Inductance and current distribution of magnetic shielded dipoles

Magnetic shielding [1] is used in applications such as pulsed energy storage and poloidal field fusion magnets [2] to reduce the a.c. losses in adjacent superconducting magnets. The shielding current distribution for circular cross section dipoles is determined analytically using toroidal coordinates. Using this method the magnetic field distribution can be directly determined at all points by differentiating the flux function, and is therefore superior to the numerical mutual inductance approach. The inductance of circular cross section dipoles is determined as a function of the aspect ratio. It is also shown in the paper that shielded dipoles have smaller inductances compared to uniform current dipoles.