 Ω, 0.5 Ω) in case#2, it means that the switch connecting the dump resistor is closed. The terminal voltages of two coils are shown in Fig. 8. We can see that in the case #1, the voltage evolution is dependent on the resistance of the dump resistor. With higher resistance, the terminal voltage is increasing more quickly. Due to the connection of the dump resistor, the current starts to share to the dump resistor when the normal zone appears in the coil, which is shown in Fig. 9. Due to the variation of the
Fig. 6. The maximum temperature difference in the transverse and longitudinal direction.
Fig. 8. The terminal voltage of two coils (*−1 means the quench protection system without the switch in the connection of dump resistor and *−2 means the quench protection with the switch in the connection of dump resistor).
Fig. 7. The T50K – Tthr under different operating conditions. 4
Physica C: Superconductivity and its applications 566 (2019) 1353523
M. Li, et al.
Fig. 9. The current flows to the dump resistor with different resistances and evolution of the normal zone length in coil #1 (*−1 means the quench protection system without the switch in the connection of dump resistor and *−2 means the quench protection with the switch in the connection of dump resistor).
Fig. 11. The temperature of the hot spot (*−1 means the quench protection system without the switch in the connection of dump resistor and *−2 means the quench protection with the switch in the connection of dump resistor).
the superconducting operation. Combining with the evolution of terminal voltage, the 0.3 Ω dump resistor is applicable for the quench protection system. Comparing these two kinds of connections of the dump resistors, we can see that the advantage of case #1 is that it only needs to operate one switch for quench protection. The advantage of case #2 is that the voltage climbing is quick and the quench protection system can have a faster response. However, the existence of the delay time for the physical opening of the switch makes the advantage of case#2 negligible and simultaneous action of two switches reduces the safety factor. So, the case #1 has more advantages in practice.
current flowing through the coil, the induced positive voltage appears in the coil, which is shown in Fig. 10(b). The voltage in RQ1 is negative (shown in Fig. 10(a)) and therefore, the terminal voltage of case#1 is smaller than that of case #2. In the case #2, because the dump resistor is disconnected with the circuit, the current flowing through the coil keeps constant and the terminal voltage is independent on the resistance value before the current supply is cut off. After the current supply is cut off, the electric circuits in two cases are the same and the voltage evolution is nearly the same. The currents start to share to the dump resistor. We can see that when the operating current is 900 A and dump resistance is 0.5 Ω, the maximum coil terminal voltage is about 450 V after the current supply is cut off. In the preliminary test of the superconducting coil, the coil withstand voltage is 500 V. In order to have a safety factor of 1.5, the maximum allowable terminal voltage is set to be 330 V. Therefore, the dump resistor is chosen to be 0.3 Ω and the maximum terminal voltage is 260 V, which is shown in Fig. 8. Fig. 11 shows the temperature evolution at the hot spot. We can see that after the current supply is cut off, the temperatures keep increasing to different levels. When the resistance of the dump resistor is 0.1 Ω, the temperature has risen to nearly 100 K. When the resistance is 0.3 Ω, the maximum temperature is stable at about 80 K, which is allowable for
4. Conclusion This paper demonstrates a method used for interplay analysis between quench protection and coil quench characteristics. Via including the quench protection electric circuit in the simulation, the method can present a comprehensive explanation of impact of the quench voltage threshold and dump resistor on the stability. By setting the temperature limit (50 K) for the quench protection action, the key parameters of the quench protection system are calculated and confirmed systematically. The results show that with a given quench protection action time
Fig. 10. The voltage profile in RQ1 (a) and coil #1 (b). (*−1 means the quench protection system without the switch in the connection of dump resistor and *−2 means the quench protection with the switch in the connection of dump resistor). 5
Physica C: Superconductivity and its applications 566 (2019) 1353523
M. Li, et al.
(tdelay + tv) and temperature limit for quench protection action, the maximum allowable operating current and appropriate dump resistor value are both specific values. The safe operation is very important for the SC magnets. Therefore, the quench protection is such a key issue for the design and optimization of SC magnets. This paper gives a feasible way for comprehensive analysis of the relationship between quench protection and coil quench characteristics.
