JP2017033976A - Superconducting magnet device - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a superconducting magnet device comprising a quenching protection circuit capable of quickly discharging an energy stored in a superconducting coil without generating a voltage larger than a withstanding voltage of the superconducting coil.SOLUTION: A superconducting magnet device 100 comprises: a superconducting coil 10; and a quenching protection circuit 120 connected in parallel to the superconducting coil 10. The quenching protection circuit 120 includes: a diode D1; a resistor RP connected in series to the diode D1; and a capacitor C1 further connected in series to the series circuit including the diode D1 and the resistor RP.SELECTED DRAWING: Figure 1

Description

  The present invention relates to a superconducting magnet device, and more particularly to a superconducting magnet device including a quench protection circuit for a superconducting coil.

  When the superconducting coil is quenched, it is necessary to cut off the power source current as soon as possible and to release the energy stored in the superconducting coil. For this reason, the superconducting magnet device is provided with a quench protection circuit connected in parallel to the superconducting coil (see, for example, Non-Patent Document 1).

  In the said nonpatent literature 1, the quench protection circuit is comprised from the diode connected in antiparallel with the superconducting coil, and the protection resistance connected in series with the diode. When the superconducting coil is quenched, when the power supply current is cut off, the energy stored in the superconducting coil is released by the current flowing through the closed circuit formed by the superconducting coil, the protective resistor, and the diode.

Yukikazu Iwasa, "Case Studies in Superconducting Magnets Design and Operational Issues Second Edition", Springer

  According to the quench protection circuit described in Non-Patent Document 1, the current flowing through the closed circuit formed by the superconducting coil, the diode, and the protection resistor is in accordance with a time constant determined by the inductance of the superconducting coil and the resistance value of the protection resistor. Attenuates.

  At this time, an induced electromotive voltage due to self-induction is generated in the superconducting coil with the temporal change of the current flowing in the closed circuit. The magnitude of the induced electromotive voltage is equal to a value obtained by integrating the inductance of the superconducting coil and the temporal change in current. Therefore, if the current flowing through the closed circuit is to be attenuated quickly, the temporal change of the current increases, and the induced electromotive voltage generated in the superconducting coil also increases. As a result, in a superconducting magnet device using a superconducting coil having a high inductance, an induced electromotive voltage exceeding the withstand voltage of the superconducting coil may be generated, thereby possibly damaging the superconducting coil.

  The present invention has been made in order to solve the above-described problems, and the object of the present invention is to quickly store the energy stored in the superconducting coil without generating a voltage exceeding the withstand voltage of the superconducting coil. To provide a superconducting magnet device with a quench protection circuit that can be released.

  A superconducting magnet device according to an aspect of the present invention includes a superconducting coil and a quench protection circuit connected in parallel to the superconducting coil. The quench protection circuit includes a diode, a resistor connected in series with the diode, a series circuit including the diode and the resistor, and a capacitor connected in series.

  According to the above, it is possible to provide a superconducting magnet device including a quench protection circuit capable of quickly releasing energy stored in the superconducting coil without generating a voltage exceeding the withstand voltage of the superconducting coil. .

It is a schematic block diagram of the superconducting magnet apparatus which concerns on embodiment. It is a block diagram of the quench protection circuit which concerns on an Example. It is a block diagram of the quench protection circuit which concerns on a comparative example. It is a figure which shows the simulation result about the change of the electric current which flows into a superconducting coil. It is a figure explaining the relationship between the capacity | capacitance of a capacitor | condenser and the decay time constant of the electric current which flows through a superconducting coil. It is a figure explaining the relationship between the capacity | capacitance of a capacitor | condenser and the generated voltage of a superconducting coil. It is a figure explaining normalization of the relation between the capacity of a capacitor and the generated voltage of a superconducting coil. It is a figure which shows the relationship between the maximum generated voltage and inductance of a superconducting coil. It is a figure which shows the result of having verified the consistency of the generalized maximum generated voltage and the relationship between the capacity | capacitance of the capacitor | condenser shown in FIG. 6, and the maximum generated voltage. It is a flowchart explaining the design procedure of the quench protection circuit which concerns on embodiment.

