Anomalous phenomena in ECRH experiments at toroidal devices and low threshold parametric decay instabilities

Transcription

1 Anomalous phenomena in ECRH experiments at toroidal devices and low threshold parametric decay instabilities Gusakov E.Z., Popov A.Yu. Ioffe Institute of RAS, SPb, Russia 17 th Joint Workshop on Electron Cyclotron Emission and Electron Cyclotron Resonance Heating

2 OUTLINE Common theoretical understanding of parametric decay instability role in ECRH experiments at toroidal machines Resent observations of anomalous phenomena at ECRH experiments in toroidal devices (non local electron transport, fast ion generation and induced backscattering phenomena) New theoretical approach to look for conditions when at least one of the daughter waves is trapped in plasma and therefore its convective losses are suppressed Drastic decrease of the decay instability threshold in the presence of nonmonotonic density profile and magnetic field inhomogeneity leading to Bernstein wave trapping across and parallel to the magnetic field Induced Backscattering t t l IB convective PDI threshold at Textor Anomalous reflection absolute instability threshold and growth rate Anomalous absorption t leb lib and t l absolute UH l UH instabilities threshold and growth rate Possible PDI role in the energy budget Conclusions.

3 The PDI thresholds in ECRH experiment Parametric decay instabilities (PDI) leading to anomalous reflection or absorption of microwave power are believed to be deeply suppressed in tokamak MW power level ECR O-mode and second harmonic X-mode heating experiments utilizing gyrotrons. According to theoretical analysis of PDI thresholds [1-3], the typical RF power at which these nonlinear effects can be excited at tokamak plasma parameters is very high (around 1 GW for induced backscattering), which is only possible with free electron laser application planned in late 8 th at MTX. [1-3]: M. Porkolab et al. Nucl. Fusion 8 (1988) 39; B. Cohen et al. Rev. Mod. Phys. 63, (1991) 949; A. Litvak et al. Phys. Fluids B 5, (1993) 4347 The high PDI threshold is due to strong convective losses of daughter waves from the decay region both along magnetic field and plasma inhomogenuity direction. 3

4 Convective losses along plasma inhomogenuity direction Three-wave resonance (decay) conditions,,, k x k x k x d 1 d 1 d 1 Interaction coherence length d k x k1 x k x l dx 1 x d Spatial amplification coefficient S l exp v v 1 (A.D. Piliya 1971, M. Rosenbluth 197) is the maximal PDI growth rate in homogeneous plasma, proportional to the pump wave amplitude PDI were only observed in 1 kw power range EBW heating experiments (M. Porkolab et Versator, 1983; M. Larionov et FT-1, 1986; G. L-, 1989, H. Laqua et WVII-AS, 1997, V. Shevchenko et al. MAST, 6), where the backscattered and pump wave group velocity is reduced and the pump electric field is increased by the presence of the UHR thus decreasing the PDI power threshold (E.Z. Gusakov et al. 7 Plasma Phys. Control. Fusion 49, 631) 4

5 The parametric decay instabilities in ECRH experiment Present day understanding wave propagation and absorption in O-mode and nd harmonic X-mode ECRH experiments where no UHR exists is well described by linear theory and thus predictable in detail. No anomalous reflection or absorption are expected. However during the last decade a critical mass of observations has been obtained evidencing presence of anomalous phenomena in ECRH experiments at toroidal devices. 5

6 (a) Non local electron transport was shown to accompany ECRH in some devices indicating that the RF power is not deposited in the regions predicted by standard theory, but is rather quickly redistributed all over the plasma. Andreev V.F. et al. Plasma Phys. Control. Fusion. 4. V.46. P The ballistic jump of the total heat flux after ECRH switching on (observations on T-1)

7 (a) Non local electron transport K. Ida et al., Multiple states of electron heat transport inside an internal transport barrier in LHD, 3rd EFDA Transport Topical Group Meeting ) Strong nonlocal power redistribution in LHD ECRH experiments just after pellet injection

8 (b) Ion acceleration accompanying ECRH experiments at TJ-II D Rapisarda, B Zurro, V Tribaldos, A Baciero and TJ-II team, Plasma Phys. Control. Fusion 49 (7)

9 Conditions of nd harmonic ECRH at TJ-II N e 1 13 cm ne(rho)(115.ms)-536 ne(rho)(19.ms)-5331 ne(rho)(174.ms)-5333 ne(rho)(174.ms)-5335 TJ-II magnetic configuration and 54 GHz nd harmonic ECRH scheme r Hollow profile typical for ECRH in TJ-II at low density 9

10 (b) Ion acceleration accompanying ECRH experiments at TCV Christian Schlatter Turbulent Ion Heating in TCV Tokamak Plasmas THÈSE NO 4479 (9)

