1 EX/11-2Ra The Isotope Effect in GAM Turbulence Interplay and - - PDF document

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EX/11-2Ra The Isotope Effect in GAM – Turbulence Interplay and Anomalous Transport in Tokamak

A.D. Gurchenko1, E.Z. Gusakov1,

• P. Niskala2,

A.B. Altukhov1, L.A. Esipov1, D.V. Kouprienko1, M.Yu. Kantor1, S.I. Lashkul1, S. Leerink2, A.A. Perevalov1

1Ioffe Institute, St. Petersburg, Russia 2Euratom-Tekes Association, Aalto University, Espoo, Finland

E-mail contact of main author: aleksey.gurchenko@mail.ioffe.ru

• Abstract. It is demonstrated experimentally for the first time at the FT-2 tokamak that the theoretically predicted

possibility of GAM control of the turbulence associated with the enhanced plasma rotation shearing manifests itself in modulation of the turbulence level at the GAM frequency. This observation is supported by ELMFIRE full-f global gyro-kinetic modeling demonstrating the modulation of density fluctuations as well as of the heat flux and diffusivity. The experimental effects were enhanced in deuterium discharges where GAM amplitude increased leading to the stronger fluctuation reflectometry signal suppression during the GAM bursts and to the decrease of the mean anomalous electron thermal diffusivity determined by the ASTRA modeling thus providing an explanation for the isotope effect in tokamak plasma anomalous transport.

• 1. Introduction

The interaction between large-scale E×B flows, in particular geodesic acoustic modes (GAM), and small-scale drift-wave turbulence has been an important area of experimental research for anomalous transport of energy and particles in toroidal plasmas during the last decade utilizing more and more sophisticated tools. GAMs, which are, according to the present day understanding, excited in plasma due to nonlinear three-wave interaction of drift waves, in their turn can influence the turbulent fluctuations and anomalous transport. The mechanism GAMs control the turbulence could be associated with large inhomogeneity of poloidal rotation accompanying GAMs possessing small radial wavelength and huge radial electric field. Dependence of GAM excitation level and, more general, long-range correlations on ion mass could be responsible [1] for the isotope effect in tokamak anomalous transport [2] which is still unclear. The present paper is devoted to investigation of these effects in the FT-2 tokamak (R = 55 cm, a = 7.9 cm) using a set of highly localized microwave backscattering diagnostics and the global gyro-kinetic (GK) modeling by ELMFIRE code [3].

• 2. The turbulence and diffusivity modulation at GAM frequency as provided by

ELMFIRE GK code The ELMFIRE simulations for ohmic 19 kA H-discharge (B  2.1 T, ne(0)  4×1013 cm-3; Zeff  3.5; Te(0)  470 eV, Ti(0)  110 eV, see profiles in FIG. 1) were successfully validated against experimental data characterizing the FT-2 tokamak turbulent dynamics and transport phenomena including GAM temporal and spatial structure [3, 4]. Strong poloidal velocity

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• scillations associated with GAMs and obtained

in [3, 4] as a result of ELMFIRE radial electric field Er simulation are shown in FIG. 2. The GAM radial wave structure is located at small radii r =4-6.5 cm. The mechanism GAMs control the turbulence discussed in theory [5] is associated with large inhomogeneity

• f

poloidal rotation accompanying GAMs possessing small radial wavelength and huge radial electric field. The stabilizing effect of strong GAM rotation shearing should be however reduced, according to theory [6] by its quick temporal variation leading to the following modification

• f

the drift-wave turbulence stabilization condition: eff = |E×B H + 0| > , where E×B and 0 are poloidal rotation shearing rates corresponding to GAM and mean flow correspondingly,  is the instability growth rate or the turbulence inverse correlation time, parameter

 

 

1/ 4 2 3

(1 3 ) 4 (1 ) 1 4 H F F F F      is a reduction factor, F  (2FG/)2 and FG is the GAM frequency. The inward propagating intensive GAM waves shown in FIG. 2 are sufficiently strong to satisfy condition eff > . A comparison of the effective shearing and the growth rate (at r = 5.5 cm) is demonstrated in FIG. 3. The absolute value of the E×B shearing rate at this radius composed

• f

the mean shear 0  66 kHz and its fluctuating part reduced by a factor H  0.2 is shown in FIG. 3b by red

• curve. The turbulence growth rate, estimated

from the ELMFIRE data as   158 kHz is shown by blue line. The mean shear 0 and the GAM frequency FG  53 kHz are shown in

