The isothermal critical-state model of hard superconductors is extended to include the effects of heating when the applied field is changed suddenly and magnetic flux enters adiabatically into the bulk. We consider the following specific situation. A semi-infinite slab of superconductor is cooled in a magnetic field lying in its surface plane. Next, the external field is raised isothermally by an amount Hs. This excess field decreases linearly to a depth δ= 10Hs/4πJc from the surface. Finally, the field is raised by an infinitesimal amount ΔH in a time short compared to the thermal diffusion time and long compared to the electromagnetic diffusion time. Each element of volume exposed to the changing field receives a thermal impulse proportional to the local-flux-change times Jc. This thermal impulse, in turn, lowers the critical current and allows more flux to penetrate. We find that if Hs exceeds some critical value Hfj, then the isothermal critical state is not the only allowed state of the superconductor. This instability field is given in terms of the critical current density Jc, derivative of the critical current density with temperature, ∂Jc/∂T, and the volume specific heat C by the formula Hfj= [−π3CJc/(∂Jc/∂T)]1/2. The application of the incremental field ΔH can initiate an avalanching process, or a flux jump, that terminates in an adiabatic critical state. Immediately following the flux jump the internal field, the induced supercurrent, and the temperature rise at each position are associated in a self-consistent way with the avalanche of flux that has entered the superconductor. In this framework a flux jump is viewed as a switching from the isothermal critical state to an adiabatic critical state. The magnitude of the jump is related to Js and is calculated.

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It is found that in two different and well-defined experimental situations the magnitude of the critical surface current changes when the direction of the transport current is reversed. This property is denoted as "partial rectification." In one case (single-surface rectifier), the asymmetry is measured when the external magnetic field (H c i