Numerical Optimization of Stellarators with Small Number of

Numerical Optimization of Stellarators with Small Number of Periods M. A. Samitov 1, W. A. Cooper 2, M. F. Heyn 3, M. Yu. Isaev 1, A. A. Ivanov 4, V. N. Kalyuzhnyj 5, S. V. Kasilov 5, W. Kerbichler 3, A. A. Martinov 4, S. Yu. Medvedev 4, M. I. Mikhailov 1, V. V. Nemov 5, C. Nührenberg 6, J. Nührenberg 6, Yu. Poshekhonov 4, V. D. Shafranov 1, A. A. Subbotin 1, K. Yamazaki 7, R. Zille 6 1 Russian Research Centre "Kurchatov Institute", Moscow, Russia 2 CRPP, Association Euratom-Confederation Suisse, EPFL, Lausanne, Switzerland 3 Institut für Theorerishe Physik, Techische Universitàt Graz, Austria 4 Keldish Institute, Russian Academy of Science, Moscow, Russia 5 IPP, NSC “Kharkov Institute of Physics and Technology”, Kharkov, Ukraine 6 Max-Planck-Institut für Plasmaphysik, IPP-EURATOM Association, Germany 7 National Institute for Fusion Science, Toki, Japan

Penalty functions include: • pseudo-symmetry condition; • condition of closure of the second adiabatic invariant contours; • Mercier, resistive and ballooning modes stability; • Cross-section geometry restrictions (to prevent high elongation, narrow angles and concaves) Obtained systems • N=3, aspect ratio A~6. 8, <β>=3. 9% • N=2, aspect ratio A~3. 9, <β>=2. 4% both with improved particle confinement and Mercier and ballooning modes stability.

Magnetic Surface, N=3 Cross-section at start, at quarter and at a half of period Poloidal Boozer angle, one period B Toroidal Boozer angle, one period Boundary magnetic surface of optimized N=3, aspect ratio A~7 and 4% system and lines B=constant on the magnetic surface corresponding to 1/2 of minor plasma radius.

Magnetic Surface, N=2 Cross-section at start, at quarter and at a half of period B Poloidal Boozer angle, one period Lines B=constant on the magnetic surface corresponding to 1/2 of minor plasma radius Toroidal Boozer angle, one period Boundary magnetic surface of optimized N=2, aspect ratio A~4 and 2. 4% system

Example of N=1 system B Boundary magnetic surface of N=1, aspect ratio A~4 and 1. 5% system

Conclusions Investigation were performed on optimization of stellarator configurations with poloidal direction of B-lines with small number of system periods. Boundary magnetic surfaces were obtained for two- and threeperiodical systems with improved collisionless particle confinement and with Mercier and ballooning modes stability. For these systems, requirement of the ballooning stability partially is in contradiction with quasi-isodynamicity condition and leads to increased losses. In future plans: - Investigate β limit for stability consistent with confinement - Optimization of N=1 system