• FIG. 3b by black and green lines respectively. As

it is seen in FIG. 3, the effective shear eff exceeds the turbulence growth rate level once or even twice times per the GAM period depending

• n the amplitude of the VE×B oscillations, which

is most likely the reason of the strong modulation

• f the magnetic surface averaged electron

thermal diffusivity demonstrated in FIG. 4. The similar phenomenon in ELMFIRE simulations was also found for TEXTOR [7]. The influence of the intensive GAM wave manifests itself initially 210 240 270 300 330 200 400

• 8
• 4

4 (b)

0

FG eff

eff ,  (kHz)

t (mks)  (a) r = 5.5 cm VExB (km/s)

• 6 -4 -2

2 4 6 150 300 450 Ti (eV) Te (eV) x (cm) 2 4 ne (10

19 m

• 3)

3 4 5 6 7 200 220 240 260 280 300 320 340 r (cm) t (mks)

• 12
• 8
• 4

4 8

Er (kV/m)

• FIG. 1. The density and temperature

equatorial profiles in 19 kA H- discharge.

• FIG. 2. Temporal variation of the

radial electric field spatial distribution computed by ELMFIRE.

• FIG. 3. The simulated E×B velocity (a)

and comparison of eff and  (b).

3 4 5 6 7 200 220 240 260 280 300 320 340 r (cm) t (mks) 1.0 1.6 2.2 2.8 3.4 4.0

e (m

2/s)

• FIG. 4. Temporal variation of the

electron thermal diffusivity spatial distribution computed by ELMFIRE.

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in the turbulence level modulation. As it is seen in FIG. 5, the coherency spectrum of magnetic surface averaged radial electric field and density fluctuations squared in the vicinity of equatorial plane (where density component of the GAM is suppressed in agreement with its sin() symmetry, where  is the poloidal angle) possesses maximum at the GAM frequency FG  53 kHz in the region where experimental measurement were performed (4.9 cm < r < 5.6 cm). In the next section of the paper we visualize this numerically predicted effect in the FT-2 tokamak experiment using complex approach utilizing microwave Doppler enhanced scattering (ES) and reflectometry diagnostics [8].

• 3. Experimental investigation of GAM-turbulence interaction

The theoretically predicted effect of turbulence control by GAMs was studied utilizing correlative Doppler microwave enhanced scattering (CDES) [9] (with X-mode out-off- equatorial plane microwave backscattering in the upper hybrid resonance off small-scale density fluctuations possessing radial wave numbers rS > 2) and reflectometry diagnostics. The medium-scale radial electric field GAM

• scillations are characterized in experiment by

the CDES technique using the backscattering spectra Doppler frequency shift fD(t) modulation [10], which is associated with

• scillations of plasma poloidal rotation velocity

V, (fD(t) = V(t)/2 where  is the turbulence wave number). The fD-signal power spectra measured in similar 19 kA H- and D- discharges at the same radial position are shown in FIG. 6a. GAM frequency radial profiles are shown in FIG. 6b. In accordance with the theory predictions [11] (shown by solid lines) they are determined by electron temperature behavior and the isotope mass. It is important that a much larger level of the GAM amplitude was observed in D-regime in comparison with hydrogen. The possible reason for this effect could be associated with the difference in ion collisionality in D- and H- discharges due to different mass and smaller atom density in deuterium. The double-frequency probing correlative scheme was used for investigation of the GAM spatial structure [12] propagating inwards. The GAM wave length r and correlation length in D- regimes (with 19 kA and 32 kA plasma currents) have systematically larger values then in

• FIG. 5. The spatial distribution of the

coherence spectrum between Er and n2 computed by ELMFIRE.

• FIG. 7. Comparison of the GAM radial

wave length measured experimentally r with G in H- and D-discharges with plasma current 19 kA and 32 kA.

5 6 7 8 30 40 50 H D (a) r (cm) F (kHz) 40 80 120 5 10 15 20 H D F (kHz) (b) fD (a.u.)

• FIG. 6. (a) Power spectra of the fD-signal in

D (red) and H (blue) discharges. (b) Radial profiles of the GAM frequency (blue triangles – for H, red circles – for D, solid curves – theoretical [11] estimation).