T. Magn. 30 (4) (1994) 1742–1745 https://doi.org/10.1109/20.305593. [4] A. Dudarev, C. Lesmond, D.E. Baynham, Quench propagation and protection analysis of the ATLAS Toroids, IEEE Trans. Appl. Supercond. 10 (2000) 365–368 https://doi.org/10.1109/77.828249. [5] E. Ravaioli, B. Auchmann, V.I. Datskov, Advanced quench protection for the Nb3Sn quadrupoles for the high luminosity LHC, IEEE Trans. Appl. Supercond. 26 (3) (2016) 4002006https://doi.org/10.1109/tasc.2016.2524464. [6] T. Salmi, A. Stenvall, M. Prioli, Quench protection analysis integrated in the design of dipoles for the Future Circular Collider, Phys. Rev. Accel. Beams. 20 (3) (2017) 032401https://doi.org/10.1103/physrevaccelbeams.20.032401. [7] I.R. Dixon, A.V. Gavrilin, J.R. Miller, Analysis of the quench protection system of a series connected hybrid magnet, IEEE Trans. Appl. Supercond. 17 (2) (2007) 2446–2449 https://doi.org/10.1109/tasc.2007.899132. [8] S.I. Bermudez, B. Auchmann, H. Bajas, et al., Quench protection studies of the 11-T Nb 3 Sn dipole for the LHC upgrade, IEEE Transactions on Applied Superconductivity 26 (4) (2016) 1–5. [9] M. Bagnasco, D. Bessette, L. Bottura, Progress in the integrated simulation of thermal-hydraulic operation of the ITER magnet system, IEEE Trans. Appl. Supercond. 20 (3) (2010) 411–414 https://doi.org/10.1109/tasc.2010.2043836. [10] M. Li, J.X. Zheng, Y.T. Song, et al., Beam optics and isocenter property of SC200 proton therapy gantry, Nucl. Sci. Tech. 29 (8) (2018) 112 https://doi.org/10.1007/ s41365-018-0446-5. [11] P.A. Farling, P.A. Flynn, G. Darwent, Safety in magnetic resonance units: an update, Anaesthesia 65 (7) (2010) 766 https://doi.org/10.1111/j.1365-2044.2010. 06377.x. [12] L. Bottura, A practical fit for the critical surface of NbTi, IEEE Trans. Appl. Supercond. 10 (1) (2000) 1054–1057 https://doi.org/10.1109/77.828413. [13] L. Bottura, C. Rosso, M. Breschi, A general model for thermal, hydraulic, and electric analysis of superconducting cables, Cryog. 40 (8–10) (2000) 617–626 https://doi.org/10.1016/s0011-2275(01)00019-4. [14] POWER, Electric network simulation of magnetic systems ver. 2.1, August 2009. [15] SuperMagnet, User's Guide, CryoSoft, 2007 Ver. 1.0. [16] R. Kang, J. Zheng, Y. Song, Stability study of Bi-2212 conductor based on perturbation spectrum for hybridsuperconducting magnet, Int. J. Energ. Res. 41 (9) (2017) 1277–1286 https://doi.org/10.1002/er.3710. [17] A. Anghel, QUELL experiment: analysis and interpretation of the quench propagation results, Cryog. 38 (5) (1998) 459–466 https://doi.org/10.1016/s00112275(98)00016-2. [18] Y. Iwasa, Case Studies in Superconducting Magnets: Design and Operational Issues, Springer Science & Business Media, 2009, https://doi.org/10.1063/1.2808214.
