Biot–Savart Approach to Analytical Computation of Magnetic Fields and Forces of CCT Magnets

The current distribution in a canted cosine theta (CCT) multipole magnet can be written starting from the equation of an azimuthal modulated helix. In the ideal case of coaxial layers of infinitely long and infinitely thin windings, both the magnetic field and Lorentz forces are analytically obtained by applying the Biot-Savart law. The calculations are extended to multiwire magnets, where the conductors are modeled as sets of infinitely thin filaments. In order to evaluate the impact of the infinitesimal conductor thickness assumption, a comparison with finite element model results was performed. A very good agreement was found, demonstrating that the analytical model can be used as a powerful tool to support CCT magnet design as well as a useful and simple approach for didactic purpose.