Normal zone acceleration: a new model to describe the quench process in superconductors with changing current N.A. Buznikov, A.A. Pukhov and A.L. Rakhmanov Institute for High Temperatures, Russian Academy of Sciences, Moscow 127412, Russia Received 16June 1993; revised 18January 1994 Quench propagation is studied in a superconductor with changing transport current I(t) placed in a varying magnetic field B(t). It is shown that the normal zone propagation velocity v increases and the quench energy ec decreases with an increase in the rate of change of transport current / and magnetic field B. Such normal zone acceleration arises due to interaction between the propagating normal zone and thermomagnetic instability induced by varying / and B. This effect takes place both for increasing and decreasing currents and changes the values of v and ec by several orders of magnitude. The analytical and numerical dependences v(I, B) and ec(/, B) are found. Analytical expressions for v and ec which are valid for a wide range of/, B values are obtained and compared with both experimental and numerical data. Good agreement is observed. The obtained results may be of importance for understanding the abnormally fast quench propagation in pulsed magnet systems (such as SMES), sectional magnets, thermally controlled switches and superconducting a.c. devices. Keywords: composite superconductors; normal zone acceleration; thermomagnetic instability; quench energy Recent experimental results ~ have demonstrated that certain features of the quench process in a composite superconductor (SC) with changing current I(t) and/or placed in a varying magnetic field B(t) cannot be explained by the conventional normal zone propaga- tion theory 7-9. These effects are connected with the dependence of quench propagation on the transport current variation rate dI/dt -- I. In references 4, 6 and 10 it was reported that the normal zone propagation velocity v depends directly on I and increases by several orders of magnitude with an increase in I. In reference 11 it is shown that the quench energy e~ of the thermal perturbations required to destroy the super- conductivity decreases sharply with the growth of I. Quench in superconductors carrying an a.c. current I(t) has been discussed previously 12'13. However, in these papers it is suggested that the effect of current variation on normal zone propagation is due to the quasi-stationary variation of heat release in the normal state. This theory does not explain the strong depend- ences of v and e~ on i. In our previous papers 14'15 a simple model is proposed which describes qualitatively the depend- ences of v and ec on i. According to references 14 and 15 the current and/or magnetic field variation may effect the quench process directly due to the thermal and electrical disturbances induced in the supercon- ducting state by ) and /~. These disturbances initiate the normal transition in the uniform superconducting state if the current is larger than some quench current />Iq(L /~)9,16,17, where lq<Is and Is is the critical current. In the d.c. regime (i =/~ = 0) the stable uniform superconducting state disappears at I -- Is. At I --~ Is the velocity v sharply increases and the quench energy ec tends to zero 7,9. It is evident that analogous behaviour of v and ec can be expected under varying I(t) and B (t.) at I --~ lq. In this case v and ec. are strong functions of I, /~ since Iq depends on i and B. Note that the described dependences of v (I) and ec (i) are also observed in the experiments detailed in references 6, 10 and 11. In this paper we present a detailed analysis, both analytical and numerical, of the normal zone propaga- tion in a SC carrying a varying transport current I(t) and placed in a varying magnetic field B(t). The proposed model of the process takes into account the current dependence of the losses in the superconduct- ing state and current sharing between the supercon- 0011-2275/94/090761-09 (~) 1994 Butterworth-Heinemann Ltd Cryogenics 1994 Volume 34, Number 9 761