Generation and confinement of uniform magnetic fields with surface currents

This paper presents the methodology for generation and confinement of a uniform magnetic field in an arbitrarily assigned polyhedral cavity enclosed by planar distribution of surface currents. The condition of existence and confinement of a uniform field is derived. An example of a practical self-shielded magnet with prismatic windings is constructed around a regular hexagonal cavity. The hexagonal magnet has the desirable property of a constant current density on each lateral winding. A field of 1 Tesla is generated by a current of 1.19×10⁶ A/m. In contrast to the field in a conventional solenoid magnet, the field generated by a structure of surface currents is perpendicular to the main axis of the cavity.