Eigenfunctions of the curl in cylindrical geometry Available to Purchase

Eigenfunctions of the equation $∇⃗×B⃗=λB⃗$ are found for finite cylindrical geometry with normal boundary condition $B⃗∙n̂=0$ and nonaxisymmetric modes $∼eimθ,m≠0$⁠. The vector field $B⃗$ can be represented by a scalar generating function of the Chandrasekhar-Kendall type with radial Bessel functions for the nondegenerate cases. A general set of solutions can also be generated by transformation of variables. A series solution in terms of radial Bessel functions is found which has excellent convergence properties $(an∼1∕n4)$ and a robust method of locating eigenvalues is described.