1. 1 ST workshop 2005 Numerical modeling and experimental study of ICR heating in the spherical tokamak Globus-M O.N.Shcherbinin, F.V.Chernyshev, V.V.Dyachenko, V.K.Gusev, Yu.V.Petrov, N.V.Sakharov A.F.Ioffe Physico-Technical Institute, St.Petersburg, Russia

2. 2 Outline 1. Specific features of ICRH experiments on spherical tokamaks. 2. Model for numerical simulation. 3. Effect of light ion content in plasma on RF heating efficiency (simulation and experiment). 4. Effect of the second hydrogen harmonic position on ion heating.

3. 3 Specific features of ICR heating at small plasma aspect ratio Due to strong variation of toroidal magnetic field along major radius, several ion cyclotron harmonics exist simultaneously in plasma cross- section. For typical conditions of spherical tokamaks (low B t and high n e ) it is necessary to use low frequency RF power (5- 10 МHZ). So the wavelength is much larger than plasma dimensions and width of resonance and cut-off zones. Tokamak Globus-M operates with high hydrogen concentration (10-50)% in deuterium plasma. The shadow of the limiter in Globus-M is too shallow to place there a multi-element antenna to excite a well shaped wave spectra.

4. 4 Cyclotron Harmonics in Globus-M Magnetic fields in equatorial plane of Globus-M  cD  cD,  cH  cD Cyclotron harmonic positions in Globus-M cross-section for 7.5 MHz at B 0 =0.4 T

5. 5 Dispersion Curves for 7.5 MHz Blue lines – FMS waves, red lines – Bernstein waves Broken lines – imaginary part of refractive indices

6. Model accepted for numerical simulation Plasma is confined between two cylindrical surfaces. All plasma parameters change in radial direction only. They follow the behavior of plasma parameters in the equatorial plane of the real Globus-M tokamak. Cyclotron absorption, magnetic pumping and Landau damping are included in the code. The effects related to poloidal inhomogeneity are absent in the calculations. Spectra of excited waves are calculated using 3-D antenna model.

7. 7 RF Energy Absorption Profiles absorption by electrons (TTMP and Landau damping) absorption by protons and by deuterons (cyclotron absorption and Bernstein wave absorption)

8. 8 Spectrum excited by a single-loop antenna The peaks correspond to resonator modes excited in the chamber (calculated in the cylindrical geometry). The broken line shows the idealized spectrum if all excited waves are completely absorbed in the plasma without any reflection from inner plasma layers.

9. 9 Spectra excited by various antennas Spectrum of single-loop antenna Spectrum of a set of 4 one- loop antennas (in 0π0π mode).

10. 10 RF Energy Absorption Profiles in case of 4 antennas absorption by electrons (TTMP and Landau damping) absorption by protons and by deuterons (cyclotron absorption and Bernstein wave absorption)

11. 11 Comparison of absorption profiles for different antennas - 1 A single-loop antenna A set of 4 antennas

12. 12 Comparison of absorption profiles for different antennas - 2 A single-loop antennaA set of 4 antennas

13. 13 Energy Spectra of Ions with/without RF pulse I P = 185 kA n e (0)=3.10 19 m -3 P inp = 120 kW f = 7.5 MHz

14. 14 Evolution of Ion Temperature with/without RF pulse I P =185 kA n e (0)=3.10 19 m -3 P inp = 120 kW f = 7.5 MHz RF

15. 15 Ion heating in dependence on H- concentration B t /B t0 =1 In OH-regime T D =T H =180-200 eV The 2nd H-harmonic is absent in the plasma volume. B 0 = 0.4 T, n e (0) ≈ 3.10 19 m -3, I P = 195 – 230 kA, f = 7.5 MHz, P inp = 120 kW.

16. 16 RF energy absorption profiles for C H =20% calculated for equatorial Globus-M parameters: B o = 0.4 T, I p = 200 kA, N e (0)= 5  10 13 cm -3. absorption by electrons (TTMP and Landau damping) absorption by protons and by deuterons (cyclotron absorption and Bernstein wave absorption)

17. Ion Temperature Behavior in dependence on B t B t0 =0.4 T I p = 190-210 kA C H =15%, 30% f = 7.5 MHz P inp = 120 kW In OH regime T D =180-200 eV

18. 18 T H /T D ratio in dependence on B t B t0 =0.4 T I p = 190-210 kA C H =15% f = 7.5 MHz P inp = 120 kW In OH regime T D =180-200 eV a=23 cm r – position of 2nd H- harmonic in cross-section at given B t /B to 26 cm21 cm r=17,5 cm 23

19. 19 Ion heating in dependence on H- concentration with/without the 2nd H-harmonic B t /B t0 =1 B t =0.8B t0 In OH-regime T D =T H =180-200 eV

20. 20 Conclusions  The ICRF heating experiments were carried out on the Globus-M spherical tokamak where conditions for several cyclotron harmonics were fulfilled simultaneously.  The experiments with hydrogen-deuterium plasma have shown that the ion heating efficiency does not practically depend of concentration of light ion component but increases slightly with rise of C H from 10% to 70%.  It is shown that presence of 2nd H-harmonic in front of the antenna diminishes efficiency of on-axis ion heating.  Experimental results are in agreement with numerical modeling by 1-D wave code.

21. 21 Globus-M RF antenna Outside arrangement

22. 22 RF antenna set-up and voltage distribution in the antenna resonator

23. 23 Globus-M characteristics ParameterDesignedAchieved Toroidal magnetic field 0.62 T0.55 T Plasma current0.5 MA0.36 MA Major radius0.36 m0.36 m Minor radius0.24 m0.24 m Aspect ratio1.51.5 Vertical elongation2.22.0 Triangularity0.30.45 Average density1  10 20 m -3 0.7  10 20 m -3 Pulse duration0.2 s0.085 s Safety factor, edge4.52 Toroidal beta25%~10% OH ICRF power1.0 MW0.5 MW Frequency8 -30 MHz7–30 MHZ Duration30 mc30 mc NBI power1.0 MW0.7 Mw Energy30 keV30 keV Duration30 mc30 mc

24. 24 Dispersion Curves for 9.1 MHz

25. 25 Magnetic Field Distribution In equatorial plane of the Globus-M chamber R 0 = 36 cm, a 0 = 23 cm B 0 = 0.4 T, I p = 250 kA, f=9 MHz blue line – toroidal vacuum field green line – poloidal field violet line – paramagnetic field red line – full magnetic field dashed red line – full magnetic field without paramagnetic component