Toroidal current density

Ampere's law (36) indicates the toroidal current density $J_{\phi}$ is given by

$$\mu_0 J_{\phi} = \frac{\partial B_R}{\partial Z} - \frac{\partial B_Z}{\partial R}$$

$$= - \frac{1}{R} \frac{\partial^2 \Psi}{\partial Z^2} - \frac{\partial}{\partial R} \left( \frac{1}{R} \frac{\partial \Psi}{\partial R} \right)$$ (39)

Define a differential operator

$$\triangle^{\ast} \Psi \equiv \frac{\partial^2}{\partial Z^2} + R ... ...rtial}{\partial R} \left( \frac{1}{R} \frac{\partial \Psi}{\partial R} \right),$$ (40)

then Eq. (39) is written

$$\mu_0 J_{\phi} = - \frac{1}{R} \triangle^{\ast} \Psi .$$ (41)