Consider the equations $$\textbf j=\mu\textbf B$$ $$\nabla \wedge \textbf B=\mu_0\textbf j=\mu_0\mu\textbf B$$ where $\mu_0, \ \mu$ are constants. Then, $$\nabla \wedge \textbf B=\mu_0\mu\textbf B$$ which in cyclindrical coordinates ${\bf B} = (B_\rho,B_\theta,B_z)$ leads to a Bessel function solution $$B_z = B_0 J_0(\mu_0\mu \rho) \\ B_\theta = B_0J_1(\mu_0\mu \rho) \\ B_\rho = 0$$
How do I do this? Isn't Bessel solution for Laplace equation, not curl?