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 I0 cos ωt and a phase-different ac magnetic field H0 cos (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 2π a, 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).