Acknowledgement This work was supported by the National Key Research and Development Program of China (2017YFE0123400, 2017YFE0300503), The China National Science Fund for Distinguished Young Scholars (51525703), Youth Innovation Promotion Association of CAS (2015266), Young Elite Scientists Sponsorship Program by CAST (2017QNRC001) and the China National Natural Science Foundation of China (51507173). Supplementary materials Supplementary material associated with this article can be found, in the online version, at doi:10.1016/j.physc.2019.1353523. References [1] A. Gerbershagen, C. Calzolaio, D. Meer, S. Sanfilippo, M. Schippers, The advantages and challenges of superconducting magnets in particle therapy, Supercond. Sci. Tech. 29 (8) (2016), https://doi.org/10.1088/0953-2048/29/8/083001. [2] Y. Iwata, T. Furukawa, Y. Hara, Superconducting gantry and other developments at HIMAC, Proceedings of PAC, Pasadena, CA USA, 2013. [3] L. Coull, D. Hagedorn, V. Remondino, LHC magnet quench protection system, IEEE
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Contents lists available at ScienceDirect
Physica C: Superconductivity and its applications journal homepage: www.elsevier.com/locate/physc
A method for interplay analysis between quench protection and quench characteristics of close-wound superconducting magnet
T
Li Minga,b, Zheng Jinxinga, , Song Yuntaoa,b, Zeng Xianhua,b, Wang Minga,b ⁎
a b
Institute of Plasma Physics, Hefei Institutes of Physical Science, Chinese Academy of Sciences, Hefei, Anhui 230031, China University of Science and Technology of China, China
ARTICLE INFO
ABSTRACT
Index Terms: Interplay analysis Quench protection Quench characteristic
The quench protection of the close-wound superconducting magnet is a key factor during the design process, especially when used on the particle therapy gantry system. Therefore, the interplay between quench protection and coil quench needs to be considered from the earliest stage of the design. For this purpose, a method using Cryosoft code is presented in this paper. Based on the quench protection electric circuit, the current and voltage evolution of the quench protection circuit and the temperature and normal zone evolution of the superconducting coil all can be obtained with this method. By studying the allowable action time for the quench protection associated with the operating current, the quench voltage threshold and the resistance of the dump resistor are determined, which is 0.4 V and 0.3 Ω. The differences of the voltage evolutions obtained with different kinds of dump resistor connections are also studied. The results show that it is better to have the dump resistor directly connected to the coil than with a switch. The advantage of this method is its integration and comprehensiveness and can be used in the design procedure of different kinds of magnets.
1. Introduction The utilization of a close-wound superconducting (SC) magnet on the proton therapy gantry system can significantly reduce the weight of the gantry and cut the costs [1]. The first SC gantry is finished by the National Institute of Radiological Science (NIRS) in Chiba, Japan. It is designed for carbon ion therapy [2]. The SC coil of the dipole magnet developed by NIRS is wound on the surface of the cylindrical mandrel with a certain angle of inclination. It adopts the conduction cooling method and its operation needs to be very careful because of the small temperature margin. As to the design process of the SC dipole magnet, the quench protection system is the key issue. It needs to consider the energy dissipation and its impact on the quench propagation. Most of the quench protection design only focus on the energy dissipation [3–5] and determine the key parameters according to the experimental data. Salmi et al. has accounted for the quench protection system in the process of developing dipole magnet [6]. They describe the usage of the quench protection in the magnet design. Dixon et al. describes the impact of the quench voltage threshold on the quench propagation [7]. However, the other parameters of the quench protection system have not been analyzed in detail. Bermudez gives detailed introduction on the quench protection of the dipole magnet for the LHC upgrade [8]. ⁎
For better knowing the quench protection system and considering the interplay between the quench protection and coil quench, we need a comprehensive analysis of the quench protection system. This paper introduces an analysis method [9], which can analyze the interplay between quench protection system and the stability characteristics. The method performs quench propagation analysis while considering the quench protection electric circuit. 2. Simulation model description 2.1. The close-wound SC magnet The 90-degree dipole magnet with saddle-shaped superconducting coil, which is shown in Fig. 1, is aiming for the upgrading of the SC200 proton therapy gantry system [10]. The radius of the magnet centerline is 1.1 m and the target maximum magnetic field in the bore region is 2 T. The SC coil is designed to be saddle-shaped in order to avoid reversing field at both ends, which makes the coil winding very difficult. The coil is hand-wound using a specially-made mold. The NbTi conductor with rectangular cross-section is selected for easier compression during the winding process. The stronger fields of the gantry magnets located near the patient also lead to more extended and stronger stray fields. In general, the magnetic field should not exceed 0.5 mT at the
Corresponding author. E-mail address: [email protected] (J. Zheng).
