Study on conditions to reuse quenched HTS coil

An HTS coil quenches despite of the high quench margin. Main origins of unexpected quench of HTS coils are non-reversible local defects, and training effects as in LTS coils are not observed in HTS coils. Therefore, when an HTS coil is quenched before the required coil performance is met, the coil cannot be reused unless the coil is safely protected from quench damage and its operating conditions are readjusted. This paper studies on the conditions to reuse the coil which experienced a quench and is not damaged by the quench to meet the required performance. The study is conducted based on the temperature and current dependences of the coil stability measures of the maximum allowable defect (MAD) and minimum propagating zone (MPZ).


Introduction
High-temperature superconductor (HTS) coils are used in various applications, such as HTS rotating machines [1,2], superconducting magnetic energy storage (SMES) [3,4], and magnetic resonance imaging MRI [5]. However, HTS coils quench and are easily damaged when the quench protection system does not work properly, even though the coils have a high quench margin [6,7]. It is known that unexpected quenches of HTS coils are caused by non-reversible local defects, and that the training effects observed in low-temperature superconductor coils are not observed in HTS coils [8]. Therefore, to reuse quenched coils, it is important to protect coils from quench damage. It has been shown that quenched HTS coils can be protected from damage by adopting a commonly used detect-and-dump method with a properly selected quench detection voltage and current decay time constant [9,10]. When a coil is prematurely quenched (i.e., before the required performance is met), it is necessary to adjust the operating conditions for the coil, such as the operating temperature and coil current.
Coils wound with rare earth-barium-copper oxide (REBCO) wires are more sensitive to quenching and easily damaged, especially those with a high winding pack current density, compared with coils wound with Bi2223/Ag-sheathed wires [7]. This study investigated the conditions required to reuse a coil wound with insulated REBCO wires that had experienced a quench without damage. The study was conducted based on the temperature and current dependences of two coil stability measures, namely the maximum allowable defect (MAD) and the minimum propagation zone (MPZ) [11,12]. The MAD and MPZ were calculated using a numerical simulation analysis of the behaviour of the resistive zone caused by a local defect in a coil wire. A local defect is defined as a part of the wire where the critical current Icd is locally lower than the critical current Ic in the defect-free part. In the analysis, it is assumed that Icd is uniform in the defect area. Here, the deterioration factor η for the defect is defined as

Analytical model
The numerical simulation analysis was conducted based on a thermal analytical model of a winding pack of a coil wound with REBCO wires. The MAD and MPZ depend on various parameters. In this study, the simulation analysis was conducted for the winding pack model shown in figure 1, which is similar to that used in the authors' previous study [12]. In the model, thin Cu strips are inserted between the insulated REBCO wires to make a co-winding coil for highly sensitive quench detection [13], which is considered necessary for medium and large scale YBCO coils. The REBCO wires are insulated by Kapton tape (12.5 µm thick × 2). The winding pack is cooled by thermal conduction to the cooling blocks at the bottom of the pack. In figure 1, the layers of insulated REBCO wires are labelled consecutively as w-n, …, w-1, w0, w1, …, wn. In the model, it was assumed that there is a defect of length ld in layer w0 and that the temperature of the cooling block T0, which corresponds to the coil operating temperature, is kept constant. Values of MAD and MPZ depend on various parameters. In this study, the simulation analysis was conducted for a case similar to that used in the reference [12]. Specifications of the REBCO wire are summarized in table 1. The following heat equilibrium equation for a wire comprising the i-th layer of the winding pack was used in the analysis, The temperature dependences of Cp, K, hl, and hb were taken into consideration in this analysis. Details of the parameters in equation (2) are in the reference [12]. The value of Ic, which depends on the temperature and the magnetic field component vertical to the wide face of the YBCO wire B⊥, was determined based on data for the lift factor given in the reference [14]. In the calculation, it was assumed that the centre of the defect part is located at x = 0, and that the highest temperature THS in the resistive zone (hot-spot temperature) is equal to T0(0, t).  The behaviour of the resistive zone that originated at the defect in the winding pack was investigated by numerically calculating THS. This was done by solving Eq. (2) for a model coil with the winding pack structure shown in figure 1 using the multi-physics modelling software COMSOL [15]. The model coil was composed of 8 double-pancake coils, whose specifications are shown in

