Reformulation of the Fourier-Bessel steady state mode solver using Ampere's and Faraday's law.

Matrix perturbation technique developed for the Fourier-Bessel mode solver.

Three forms of the system matrix and perturbation matrix are provided.

Matrix generating expressions provided.

System matrix order reduction is presented which is possible using structure symmetry and sectioning eigenstates into mode families.

Discussion of rotational space mode families, mixing and field properties.

Two perturbation symmetry examples are presented, one for on symmetry perturbation, one for off symmetry perturbation.

The simplified nature of the reformulated perturbative Fourier-Bessel numerical solver makes it attractive to all researchers with a moderately performant desktop PC.