The stability of the equilibrium between flux pinning and Lorentz forces acting on the flux structure in the mixed state is investigated. Complete stability is expected only if the temperature gradient of the flux pinning forces, $\frac{\partial F_P}{\partial T}$, is positive; otherwise the stability is affected by external field and geometry considerations. For the simple case of a semi-infinite slab, cooled in zero field, a calculation is given using standard empirical formulas for $F_P(B, T)$; the field above which instability is found then becomes $H_{\mathrm{fi}}=\frac{1}{2}{\pi }^{\frac{3}{2}}{\left[\frac{c({T_c}^2-T^2)}{T}\right]}^{\frac{1}{2}}$, where $c$ is the specific heat per unit volume and $T_c$ the critical temperature. For $H_{\mathrm{fi}}<H<\mathrm{}{H}_{\mathrm{fj}}$, the flux lines are accelerated by the Lorentz force until thermal recovery restores $F_P$. This is called a limited instability. Above $H_{\mathrm{fj}}$, the acceleration becomes too large compared to the thermal recovery and a runaway speed is reached. This runaway instability is identified with flux jumping. A simplified approach to the heat equation allows an estimate to be made of the maximum speed during a limited instability and of the flux-jumping field $H_{\mathrm{fj}}$, if the thermal diffusivity is known. The applicability of the given calculations and the influence of various parameters are discussed, as well as some pertinent experimental results.

• Received 6 March 1967

DOI:https://doi.org/10.1103/PhysRev.161.404