O L Krutkin

E Z Gusakov

S Heuraux

C Lechte

Nonlinear Doppler reflectometry power response

Introduction

Turbulent transport plays a key role in limiting confinement in magnetic fusion devices.

Investigation of underlying physical processes behind it requires suitable tools to study plasma turbulence. One of such tools is Doppler reflectometry (DR) diagnostic, which employs the probing of the plasma with the microwave beam in the presence of cut-off. The probing beam is tilted with respect to the magnetic surface and backscattered signal is measured. The vicinity of the probing wave turning point provides the dominant contribution to the DR signal [1]. Using the Doppler effect, the poloidal velocity of density fluctuations is determined. The Bragg resonance condition makes the measurement of fluctuation poloidal wavenumber spectrum possible by varying the probing angle.

However, such a straightforward interpretation is only possible in the linear regime of scattering, where the Born approximation over the amplitude of density fluctuations is applicable. This case was extensively studied both analytically [1] and numerically [2]. Analytical predictions have also been made for the strongly nonlinear (or saturated) case [3] when multiple forward scattering is dominant and nonlinear effects were observed in fullwave numerical modeling [START_REF] Krutkin | Proc. 44th EPS Conf. on Contr. Fusion and Plasma Physics (Belfast) ECA[END_REF][START_REF] Lechte | [END_REF].

Finally, a study of the intermediate nonlinear regime, when the amplitude of the scattered signal scales nonlinearly with density fluctuations r.m.s. was performed [6] and the criterion of transition from linear regime to nonlinear regime was derived. This analysis, however, utilized the physical optics approximation, which has limited and uncertain domain of validity due to the fact that only backscattering in plasma at cut-off region is taken into consideration.

In the present paper, the intermediate nonlinear regime of Doppler reflectometry will be considered in the framework of perturbation theory applied to the Helmholtz equation, to overcome the limitations of the physical optics.

Analytical treatment

In this work, plasma probing with the microwave beam of O-polarization is considered.

Analysis is performed in slab geometry, the background density profile is assumed to be linear over radial coordinate x and uniform over the poloidal coordinate y. Density fluctuations in the analytical treatment on the other hand are assumed to be uniform over x, which corresponds to the large radial correlation length. This assumption, which resembles the physical optics approach, is made to simplify the derivation. However we will not limit the analysis to only the turning point vicinity and will consider contribution of all the plasma volume to the backscattering signal. The microwave propagating through plasma is described by the Helmholtz equation:

2 2 22 2 2 ( , ) ( , ) ( ) ( ) ( , ) 0 dd E x y E x y k x k y E x y dx dy   + + - =  (1)
where k(x) 2 = ω 2 /c 2 (1-n(x)/nc); δk(x) 2 =ω 2 /c 2 (δn(y)/nc) and nc=meω 2 /(4πe 2 ). To obtain the solution of this equation we will use the WKB approximation. Unperturbed solution for a single poloidal harmonic takes the form:

( ) ( ) () 0 0 (0, ) ( , ) ( ) exp cos ( , ) ( , , ) 4
4 y y Lk Lk y y y y y x y k x k dx kk E x k f k i i k x k dx k x k     = + +        (2)
where f(ky) is probing beam's angular diagram. L(ky) is radial cutoff position for a given poloidal wave number and k(x,ky) 2 =k 2 (x)-ky 2 . The first order correction to the solution -E 1 , describing scattering in the Born approximation can be obtained by solving equation:

( ) ( ) 2 2 2 1 2 1 2 2 2 () 0 (0, ) () ( , ) ( , ) ( , ) ( ) ( , ) exp cos ( ', ) ' 4 4
,

y y y y y y y y c q L k q Lk y y x kk d c c n q E x k k x k E x k f k q dx k x k n i q i k x k q dx dq k x k dx       - - - + = -        - + - +              (3)
To find the amplitude of the scattered signal we utilize the reciprocity theorem [7]:

2 2 2 () ( , ) 4 s e c ie n y A P E x y dxdy m n     - - =  (4)
Next, by substituting formula (2) and a solution of (3) into (4) we can derive a linear response, "proportional" to δn and a quadratic one, "proportional" to δn 2 . The value of δn corresponding to these two terms being equal will give us the threshold for transition from linear to nonlinear regime.

