Reduction in energy dissipation rate with increased effective applied field

Dynamics of the response of type-II superconductors to a time-varying magnetic field can exhibit a rate-independent or rate-dependent hysteresis. An energy dissipation rate in a superconductor placed in a time-varying magnetic field depends on its wave form and type of hysteresis, which depends on temperature. The same wave form may reduce the energy dissipation rate in the case of true hysteresis, while it may increase the energy dissipation rate in the case of dynamic hysteresis compared with an energy dissipation rate in a pure sinusoidal field. We present experimental data which confirm the energy dissipation rate calculated using the critical state theory for the case of rate-independent hysteresis and limiting behavior in a normal state for the case of rate-dependent hysteresis.