  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.
