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 $I_0\cosωt$ and a phase-different ac magnetic field $H_0\cos(ωt+θ_0)$. On the basis of Bean's critical state model, we calculate $Q$ for small current amplitude $I_0\ll I_c$, for small magnetic field amplitude $H_0\ll I_c/2πa$, and for arbitrary phase difference $θ_0$, where $I_c$ is the critical current and $2a$ is the width of the strip. The resulting expression for $Q=Q(I_0,H_0,θ_0)$ is a simple biquadratic function of both $I_0$ and $H_0$, and $Q$ becomes maximum (minimum) when $θ_0=0$ or $π$ ($θ_0=π/2$).

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