Quick methods of improving the field homogeneity of Atherton's type minimum volume superconducting coils

Atherton (J. Appl. Phys.; 40:2246 (1969)) has studied the problem of minimum volume superconducting coils having a given Fabry factor, but with the superconducting current density inversely proportional to field. This is a feature common to all superconducting coils. Plots of the second and fourth derivatives values, involved in the calculation of the field near the centre of the coil, as a function of the coil parameters are presented. Thus families of coils having identical values of the second and/or fourth derivatives can be easily found. Plots are presented for problems in which the internal bore of the superconducting magnet is given and those where the given parameter is the external radius of the magnet. The later plots are useful where a 'best fitting, high field, cheap magnet' is required to enter inside a certain cryostat and allowances can be made for miniaturization of the measuring equipment and samples fitting within the internal radius of the magnet. (author)