0.8 1.2 2 4 6

r = G G = 4i

2/3LT 1/3 (cm)

r (cm)

H 19kA D 19kA H 32kA D 32kA

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• hydrogen. The correlation length values were in

the range 0.6-1 cm. Experimentally measured GAM wave length manifold significantly exceeds the maximal value G predicted in theory [13] for free-propagated waves (FIG. 7). This result indicates that GAMs observed in FT-2 tokamak plasmas are non-linearly induced by low frequency beats of the drift turbulence. It should be mention that the turbulence radial correlation length, as measured by radial correlation Doppler reflectometry [14], is also larger in deuterium. The long-scale drift-wave turbulence behavior is investigated with 30 GHz frequency range O-mode reflectometer quadrature scheme utilizing equatorial probing from low-field side. The equatorial probing for reflectometer scheme was utilized in order to exclude the GAM minor density oscillations component from the scattering spectrum (see FIG. 8). The first evidence for GAMs interaction with the small- scale plasma turbulence component (both measured by CDES) via three-wave coupling was found by the bicoherency analysis [10, 12]. However, only weak influence of the GAM intermittency was observed (both in H- and D-regimes) in the small-scale turbulence radial wave number spectra obtained by CDES diagnostic [12]. On contrary, a strong modulation of the large-scale turbulence level at the GAM frequency was for the first time found by cross-method utilizing both ES and reflectometry

• techniques. The experimental geometry for this combined

approach is shown in FIG. 9. The evolution of density fluctuations was measured by reflectometer from low field side whereas the poloidal velocity V oscillations were reconstructed from the ES measurements. The probing frequencies were 35 GHz for the O-mode reflectometer and 65 GHz for the ES, providing the radial overlapping (r  5.8 cm) for scattering regions shifted by 90 degrees toroidally. The temporal variation of the CDES Doppler frequency shift fD, obtained as a mean value from the backscattering spectrum at 65 GHz measured during 3.2 ms in 19 kA H-discharge is shown in

• FIG. 10. Strong oscillations of fD seen in FIG. 10a,

as it was proved in [10], are related to the intensive GAM excited in plasma. The temporal evolution of the reflected signal power PIQ(t) = C2 + S2 determined using the IQ detected cosine and sine homodyne signals C(t) and S(t), is shown in FIG. 10b. As it is seen in the figure, the

• scillations possessing periodicity similar to that of FIG. 10a and corresponding to GAM

100 200 300 400 1 FG Pr (a.u.) vertical F (kHz) equatorial

• 6

6

• 6

6 cutoff UHR Refl. y (cm) x (cm) ES

(b)

• FIG. 10. fD and PIQ time traces in 19 kA

H-discharge.

• FIG. 8. The reflectometer power spectra

in 19 kA H-discharge: one with equatorial probing from low-field side (red) and another with top launching and vertical probing (blue).

• FIG. 9. (a) The ES and O-mode

reflectometer disposition (top view). (b) Ray trajectories for ES (red) and equatorial reflectometer (green).

0.60 0.62 0.64 0.66 0.68 1 2 (b) PIQ (a.u.) t (ms) 1 2 (a) fD (MHz)

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exist in behavior of reflectometry signal, as

• well. Otherwise, when GAM oscillations are

invisible the PIQ(t) signal become more uniform. Results of the statistical spectral analysis of these signals are shown in FIG. 11. The power spectra averaged in 3.44 ms time interval (with 84 samples) of the fD(t), C(t) and S(t) (taken before the amplification level’s adapting), PIQ(t) signals are shown in

• FIG. 11a-c. A well pronounced line related

to the plasma poloidal oscillations at the GAM frequency is seen in fD-spectrum, whereas in reflectometer measurements it was seen only for vertical probing and not

• bserved

in the equatorial plane in agreement with the GAM’s sin()

• symmetry. Nevertheless, as it is seen in
• FIG. 11c, the line at the GAM frequency is

also observable in the spectrum of the reflectometry signal total power indicating the possibility of turbulence amplitude modulation by the GAM. This assumption is confirmed by the analysis of the coherence spectrum between two signals fD(t) and PIQ(t) shown in FIG. 11d demonstrating the coherence value at the GAM frequency (35%) higher than the noise level (shown by grey color). The value of the cross- phase between two signals at the GAM frequency (172) is close to 180. In order to check whether the observed modulation of the turbulence level is consistent with criteria eff >  and therefore may be attributed to the GAM poloidal rotation shear we determine the related quantities from the

• experiment. The turbulence inverse correlation time was estimated as the half-width of the IQ

reflectometer power spectrum provided by C(t) and S(t) signals and shown in FIG. 12. The corresponding inverse correlation time value, as it is seen in the figure is   270 kHz. The time-averaged values of poloidal rotation velocity <V> measured in the region of interest using CDES diagnostic [4, 9] are shown in FIG. 13. The corresponding radial velocity gradient is estimated from this figure as

