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Numerical Optimization of Stellarators with Small Number of Periods

Numerical Optimization of Stellarators with Small Number of Periods.

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Numerical Optimization of Stellarators with Small Number of Periods

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  1. Numerical Optimization of Stellarators with Small Number of Periods M.A.Samitov1, W.A.Cooper2, M.F.Heyn3, M.Yu.Isaev1, A.A.Ivanov4, V.N.Kalyuzhnyj5, S.V.Kasilov5, W.Kerbichler3, A.A.Martinov4, S.Yu.Medvedev4, M.I.Mikhailov1, V.V.Nemov5, C.Nührenberg6, J.Nührenberg6, Yu.Yu.Poshekhonov4, V.D.Shafranov1, A.A.Subbotin1, K.Yamazaki7, R.Zille6 1Russian Research Centre "Kurchatov Institute", Moscow, Russia 2CRPP, Association Euratom-Confederation Suisse, EPFL, Lausanne, Switzerland 3Institut für Theorerishe Physik, Techische Universitàt Graz, Graz, Austria 4Keldish Institute, Russian Academy of Science, Moscow, Russia 5IPP, NSC “Kharkov Institute of Physics and Technology”, Kharkov, Ukraine 6Max-Planck-Institut für Plasmaphysik, IPP-EURATOM Association, Germany 7National Institute for Fusion Science, Toki, Japan

  2. Penalty functions • 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.

  3. Magnetic Surface, N=3 Cross-section at start, at quarter and at a half of period B Poloidal Boozer angle, one period 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.

  4. Magnetic Surface, N=2 Cross-section at start, at quarter and at a half of period B Lines B=constant on the magnetic surface corresponding to 1/2 of minor plasma radius Poloidal Boozer angle, one period Toroidal Boozer angle, one period Boundary magnetic surface of optimized N=2, aspect ratio A~4 and 2.4% system

  5. Example of N=1 system B Boundary magnetic surface of N=1, aspect ratio A~4 and 1.5% system

  6. 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 three- periodical 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

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