Magnet system design with cost optimization

The problem of optimizing the design of magnet systems to simultaneously satisfy a set of constraint equations for field, geometry, protection, and stability while minimizing the total system cost is considered. A mathematical description of the problem is given, along with details concerning possible constraint algorithms and cost functions. Rules for the optimal selection of magnet technology (potted, ventilated, and cable-in-conduit coils) are presented. The resulting sets of equations can be solved by different numerical methods; the final choice is based on considerations of functional form as well as computational speed and accuracy. Depending on the choice of constraint equations, the resulting problem may or may not be smooth, and may or may not admit multiple minima. The choice of minimization algorithm can be tailored to the situation at hand to yield optimal performance. We present results pertaining to an alternating-field solenoid system being considered by the MuCool collaboration. The system design requires consideration of field profile, magnet stability, magnet structure, and protection, as well as total cost. A key application of the optimization code is the analysis of cost trade-off with respect to the imposed constraints, and examples are given in the alternating-solenoid case.