[Description of Embodiment of the Present Invention]
First, embodiments of the present invention will be listed and described.

  (1) A superconducting magnet device (see FIG. 1) according to an aspect of the present invention includes a superconducting coil 10 and a quench protection circuit 120 connected in parallel to the superconducting coil 10. The quench protection circuit 120 includes a diode D1, a resistor (protection resistor) RP connected in series with the diode D1, and a capacitor C1 connected in series to a series circuit including the diode D1 and the resistor RP.

  In this way, when power supply to the superconducting coil 10 is interrupted by detecting a quench, a current flows through a closed circuit composed of the superconducting coil 10, the capacitor C1, the resistor RP, and the diode D1, and thus the superconducting coil 10 is detected. The energy stored in is released. In the closed circuit composed of the superconducting coil 10, the capacitor C1, the resistor RP, and the diode D1, an LCR series resonance circuit is formed. Therefore, the voltage exceeding the withstand voltage of the superconducting coil 10 is adjusted by adjusting the capacitance of the capacitor C1. The energy stored in the superconducting coil 10 can be quickly released without generating.

  (2) Preferably, in the superconducting magnet device 100 according to (1) above, in the closed circuit formed by the superconducting coil 10, the diode D1, the resistor RP and the capacitor C1, the maximum voltage generated in the superconducting coil 10 by self-induction is: It is represented by the following formula (1).

V = 1.005 * Io * C- ^0.498 * L ^0.510 ... (1)
(In the formula (1), V represents the maximum voltage, Io represents the current flowing through the superconducting coil 10 in a normal state where no quench has occurred, L represents the inductance of the superconducting coil 10, and C represents the capacitance of the capacitor C1. Represents.)
In this way, the maximum voltage generated in the superconducting coil 10 by self-induction can be generalized as a function of the inductance L of the superconducting coil 10, the capacitance C of the capacitor C1, and the energizing current Io. Thereby, it is possible to easily set the capacitance C of the capacitor C1 suitable for quickly attenuating the current flowing through the closed circuit without generating a voltage exceeding the withstand voltage of the superconducting coil 10. However, the maximum voltage is not limited to the value represented by the above formula (1), and has a slight variation depending on the characteristics of the diode D1.

  (3) Preferably, in the superconducting magnet device 100 according to the above (2), the capacitance C of the capacitor C1 satisfies the condition that the maximum voltage V is equal to or lower than the withstand voltage of the superconducting coil 10.

  In this way, the energy stored in the superconducting coil 10 can be quickly released without generating a voltage exceeding the withstand voltage of the superconducting coil 10.

[Details of the embodiment of the present invention]
Hereinafter, embodiments of the present invention will be described with reference to the drawings. In the following drawings, the same or corresponding parts are denoted by the same reference numerals, and description thereof will not be repeated.

[Configuration of superconducting magnet device]
FIG. 1 is a schematic configuration diagram of a superconducting magnet apparatus according to an embodiment.

  Referring to FIG. 1, superconducting magnet device 100 includes superconducting coil 10, excitation power supply 20, circuit breaker 30, quench detection circuit 110, and quench protection circuit 120.

  Superconducting coil 10 is formed by winding a superconducting wire. For example, the superconducting wire is an oxide superconducting wire having a strip shape. The oxide superconducting wire has a Bi-based superconductor extending in the extending direction, and a sheath covering the superconductor. The sheath is made of, for example, silver or a silver alloy.

  Superconducting coil 10 is cooled by a cooling device (not shown). The cooling device has a cooling head thermally connected to the superconducting coil 10, and causes the cooling head to generate a cryogenic temperature below the critical temperature of the superconductor constituting the superconducting coil 10. Thereby, the superconducting coil 10 is cooled to a cryogenic temperature. In addition, it is good also as a structure which immerses the superconducting coil 10 in refrigerant | coolants, such as liquid helium or liquid nitrogen accommodated in the heat insulation container, without using a cooling device.