https://doi.org/10.1016/j.physc.2019.1353523 Received 12 March 2019; Received in revised form 18 August 2019; Accepted 31 August 2019 Available online 06 September 2019 0921-4534/ © 2019 Elsevier B.V. All rights reserved.
Physica C: Superconductivity and its applications 566 (2019) 1353523
M. Li, et al.
Fig. 1. The 90-degree superconducting magnet with saddle-shaped coil. Table 1 The specifications of the NbTi conductor and the coils.
Conductor parameters
Coil parameters
Parameter
Unit
Value
Conductor type Bare nominal dimension Insulated nominal dimension Superconductor cross section Copper cross section Copper residual resistivity ratio Critical current @ 3 T, 4.2 K Number of layers Number of turns in each layer Inductance of single coil Mutual inductance of the two coils
– mm mm mm2 mm2 – A – – H H
WIC NbTi 2.286 × 1.524 2.553 × 1.765 0.401 3.083 200 1977 12 10 0.128 0.05
Fig. 3. Schematic representation of the electrical network used for the simulation.
an optical isolation circuit and then sent to the quench trigger circuit. For safe operation, the dump resistor is always connected in the quench protection circuit. Under normal operation, the resistance of the dump resistor is always greater than the superconducting coil and the switch S1 keeps closed. When the quench voltage exceeds the quench voltage threshold, the energy of the two coils can be dissipated with the dump resistor as soon as possible and the current supply will be cut off. 2.3. Simulation model
patient position [11]. Two warm iron yokes are used to generate the desired magnetic field with acceptable field uniformity and shield the stray fields around the magnet. The critical current density is parameterized with the equation proposed in [12] and the fitting parameters are also listed in Table. 1. When the operating current is 800 A/ turn, the maximum magnetic field density within the conductor is about 3 T and the maximum magnetic field in the bore region is 2.4 T. The GM Cryocoolers can only be installed at both ends of all the coils. The total heat leakage of the all coils and coil supports is about 3 W. The practical heat leakage may be greater. The practical cooling capacity of the four GM cryocoolers is only 4.8 W (rated power is 6 W @ 4.2 K). Due to the restriction of the conduction cooling system, the heat cannot dissipate immediately. Therefore, the operating environment is simplified to an adiabatic environment.
For realizing the integrated analysis of the quench protection, an integrated simulation model is established. The model is based on the quench protection circuit, which is shown in Fig. 3. We can see that RQ1 and RQ2 indicate the normal zone resistance of coil #1 and coil #2 separately. RD is the dump resistor and the resistance value is Rdump. The whole model is established with THEA code [13] and POWER code [14]. The THEA code is used for thermal analysis and the POWER is used for the electrical circuit calculation. The total cable current used for simulation by THEA can be obtained by a simulation of an electric network with POWER. The normal zone resistance (RQ1 and RQ2) used for the electric circuit calculation is obtained from THEA code, similarly, the operating current used in THEA code is obtained from POWER code. The communication between THEA and POWER code is governed by SUPERMAGNET (Multitask Code Manager) [15]. The THEA code is usually used for the analysis of cable-in-conduit cable (CICC) [16,17]. In order to use THEA software for tightly wound magnets operated under adiabatic environment, the transverse heat conductions between turns and layers needed to be taken into consideration. The heat which is expressed with (1), in which the heat capacity of the insulation is omitted because it is very thin compared to the conductor.