θ

< > 20 42 kHz d V dr   , whereas the mean part of the E×B shearing rate

θ θ

ω 50 42 kHz d V r d q V dr q dr r           (where q is the safety factor computed as a result of ASTRA code modelling based on experimentally measured profiles of all quantities). The V rms value associated with GAMs is estimated from fD-signal rms using poloidal wave number of fluctuations contributing to backscattering in the UHR which is determined from the CDES measurements [9]. The corresponding GAM amplitude is VG  1.7 km/s whereas the typical GAM radial wave number, measured in this discharge by

1 2 4

(b) Refl.

Pr (a.u.) 0.0 0.4 0.8

(a)

fD (a.u.)

ES (c)

PIQ (a.u.) 100 200 300 0.0 0.2 0.4

(d)

F (kHz)

fD&PIQ

coh

• FIG. 11. Power spectra of fD(t) (a); both IQ

reflectometry signals (b); PIQ(t) (c) and coherence between fD and PIQ (d) in 19 kA H- discharge.

• 200

200 2 Prfl (a.u.) F (kHz)

/

• FIG. 12. The IQ reflectometer spectrum.

5.0 5.5 6.0 6.5

• 2
• 1

<V> (km/s) r (cm)

• FIG. 13. The measured averaged V.

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two channel radial CDES approach [10], is kG  2.6 cm-1. Accordingly the oscillating part

• f

the E×B shearing rate E×B = kGVG  442 kHz. At the GAM frequency FG  43 kHz the shearing reduction factor is H  0.5 and an effective shearing rate eff  27142 kHz is very close to the turbulence growth rate, providing the possibility for the turbulence suppression once per the GAM period. The intermittency of GAMs was also taken into account during the integration of the total reflectometer power

IQ IQ

P P dt t   



by selection and recombining of time intervals where GAMs are excited or suppressed. The quality of this selection is seen in FIG. 14a where the power spectra of fD-signals with and without GAMs are demonstrated. In the timed intervals the corresponding PIQ signals were also recombined and their power spectra characterizing the turbulence power are shown in FIG. 14b. The difference between PIQ spectra with and without GAMs is not obvious, but the turbulence total power has a slightly smaller level when analysed during intervals where GAMs are excited:

IQ with GAM IQ w/o GAM

0.8 P P    . The more clear effect was found in deuterium 19 kA discharge (B  2.3 T, ne(0)  2.6×1013 cm-3; Zeff  2.8, Te(0)  400 eV, Ti(0)  105 eV). The amplitude

• f

GAM like

• scillations

increased in the fD(t) time trace by a factor

• f 2, the shape of PIQ-peaks also became

more distinct (see FIG. 15). The power spectra and coherence in D-case are shown in FIG. 16. GAM line amplitude increases in comparison with H-case. The coherence between fD-signal and the total reflectometry power PIQ at GAM frequency reaches the level 38% thus proving the turbulence level modulation by GAMs. The cross-phase value at GAM frequency in this case is 161. We have also studied the width of the turbulence frequency range modulated by GAMs. For this purpose the fast evolution of the IQ reflectometer power spectrum provided by C(t) and S(t) signals was calculated first Prfl(F, t). Then the spectral power evolution PF(t) was calculated in the frequency band |F|>F0 in the following manner:

rfl F F F

P P dF



   for

200 400 1 (b) PIQ (a.u.) w/o GAM with GAM F (kHz) 2 4 (a) fD (a.u.) w/o GAM with GAM

• FIG. 14. Power spectra of fD(t) (a) and PIQ(t)

(b) for recombined signals with intervals of excited (red) or suppressed (blue) GAM in 19 kA H-discharge.

0.82 0.84 0.86 0.88 0.90 2 4 (b) t (ms) PIQ (a.u.) 2 (a) fD (MHz)

• FIG. 15. fD and PIQ time traces in 19 kA D-

discharge.

1 2 2

Refl. (b)

Pr (a.u.) 2

ES (a)

fD (a.u.)

(c)

PIQ (a.u.) 100 200 300 0.0 0.2 0.4

(d)

F (kHz)

fD&PIQ

coh

• FIG. 16. Power spectra of fD(t) (a); both IQ

reflectometry signals (b); PIQ(t) (c) and coherence between fD and PIQ (d) in 19 kA D- discharge.

