1. Mariya Korzhavina Budker Institute of Nuclear Physics, Novosibirsk, Russia Study of microinstabilities in anisotropic plasmoid of thermonuclear ions 8 th International Conference on Open Magnetic Systems for Plasma Confinement

2. View of the Gas Dynamic Trap facility

3. General layout of gas dynamic trap (GDT) Length 7 m Magnetic field: center 0.3 Т mirror up to 12 Т Mirror ratio B m /B c ≈ 35 Target plasma: 10 13 -10 14 cm -3, 150 eV Fast ions (H +,D + ): ~10 13 cm -3, ≈10 keV

4. Experiment with compact mirror cell at the Gas Dynamic Trap

5. Compact mirror at GDT Experiment: 2ρ fi >1; β >E ||. Compact mirror cell (CM): L = 30 cm, D = 70 cm. Magnetic field: B 0 = 2.4 T, B m = 5.2 T Background plasma: hydrogen, n w ≈ 10 13 cm -3, T w ≈ 150 eV, a w = 9 cm. CM NBI system: hydrogen, E 0 = 20 keV, θ = 90º, P inj ≈ 1 MW, τ inj = 4 ms, a f = 8-10 cm. Strong high-frequency oscillations of plasma potential during accumulation of the fast ions in the compact mirror Compact mirror cell GDT central cell

6. Early studies of microinstabilities M.S.Ioffe, B.B.Kadomcev, Uspekhi Fizicheskih Nauk, vol. 100, № 4, 1970 R.F.Post, Nuclear fusion, Vol.27, 1987 F.H.Coensgen, et al. Phys.Rev.Letters, Vol.35, 1975, [2XIIB] T.A.Casper, G.R.Smith, Phys.Rev.Letters, Vol.45, 1982, [TMX] M. Ichimura, et al. Phys.Rev.Letters, Vol.70, 1993, [Gamma-10]

7. DCLC The drift-cyclotron losscone instability k ║ « k ┴ k || = 0 ω ≈ ω ci AIC The Alfven ion- cyclotron instability k ║ » k ┴ k ┴ = 0 ω < ω ci Microinstabilities in anisotropic plasma

8. Estimation of developing DCLC and AIC in the compact mirror of GDT DCLC Stabilization by addition of small amount of warm ions: n w /n f > 0.06 GDT CM: n w /n f ≈ 0.1 AIC Instability grows if: β ┴ A > const GDT CM: A ≡ / ≈ 50, β ┴ ≈ 0.02 βA ≈ 1 R.F.Post, Nuclear fusion, Vol.27, 1987 M.J.Gerver, The Phys. of Fluids, Vol.19,1976 D.C.Watson, Phys.Fluids 23,1980

9. High-frequency oscillations in plasmoid have been observed with special HF Langmuir and magnetic probes Set of special HF Langmuir probes Tree orthogonal loops of the HF magnetic probe. 10 mm

10. Modes: k = m/r p r p = 4.5 cm m ≈ 1-6 Layout of the HF Langmuir probes system in the compact mirror of GDT

11. HF magnetic probe

12. Oscillation frequency: f osc = 39.7 ± 0.2 MHz B midplane = 27.6 ± 0.3 kGs f ci = 42 ± 0.5 MHz Cross amplitude spectrum f osc f ci

13. Voltage oscillations induced in loops of magnetic probe

14. Rotation of the wave magnetic field vector Rotation in the direction of ion gyration

15. Mode structure analysis, azimuthal modes Azimuthal mode m = 1, rarely 2.

16. Observation of AIC in the compact mirror of the GDT Частотный спектр колебаний f0f0 f ci Cross amplitude spectrum f0f0 f ci Phase variation, radian Azimuthal probe separation, radian m=1 m=2 RF Langmuir probes : frequency, azimuthal modes Magnetic probes: polarization Azimuthal vs radial induced loop voltages. The field vector rotates in the direction of ion gyration. Azimuthal number m ~ 1- 2 Main frequency f 0 < f ci The magnetic field vector of the wave rotates in the direction of ion gyration. AIC

17. Threshold of the oscillations Diamagnetism of fast ions in the compact mirror Amplitude of HF oscillations induced on magnetic probe n >3 х 10 13 сm -3 A ≈ 40; β ┴ = 0.02 =>  ┴ A ~ 1.  сi /а p ≈ 0.23 Anisotropy of the ion plasmoid

18. Results: Microinstability developing in the compact mirror is Alfven ion- cyclotron (AIC). This was proved by observing small azimuthal modes numbers m = 1–2, oscillation frequency below the diamagnetically depressed ion-cyclotron frequency and rotation of the magnetic field of the wave in the direction of ion gyration. The threshold of the AIC fluctuation was determined relative to the density of hot ions, ratio of ion pressure to magnetic field pressure β, anisotropy A and the ion gyroradius to the plasmoid radius ratio a i /R p. AIC microinstability developed when the density of hot ions n f was greater than 3x10 13 cm -3, β ≈ 0.02, anisotropy A ≈ 50, for the ratio a i /R p of about 0.23. Experimentally was confirmed the criteria which defines the stability region  A < 1. Alfven ion cyclotron instability developing in the CM GDT does not lead to the significant particle loss and plasma parameters limitation.

19. Thank you!

20. Dots – experimental data, solid line – calculation (ITCS). Dependence of fast ion density in the compact mirror of GDT on the trapped power

21. Регистрация AIC на TMX Электрические зонды: частота и модовый состав Магнитные зонды: поляризация T.A.Casper, G.R.Smith, Phys.Rev.Letters, Vol.45, 1982 |m| ≈ 4 f 0 < f ci Вращение магнитного поля волны в направлении ларморовского движения ионов AIC

22. Анализ модового состава, продольные моды DCLC: набег фазы между средним зондом в КП и зондом в расширителе, силовая линия 15.5 cm – от выстрела к выстрелу случайный DCLC нет

23. Параметры ГДЛ: c / R p ω ci ≈ 18 ; ω 2 ci / ω 2 pi ≈ 6.410 -4 Стабилизация теплыми ионами: n w /n f > 0.06 ГДЛ: n w /n f ≈ 0.1 R.F.Post, Nuclear fusion, Vol.27, 1987 M.J.Gerver, The Phys. of Fluids, Vol.19,1976 Оценки для DCLC мод в КП ГДЛ

24. Оценки для AIC мод в КП Критерий развития неустойчивости: ГДЛ: A ≡ / = 50, β = 0.02 βA ≈ 1 При β ║ ~ β ┴ « 1 β ║ < const * β ┴ 2 или (β ║, β ┴ ) → (A, β ┴ ) : β ┴ A > const D.C.Watson, Phys.Fluids 23,1980 T.A.Casper, G.R.Smith, Phys.Rev.Letters, Vol.45, 1982 βA 2 > 8 TMX ? Параметры ГДЛ: β ║ < β ┴ ~ 0.02

25. DCLC и AIC на установках 2X||B и TMX 2XIIB : основная неустойчивость – DCLC, TMX: основная неустойчивость – AIC,

26. Корреляционный анализ Взаимная корреляционная функция: Сигналы с зондов φ 1 (t), φ 2 (t) → БПФ → Спектральная плотность взаимной корреляционной функции:

27. Сделаем преобразование Фурье