What happens in a typical first magnet?
1. Pre-stress (and/or effective cable thickness) is not right by a significant amount. An attempt to get right compression messes up field quality.
2. Higher order harmonics are OK but lower order are not (generally first two).
- Need 1+2 = 3 parameters to fix the above three quantities.
But usually we are almost there: measured harmonics are 10-3 instead of required 10-4 .
And corresponding relative mechanical errors are small as compared to the overall coil dimensions.
Change cross-section (change wedges, cable size, coil tooling, etc.) which makes mechanical changes relatively large. As a result the process becomes time consuming and expensive and due to a large change it does not always converge in one iteration.