There’s a lot we know about magnetic core loss, and at lot we don’t know. The situation is summarized in presentation slides from my presentation at the PSMA/IEEE Magnetics Workshop. The slides have the references added at the end with reference numbers sprinkled through.
People were intrigued by the three simple flux crowding simulations shown here. These aren’t intended to be highly accurate–they are based on constant permeability, and as pointed out by Bruce Carsten, the real behavior is nonlinear. But the results are still interesting and somewhat surprising. Based on loss proportional the flux density raised to the 2.5 power, the second picture–the circular hoop–doesn’t reduce loss as you might expect. Rather, it raises loss by about 3%, compared to the simple square corners at the top. But the bottom design does reduce loss, by about 8%, compared to the simple square corners.
Great Mr. Charles Sullivan, Always design plays a very important while at designing the magnetic cores. As it can be seen from the analysis of second core image. Great Work.