  The excitation power supply 20 supplies a current to the superconducting coil 10. When the superconducting coil 10 is not quenched, the current flows through the superconducting coil 10 and no current flows through the quench protection circuit 120.

  The circuit breaker 30 is connected between the excitation power supply 20 and the superconducting coil 10. The circuit breaker 30 is driven from a conduction (on) state to a non-conduction (off) state in response to an abnormal signal given from the control unit 114 of the quench detection circuit 110. Thereby, the electric power feeding to the superconducting coil 10 is interrupted.

  The quench detection circuit 110 detects the quench of the superconducting coil 10. The quench detection circuit 110 employs a voltage detection method, which is the most basic method of quench detection. The quench detection circuit 110 includes a method using acoustic emission detection, an acoustic method using ultrasonic waves, an optical method using an optical fiber, a method for detecting an increase in refrigerant pressure, etc., instead of a detection method using voltage. A known quench detection method may be employed.

  The quench detection circuit 110 includes terminals MT, ETA, ETB, a voltage difference detection unit DU, a voltmeter 112, and a control unit 114. Terminal MT is connected to midpoint MP of superconducting coil 10. Terminals ETA and ETB are connected to both ends EPA and EPB of superconducting coil 10, respectively. Among the coil conductors of the superconducting coil 10, the middle point MP to the end point EPA is referred to as a section SGA, and the middle point MP to the end point EPB is referred to as a section SGB. The section SGB is symmetric with the section SGA with respect to the midpoint MP.

  The voltage difference detection unit DU includes a voltage applied to both ends EPA and MP of the section SGA (that is, a voltage between the terminals ETA and MT) and a voltage applied to both ends EPB and MP of the section SGB (that is, a voltage between the terminals ETB and MT). ) To detect these voltage differences.

  Specifically, voltage difference detection unit DU includes a variable resistor PM (also referred to as a potentiometer) having a movable terminal T1 and fixed terminals T2 and T3, and a voltmeter 112. Fixed terminals T2 and T3 are connected to terminals ETA and ETB, respectively. The voltmeter 112 is connected between the movable terminal T1 and the terminal MT. The resistance value between the terminals T1 and T3 and the resistance value between the terminals T2 and T3 change according to the position of the movable terminal T1.

  The variable resistor PM is replaced with a resistor RC connected between the movable terminal T1 and the fixed terminal T2 and a resistor RD connected between the movable terminal T1 and the fixed terminal T3 connected in series. Can do. As the position of the movable terminal T1 changes, one resistance value of the resistors RC and RD increases and the other resistance value decreases. More generally, it is sufficient that at least one resistance value of the resistors RC and RD is adjustable.

  The position of the movable terminal T1 is adjusted so that the voltage detected by the voltmeter 112 becomes zero at a normal time when no quench occurs. In this way, in any one of the sections SGA and SGB, when the superconducting wire transitions to the normal conduction state and quenching occurs, the voltmeter 112 detects a voltage exceeding the threshold value. In the following description, the voltage generated between the bridges (that is, the detected value of the voltmeter 112) is also referred to as “balance voltage Vb”.

  The control unit 114 determines that there is an abnormality when the detected voltage (balance voltage) Vb of the voltmeter 112 exceeds a threshold value, and outputs an abnormality signal to the circuit breaker 30. In response to the abnormal signal, the circuit breaker 30 is driven to a non-conduction (off) state, whereby the power supply from the excitation power supply 20 to the superconducting coil 10 is interrupted. After the power supply from the excitation power supply 20 is cut off, the quench protection circuit 120 quickly releases the energy stored in the superconducting coil 10. This avoids damage to the superconducting coil 10 due to quenching.

[Configuration of quench protection circuit]
The quench protection circuit 120 is connected in parallel to the superconducting coil 10. The quench protection circuit 120 includes a diode D1, a protection resistor RP, and a capacitor C1.

  The protective resistor RP is connected in series with the diode D1. Capacitor C1 is further connected in series to a series circuit including diode D1 and protective resistor RP. That is, the quench protection circuit 120 is configured by a series circuit including the diode D1, the protection resistor RP, and the capacitor C1.