In the further derivation we will assume that the probing antenna has a narrow angular diagram centered around K= ω/c sinϑ, ϑ is a probing angle with respect to normal to the magnetic surface (which in our case is directed along x). To simplify the derivation, we will also assume a Gaussian spectrum of turbulence

n c c c a n l L L n c c c b n l L l Kl n c c n l                         -      (6)
Numerical factors in these formulae were excluded, as some of them are just estimations of the scattered field, not exact values. It should be noted, that these criteria are in agreement with each other in intermediate parameter which means they properly describe all possible parameter values. Finally, using the fact that nonlinearity criterion and saturation criterion coincide in case of normal probing beam incidence [6,8], formulae [START_REF] Lechte | [END_REF] can be generalized for arbitrary radial correlation length lcx:

Here, formula (7a) is in agreement with the one obtained with the help of the physical optics model [6]. However, the physical optics model does not reproduce the other formulae obtained, in particular, expression 5b, which corresponds to the most realistic situation of the DR experiment. Generalized version of ( 6) can also be obtained by taking into account the consistency between ( 5) and (6).

Numerical modeling

To validate the obtained theoretical results and highlight the differences with the physical optics description, a full-wave numerical modelling with the IPF-FD3D code [START_REF] Lechte | [END_REF] was performed. To generate random turbulence, a Gaussian spectrum with random phases added to it was used. Each random turbulence was normalized to have r.m.s. of 1 and then scaled to a certain fraction of nc.

The amplitude of the scattered signal and power dependence ni=ln(Pi+1/Pi)/ ln(ai+1/ai) for two calculations can be seen at figures 1 and 2. Green, orange and brown vertical lines correspond to the nonlinear transition values provided by (7b), the phys. optics and the saturation criterion [8] respectively. As it can be seen from above figures, new nonlinearity threshold describes the actual nonlinear transition better than the criterion provided by physical optics [6]. However, in the case when nonlinear criterion suggested exceeds saturation threshold calculation results

were not in agreement with theory. This discrepancy is currently under investigation.

Conclusions

By applying the perturbation method to the Helmholtz equation, the new threshold for transition to nonlinear regime was suggested without relying on physical optics. It was validated numerically for a wide range of parameters, however, there are still some inconsistencies to investigate.

Financial support of RSF grant 17-12-01110 is acknowledged by E.G., whereas support of RFBR grant 18-32-00031 and Vernadsky scholarship for Ph.D. students is acknowledged by O. K.

Fig 1 .

 1 Fig 1. Calculation results for f=30GHz, L=20cm, lcx=1.3 cm, lcy=1.3. cm, ϑ=40°.

Fig 2 .

 2 Fig 2. Calculation results for f=30GHz, L=20cm, lcx=1.7 cm, lcy=1.7. cm, ϑ=30°.

  signal is too lengthy to write it here, in the end one can arrive at a number of nonlinearity thresholds corresponding to different parameter ranges.

	For lcy 2 >>Lc/ω:
	c c n n n n  	 	22 4 22 4 cy cy Kl Kl  -    exp sin exp 2 cos c L       -	sin  cos c L     cos sin c L  	( ) ( ) a b	(5)
	In the opposite case of lcy 2 <<Lc/ω:
					;		sin		(	)
					cos			cos
	c		cy
		sin
					;			sin	(	)
								cos
	c			cy					cy
					22
		sin	2	exp	cy	;	sin	(	)
					4
	c						cy
								22 y cy k l  / 8 =- , 0 exp cy n l  ( ) y n k

where lcy is the poloidal correlation length of fluctuations. While the expression for the quadratic scattered


A B Altukhov
email: a.altuhov@mail.ioffe.ru

A D Gurchenko

E Z Gusakov

M A Irzak

O L Krutkin

L A Esipov

P Niskala

T P Kiviniemi

S Leerink

C Lechte

BENCHMARKING OF FULL-F GLOBAL GYROKINETIC MODELING RESULTS AGAINST THE FT-2 TOKAMAK DOPPLER REFLECTOMETRY DATA USING SYNTHETIC DIAGNOSTICS

