Magnetic field, Lorentz forces and stored energy of multipole cos(nθ) and sector magnets with and without iron yoke

When approaching the design of a multipole magnet, such as a dipole, quadrupole, sextupole, and so on, it is highly advantageous to initiate the process by establishing the fundamental parameters. These parameters include conductor size, current density, inner and outer radius of the iron yoke, and more. This preliminary dimensioning enables the acquisition of the necessary specifications for the design. Within this report, analytical expressions for the magnetic field, Lorentz forces, and stored energy of multipole magnets with the cos(nθ) and sector coil configurations, both with and without the presence of an iron yoke, are derived. These derivations are based on the vector potential of a current line.