Analytical Field Calculation of Modulated Double Helical Coils

We develop analytical expressions for the magnetic vector potential and the magnetic field of modulated double helical coils (MDHC). It is assumed that the coils are tightly wound and can be approximated by two infinite thin current sheets. From each coil parametric equation, the surface current density is derived by considering the turn-to-turn spacing. The field inside and outside each coil is then calculated by decomposing the surface current density into three contributions. By summation, the field of any MDHC can be obtained. As a validation, we evaluate the field of a superconducting double helical quadrupole. A good agreement is found between analytical and numerical results. From the field, the main coil parameters can be quickly estimated with a fair accuracy. This can be useful for the design an optimization of advanced magnets, both conventional and superconducting.