Hysteretic ac loss of superconducting strips simultaneously exposed to ac transport current and phase-different ac magnetic field

A simple analytical expression is presented for hysteretic ac loss Q of a superconducting strip simultaneously exposed to an ac transport current I0cosωt and a phase-different ac magnetic field H0cos(ωt+θ0). On the basis of the critical state model, the authors calculate Q for small current amplitude I0⪡Ic, for small magnetic field amplitude H0⪡Ic∕2πa, and for arbitrary phase difference θ0, where Ic is the critical current and 2a is the width of the strip. The resulting expression for Q=Q(I0,H0,θ0) is a simple biquadratic function of both I0 and H0, and Q becomes maximum (minimum) when θ0=0 or π (θ0=π∕2).