Two versions of the X-mode Doppler reflectometry (DR) synthetic diagnostics are developed in the framework of the ELMFIRE global GK modeling of the FT-2 tokamak ohmic discharge. In the "fast" version DR signal is computed in the linear theory approximation using the reciprocity theorem utilizing the probing wave field pattern provided by computation taking into account the 2D plasma inhomogeneity effects, whereas the alternative "slow" version of DR synthetic diagnostic is based on the full-wave code IPF-FD3D describing the probing and scattered wave propagation in turbulent plasma. The DR signal frequency spectra and the dependence of their frequency shift, width and shape on the probing antenna position are computed and shown to be similar to those measured in the high field side probing DR experiment at the FT-2 tokamak. The GAM characteristics provided by the measurements and by the synthetic DR are close within a 12% accuracy. However the variation of the DR signal at growing incidence angles in experiment is slower than predicted by both synthetic diagnostics. The substantial difference was found also in the decay of the DR signal CCFs with growing frequency shift in the probing wave channels. The quick decrease of the RCDR coherence observed in the experiment and full-wave synthetic diagnostic compared to the fast synthetic RCDR is attributed to the phase modulation of the probing wave in the former two cases due to the long-scale density fluctuations, which is shown to be close to π/4 both in the specially performed measurements and in the GK modelling. In spite of the fact that this value indicates only the beginning of the transition to the fluctuation reflectometry nonlinear regime, which therefore is not influencing the DR spectra, it already has a strong influence on the RCDR performance.

INTRODUCTION

The anomalous energy transport remains the main unresolved enigma on the way to the realisation of magnetic confinement fusion using the tokamak concept. According to the present day understanding [1,2] the anomalous transport is determined by the multi-scale drift-wave turbulence and is strongly dependent on the nonlinear interaction of its components, such as large-scale mean EB flows, meso-scale zonal flows and fine-scale microturbulence excited due to specific profiles of plasma parameters. That interaction controlling the anomalous transport has been in the focus of theoretical and experimental research in magnetically confined plasmas for a long time. The massively parallelized particle-in-cell simulations of the gyrokinetic (GK) distribution function and the electric field [3,4] provide an efficient theoretical tool for studying the nonlinear turbulent plasma dynamics, which, however, needs a validation and comprehensive benchmarking against the experimental data. In the recent papers [5,6] such simulations of the electron and ion distribution function from the first principles were performed for the small research limiter tokamak FT-2 [4]. The complex interplay of the multi-scale turbulence components was studied in simulations and successful quantitative comparison was presented with measurements carried out at the low magnetic field side of the machine with O-mode Doppler reflectometry and enhanced microwave scattering in the upper hybrid resonance [5,6]. In the present paper the results of the global GK particle-in-cell simulations will be quantitatively compared to the X-mode Doppler reflectometry experimental data obtained at the high magnetic field side of the FT-2 tokamak (these data characterize the tokamak turbulent dynamics and transport phenomena at micro, macro and meso-scale). Doppler reflectometry (DR) is the microwave diagnostic widely used nowadays in toroidal fusion experiments to get information on the multi-scale anomalous transport phenomena -namely, on plasma rotation at ASDEX UG (the mean value and its oscillations) [7] and turbulence poloidal wavenumber spectrum at Tore Supra [8]. Just recently the radial correlation modification of this technique proposed at ASDEX UG [9] providing information on the turbulence radial structure was justified [10,11]. Unfortunately, the interpretation of DR data is complicated by the contribution of the poorly localized small-angle scattering along the wave trajectory, which can lead to the overestimation of the turbulence radial correlation length in the linear scattering regime, and to its underestimation in the strongly nonlinear regime. In the latter case the turbulence wavenumber spectrum measurements are questionable, and only the plasma turbulence mean velocity could be determined (however, with poor spatial resolution) [12]. Moreover, in the case of X-mode DR the turning point can not be determined unambiguously due to the 2D propagation effects, which additionally complicates the experimental data interpretation and its comparison with the theory predictions. Development of a synthetic diagnostics, allowing the direct signal computation based on the results of GK modeling, could be helpful in this case both for the interpretation of the experimental results and for the code benchmarking. In this paper two versions of the X-mode DR synthetic diagnostics are developed in the framework of the ELMFIRE global GK modeling of the FT-2 tokamak ohmic discharge [6]. The X-mode DR signal is computed both in the linear theory approximation using the reciprocity theorem utilizing the probing wave field pattern provided by computation taking into account the 2D plasma inhomogeneity effects [13] and by the full-wave code IPF-FD3D describing the probing and scattered wave propagation in turbulent plasma [14]. The temporal behavior of the DR signal frequency spectra and the dependence of its amplitude, frequency shift and shape on the probing antenna position are computed and compared to those measured in the experiment at the FT-2 tokamak. In the case of multifrequency probing the radial correlation (RC) DR cross-correlation function (CCF) is also determined by both synthetic diagnostics and compared to that obtained in the experiment. The role of probing wave phase modulation in performance of RCDR is investigated both in computations and experimentally.

THE EXPERIMENTAL APPROACH.

