Pfirsch-Schlüter Current
Abstract
The Pfirsch-Schlüter 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-Schlüter current, and it is desirable to minimize both the strength and the distance this current flows along the magnetic field lines. The Pfirsch-Schlüter current is localized within a half period of a stellarator when dℓ/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 ℓs required for a field line to cross the half period being the same for all lines in the surface. To make the ℓs's the same, the lines started on the small major radius side of the plasma must undergo wiggles to make their ℓs as long as those started on the outboard side. This is generally achieved using modular coils with a large helical component on the small major radius side but could be achieved with a central column carrying a helical current.
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BibTeX
@misc{boozer2026pfirschschlüter,
title = {{Pfirsch-Schlüter Current}},
author = {Allen H Boozer},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2605.21637},
eprint = {2605.21637},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.21637},
}
RIS
TY - UNPB
TI - Pfirsch-Schlüter Current
AU - Allen H Boozer
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2605.21637
UR - https://arxiv.org/abs/2605.21637
AB - The Pfirsch-Schlüter 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-Schlüter current, and it is desirable to minimize both the strength and the distance this current flows along the magnetic field lines. The Pfirsch-Schlüter current is localized within a half period of a stellarator when dℓ/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 ℓ_s required for a field line to cross the half period being the same for all lines in the surface. To make the ℓ_s's the same, the lines started on the small major radius side of the plasma must undergo wiggles to make their ℓ_s as long as those started on the outboard side. This is generally achieved using modular coils with a large helical component on the small major radius side but could be achieved with a central column carrying a helical current.
ER -