  With this configuration, when quenching occurs in the superconducting coil 10, when the quench detection circuit 110 detects quenching and power supply from the excitation power supply 20 is cut off, the superconducting coil 10 and the capacitor A current flows through a closed circuit including C1, the protective resistor RP, and the diode D1. Thereby, the energy stored in the superconducting coil 10 is released.

  Here, an LCR series resonance circuit is formed in the closed circuit including the superconducting coil 10, the capacitor C1, the protective resistor RP, and the diode D1. Therefore, the current flowing through the closed circuit attenuates while vibrating. Specifically, in the LCR series resonance circuit, vibration is maintained by repeating the exchange of energy between the superconducting coil 10 and the capacitor C1, while the loss of energy occurs in the protective resistor RP. The amplitude decreases exponentially.

  How the oscillation amplitude of the current flowing through the closed circuit is attenuated depends on the frequency characteristics of the LCR series resonant circuit. From the viewpoint of quench protection of the superconducting coil 10, it is required that the current flowing through the closed circuit is quickly attenuated.

  On the other hand, as the current flowing through the closed circuit attenuates, an induced electromotive voltage is generated in the superconducting coil 10 due to self-induction. When the inductance of the superconducting coil 10 is L and the time change of the current I flowing through the closed circuit is dI / dt, the induced electromotive voltage generated in the superconducting coil 10 is expressed by L × dI / dt. Therefore, when the current decay becomes faster, dI / dt increases and the induced electromotive voltage increases. For this reason, in the superconducting coil 10 having high inductance, there is a possibility that an induced electromotive voltage exceeding the withstand voltage of the superconducting coil 10 may be generated due to faster current decay.

  As described above, in the quench protection circuit, there is a trade-off between increasing the decay rate of the current flowing through the closed circuit and reducing the voltage generated in the superconducting coil. In the quench protection circuit 120 shown in FIG. 1, the inventors have made a trade-off by examining the relationship between the capacitance of the capacitor C1, the attenuation characteristics of the current flowing through the closed circuit, and the induced electromotive voltage generated in the superconducting coil 10. It was found that improvement can be achieved.

  Hereinafter, a result of verifying that the tradeoff is improved by the quench protection circuit 120 according to the present embodiment will be described.

(Relationship between capacitor capacity and current attenuation characteristics)
First, in the quench protection circuit 120 according to the present embodiment, the relationship between the capacitance of the capacitor C1 and the attenuation characteristic of the current flowing through the superconducting coil 10 was verified by simulation. In the simulation, for each of the example shown in FIG. 2 and the comparative example shown in FIG. 3, the change in the current flowing through the superconducting coil 10 after the circuit breaker 30 was turned off was calculated.

  As shown in FIG. 2, in the quench protection circuit 120 according to the embodiment, the inductance L of the superconducting coil 10 is set to 100H (L = 100H), and the resistance value R of the protection resistance RP is set to 1Ω (R = 1Ω). For the capacitor C1, the capacitance C was changed between 0.1F, 1.0F, 10F, 100F, and 1000F. In addition, the energization current Io of the superconducting coil 10 in a normal state where no quench occurs is set to 200A (Io = 200A).

  On the other hand, as shown in FIG. 3, the quench protection circuit 130 according to the comparative example is configured by a series circuit of a diode D1 and a protection resistor RP. That is, the comparative example is different from the example in that a capacitor is not further connected in series to the series circuit of the diode D1 and the protective resistor RP. In the comparative example, the superconducting coil 10, the diode D1, and the protective resistor RP each have the same structure as that of the example. The energization current Io was set to 200 A as in the example.

  FIG. 4 shows the simulation results. The horizontal axis in FIG. 4 indicates time [s] that has elapsed since the circuit breaker 30 is turned off (time t = 0), and the vertical axis indicates the current [A] that flows through the superconducting coil 10.