2.2. Quench protection circuit A schematic of the passive quench protection circuit is shown in Fig. 2. For clarity, the signal processing circuit and the quench detection circuit is not shown. The two coils are connected in series and driven by a 1000A regulated DC power supply. The voltage signal is processed by
Pconductor = (k ins/ th ins) d (Tconductor
Tx )
(1)
Where, Tx indicates the temperature at position x. Tconductor indicates the temperature of the adjacent conductor. Pconductor is the turn to turn (layer to layer) heat conduction. kinsand thins is the thermal conductivity and thickness of the insulation separately. d is the nominal dimension of the NbTi conductor, which is shown in Table 1. The transverse heat conduction is defined in the user-routine (UserSHeating) [14] in the THEA code. For simulating practical quench protection process, the resistance value of the dump resistor (Rdump) is also defined in the user-routine (UserBranchResistance) [15].
Fig. 2. The schematic of the quench protection. 2
Physica C: Superconductivity and its applications 566 (2019) 1353523
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3. Results
difference is calculated with the temperature data of the point A1 (A2) and point B1 (B2). The longitudinal-inner temperature difference is calculated with the temperature data of point A1 (A2) and A3. The longitudinal-outer temperature difference is calculated with the temperature data of the point B1 (B2) and point B3. The definitions of the points are shown in Fig. 5. The cross section #1 is the position where the perturbation is applied. The cross section #2 is 1 m away from cross section #1. The cross section #3 is the farthest section from cross section #1. We can see that the temperature difference in the cross section increases very quickly when the perturbation is applied and then decays to nearly 0 in very short time. It means that the temperature in the cross section reach equilibrium very quickly. Due to the fast quench propagation velocity, the temperature difference between cross section #1 and cross section #3 in the longitudinal direction starts to decay at 0.25 s. The temperature difference between the cross section #2 and cross section #3 appears at 0.15 s, which means that the longitudinal quench propagation velocity is about 10.75 m/s. In the Fig. 4, the T50K indicates the time when the temperature of the magnet reaches 50 K and the Tthr indicates the time when the terminal voltage of the magnet reaches quench voltage threshold. We can see from Fig. 7 that the T50K – Tthr is strongly dependent on the operating current. The T50K – Tthr is less than 300 ms when the operating current is greater than 900 A and the voltage threshold is greater than 0.5 V. However, the total time (tdelay + tv) for the quench detection and quench protection action is 305 ms. So, for safe operation, the operating current of the 90-degree dipole magnet should be less than 900 A, which is 45% of the critical current. Due to the existence of the delay time for the action of quench protection system, the T50K – Tthr is much larger than Tthr and the impact of the quench voltage threshold on the quench protection system is weakened. In comprehensive consideration of the sensitivity of quench detection, the quench voltage threshold is set to be 0.4 V.
