poloidal magnetic flux

source current

source radius

source height

field point radius

field point height

max distance parameter $k_{\max}^{2}$

$k_{\max}^{2} = \frac{4 r r_{0}}{\left( r + r_{0} \right )^{2} + \left( z - z_{0} \right )^{2}}$

min distance parameter $k_{\min}^{2}$

$k_{\min}^{2} = \frac{4 r r_{0}}{\left( r - r_{0} \right )^{2} + \left( z - z_{0} \right )^{2}}$

Green function G

$G \left( r , z ; r_{0} , z_{0} \right ) = \frac{\mu_{0}}{\pi k} \sqrt{r r_{0}} \left[ \left( 1 - 0.5 k^{2} \right ) K \left( k \right ) - E \left( k \right ) \right ]$

poloidal magnetic flux $\Psi$

$\Psi = G I_{0}$

max distance $d_{\max}$

$d_{\max}^{2} = \left( r_{1} + r_{0} \right )^{2} + \left( z_{1} - z_{0} \right )^{2}$

min distance $d_{\min}$

$d_{\min}^{2} = \left( r_{1} - r_{0} \right )^{2} + \left( z_{1} - z_{0} \right )^{2}$

Green function  $G_{2}$

$G_{2} = \frac{\mu_{0}}{2} \left[ - d_{\min} E \left( - k_{\min}^{2} \right ) - d_{\max} E \left( k_{\max}^{2} \right ) + \left( k_{\min} + d_{\min} \right ) K \left( - k_{\min}^{2} \right ) + \left( d_{\max} - k_{\max} \right ) K \left( k_{\max}^{2} \right ) \right ]$