  In FIG. 4, a waveform k1 indicates the current flowing through the superconducting coil 10 in the comparative example (FIG. 3). Waveforms k2 to k6 indicate currents flowing through the superconducting coil 10 in the embodiment (FIG. 2). Specifically, the waveform k2 is a current waveform when the capacitance C of the capacitor C1 is 0.1F, the waveform k3 is a current waveform when C = 1F, and the waveform k4 is a current waveform when C = 10F. The waveform k5 is a current waveform when C = 100F, and the waveform k6 is a current waveform when C = 1000F.

  As shown in FIG. 4, the current decay is faster in the example than in the comparative example not having the capacitor C1. However, when the capacitance C of the capacitor C1 is 1000F (waveform k6), the speed of current decay is similar to that of the comparative example, and as the capacitance C decreases in the order of 100F, 10F, 1F, and 0.1F. The difference from the comparative example is large. In addition, when the capacitance C = 1000F, 100F, 10F (waveforms k6, k5, k4), no oscillation amplitude of the current is observed, while when the capacitance C = 1F, 0.1F (waveforms k3, k2). Shows the oscillation amplitude of the current.

Since the closed circuit composed of the superconducting coil 10, the capacitor C1, the protective resistor RP, and the diode D1 is configured by an LCR series resonance circuit, the time when the circuit breaker 30 is turned off is set to t = 0, and the time t (t> 0) the terminal voltage _{V C} of the capacitor C1, the terminal voltage _{V L} of the superconducting coil 10, the voltage between the terminals of the protection resistor RP and _{V R,} the Kirchhoff's law, equation (1) is derived.

Since there are relationships of V _C = Q / C, V _R = RI, V _L = L × dI / dt, and I = dQ / dt, the second-order differential equation shown in Equation (2) is obtained.

Since t = 0, I = Io, and V _C = 0, assuming that I = Ioexp (−st), the solution of the above equation (2) is given by Q = −I / s. Thereby, Formula (3) is obtained from the above Formula (2).

  Further, the current I can be expressed as shown in the equation (4) by modifying the equation (3).

In the above formula (4), at 4L / C> ^{R 2,} the current I is oscillating with amplitude attenuated. In contrast, when the 4L / C ≦ R ^2, the current I is attenuated without vibration. The state of 4L / C> R ² is called vibration damping, the state of 4L / C = R ² is called critical damping, and the state of 4L / C <R ² is non-vibration damping (or overdamping). be called. When the inductance L of the superconducting coil 10 and the resistance value R of the protective resistance RP are respectively determined, the current I takes one of vibration damping, critical damping, and non-vibration damping depending on the capacitance C of the capacitor C1. .

  In FIG. 4, when the capacitance C = 10F (waveform k4), the current I is rectified by the diode D1, so that a current waveform without vibration is obtained. As a result, the current I reaches I = 0 the fastest when the capacitance C = 10F.

  As described above, in the quench protection circuit 120 according to the embodiment, the capacitor C1 is adjusted by adjusting the capacitance C of the capacitor C1 by further connecting the capacitor C1 in series to the series circuit of the diode D1 and the protection resistor RP. Compared with the comparative example which does not have, the electric current which flows into the superconducting coil 10 can be attenuate | damped more rapidly. In the following description, an attenuation time constant is used as an index representing the speed of attenuation of the current flowing through the superconducting coil 10. In this specification, the decay time constant means the time until the current amplitude decays to about 37%.

  FIG. 5 is a diagram for explaining the relationship between the capacitance of the capacitor C1 and the decay time constant of the current flowing through the superconducting coil 10. In FIG. The horizontal axis of FIG. 5 represents the capacitance C [F] of the capacitor C1, and the vertical axis represents the decay time constant [s] of the current flowing through the superconducting coil 10. The decay time constant was calculated from the change in the current flowing through the superconducting coil 10 after the time when the circuit breaker 30 was turned off, which was calculated for the embodiment shown in FIG. The resistance value R of the protective resistance RP of the superconducting coil 10 was set to 1Ω (R = 1Ω), and the inductance L of the superconducting coil 10 was changed between 1H, 10H, 100H, and 1000H.