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different frequencies F0. Finally the coherence between fD(t) and PF(t) signals was

• calculated. The corresponding level of the

coherence at GAM frequency was 43% for |F| > 110 kHz, 36% for |F| > 200 kHz, 23% (at the boundary of the noise level) for |F| > 250 kHz and at mean noise level without any peaks for |F| > 300 kHz. This result demonstrates existence of the wide turbulence spectral band modulated at the GAM frequency. The power spectra of fD-signals calculated in GAM-active and GAM-free periods are demonstrated in FIG. 17a for 19 kA D-discharge. The corresponding power spectra of the PIQ signals are shown in FIG. 17b. As it is seen, the turbulence modulation at the GAM frequency (FIG. 16d) results in D-case in strong drift-wave turbulence spectrum suppression during the GAM bursts compared to the GAM-free periods and significant drop of the total reflectometry signal power:

IQ with GAM IQ w/o GAM

0.6 P P    . The observed turbulence suppression by GAMs provides an explanation for the anti-correlation of the GAM amplitude and the effective electron thermal diffusivity typical for the FT-2 experiments [12]. In the case of similar deuterium and hydrogen discharges the above effect is shown in FIG. 18, providing a striking example of the isotope effect.

• 4. Conclusion

It is demonstrated experimentally for the first time that the theoretically predicted possibility

• f GAMs control of the turbulence manifests itself in modulation of the turbulence level at the

GAM frequency. This observation is supported by ELMFIRE full-f global GK modeling demonstrating the modulation of density fluctuations as well as of the heat flux and

• diffusivity. The effect was enhanced in D-discharge where GAM amplitude increased leading

to the fluctuation reflectometry signal suppression during the GAM bursts and to the decrease

• f the mean anomalous electron thermal diffusivity determined by the ASTRA modeling. The
• btained experimental results appeal for the further comparative investigation of the

anomalous transport phenomena in the hydrogen and deuterium discharges using localized diagnostics and full-f global GK modeling.

200 400 2 4 (b) PIQ (a.u.) w/o GAM with GAM F (kHz) 2 4 (a) fD (a.u.) w/o GAM with GAM

• FIG. 17. Power spectra of fD(t) (a) and PIQ(t)

(b) for recombined signals with intervals of excited (red) or suppressed (blue) GAM in 19 kA D-discharge.

4 5 6 3 6 (b)

eff (m

2/s)

H D D r (cm) 10 20 30 (a) GAM ampl. H

noise

• FIG. 18. (a) GAM amplitude and (b)

electron thermal diffusivity radial distributions in 19 kA H- (blue) and D- (red) discharges.

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• 5. Acknowledgements

Partial financial supports of RFBR grant13-02-00614, NWO-RFBR Centre of Excellence on Fusion Physics and Technology (grant 047.018.002) and the Russian Academy of Science Presidium program 12 are acknowledged.

• 6. References

[1] XU, Y., et al., Phys. Rev. Lett. 110 (2013) 265005. [2] STROTH, U., Plasma Phys. Control. Fusion 40 (1998) 9. [3] LEERINK, S., et al., Phys. Rev. Lett. 109 (2012) 165001. [4] GUSAKOV, E.Z., et al., Plasma Phys. Control. Fusion 55 (2013) 124034. [5] DIAMOND, P.H., et al., Plasma Phys. Control. Fusion 47 (2005) R35. [6] HAHM, T.S., et al., Phys. Plasmas 6 (1999) 922. [7] NISCALA, P., et al., 41th EPS Conf. on Plasma Physics (Europhysics conf. abstracts, Berlin, 2014), Vol. 38F, European Physical Society, P1.053. [8] GURCHENKO, A.D., et al., 41th EPS Conf. on Plasma Physics (Europhysics conf. abstracts, Berlin, 2014), Vol. 38F, European Physical Society, O2.111. [9] GUSAKOV, E.Z., et al., Plasma Phys. Control. Fusion 48 (2006) B443. [10] GURCHENKO, A.D., et al., Plasma Phys. Control. Fusion 55 (2013) 085017. [11] GUO, W., et al., Phys. Plasmas 17 (2010) 112510. [12] GURCHENKO, A.D., et al., 40th EPS Conf. on Plasma Physics (Europhysics conf. abstracts, Espoo, 2013), Vol. 37D, European Physical Society, P2.181. [13] ITOH, K., et al., Plasma Fusion Res. 1 (2006) 037. [14] ALTUKHOV, A.B., et al., 40th EPS Conf. on Plasma Physics (Europhysics conf. abstracts, Espoo, 2013), Vol. 37D, European Physical Society, P1.170.