A scaling law for the magnetic fields of superconducting undulators

A scaling law for the calculation of the peak magnetic fields in the midplane of planar superconducting undulators (SCUs) was deduced from numerical analyses. The scaling law, which is a constant of (current density)×(period), requires the scaling of the SCU dimensions according to a period ratio. Under the scaling law, not only the peak field and coil maximum field, but also the whole field distribution remained unchanged. Using the scaling law, the peak fields for a period range of 8-40 mm were calculated from a data set computed for SCUs with NbTi superconducting coils for a period of 16 mm and a gap/period ratio g/λ=0.5. From numerical analyses for one case of coil dimensions, the dependence of the peak field on g/λ was deduced to exp(-πg/λ), which underestimated the peak field up to 4% for g/λ>0.2.