The experiment was performed at the FT-2 tokamak (a major radius R = 55 cm, limiter radius a = 7.9 cm) in the hydrogen ohmic discharge (with plasma current I p = 19 kA, central density n e (0) = 410 13 cm -3 and electron temperature T e = 470 eV). The discharge is similar to that utilized for successful comprehensive benchmarking of the ELMFIRE GK code in [5,6], however, the toroidal magnetic field at the discharge axis is slightly smaller (B t (0) = 1.7 T instead of 2.1 T). The actual measured electron density and temperature profiles for this discharge used in the GK modelling, as well as the ion temperature profile are shown in Fig. 1. The vertically movable (by ±2 cm) X-mode double antenna set (shown in Fig. 2) installed at high magnetic field side in equatorial plane allowed plasma probing at variable incidence angle with frequencies in the range f i = (50-75) GHz. It was used both in standard DR measurements utilizing the quadrature scheme and in the RCDR technique based on the scheme described in [15]. In the former case the DR spectrum was obtained via averaging of 155 random DR power spectra obtained by using Fourier transform of 12.8 microsecond samples of the DR signal. In the latter case the reference channel generator was tuned to the master frequency f 0 =70 GHz determining the measurement position in the vicinity of r = 5 cm, whereas another generator producing probing signal at a slave frequency varied in the interval [1.2; 1.2] GHz around the master frequency in 100 MHz steps was used in the second, (signal), channel to determine the turbulence two-point CCF. The backscattering (BS) spectra ( ) ( )

s s i s P f f P f  
(f i and f s are probing and scattering frequencies accordingly) measured by the X-mode DR diagnostics at different vertical antenna displacements were presented in [12, 12A]. It was shown there that the BS power is decreasing with growing antenna vertical shift corresponding to increase of the probing wave incidence angle, whereas the spectra frequency shifts and width are increasing.

THE GK COMPUTATION APPROACH AND THE SYNTHETIC DIAGNOSTICS.

The simulations are performed with the global electrostatic particle-in-cell code ELMFIRE [3] to model the evolution of the full distribution function of drift kinetic electrons and gyrokinetic protons and O 6+ ions. The simulation geometry has a circular cross-section and covers all the radial range. The time step is set to t = 30 ns and spatial grid to 1105158 cells in radial (r), poloidal (), and toroidal () direction. Approximately 2400 electrons and ions are simulated per grid cell. Momentum and energy conserving binary collision operator [16] is applied allowing the inclusion of neoclassical physics in the simulations.

The particles are initialized according to a prescribed temperature and density profiles taken close to the experimentally measured ones (see Fig. 1). The profiles are allowed to develop self-consistently in time, while turbulence develops and heat sources and sinks, namely Ohmic heating and radiation losses, are applied. The Ohmic heating is induced by a spatially homogeneous loop voltage [17,18], while electrons are cooled using a Monte Carlo model according to an impurity radiation loss distribution measured by the bolometry diagnostics.

The initial oxygen O 6+ impurity density is chosen in order to provide the experimental value of Z eff = determined using ASTRA modeling and experimental loop voltage measurements, with equal temperatures for the impurities and main ions. Neumann and Dirichlet boundary conditions are used at the inner and outer boundary of the simulation geometry for the electrostatic potential. Particles passing the inner boundary are reflected back into the simulation domain whereas particles passing the outer boundary are returned to the simulation domain as an electron-ion pair according to a probability distribution proportional to the measured radial profile of neutral hydrogen density and at the wall temperature.

The fast synthetic X-mode DR diagnostics developed for this code [13] is based on the reciprocity theorem of electrodynamics [19] relating the high-frequency current in the plasma volume and the signal radiated by it and received by the antenna. The probing and backscattering wave propagation in the plasma not perturbed by turbulence is described in the fast synthetic diagnostic by full-wave code WaveTOP2D [20]. The code solves complete Maxwell equations in toroidal geometry accounting for the magnetic field shearing. Turbulent density fluctuations computed in the eight toroidal cross-sections were used to obtain the DR signal lasting 0.96 ms. This realization was divided into 0.012 ms samples in which the random Fourier spectra were calculated later used to obtain the average DR spectrum. It should be mentioned however that the approach based on the reciprocity theorem neglects the perturbations of the probing wave propagation caused by the density fluctuations, in particular, multiple small-angle scattering or its strong phase modulation. In this sense it is equivalent to the so called Born approximation linear in the fluctuation amplitude. The main merit of this approach is the possibility of fast computations, whereas the main drawback is related to the neglecting the nonlinear effects. The alternative "slow" DR synthetic diagnostic is free from this drawback. It is based on the full-wave code IPF-FD3D describing the probing and scattered wave propagation in turbulent plasma [14] It is accounting for perturbations introduced by density fluctuations and therefore is not limitted to the linear approximation, however solves Maxvell equations for a single mode in the case of propagation perpendicular to the magnetic fieild and neglecting its poloidal component and toroidicity.

