4. Alternative losses (ac losses)

While a superconductor has no losses in a constant electromagnetic environment, losses, known as alternating or ac losses, appear as soon as the induction or current varies over time. The Maxwell-Faraday law $\left(\text{rot}\overrightarrow{E}+\frac{\partial \overrightarrow{\beta }}{\partial t}=0\right)$ states that a time-varying magnetic induction automatically generates an electric field. The induction is either external or linked to the transport current (self-field). The electric field and the critical current density (critical state) then create density losses $$