Eigenfunctions of the curl in cylindrical geometry

Abstract

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.