The efficiency and the demagnetization field of a general Halbach cylinder

TL;DR

This paper analyzes the magnetic efficiency and demagnetization field of general multipole Halbach cylinders, deriving optimal design ratios and identifying conditions that maximize demagnetization to inform better magnet design.

Contribution

It provides a mathematical analysis of efficiency and demagnetization in general p-order Halbach cylinders, including optimal ratios and demagnetization field locations.

Findings

Efficiency decreases with increasing |p|

Optimal inner/outer radius ratio tends to zero for large |p|

Demagnetization peaks at specific angular positions depending on p

Abstract

The maximum magnetic efficiency of a general multipole Halbach cylinder of order $p$ is found as function of $p$. The efficiency is shown to decrease for increasing absolute value of $p$. The optimal ratio between the inner and outer radius, i.e. the ratio resulting in the most efficient design, is also found as function of $p$ and is shown to tend towards smaller and smaller magnet sizes. Finally, the demagnetizing field in a general $p$-Halbach cylinder is calculated, and it is shown that demagnetization is largest either at $\cos 2p\phi=1$ or $\cos 2p\phi=-1$. For the common case of a $p=1$ Halbach cylinder the maximum values of the demagnetizing field is either at $\phi = 0,\pi$ at the outer radius, where the field is always equal to the remanence, or at $\phi = \pm \pi/2$ at the inner radius, where it is the magnitude of the field in the bore. Thus to avoid demagnetization the coercivity of the magnets must be larger than these values.