Abstract: A numerical methodology for optimizing axisymmetric coil systems is described in this brief tutorial. This methodology combines a classical theory of axisymmetric magnetic fields with modern optimization techniques. Corresponding field analysis involves Biot-Savart integral, zonal harmonic expansions, and spectral analysis. Both higher-order deterministic and zeroth-order stochastic optimization methods are briefly discussed. An Evolution Strategy is described in more detail, and a powerful concept of Meta-Evolutionary optimization is introduced. Nuclear Magnetic Resonance (NMR) is a typical area where this numerical methodology is very useful for optimizing superconductive magnets with strong and highly homogeneous magnetic fields. Some examples are shown.
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