Eddy current interaction loss of randomly distributed magnetic domain walls with speeds in field equilibrium

Eddy current losses are calculated for a domain model of the R.H. Pry and C.P. Bean (1958) type in which the domain walls are distributed randomly with mean spacing W across a lamination of thickness D. Two cases are considered. In the first, all walls are constrained to reverse flux at the same rate. The resulting eddy loss exceeds the classical loss (for uniform dB/dt) by a factor of η₀+1, where η₀=1.628 W/D is the value in the limit of negligible wall-to-wall eddy overlap. This confirms earlier work and G. Bertotti´s (1983) rule that independent random eddy interactions between walls make a classical loss contribution. In the second case, each wall adjusts its individual flux rate to balance the eddy current drag against the applied field pressure; a lower loss ratio η_A=η₀+η _I results. η₁ decreases from 1 for W≪D, to 0.7 for W≫D. This is contrary to Bertotti´s rule that correlated magnetic activity enhances eddy current loss