Some thoughts on an eddy current septum magnet

It is the purpose of this report to describe the thinking and work that went into thoroughly understanding, a specific eddy current septum magnet that will be used in the APS and needs ``fixing.`` The goal is to go beyond mere qualitative understanding and carry the analysis far enough to recognize the real problems of this magnet and to develop the tools to solve them. While it would be very tempting to write this report in very general terms, it would be very difficult to achieve complete generality, and one would risk losing the focus on this specific magnet that needs to have an improved performance. The discussion contains, however, so many generally useful concepts and procedures that it might further be useful for designers of other eddy current septum magnets both at the APS and elsewhere. Since it is necessary not only to have a deep qualitative understanding of several aspects of this type of magnet, but also to quantitatively assess what has to be done to achieve the desired performance, fairly heavy use of mathematical tools was made. In doing so it became clear that the extensive use of these tools is essential not only for this purpose, but also to get the required good qualitative understanding of the device. For instance, it turns out that in this particular instance, an important part of the underlying physics does not become clear until one seems to run into what one might consider, at first, a mathematical problem, whose resolution is not clear until one has found the solution, which then seems ``obvious.`` Even though iron in the septum has a nonlinear relationship between B and H, assuming a constant permeability is sufficient to obtain the information needed to develop a sufficient understanding of the magnet to make some crucial decisions