11 Conditions of nd harmonic ECRH at TCV,E+19 n (m -3 ) 1,E+19,85,9,95 1, 1,5 1,1 R (m) TCV magnetic configuration and nd harmonic ECRH scheme Hollow profile typical for 8.4 GHz ECRH in TCV at low density 11

12 (c) TEXTOR backscattering observations Finally the first observations of the backscattering signal in the 6 kw nd harmonic ECRH experiment at TEXTOR tokamak were reported. This signal down shifted in frequency by approximately 1 GHz, which is close to the lower hybrid frequency under the TEXTOR conditions, was surprisingly strongly modulated in amplitude at the m= magnetic island frequency. E. Westerhof et al. PRL 13, 151 (9) 1

13 (c) TEXTOR backscattering observations This observations performed at the modest RF power under conditions when no UHR was possible for the pump wave provides an indication that probably a novel low threshold mechanism of the PDI excitation is associated with the presence of a magnetic island. E. Westerhof et al. PRL 13, 151 (9) 13

14 The candidates for the role of decay waves Backscattered wave - X-mode vs c t t l 1 Low frequency wave lower hybrid or high harmonic ion Bernstein wave S k l exp v v i s k i k s Ion Bernstein (IB) wave turning point Though the convective losses are supressed in a vicinity of turning points. Still high threshold of PDI (5 MW) at a single turning point due to small size of decay region 14

15 4 x x-bottom o-top o-bottom x-top Shot 1718: q= island phases D IBW localization IBW localization In the radial direction due to local density maximum at O-point of the island ne, m z, m M. Yu. Kantor et al. 9 Plasma Phys. Control. Fusion b ki,x k s,xqx (cm-1 ) ki,xk s,x n qx 3 1 n (1 13 cm -3 ) x (cm) The polidal phase portrait q y (y) showing IBW poloidal localization (Ray tracing procedure) E.Z. Gusakov, A.Yu. Popov PRL15 (1) 1153

16 The ion Bernstein daughter wave equation The coupled wave equations drd r r, r r / r 4 r r r r dq Dr r, Dq, exp iqr r ; 3 D D id pe pe pi D q 1 q 1 X Y cot ce ti qti qti ci exp t X iy dt t io x j ksx Esy i sy The high frequency daughter wave equation 4s c e pe enu iy E 4mes ce x j sy iy (A.Piliya and A. Saveliev 1994 PPCF 36 59) The nonlinear charge density responsible for coupling of low and high frequency waves is provided by a 1 e 4 m e ponderomotive force pe cei Es y E Eiy Es y x x x iy 16

17 In the vicinity of magnetic island O-point situated in the equatorial plane of the torus and coincident to the IB wave turning point the above system can be reduced to differential equation D pe x x y D sin q x q x D b 4 b x, y qx x y L nx L b Solution of the unperturbed equation perturbations xx y xx y bxy (, ) k xly H k Hl exp x y x y 1 L q D q L q 1/4 1/ 1/ / / / ; sin / / x nx x x y b x pe 1 D D q x pe q x kl, k 1sin l1 qx L nx L b 17

18 .. & waveguide perturbation theory k x l y Dk x l y 4 k x l y exp iqxx dydx D id i q 1 D D 3 D 4sin 3 z 3 qx qx qx qx x q x qx y damping correction due to decay instability for the IB waveguide 3 4 x q pe ai x y z bx, y i exp ik exp sy y dx ikxx b x, y 16 i ce H D q pe pi x exp sec 3 ei ce ti qxti qxti ci ci K q k k x ix, sx, ii pi 1 p m ci ci exp ti q x ti q x ti q ti m q ti ex 18

19 The convective PDI threshold t t l IB The imaginary q correction due to decay instability for the IBW cavity The IBW gain coefficient & PDI power threshold q 5/ 3/ pe ai z sin qx x k, l i ce H cot q 1 y z, q x K exp x 3 D x D y q x y q x P th ch i ce kl, pe l 1 y qx x 19

20 The convective PDI power threshold in TEXTOR TEXTOR experimental parameters 13-3 H 19 kgs, f 14 GHz, n31 cm, i Ti 6 ev, 1 cm for the fundamental IB mode Pth 45 kw /.9 GHz,, / 1 MHz,.8 cm,.6 cm y x exp, 1 Dependence of frequency corresponding to maximal IB wave gain on plasma density. (triangles-ti=3ev, circles- Ti=6eV, stars- Ti=9eV) density variation in a nn.1 magnetic island Dependence of the IB wave gain on the radial mode number at P = 4 kw, Circles n = 1 13 cm -3, Stars - n = cm -3 a magnetic island width w 3 cm

