where J m is the Bessel function, k = ± ± 2 π π n / L , n = 0 , 1 , 2 , … … , the integers m = 0 , ± ± 1 , ± ± 2 , … … and μ μ j is determined by the boundary condition a k μ μ j J m ′ ( μ μ j a ) + m λ λ J m ( μ μ j a ) = 0. The eigenvalues for m = n = 0 has to be dealt separately. Since here n ^ ^ = e z , we can think of z direction to be toroidal and θ θ direction to be poloidal, consistent with the convention.