DR FREQUENCY SPECTRA COMPARISON

The DR spectra obtained in the experiment and provided by synthetic diagnostics are compared in Fig. 3 for vertical antenna shifts of different sign. As it is seen in the figures, spectra provided by both synthetic diagnostics fit reasonably well the experimental ones for all the antenna positions. Not only are the shifts of both spectra close in all cases, but their shapes also look alike. This impression is confirmed in Fig. 4 and Fig. 5, where the mean frequency shift

      1 2 2 D s s f f f P f df P f df            
of the experimental and synthetic spectra obtained as the first and the second moment of the spectrum accordingly are plotted as functions of the antenna vertical displacement and the turbulence poloidal wavenumber. The relation between the antenna displacement and the fluctuation poloidal wavenumber was obtained using the X-mode ray-tracing (the doubled value of the probing wave poloidal wavenumber at the trajectory minimal radial coordinate). The spectral shift data provided by the experiment and GK modeling agree surprisingly well. The meaningful difference is only observed at the largest antenna displacement y a = ±2.0 cm. This difference is probably due to a contribution of experimental spectrum tails becoming especially heavy and asymmetric at high antenna displacement and correspondingly fluctuation poloidal wavenumber. The tail is opposite to the mean frequency shift of the spectrum and presumably caused by drift modes excited in plasma at a low level and rotating in the direction of the ion diamagnetic drift.  for the full-wave one. The obtained agreement between the measured and computed DR spectra, which are determined by the plasma flows, provides evidences in favor of correct modeling of plasma poloidal rotation and a correct reproduction of the radial electric field behavior in the FT-2 tokamak by the ELMFIRE code. As it is seen in Fig. 5, the mean width of synthetic spectra is systematically smaller than in experiment. However the difference is in the range of only 20 -30 %. It could be attributed to the contribution of the spectra tails, which are higher in the experiment. The large backscattering spectrum width seen in Fig. 5 is partly associated with strong plasma potential oscillations caused by geodesic acoustic mode (GAM) excited in the FT-2 plasma [5,6,21]. These oscillations could be extracted from the DR signal using information on the temporal behavior of frequency shift of its spectrum [7]. Utilizing 5 s samples of experimental and synthetic DR signal the following dynamics of the plasma poloidal velocity shown in Fig. 6 was obtained. The oscillations in the v θ (t) behavior are caused by the GAM. The velocity oscillation amplitudes provided by measurement and fast synthetic diagnostics are close (1.9±0.3 km/s and 1.7±0.2 km/s accordingly). The standard deviation of the velocity fluctuations determined using DR data are also similar: 1.1 km/s is obtained in experiment and 0.9 km/s is given by the fast synthetic diagnostics. The GAM is represented by a line in Fourier spectrum of velocity shown in Fig. 7. As it is seen in the figure, the experimental value of the GAM frequency is 40 kHz, whereas the computational value provided by the fast synthetic diagnostics is slightly higher -45 kHz. We have also compared the DR signal intensity ( )

s s P f df 
dependence on the vertical antenna displacement, which is expressed in Fig. 8 in terms of the poloidal wavenumber of the turbulence. As it is seen in Fig. 8, the decrease of the DR signal power with growing fluctuation poloidal wavenumber is substantially faster than in experiment for both synthetic diagnostics. The difference could be attributed to an underestimation of the turbulence poloidal wavenumber spectrum in the intermediatescale domain

1 10 cm    
which occurs in spite of a sufficiently high density of the GK code grid (poloidal cell size 0.06 cm).