21 Absolute PDI threshold for toroidal IBW cavity parametric excitation t t l IB APDI threshold in hollow density profile tokamak: IB D D 1 P th, EC c x IB EC V V PDI damp V V damp PDI R pol APDI threshold in homogeneous plasma: P th P E IB P i EC 1

22 Threshold and growth rate of reflective absolute PDI t t l IB For JET-like tokamak parameters 14-3 n 11 cm T D T e 3 kev f 17GHz H 3 kgs / 1.35GHz

23 nd harmonic EBW trapping and possibility of anomalous absorption For the typical conditions of TCV ECRH experiments Radial trapping of EBW satisfying decay condition for the process t l l EB IB 3

24 nd harmonic EBW trapping and possibility of anomalous absorption For the typical conditions of TCV ECRH experiments Radial and poloidal trapping of second harmonic EBW 4

25 Instability threshold and growth rate For the typical conditions of TCV ECRH experiments / 8.4GHz H 14 Gs, I /.55GHz nm qebx.1 cm 13 3 Ti 1 94 cm, 1 qibx cm 35eV T 36eV 77, e 5

26 UH wave trapping by density maximum and low-threshold two-plasmon decay t l l UH UH pe ce 4 Trapping of UH waves in radial direction in the vicinity of density maximum for Textor magnetic island D localization of UH waves by the pump beam at high enough power corresponding to absolute instability onset 6

27 Absolute PDI growth rate and threshold for two-uh-plasmon decay P 6kW The dependence of the growth rate on the pump wave power for Textor magnetic island parameters. s p1, T 5 ev, w w 1 cm, e y z /, q, k l 13, P 16 kw. th y The dependence of the growth rate on the waist of the beam along the magnetic field. See A. Popov On possibility of low-threshold two-plasmon decay instability in second harmonic ECRH experiments at toroidal devices P1-1 at EC-17

28 Possible role of PDI in energy balance in ECRH experiments D Rapisarda, B Zurro, V Tribaldos, A Baciero and TJ-II team, Plasma Phys. Control. Fusion 49 (7) Up to 38 kw absorbed by ions is needed at TJ-II to explain observed ion heating at ECRH power of 4 kw which is a lot because energy is distributed in PDI proportionally to wave frequency 8

29 Possible role of PDI in non local electron transport Nonlocal Transport Phenomena is observed when the electron density profile becomes hollow! 9

30 Conclusions-1 Drastic decrease of parametric decay instability power threshold is provided by non monotonous profile of plasma density, which is routinely observed at the discharge axis, in the vicinity of magnetic islands or blobs and at the plasma edge due to electron pump out effect or pellet injection. Acting in parallel with poloidal magnetic field inhomogeneity it makes possible localization of Bernstein decay waves and suppression of their convective losses. The typical backscattering t t l IB convective parametric decay instability pump power threshold is estimated at the level of less than 1 kw. Based on the convective PDI the absolute t t l IB decay instability can be excited for hollow density profile in tokamak. The non monotonous density profile can lead to trapping of decay EBWs as well, thus making possible the low-threshold anomalous absorption t l l at ECRH Trapping of the UH waves at the non monotonous density profile leads to lowthreshold excitation two-plasmon absolute decay instability t l l UH EB UH IB 3

31 Conclusions- The low threshold anomalous absorption and reflection most likely play a role in anomalous backscattering at TEXTOR and ion acceleration and heating at TJ-II and TCV accompanying ECRH. The low threshold anomalous absorption and reflection can, in principle, lead to reduction of ECRH efficiency and quick change of its localization which is interpreted in terms of so called non local electron transport effect. The low threshold PDIs are potentially dangerous for ECRH in ITER therefore their excitation and consequences should be studied in the present day experiments. The physical reasons of density peaking in the magnetic island and electron-pumpout effect deserve systematic investigation as well. 31

32 PDI and non local electron transport in ECRH experiments Local maximum of the density profile Threshold of the PDI decreases drastically Excitation of the backscattered EC wave with downshifted frequency, which is then reflected from the wall and absorbed diffusively Power deposition profile of daughter EC waves differs from the one predicted by linear theory 3

33 Quasi-linear saturation of absolute PDI Strong stochastic damping of the IBW ci t, th B 4q 1/3 ci q c x x C.F.F. Karney and A. Bers Phys. Rev. Lett. 39, 55 (1977)

34 Quasi-linear saturation of absolute PDI D QL th pi th exp H 1 ti qxti qx ti For JET-like parameters H th -Heaviside function When the PDI pumping exceeds the perpendicular Landau damping the quasi-linear saturation fails. Above this second threshold ion tails generation, spectral cascades and significant modification of power deposition profile can occur.