3.1. Analysis of quench protection As to the quench protection, the quench voltage threshold (Vthr) is a key parameter and needs to be confirmed by the user. The quench detection time (td) depends on the sensitivity and thresholds of quench detection system. The validation time (tv) is typically defined by the hardware. Typically, for LTS (Low Temperature SC) magnets (td + tv) is 7–15 ms. So, we take 5 ms for tv in our calculation. When the quench voltage exceeds Vthr for the given tv, the SC coil is considered to be quenched. When the quench is validated, there is a time delay (tdelay) between the validation of quench and the cutting off of the current supply. The delay is included for the physical opening of the circuit breaker and avoiding the voltage spikes, which is assumed to be 300 ms in the computations. So, as to the quench protection system, when the coil terminal voltage exceeds the quench voltage threshold, it takes tv + tdelay for the current supply to be cut off. With different operating currents, the ramp rate of the coil terminal voltage and temperature is different. The given Vthr needs to be able to meet different operating conditions. Different Vthr of the quench protection will result in different maximum temperature in the coil. According to Iwasa [18], the quench protection should be able to limit the stresses and strains in the coils by limiting the maximum temperature within the coils to be under 200 K (considered safe). Because the SC dipole introduced in this paper is used on the gantry, the safe operation is in the dominated position. So, the temperature limit for cutting off the current supply is set to be 50 K from the engineering point of view. The coil terminal voltage and temperature evolution are analyzed under different operating currents. The thermal conductivity of insulation (kins) is 0.05 Wm−1 K−1 in this case. The quench of coil #1 is triggered with minimum quench energy and there is no perturbation in coil #2. The duration of the perturbation is 0.1 s and the perturbation length is 0.1 m in the central position of the coil. The evolution of current in copper, normal zone length, temperature and terminal voltage is shown in Fig. 4. We can see that the current in the perturbation position shares to the copper region immediately. The normal zone propagates very quickly and the whole superconducting coil turns to normal state at about 0.23 s. The temperature difference in the transverse direction and longitudinal direction is shown in Fig. 6. The transverse temperature
3.2. Interplay analysis For better analyzing the interplay between the quench protection system and the quench characteristics, the stability analysis of coil #1 is conducted in detail. The quench is triggered with the 110% of the minimum quench energy (MQE) in the coil #1. The quench voltage threshold is set to be 0.4 V and the tdelay + tv is set to be 0.305 s. The operating current is 900 A. When the terminal voltage exceeds the
Fig. 4. The evolution of temperature, terminal voltage, Cu current and normal zone length during quench triggered by minimum quench energy, Iop = 600 A. 3
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Fig. 5. The schematic view of the temperature difference calculation.
quench voltage threshold, the current supply is cut off after tdelay + tv. The energy stored in the coil is dissipated in the dump resistor. The analysis is based on two kinds of quench protection connections. Case #1 is shown in Fig. 2. Case #2 is similar to the first one and the difference is that the dump resistor is connected with a switch. In the simulation, the dump resistance value is set to be 0.1 Ω, 0.3 Ω, 0.5 Ω in case#1. In the case#2, the dump resistance value is the piecewise function of time and changes from infinity to 0.1 Ω (0.3 Ω, 0.5 Ω) when the quench protection is triggered. The dump resistance value is set to be infinity to indicate that the dump resistor is connected with a switch and the switch is open. When the resistance value changes to 0.1 Ω (0.3 Ω, 0.5 Ω) in case#2, it means that the switch connecting the dump resistor is closed. The terminal voltages of two coils are shown in Fig. 8. We can see that in the case #1, the voltage evolution is dependent on the resistance of the dump resistor. With higher resistance, the terminal voltage is increasing more quickly. Due to the connection of the dump resistor, the current starts to share to the dump resistor when the normal zone appears in the coil, which is shown in Fig. 9. Due to the variation of the
Fig. 6. The maximum temperature difference in the transverse and longitudinal direction.
Fig. 8. The terminal voltage of two coils (*−1 means the quench protection system without the switch in the connection of dump resistor and *−2 means the quench protection with the switch in the connection of dump resistor).
Fig. 7. The T50K – Tthr under different operating conditions. 4
Physica C: Superconductivity and its applications 566 (2019) 1353523
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Fig. 9. The current flows to the dump resistor with different resistances and evolution of the normal zone length in coil #1 (*−1 means the quench protection system without the switch in the connection of dump resistor and *−2 means the quench protection with the switch in the connection of dump resistor).
