Analytical solutions of the magnetic field generated by two-pole nested Halbach cylinders.

One of the most common permanent magnet configurations employed in room-temperature magnetic refrigeration applications is the Halbach cylinder, a structure whose magnetic remanence is defined as a sinusoidal curve. We present an analytical solution of the magnetic field generated in the air gap between two concentric Halbach cylinders (where the active magnetic regenerators are placed). The model has been adapted from previous works and the solution has been extended to the case of two concentric cylinders with two magnetic poles so as to simplify the manufacture of this permanent magnet configuration. The two Halbach cylinders are assumed to be infinite in length and built from Nd-Fe-B permanent magnets with a magnetic remanence of 1.47 T. In the present analysis, the radial dimensions of the magnets are varied to quantify the influence of the air gap size on the magnet performance and identify optimal configurations.