Equilibrium Plasma Current Density

Let ${\bf j}$ be the equilibrium electric current density. The Maxwell equation $\mu_0\,{\bf j} = \nabla\times{\bf B}$ yields

$$\mu_0\,{\cal J}\,j^{\,r} =0,$$ (14.27)

$$\mu_0\,{\cal J}\,j^{\,\theta} = - B_0\,R_0\,\frac{dg}{dr},$$ (14.28)

$$\mu_0\,{\cal J}\,j^{\,\varphi} = B_0\,\frac{\partial}{\partial r}\!\left(r\,f\,\vert\nabla r\ver... ...,\frac{\partial}{\partial\theta}\!\left(r\,f\,\nabla r\cdot\nabla\theta\right),$$ (14.29)

where use has been made of Equations (14.14)–(14.16) and (14.22)–(14.24).