This paper is concerned with the stability against flux jumpes of current and temperature distribution in a composite superconductor which has internal cooling channels. The stability and perturbation increments have been found. Rux jumps in intemally cooled composite superconductors R.G. Mints and/EL. Ra'khmanov It is known h2 that thermomagnetic instabilities, flux jumps, may arise in hard superconductors or superconducting composites. In the case of composites, the stability criterion strongly depends on the external cooling. For this reason, the cooling channels in conductors consisting of composite wires are usually provided in the bulk of the material. The present paper is concerned with the stability of such conduc- tors with respect to small perturbations covering a large portion of the sample volume. Although similar, this problem is different from the cryostatic stability which has been discussed in the literature 3. To initiate the instability in question, there must be an initial perturbation covering the entire sample cross-section and having a longitudinal dimension greater than the cross- section perimeter 2. Such a perturbation may be brought about by a flux jump in individual sample elements caused by current input and output, displacement of coil turns, etc. Note that this presentation of the problem eliminates the effect of twisting on the stability ~'s To find the stability criterion one has to derive the equations describing the evolution of small perturbations of the electric field E and the temperature T. Following the methods Used in 4,s, the inhomogeneous conductor with cooling channels is considered here as the continuous medium with parameters averaged over a small volume. The feasibility of such an approach has already been discussed in detail s . The averaged Maxwell equation has the following standard form: curl curl•- 47r 37 (1) c 2 3t where the current density j is given by: Yi= & (T, H) + ~k Oik Ek Js and oik are the averaged density of the supercurrent and conductivity tensor, respectively; i and k are tensor indices (X 1 =X,X 2 =y, X 3 =Z). Analogous to, for example, reference five, one may find in the linear approximation with respect to the temperature disturbance 0 = T-To. The authors are at the Academy of Sciences, Moscow, USSR. Paper received 26 November 1979. 30 ~ 320 217 H (2) I) -~- = Z~LkKik-~i~X x + js E- ro qH Where v and Kik are averaged heat capacity (without allowance of the helium circulating in the channels) and thermal con- ductivity tensor, ~H is the portion of the cross-section occu- pied by the channels, ro is the channel radius, qH is the heat flux to the helium from the unit cooling channel surface. Similarly for helium temperature TH we have: ~0H 2qH 11 H -- = __ _ Ul) H -- 3t r o ~OH OZ OH = T H - T o (3) where v H is the helium heat capacity, and u the helium velo- city. For simplicity it is assumed that the cooling channels are oriented along the axis oz. The averaged values of is, v, o, K appearing in (1) - (3) have been discussed4,s. To determine the value qH exactly is extremely difficult since convection and boiling of helium and the specific structure of the composite must be taken into account. If the helium flow rate u is small the helium has enough time to receive heat so that OH = O and then qH = VH 2/roO. It is easily seen that the perturbation equations will in this case be identical with those for a composite without channel¢ 's, provided that the corrections in/'s, v, o, K have been properly taken into account. The values of o, K,/s decrease and the effective heat capacity v + 1) H I"/H increases when cooling channels are provided. However, in the first approximation the stability criterion for the composites is independent of the heat capacity4,s. Therefore, the internal cooling will fail to be effective if the helium velocity is small. Note, that for hard superconductors without normal metal, the situation is quite different: the stability increases with heat capacity 2. When helium flows rapidly, its heating is insignificant: O >>OH Then we may use the conventional empirical equation for qH: qH = Wo (T- Trt), where TH ~-- To, Wo is the heat transfer coefficient. Then from (3) it follows that: PHrO 0 ~ u --OH wd Here, we have used the estimate: ()0H/DZ ~ OH/l and I is the 0011-2275/80/060326-03 ~;02.00 ©1980 IPC Business Press 326 CRYOGENICS. JUNE 1980