Monel contribution to AC losses in MgB$_{2}$ wires in frequencies up to 18 kHz

AC losses for a wide range of AC amplitudes and frequencies have been studied in MgB2 superconducting wire with 36 filaments and Monel sheath at different temperatures and DC current levels. The results show a strong nonlinear frequency dependence below 1 kHz which crosses over to a more moderate linear behavior at frequencies up to 18 kHz. Surprisingly, the introduction of DC current causes a significant reduction in the AC losses. Finite Element simulations yield AC losses consistent with that observed experimentally. The simulations show that the magnetic Monel sheath is a dominant source for AC losses in zero DC current, and that non-zero DC current saturates the magnetization, thus reducing the AC losses.