\nabla\times\mathbf{H}=\mathbf{a}_r\left(\frac{\partial H_z}{r\partial \alpha}-\frac{\partial H_\alpha}{\partial z}\right)+
\mathbf{a}_\alpha\left(\frac{\partial H_r}{\partial z}-\frac{\partial H_z}{\partial r}\right)+
\mathbf{a}_z\left[\frac{\partial (rH_\alpha)}{r\partial r}-\frac{\partial H_r}{r\partial \alpha}\right]