1
$\begingroup$

$\newcommand{\dv}[2]{\frac{\mathrm{d} #1}{\mathrm{d}#2}}$ I'm trying to find the path a magnetic field line takes along an axially symmetric magnetic surface.

I'm given: - $r,z$ points along a poloidal contour (ie a slice at one toroidal position) - $B_r$, $B_z$, $B_\phi$ at each one of these points - the number of times it must wrap around poloidally for each time it goes around toroidally - It wraps back onto itself (ie the last point is the first point)

So basically I need the $\phi$ points for each one of these $r,z$ points. So I know that $$\dv{r}{z}= \frac{B_r}{B_z}$$, but how would that work for phi because $\dv{\phi}{r}$ does not equal $\frac{B_\phi}{B_r}$.

$\endgroup$
0
$\begingroup$

The answer for small $\mbox{d}r$ and $\mbox{d}\phi$ is to use \begin{equation} \frac{r\mbox{d}\phi}{\mbox{d}r} = \frac{B_\phi}{B_r} \end{equation}

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.