  In FIG. 5, a waveform k7 shows a relationship when L = 1000H, a waveform k8 shows a relationship when L = 100H, a waveform k9 shows a relationship when L = 10H, and a waveform k10 shows that L = 1H. Show the relationship.

  As shown in FIG. 5, when the inductance L of the superconducting coil 10 and the resistance value R of the protective resistance RP are constant, the current decay time constant tends to increase as the capacitance C of the capacitor C1 decreases. For this reason, even when the inductance L of the superconducting coil 10 is as high as 1000H, it can be seen that the current decay time constant can be reduced by reducing the capacitance C of the capacitor C1.

(Relationship between capacitor capacity and superconducting coil voltage)
Next, the relationship between the capacitance of the capacitor C1 and the voltage generated in the superconducting coil 10 in the quench protection circuit 120 according to the present embodiment was verified by simulation. In the simulation, in the quench protection circuit 120 (FIG. 2) according to the embodiment, the superconducting coil 10 is switched to the superconducting coil 10 after the circuit breaker 30 is turned off for each of the inductances L = 1H, 10H, 100H, and 1000H of the superconducting coil 10. The change in flowing current was calculated. For the protective resistor RP, the resistance value R was changed between 0.1Ω, 1Ω, and 10Ω.

  FIG. 6 is a diagram for explaining the relationship between the capacitance of the capacitor C1 and the generated voltage of the superconducting coil 10. In FIG. The horizontal axis of FIG. 6 indicates the capacitance C [F] of the capacitor C1, and the vertical axis indicates the maximum absolute value of the voltage generated by the superconducting coil 10 (hereinafter also referred to as “maximum generated voltage [V]”).

  In FIG. 6, a waveform group k11 shows a relationship when L = 1000H, a waveform group k12 shows a relationship when L = 100H, a waveform group k13 shows a relationship when L = 10H, and a waveform group k14 The relationship when L = 1H is shown. In each waveform group, the solid line indicates the relationship when R = 10Ω, the dotted line indicates the relationship when R = 1Ω, and the broken line indicates the relationship when R = 0.1Ω.

  As shown in FIG. 6, when the inductance L of the superconducting coil 10 is constant, the maximum generated voltage of the superconducting coil 10 tends to increase as the capacitance C of the capacitor C1 decreases. In addition, when the capacitance C of the capacitor C1 is constant, the maximum generated voltage increases as the inductance L of the superconducting coil 10 increases.

  Here, when the relationship between the capacitance of the capacitor C1 and the decay time constant of the current (FIG. 5) and the relationship between the capacitance of the capacitor C1 and the maximum generated voltage of the superconducting coil 10 (FIG. 6) are compared, It can be seen that, when the inductance L is constant, as the capacitance C of the capacitor C1 is reduced, the current decay time constant is reduced while the maximum voltage generated in the superconducting coil 10 is increased. According to this, a voltage exceeding the withstand voltage is generated in the superconducting coil 10 by making the capacity of the capacitor C1 as small as possible within a range where the maximum generated voltage of the superconducting coil 10 does not exceed the withstand voltage of the superconducting coil 10. It is possible to quickly attenuate the current flowing through the superconducting coil 10 while suppressing the above.

[Generalization of maximum voltage of superconducting coil]
Referring to FIG. 6, the relationship between the capacitance of capacitor C1 and the maximum generated voltage of superconducting coil 10 is represented by a straight line on the log-log graph. The inclination of this straight line is constant regardless of the inductance L of the superconducting coil 10. Further, the maximum generated voltage in an arbitrary capacitance of the capacitor C1 is proportional to log ₁₀ L. According to this, it can be seen that the maximum generated voltage can be expressed as a function of the inductance L of the superconducting coil 10 and the capacitance C of the capacitor C1.

  Therefore, in the following, in the quench protection circuit 120, the relationship between the maximum generated voltage of the superconducting coil 10, the inductance L of the superconducting coil 10, and the capacitance C of the capacitor C1 is generalized.

