Longitudinal impedance from ferrite

General expressions for the complex permeability of ferrites are derived. The imaginary part of this permeability, related to magnetic losses, is of particular interest. It leads to a resistive impedance that extends in frequency as high as ~ 10 GHz. This impedance initially rises with frequency from zero to a maximum and then decreases again due to the decreasing penetration depth. The longitudinal resistive impedance is computed for the ferrites installed in the SPS machine. It amounts to Z/n < 1 W at 1.5 GHz, which is negligible as compared to the measured values of Z/n which range from 20 to more than 30 W. The contribution of the ferrites to the imaginary part of longitudinal impedance is computed as well. It is capacitive at 1.5 GHz and its magnitude is of the same order as the resistive part.