Analytical results
2.1.1. Behaviour of resistive zone -MAD and MPZ. The MAD length, ldMAD, at a coil operational current I0 is defined as follows. When ld > ldMAD, the resistive zone in the wire that originated at the defect area keeps spreading, eventually leading to coil quenching, and when ld < ldMAD, the coil can be operated free from quenching [12]. MAD is explained in figure 3, which shows examples of numerically calculated time traces of the hot-spot temperature THS for the cases of ld = 5.85 and 5.86 cm with I0 = 140 A, T0 = 25 K, and η = 60%. As shown, for ld = 5.85 cm, THS is steady. However, when ld is slightly increased to 5.86 cm, thermal runaway occurs, with THS suddenly and sharply rising, which may damage the wire. ldMAD can thus be estimated to be a value between 5.85 and 5.86 cm. When ld is equal to ldMAD, the resistive zone around the defect area (i.e., the area around the hot-spot) is the MPZ. In figures 4(a) and 4(b), the temperature distribution in the wire in the direction of the wire length (x-direction) and the layer (y-direction) around MPZ, respectively, are shown. As an example, figure 5 shows time traces of the voltage across the resistive zone Vs for the cases shown in figures 3 and 4. The voltage VMPZ across the MPZ is estimated to be 6.9 mV from figure 5. If Vs appears during the operation of a coil whose winding configuration is that shown in figure 1, the coil will not quench for Vs < VMPZ, but will quench for Vs > VMPZ. Therefore, if a resistive voltage larger than VMPZ appears between the coil current terminals, the coil will be damaged unless a proper quench protection measure is taken.

Dependence of MAD and MPZ on temperature and current in coil.
In figures 6(a)-(c), ldMAD as a function of I0 is plotted for various values of T0 and η = 60, 80, and 100%, respectively. As shown, ldMAD increases as T0 decreases for given values of I0 and η, except for the case with I0 = 145 A at T0 = 30 K and 35 K, where ldMAD = 0 regardless of the value of η because the load factor α = I0 / Ic0 exceeds 100% (where Ic0 is the critical current for the wire in the coil at T0). When a coil quenches at I0 = I01 and T0 = T01, the results in figure 6 suggest that ld is higher than the value of ldMAD at I0 = I01 and T0 = T01, and that the coil can potentially be reused if T0 < T01 and/or I0 < I01 are set to increase the value of ldMAD.
In figures 7(a)-(c), VMPZ is plotted as a function of I0 for various T0 and η = 60, 80, and 100%, respectively. As shown, VMPZ increases as T0 and I0 decreases for given values η, which also indicates that the stability of the coil can be increased and reused by decreasing the values of T0 and/or I0.

Conditions required for coil reuse
If a coil that is prematurely quenched is not damaged, there is a possibility that it can be reused, as mentioned above. In the following, the conditions required to reuse a quenched coil are studied by taking two cases of a model magnet, whose specifications are shown in table 1.

