High resolution locating of normal transitions in a high temperature superconducting coil by capacitor type voltage terminals

It is important to locate positions of normal transitions in a high temperature superconducting coil for identifying its design and fabrication weakness. The authors have proposed capacitor type voltage terminals as a contactless method to measure voltages of the coil windings through insulation of the windings. This method was useful for locating the positions of the normal transitions. Higher resolution of the location is achieved by attaching many terminals to the coil. Then shorter electro-conductive sheets of capacitor type voltage terminals are needed. However, the shorter sheets make the measured voltage signals small and the signals are supposed to be incorrectly measured. In this paper, the authors propose a method to achieve high resolution locating by long electro-conductive sheets of capacitor type voltage terminals. Numerical values of the measured voltage by the terminals depend on the positions of the normal transitions and therefore analysis of the values can achieve high resolution locating without increasing the number of the terminals. Through experimental results for a Bi2223 HTS coil, it was confirmed that the proposed method could achieve the high resolution locating.


Introduction
Locating normal transitions in high temperature superconducting (HTS) coils is important to discuss thermal stability of the coils. The authors have presented capacitor type voltage terminals as a contactless method to measure voltages of the coil windings [1][2][3]. References [2,3] show that the method is useful for locating the positions of the normal transitions. It is needed in order to make resolution of the location much higher that many voltage terminals are mounted on the windings, and then distance between adjacent two terminals are shorten. However, it makes the measurement system complex and makes measured voltage values small and then it is supposed to cause incorrect measurement. In this paper, the authors propose a method to achieve high resolution locating by using less voltage terminals based on the capacitor terminal method. Numerical values of the measured voltage by the terminals depend on the positions of the normal transitions and therefore analysis of the values can achieve high resolution locating without increasing the number of the terminals. Experimental results for a Bi2223 HTS coil showed that the proposed method could achieve the high resolution locating.  Figure 1 shows an outline of the contactless voltage measurement method [1]. A pair of electrically conductive sheets is attached on the surface of an HTS coil and is connected with an outside capacitor. Then a capacitor is formed at the each sheet and a voltage of the coil winding is measured as a voltage of the outside capacitor based on voltage dividing by the three capacitors. and are capacitances at the two sheets, and and are respectively a capacitance and a voltage of the outside capacitor. Figure 2 shows two states at a certain time after occurrence of the normal transitions as a 1D model on distribution of the normal zones in the HTS wire. When the normal zone occurs at (A) in Figure 2 which is between two sheets, relationship between the voltage of the HTS wire and the voltage of the outside capacitor is shown as follows [2].

Principle of location method
, where . (2) Whereas the normal zone occurs at (B) in Figure 2 which is under the sheet, a following equation is obtained [2].

.
( Here, is the length between the left end of the electro-conductive sheet (point "a") and the left end of the normal zone, is the length of the normal zone, is the length between the right end of the normal zone and the right end of the sheet, is the length of the sheet, is the resistance of the From the equations (1) and (3), the closer the position of the normal transition is the area between two sheets, the smaller the second term of the equation (3) becomes, and then the ratio of / increases. In case of (A), / becomes 100 % and in case of (B) / becomes smaller than 100 % with dependence of the position of the normal transition. Therefore locating normal transitions can be achieved by measuring the ratio of / . Based on this method, high resolution locating can be achieved by less electro-conductive sheets of capacitor type voltage terminals. Moreover less sheets can actualize long sheets to make measured voltages larger for more correct measurement.

Experimental setup
Experiments on the locating of the normal transitions were carried out for a Bi2223 HTS coil. Figure 3 and Table 1 show an outline of a test Bi2223 HTS coil and its specifications, respectively. AC current of 60 Hz and 150 A peak was supplied to the HTS coil which was cooled in liquid nitrogen. The normal transitions were caused by four heaters mounted on the positions I to IV of the 2nd turn of the HTS coil shown in Figure 4. Voltage terminals except the capacitor terminal were soldered to the windings to confirm the positions of the normal transitions and measured voltages by the terminals were to . Distances between adjacent two terminals were 30 mm except 60 mm for . Table 2 shows specifications of the capacitors.
The other capacitor terminal was attached on the 7th turn of the HTS coil. A voltage of the 2nd turn had an inductive voltage and therefore it was cancelled by subtracting a voltage of the 7th turn from as follows. .
was a ratio of an inductive voltage in to that in in superconducting state. had some electromagnetic noise and therefore it was transformed into an active power and filtered shown as following equations to locate the positions of the normal transitions more precisely. , 1 .   Equation (6) is expressed by Laplace transform and is a time constant of the filter. As well as the inductive voltage in , that in is removed resulting in . As the results, the ratio of / was shown as a following equation.
means filtered . By using the s and the s, the each ratio of / was calculated for the normal zone size of 30 mm in each case. For example, in case of II, following calculations were carried out.  Experimental value of equation (7)  Normal zone size became 30 mm at 15.5 s when and started to increase as shown in Figure 6 (a).  Based on the equation (7), experimental value of / was calculated from the and which were values at 15.5 s in Figures 6 (b) and (c), respectively. 120/√2.  The experimental value was normalized by / measured in case of I in order to supress measurement errors.  Theoretical value of equation (3)  Equation (3) was transformed into following one.

Experimental results
 was assumed to have a liner resistivity for and then the equation (8) could be derived as 2 2 . (9)  In case of II, the theoretical value was obtained for 30 mm and 120 mm. Table 3 shows the calculation results. Experimental results were in good agreement with the theoretical values. The results show that the proposed method can locate the position of the normal zone for the normal zone size of 30 mm. However, it was found from other experimental results that it was hard to locate the position of shorter normal zone than 30 mm. In case of IV, the value of / becomes very small value according to equation (9)   signal for the shorter normal zone in case of IV and it was hard to be measured correctly. The authors will study on locating for the shorter normal zone especially for case IV hereafter.
In these experiments, many voltage terminals were soldered on the superconducting wire for verifying the principle of the proposed method, however, only two soldered terminals on the both ends of the HTS coil are needed for in actual use. Then the inductive voltage in is removed by a cancel coil [4].

Conclusions
In this paper, the authors proposed a method to achieve high resolution locating of the normal transitions in the HTS coil by less and long electro-conductive sheets of capacitor type voltage terminals. The proposed method achieves the location by calculating a ratio of a voltage of a capacitor voltage terminal to a voltage of the HTS coil wire. Experimental results for a Bi2223 HTS coil showed the proposed method could locate the position of the normal zone of 30 mm. The authors will study on higher resolution method.