Halbach Array - Halbach Spheres

Halbach Spheres

If the two dimensional magnetic distribution patterns of the Halbach cylinder are extended to three dimensions, the result is the Halbach sphere. These designs have an extremely uniform field within the interior of the design, as they are not affected by the 'end effects' prevalent in the finite length cylinder design. The magnitude of the uniform field for a sphere also increases to 4/3 the amount for the ideal cylindrical design with the same inner and outer radii. However, being spherical, access to the region of uniform field is usually restricted to a narrow hole at the top and bottom of the design.

The equation for the field in a Halbach sphere is:

Higher fields are possible by optimising the spherical design to take account of the fact that it is composed of point dipoles (and not line dipoles). This results in the stretching of the sphere to an elliptical shape and having a non-uniform distribution of magnetization over the component parts of the sphere. Using this method, as well as soft pole pieces within the design, 4.5 T in a working volume of 20 mm3 was achieved by Bloch et al. in 1998 and this was increased further to 5 T in 2000, although over a smaller working volume of 0.05 mm3. As hard materials are temperature dependent, refrigeration of the entire magnet array can increase the field within the working area further as shown by Kumada et al. This group also reported development of a 5.16 T Halbach dipole cylinder in 2003.