I am trying to determine if the following problem has an analytical solution using the method of images. The problem is an infinitely long (in $z$) cylinder of a material with permeability $\mu_2$ of radius $r_0$, where the region outside the cylinder has permeability $\mu_1$. In the latter region there is a ring of constant current $I$ of negligible thickness, and with radius $r_1 > r_0$. This situation is illustrated in the following diagram:
The question is whether the method of images could be used to place image rings of current to solve for the fields in either region. I've done a little investigation into this question and this is leading me to believe that no simple configuration of image rings can meet the necessary boundary conditions at the region interface. This is after seeing this similar question and also after working with the equations in this paper for the magnetic field from a ring of current. So does anyone know for sure whether this can be solved using the method of images or not?
Note that the analogous electrostatics problem (I think) is a ring of charge around a cylindrical region of different permittivity or a perfect conductor.