Electric current dynamics in the stellarator coil winding surface model
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866917314023129088 |
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| author | Gerner, Wadim Nicolopoulos-Salle, Anouk Botelho, Diego Pereira |
| author_facet | Gerner, Wadim Nicolopoulos-Salle, Anouk Botelho, Diego Pereira |
| contents | In stellarator design, the coil winding surfaces $Σ\subset\mathbb R^3$ support current distributions $j$ that shape the magnetic field. This work provides a theoretical framework explaining the emergence of centre and saddle point regions, a key feature in coil optimisation. For coil winding surfaces with a toroidal shape, we prove a dichotomy principle: the current distribution has both centre and saddle point regions or is no-where vanishing. For coil winding surfaces that consist of piecewise cylinders, we show that if $j$ is oppositely oriented on the two boundary circles, centre and saddle points appear, and all but finitely many field lines of $j$ are periodic. When $j$ admits a harmonic potential, all field lines are closed poloidal orbits. These results offer insights into current patterns on winding surfaces, with implications for coil design strategies and their simplification. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_04085 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Electric current dynamics in the stellarator coil winding surface model Gerner, Wadim Nicolopoulos-Salle, Anouk Botelho, Diego Pereira Plasma Physics Mathematical Physics Dynamical Systems 31A35, 37E35, 37N20, 37C25, 37C27, 37C10, 37C20, 78A30, 78A55 In stellarator design, the coil winding surfaces $Σ\subset\mathbb R^3$ support current distributions $j$ that shape the magnetic field. This work provides a theoretical framework explaining the emergence of centre and saddle point regions, a key feature in coil optimisation. For coil winding surfaces with a toroidal shape, we prove a dichotomy principle: the current distribution has both centre and saddle point regions or is no-where vanishing. For coil winding surfaces that consist of piecewise cylinders, we show that if $j$ is oppositely oriented on the two boundary circles, centre and saddle points appear, and all but finitely many field lines of $j$ are periodic. When $j$ admits a harmonic potential, all field lines are closed poloidal orbits. These results offer insights into current patterns on winding surfaces, with implications for coil design strategies and their simplification. |
| title | Electric current dynamics in the stellarator coil winding surface model |
| topic | Plasma Physics Mathematical Physics Dynamical Systems 31A35, 37E35, 37N20, 37C25, 37C27, 37C10, 37C20, 78A30, 78A55 |
| url | https://arxiv.org/abs/2603.04085 |