Some Rate-Dependent Aspects of Flux Jumping in Nb-25% Zr Tubes

Abstract

A series of experiments have been performed on rate dependence of flux jumping in tubular samples of Nb-25% Zr using pulsed magnetic fields. The field H1 for which the first flux jump occurred was studied as a function of the rate of change of field Ḣ1 at the time of the flux jump. The range of Ḣ1 was 101<Ḣ1<105 kOe/sec. The data were taken using a specially designed inductance-resistance-capacitance circuit for producing pulsed magnetic fields.1 Silicon-controlled rectifiers were used as switching elements in the circuit. The dependence of H1 on Ḣ1 was studied for a series of tubular samples of varying wall thickness (10, 20, 40, and 100 mil). These samples had a 0.36 cm i.d. and were 3.2 cm in length. The results are shown in Fig. 1. It was found that H1 is constant for 101<Ḣ1<103 kOe/sec. The level of H1 in this region increases as the tube outer diameter increases. At some value of rate Ḣ1A, H1 begins to increase monotonically from its constant value and continues to do so up to the highest rates attainable with the present apparatus. Ḣ1A increases for thinner-walled samples and represents the point where the power density S at the surface of the tube begins to exceed S=0.8 W/cm2, the value which characterizes the onset of film boiling2 in the helium bath. The magnitude of the departure of H1 from its constant value is greater for the thicker-walled samples. At Ḣ1≃105 kOe/sec, H1 has increased by a factor of two to three over its value in the plateau region. These results can be interpreted in terms of a recently proposed criterion3–7 for the onset of magnetic instabilities in hard superconductors at a field Hfj=[−π3CJc/(∂Jc/∂T)]1/2,where Jc is the critical current density, ∂Jc/∂T the derivative of the critical current density with temperature, and C the volume specific heat of the superconductor. This function increases from zero at T=0 and rises to a maximum at T≃0.7 Tc for Nb-26% Zr. Thus, increased stability is predicted with rising temperature in the range 0<T<0.7 Tc. It is felt that the present results reflect a heating effect due to the poor heat transfer to the helium bath once the surface power density exceeds 0.8 W/cm2. This result points to the possible stability advantage to be had by operating superconducting devices made with type II materials at a somewhat elevated temperature.

Damping effects and flux kinetics in a type II superconducting disk

“…If calculations of Hfj and field sweep are made without taking into account the self-inductance of the superconducting solenoid [ignoring Eqs. (2)-(5)], these will result in an apparent strong dependence of H o on sweep rate, similar to that reported by Rothwarf et al 6 We have demonstrated that the time constant zu of the first large flux jump into NZP5 is independent of the field sweep rate for these experimental conditions. This is understandable in view of the independence of Hfj and sweep rate.…”

“…This would indicate that isothermal conditions must exist within the specimen until the flux jump occurs. Under these conditions, Wipf's la stability limit should hold and Hfj should depend on the specific heat, temperature, and critical temperature of the material according to Hfj = 89 2 -T2)/T~l/2 (6) When the superconductor is in the Meissner state the energy gained per unit volume as a consequence of the field expulsion is H2/8n. During the field sweep the external field penetrates a small volume V of the sample around the perimeter so that an amount of energy (H2/8n)V is dissipated as heat during the sweep.…”

Flux jumps under time-dependent external conditions

“…In some experiments the growth in Ha=Ha(Be) has been registered in the region of high f i e , which is apparently explained by sufficient heating of the sample (Rothwarf et al 1968, Chikaba et al 1968. We shall not discuss it.…”