  First, the relationship between the capacity of the capacitor C1 and the generated voltage of the superconducting coil 10 is normalized. FIG. 7 illustrates a normalized relationship when the inductance L = 1H of the superconducting coil 10.

  In normalization, an approximate curve was derived for the relationship shown in the waveform group k14 in FIG. In derivation, the inductance L of the superconducting coil 10 was set to 1H (L = 1H), and the initial value Io of the current flowing through the superconducting coil 10 was set to 200A (Io = 200A). The current Io corresponds to the energization current of the superconducting coil 10 at the normal time when no quench occurs.

  When the maximum generated voltage of the superconducting coil 10 when the inductance L of the superconducting coil 10 is 1H is V (L = 1, C, Io = 200), the approximate curve is expressed as the equation (5).

  Next, the relationship between the inductance of the superconducting coil 10 and the maximum generated voltage is normalized. In normalization, the maximum generated voltage when the capacitance C of the capacitor C1 is 1F is extracted for each inductance from the relationship shown in FIG. FIG. 8 shows the relationship between the maximum generated voltage of the superconducting coil 10 and the inductance when the capacitance C of the capacitor C1 is 1F and the resistance value R of the protective resistor RP is 0.1Ω. The horizontal axis of FIG. 8 shows the inductance of the superconducting coil 10, and the vertical axis shows the value obtained by normalizing the maximum generated voltage at each inductance with the maximum generated voltage when the inductance L = 1H. When the maximum generated voltage at each inductance is V (L, C, Io = 200), the normalized maximum generated voltage is V (L, C, Io = 200) / V (L = 1, C, Io). = 200).

  An approximate curve was derived for the relationship shown in FIG. The approximate curve is expressed as Equation (6).

  Subsequently, by deforming the approximate curve of the above formula (5) using the approximate curve of the above formula (6), the maximum generated voltage V (L, C, Io = 200) at each inductance is expressed by the formula ( 7).

  By further generalizing the above equation (7) with respect to the energization current Io, the maximum generated voltage finally becomes the inductance L of the superconducting coil 10 and the capacitance C of the capacitor C1, as shown in equation (8). And can be expressed as a function of the conduction current Io.

  However, it is assumed that the maximum generated voltage V (L, C, Io) satisfies the condition (V (L, C, Io) ≧ R × Io) that is equal to or higher than the voltage R × Io generated in the protective resistor RP. Further, the maximum generated voltage V (L, C, Io) is not limited to the value represented by the above formula (8), and has a slight variation depending on the characteristics of the diode D1.

  Further, in order to protect the superconducting coil 10 from overvoltage, it is necessary to suppress the maximum generated voltage V (L, C, Io) to be equal to or lower than the withstand voltage of the superconducting coil 10. That is, when the withstand voltage of the superconducting coil 10 is Vw, it is required to satisfy the condition of V (L, C, Io) ≦ Vw.

  In summary, the maximum generated voltage V (L, C, Io) needs to satisfy the relational expression shown in Expression (9).

  In other words, in the superconducting magnet device 100 shown in FIG. 1, when the energizing current Io and the inductance L of the superconducting coil 10 are determined, the capacitor C1 in the quench protection circuit 120 satisfies the above relational expression (9). A capacity C is set. As a result, when the quench is detected and the current supply to the superconducting coil 10 is interrupted, the energy stored in the superconducting coil 10 is quickly released without causing the superconducting coil 10 to generate a voltage exceeding the withstand voltage Vw. Can be made.

  FIG. 9 verifies the consistency between the maximum generated voltage V (L, C, Io) generalized by the above equation (8) and the relationship between the capacity of the capacitor C1 and the maximum generated voltage shown in FIG. The results are shown. In the graph of FIG. 9, the relationship between the maximum generated voltage calculated using the above equation (8) and the capacitance of the capacitor C1 is superimposed on the relationship between the capacitance of the capacitor C1 and the maximum generated voltage shown in FIG. It is shown.

