1 ST workshop 2008 Conception of LHCD Experiments on the Spherical Tokamak Globus-M O.N. Shcherbinin, V.V. Dyachenko, M.A. Irzak, S.A. Khitrov A.F.Ioffe Physico-Technical Institute, St.Petersburg, Russia

2 Outline 1. Specific features of LHCD experiments on spherical tokamaks. 2. Ray tracing in spherical tokamaks. 3. Full-wave 2D modeling of wave propagation in the Globus-M. 4. Simulation of the GRILL antenna. Spectra. Wave reflection. 5. Design of the LHCD system for the Globus-M.

3 The Main Problems in LHCD Experiments on Spherical Tokamaks In conventional tokamaks: ω pe ≈ ω Be N ||cr  1.5–1.8 In spherical tokamaks: ω pe » ω Be N ||cr  7–10 1.for such high N || the coupling efficiency is very poor and 2.RF energy is absorbed at the periphery

4 The New Approach in LHCD Experiments on Spherical Tokamaks In spherical tokamaks the strong poloidal inhomogeneity of the magnetic field (due to low aspect ratio and high elongation) allows a new approach: 1. Waves with comparatively low N || (3–5) should be excited in poloidal rather than toroidal direction. 2.Waves propagate at first at the plasma periphery, their N || is increased due to the poloidal inhomogeneity, and finally they penetrate into the dense plasma. 3.Absorption of the waves takes place in the vicinity of poloidal resonance by Landau damping on electrons.

5 Experimental Set-up for LHCD in Globus-M R=0.36 m, a=0.24 m, B 0 =0.4 T, I p =0.25 MA, vertical elongation – 1.6, triangularity – 4 cm, n 0 =4·10 13 cm -3, n b =1·10 11 cm -3, T e0 =400eV f=2450 MHz x y z x y z R B pol I pl, B 0

6 Poloidal Resonances I p =250 kA f=2450 MHz f=3000 MHz N  N   In 2D geometry 2 conditions are necessary: I p =210 kA f=2450 MHz (blue curves) (red ovals)

7 Ray Trajectory at N tor0 = 0, N pol0 = Red lines – ray trajectory, blue line – N par, green line – wave absorption a) b) c) x, cm

8 Ray Trajectory at Starting Stage 1.Ray is allowed to propagate in one poloidal direction only. 2.Ray starts in a kind of plasma waveguide, between conversion layer and critical density. 3.Ray turns gradually in toroidal direction and runs against plasma current. “Projection on the wall” Projection on the poloidal cross-section

9 Ray Trajectory at N tor0 = 0, N pol0 = -3.8 Red lines – ray trajectory, blue line – N par, green line – wave absorption

10 Full absorption position (in rho units) in the range of N pol0 = -3.3 – -4.1 This range of N pol corresponds roughly to excited wave spectra (calculated)

11 Simulation by Full-Wave 2D Code Simplifying assumptions: 1. The dimensions of the installation and plasma current value were diminished by 2 times 2. The shape of magnetic flux surfaces was calculated by formula, but not by equilibrium code 3. The electric fields at the antenna output were taken not self- consistent with plasma response The external field spectrum, created by the grill antenna: 8 waveguides, 

12 Comparison of Full-Wave Modeling and Ray-Tracing Result 8 waveguides with  Black “islands” – Landau damping regions N pol0  3.8 RF field distribution

13 Excitation of Fields with Opposite Phasing 8 waveguides with  N pol0 =

14 RF Energy Deposition Profiles 1.Waves propagate in -  direction only. 2.At opposite phasing the wave excitation is determined by additional (smaller) peak in the external field spectrum. 8 waveguides Solid line -  Dashed line - 

15 Self-consistent Grill Modeling 1.The surface impedance matrix was found by solving the problem of wave propagation in a 1D plasma slab with parameters corresponding to the Globus-M equatorial plane. 2. The waves entering the plasma were assumed to be absorbed in the plasma depth. 3. The impedance matrix played the role of boundary condition for 3D simulation of antenna operation. 4. The basic configuration of grill includes 12 waveguides of 8.5 mm height, stacked vertically, one atop the other. No multi-junction scheme was used. 5. Higher reflected modes in waveguides were taken into account to obtain self-consistent solution.

16 Grill Modeling. Wave Spectra. K refl =25%   K refl =44%  

17 2D Wave Spectra     Solid blue line – magnetic field direction

18 Waveguide Phasing 1 st peak2 d peak ΔφN pol PowerN pol PowerK refl 60° % %53.7% 90° % %25.2% 105°-4.047% %22% 120° % %25% 150°-5.842% %40%

19 Waveguide Phasing Optimal range of phasing – degrees. Coefficients of total reflection at change of phasing

20 Change of Spectra at Grill Tilting. Δα=+12° Δα=+8° Δα=−8° 1 st peak 17% 34% 43% 50% 2 nd peak 80% 60% 41% 24% Solid blue line – magnetic field direction, red – waveguide broad side direction

21 Ray Trajectory at N tor0 = -1.5, N pol0 = -17.8

22 RF System Set-up

23 Conclusions 1. It was found that there exists a rather wide range of experimental condition when LH waves excited by a grill in poloidal direction propagate in peripheral plasma layer, turn gradually in toroidal direction and enter the bulk plasma. The allowed direction of poloidal propagation is determined by direction of toroidal magnetic field. The waves propagate toroidally against plasma current that is favorable for current drive perspective. 2. The absorption of the waves in present experimental condition in Globus-M takes place at ρ = 0.6 – 0.8. At higher plasma current the absorption region shifts to ρ ≈ The lowest reflection coefficients in grill operation are 20% – 25%. At later stages the multi-junction scheme will be used, which will enhance the efficiency of the antenna operation. 4.The starting stage, when the waves propagate in peripheral plasma layer, is the most dangerous for success of experiments. It is difficult now to evaluate parasite wave absorption in this stage and role of vessel walls in the process. The classical collisions do not seem to be dangerous in this respect. The work was supported by the RFBR grant

24 Wave Spectra at out-phase excitation 6 waveguides of 17 mm height   K refl =34% 9% 24.4% 44% 20%

25 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 ratio Vertical elongation Triangularity Average density1  m  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