Fig. 11. The temperature of the hot spot (*−1 means the quench protection system without the switch in the connection of dump resistor and *−2 means the quench protection with the switch in the connection of dump resistor).
the superconducting operation. Combining with the evolution of terminal voltage, the 0.3 Ω dump resistor is applicable for the quench protection system. Comparing these two kinds of connections of the dump resistors, we can see that the advantage of case #1 is that it only needs to operate one switch for quench protection. The advantage of case #2 is that the voltage climbing is quick and the quench protection system can have a faster response. However, the existence of the delay time for the physical opening of the switch makes the advantage of case#2 negligible and simultaneous action of two switches reduces the safety factor. So, the case #1 has more advantages in practice.
current flowing through the coil, the induced positive voltage appears in the coil, which is shown in Fig. 10(b). The voltage in RQ1 is negative (shown in Fig. 10(a)) and therefore, the terminal voltage of case#1 is smaller than that of case #2. In the case #2, because the dump resistor is disconnected with the circuit, the current flowing through the coil keeps constant and the terminal voltage is independent on the resistance value before the current supply is cut off. After the current supply is cut off, the electric circuits in two cases are the same and the voltage evolution is nearly the same. The currents start to share to the dump resistor. We can see that when the operating current is 900 A and dump resistance is 0.5 Ω, the maximum coil terminal voltage is about 450 V after the current supply is cut off. In the preliminary test of the superconducting coil, the coil withstand voltage is 500 V. In order to have a safety factor of 1.5, the maximum allowable terminal voltage is set to be 330 V. Therefore, the dump resistor is chosen to be 0.3 Ω and the maximum terminal voltage is 260 V, which is shown in Fig. 8. Fig. 11 shows the temperature evolution at the hot spot. We can see that after the current supply is cut off, the temperatures keep increasing to different levels. When the resistance of the dump resistor is 0.1 Ω, the temperature has risen to nearly 100 K. When the resistance is 0.3 Ω, the maximum temperature is stable at about 80 K, which is allowable for
4. Conclusion This paper demonstrates a method used for interplay analysis between quench protection and coil quench characteristics. Via including the quench protection electric circuit in the simulation, the method can present a comprehensive explanation of impact of the quench voltage threshold and dump resistor on the stability. By setting the temperature limit (50 K) for the quench protection action, the key parameters of the quench protection system are calculated and confirmed systematically. The results show that with a given quench protection action time
Fig. 10. The voltage profile in RQ1 (a) and coil #1 (b). (*−1 means the quench protection system without the switch in the connection of dump resistor and *−2 means the quench protection with the switch in the connection of dump resistor). 5
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(tdelay + tv) and temperature limit for quench protection action, the maximum allowable operating current and appropriate dump resistor value are both specific values. The safe operation is very important for the SC magnets. Therefore, the quench protection is such a key issue for the design and optimization of SC magnets. This paper gives a feasible way for comprehensive analysis of the relationship between quench protection and coil quench characteristics.
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Acknowledgement This work was supported by the National Key Research and Development Program of China (2017YFE0123400, 2017YFE0300503), The China National Science Fund for Distinguished Young Scholars (51525703), Youth Innovation Promotion Association of CAS (2015266), Young Elite Scientists Sponsorship Program by CAST (2017QNRC001) and the China National Natural Science Foundation of China (51507173). Supplementary materials Supplementary material associated with this article can be found, in the online version, at doi:10.1016/j.physc.2019.1353523. References [1] A. Gerbershagen, C. Calzolaio, D. Meer, S. Sanfilippo, M. Schippers, The advantages and challenges of superconducting magnets in particle therapy, Supercond. Sci. Tech. 29 (8) (2016), https://doi.org/10.1088/0953-2048/29/8/083001. [2] Y. Iwata, T. Furukawa, Y. Hara, Superconducting gantry and other developments at HIMAC, Proceedings of PAC, Pasadena, CA USA, 2013. [3] L. Coull, D. Hagedorn, V. Remondino, LHC magnet quench protection system, IEEE
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