  In FIG. 9, the waveform group k15 shows the relationship when L = 1000H and R = 0.1Ω, the waveform group k16 shows the relationship when L = 100H and R = 0.1Ω, and the waveform group k17 shows L = 10H. , R = 0.1Ω, and the waveform group k18 shows the relationship when L = 1H and R = 0.1Ω. In each waveform group, the solid line shows the relationship obtained from the simulation, and the broken line shows the relationship obtained using the above equation (8).

  Referring to FIG. 9, it can be seen that in any waveform group, the relationship obtained from the simulation and the relationship obtained from the above equation (8) coincide with each other with high accuracy. That is, FIG. 9 proves that in the quench protection circuit 120 according to the present embodiment, the maximum generated voltage of the superconducting coil 10 can be generalized by the above equation (8).

[Quench protection circuit design procedure]
Finally, the design procedure of the quench protection circuit 120 using the above equation (8) will be described. FIG. 10 is a flowchart for explaining a design procedure of the quench protection circuit 120 according to the embodiment.

  As shown in FIG. 10, first, in step S10, the conduction current Io and the inductance L of the superconducting coil 10 are substituted into the above equation (8). Thereby, the maximum generated voltage V (L, C, Io) of the superconducting coil 10 is substantially expressed as a function of the capacitance C of the capacitor C1.

  Next, in step S20, the maximum generated voltage V (L, C, Io) derived in step S10 is equal to or lower than the withstand voltage Vw of the superconducting coil 10, that is, so as to satisfy the relational expression (9). The capacitance C of the capacitor C1 is set.

  Specifically, in step S20, the allowable range of the capacitance C of the capacitor C1 is obtained by solving the relational expression (9). As shown in FIG. 5, the smaller the capacitance C of the capacitor C1, the smaller the decay time constant of the current flowing through the superconducting coil 10. Therefore, it is preferable to set the capacity C in the vicinity of the lower limit value of the obtained allowable range.

When the capacitance C of the capacitor C1 is set in step S20, the resistance value R of the protective resistor RP is set in step S30. As described with reference to FIG. 4, in a closed circuit composed of an LCR series resonance circuit, the current I oscillates when 4L / C> R ² with a boundary of 4L / C = R ² (critical damping) as a boundary. while attenuation, when the 4L / C <R ² current I is attenuated without vibration. However, even when the current I is damped by vibration, the amplitude is suppressed by the rectifying action of the diode D1 (see the waveform k4 in FIG. 4). Therefore, it is preferable to set the resistance value R of the protective resistor RP to a value in the vicinity of the resistance value Rc (Rc = 2 (L / C) ^1/2 ) when critical damping is achieved.

  The embodiment disclosed this time is to be considered as illustrative in all points and not restrictive. The scope of the present invention is shown not by the above-described embodiment but by the scope of claims, and is intended to include meanings equivalent to the scope of claims and all modifications within the scope.

DESCRIPTION OF SYMBOLS 10 Superconducting coil 20 Excitation power supply 30 Breaker 110 Quench detection circuit 112 Voltmeter 114 Control part 120 Quench protection circuit C1 Capacitor D1 Diode DU Voltage difference detection part RP Protection resistance PM Variable resistor

Claims (3)

A superconducting coil;
A quench protection circuit connected in parallel to the superconducting coil,
The quench protection circuit includes:
A diode,
A resistor connected in series with the diode;
A superconducting magnet device, further comprising a capacitor connected in series to a series circuit including the diode and the resistor. 2. The superconductivity according to claim 1, wherein a maximum voltage generated in the superconducting coil by self-induction in a closed circuit formed by the superconducting coil, the diode, the resistor, and the capacitor is represented by the following formula (1): Magnet device.
V = 1.005 * Io * C- ^0.498 * L ^0.510 ... (1)
(In the formula (1), V represents the maximum voltage, Io represents the energization current of the superconducting coil in a normal state where no quench occurs, L represents the inductance of the superconducting coil, and C represents the capacitance of the capacitor. Represents capacity.)   The superconducting magnet apparatus according to claim 2, wherein a capacity of the capacitor satisfies a condition that the maximum voltage is equal to or lower than a withstand voltage of the superconducting coil.

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