Pfirsch-Schl\"uter Current

The Pfirsch-Schl\"uter current is a current that flows along the magnetic field lines in a toroidal plasma equilibrium that is required to make the plasma current density divergence free in the presence of a plasma-pressure gradient. A distortion in the plasma shape is caused by the Pfirsch-Schl\"uter current, and it is desirable to minimize both the strength and the distance this current flows along the magnetic field lines. The Pfirsch-Schl\"uter current is localized within a half period of a stellarator when $d\ell/B$ integrated over the half period is the same for all lines in the magnetic surface. It is shown that within parts in a thousand this is the same condition as the distance $\ell_{p/2}$ required for a field line to cross the half period being the same for all lines in the surface. To make the $\ell_{p/2}$'s the same, the lines started on the small major radius side of the plasma must undergo wiggles to make their $\ell_{p/2}$ as long as those started on the outboard side. This is achievable either using modular coils with a large helical component on the small major radius side or with a central column carrying a helical current.