Case studies
3.1.1. Case 1: Model coil designed to operate at I0 = 135 A and T0 = 35 K. I0 can reach 135 A without quenching if there are no defects in the wire, because α for the model coil wire is 95% at I0 = 135 A and T0 = 35 K ( figure 2). However, if Vs at I0 = 120 A starts to increase rapidly and exceeds VMPZ while I0 is gradually increased from 0 A, that suggests that there exists a defect with a length ld just exceeding ldMAD = 2.8 -1.2 cm dependent on η = 60-100% of the defect (see figures 6(a)-(c)). Figure 8 shows ldMAD versus T0 for η = 60-100% at I0 = 135 A. When the magnet is safely protected from quench damage, I0 can be increased to 135 A without quenching by decreasing T0 to lower than 30.4 K for η = 60 and 30.6 K for η = 100%, because the values of ldMAD at 135 A for η = 60-100% are larger than those at 120 A at T0 = 35 K (see figure 8). If the coil is quenched at I0 =110 A at 35 K, then T0 needs to be decreased to lower than 26.8 K for η = 60% and 27.8 K for η = 100% for I0 to reach 135 A, as seen in figure 8. ). However, if the coil is quenched at I0 =120 A due to Vs exceeding VMAD at 30 K, there exists a defect with a length ld just exceeding ldMAD = 0.93 -1.86 cm dependent on η = 60-100% of the defect (see figures 6(a)-(c)). Then, T0 needs to be decreased to lower than 22.8 K for η = 60% and 24.1 K for η = 100% for I0 to reach 145 A, as shown in figure 9, where ldMAD versus T0 for η = 60-100% at I0 = 145 A is shown. When the coil is quenched at I0 =130 A, I0 can reach 145 A if T0 is decreased to lower than 25.8 K for η = 60% and 26.5 K for η = 100%. Figure 9. ldMAD versus T0 for η = 60-100% at I0 = 145 A.

Safe limit of quench detection voltage.
The safe limit of quench detection voltage Vqs is defined as follows. When Vq is smaller than Vqs, the coil is protected from damage, but when Vq is larger than Vqs, THS exceeds the safe limit THSs and the coil is damaged. Values of Vqs are dependent of T0, I0 and the current decay time constant τ during the quench protection sequence of the detect and dump method. A value of τ is determined so that the peak of the coil terminal voltage Vcp = LI0 / τ (L: inductance of the model coil) is to be below the withstand voltage Vcps of the coil. Values of Vqs were estimated by calculating time traces of Vs and THS during the quench protection sequence of the detect-and-dump method based on equation (2) for the above cases 1 and 2. In the calculation, it was found that values of Vqs were estimated lowest for at η = 100% and 8.2 mV for both cases of I0 = 135A at T0 = 35K and I0 = 145A at T0 = 30K assuming Vcps = 1kV (τ = 14.7s for I0 = 135A and 15.8s for I0 = 145A), which means the coil can be safely protected from quench by setting Vq < 8.2mV, regardless the value of η.

Discussions
As shown in the above analysis, the coil temperature T0re at which a quenched coil can be used to meet the designed value of I0 is dependent on the value of η. Generally, it is difficult to know the value of η. In that case, the following procedure is taken to find proper value of T0re, when a coil is quenched prematurely while setting Vq smaller than Vqs at the designed values of I0 and T0 for η = 100%. T0 is adjusted to lower than T0re which is estimated for η = 100% by the method explained above. When the coil prematurely quenches again, then T0 is reduced repeatedly more until for I0 to meet the required value. During this procedure, the value of Vq is not necessarily changed, because Vqs increases as T0 decreases.

Conclusions
This paper studies on the conditions required to reuse a quenched coil wound with insulated REBCO wires that was quenched before the required performance was met were studied by calculating the temperature-and current-dependent values of ldMAD. A simple way to reuse the quenched coil is to degrade the required performance which is met at the coil current smaller than the quenched current, if possible. The other way is to readjust the operating temperature of the coil. When a coil quenched at a coil current I01 at coil operating temperature T01 and was protected from quench damage, the coil can be reused by lowering T0 from T01 and increasing the quenching current until I0 reaches the required value. In this study, the value of T0 at which the required value of I0 can be reached was estimated from the curves of ldMAD versus T0.
This study was conducted using a winding pack of a model coil. However, the results can be generalized for other types of coil, if the structure of the winding pack is known because quenching originates at a local part of the coil wire.