RCDR CCF COMPARISION

Inspired by a reasonable agreement of the experimental and synthetic DR spectral data we have performed the comparison of the computed and measured RCDR CCFs using the X-mode DR antenna displaced by 2.0 cm from the equatorial plane at the high-field side of the FT-2 tokamak. The corresponding CCFs shown in Fig. 9 as functions of the frequency difference in the master and slave channels (a) and of turning point separation (b) appear to be different whereas the density fluctuations two-point CCF for frequency f = f s -f i = 300 kHz computed in the measurement region based on the GK data and shown in Fig. 9b is close to the measured RCDR CCF, as it was mentioned in [15]. The CCF provided by the fast synthetic RD is much wider than the experimental one, whereas the ful-wave synthetic CCF is situated in between, as it is seen in Fig. 9a. The slow decay of the CCF provided by fast synthetic diagnostics shown in Fig9a,b is most likely determined by the small-angle-scattering contribution to the DR signal [10], which is not suppressed at the angle of incidence corresponding to y a =2.0 cm. There are two possible reasons of the drastic difference between the experimental and the fast synthetic RCDR CCFs. The first one is related to nonlinear effects, in particular, the multiple smallangle scattering, or strong probing wave phase modulation, according to theory [12,22,23], coming into play with growing turbulence level. The importance of this effect for the DR diagnostics performance was shown recently at ASDEX-upgrade [24]. The second is related to the GK code spatial grid limitations leading to underestimation of the turbulence radial wavenumber spectrum width and thus -to overestimating of the RCDR CCF width. To check the role of nonlinear effects in the FT-2 X-mode RCDR experiment we have computed and measured the random phase perturbation of the backscattered wave and determined its rms. In the computation only the contribution of the long-scale turbulence to the probing and scattered wave phase was taken into account. The calculation was performed along the ray trajectory unperturbed by density fluctuations using the expression [20]  

    2 2 0 ( , ) , , X X l c h l k l n l t t l dl n c             (1)
where the density fluctuation ( , ) n l t  is provided by the GK computation, whereas the factor ( , ) X h l  , according to [23] is given by expression

          2 2 2 2 4 2 2 2 2 2 ( , ) pe ce pe X pe ce l l l h l l l                            (2)
and

                2 2 2 2 2 2 ( , ) ce pe ce pe X pe ce l l l l k l l l c                               
is the X-mode wavenumber;

Dependencies of the random density fluctuation amplitude and factor ( , )

X X h l k c
  on the coordinate along the ray trajectory are shown in Fig. 10a for different computation moments. As it is seen in the figure the factor h X is substantially larger than unity all over the trajectory and increases further when approaching the cut-off surface. This enhancement is associated with a small separation of the cutoff and the UHR layers in our experiment. Due to this effect the phase integral (3) is steeply growing when approaching the turning point c l , as it is seen in Fig. 10b, and gets the value close to π/4. The temporal variation of the DR signal phase was also measured experimentally utilizing a quadrature scheme with the intermediate frequency reference signal inversion. The example of the reconstructed phase temporal behaviour is shown in Fig. 11 by the solid curve. The interval of the DR signal random phase variation appears to be close to that determined numerically. The standard deviation of the computed DR signal phase there is 0.93, whereas for the measured phase SD it is 1.23. The latter value is close to the computed one and to the level, which indicates the borderline for the DR diagnostics transition into the nonlinear regime of operation. In this parameter domain, strictly speaking, the reciprocity theorem ( 1) is not applicable. The obtained agreement of the measured and computed DR signal random phase standard deviation and its relatively high value demonstrates importance of the first, based upon nonlinear effects, explanation of the drastic disagreement of the experimental and fast synthetic RCDR diagnostics results. A comparatively low threshold of the X-mode DR transition to the regime nonlinear in the turbulence amplitude is explained by the probing wave strong dispersion.

In the nonlinear wave propagation and scattering regime the synthetic DR diagnostics should be based upon a full-wave code accounting for the turbulence influence on the probing and scattering wave propagation [25]. Nevertheless an estimation of the multiple small-angle scattering effect onto the RCDR CCF could be obtained just by multiplying the DR signal   The corresponding modified fast synthetic DR CCF appears to be close to the CCF provided by the full-wave synthetic diagnostics, as it is seen in Fig. 9a, thus confirming this approach based on the natural assumption justified in theory that the backscattering in DR is well localised in the trajectory turning point vicinity [26] whereas the phase modulation is performed by the long-scale fluctuations all over the trajectory [12]. It should be underlined that the CCF provided by the full-wave synthetic diagnostics is very close to the experimental one, thus demonstrating a minor role of the second reason mentioned above, namely, providing an argument in favour of correct description of the turbulence radial wavenumber spectrum by the GK code with the utilized grid. It is necessary to stress that the computational grid cell sizes (0.07cm -radial and 0.06cmpoloidal) are sufficient for adequate description of fluctuations contributing to the DR signal (poloidal wavenumber -0.4cm) and corresponding to the measured radial correlation length (radial wavelength -0.7cm). Therefore possibly distortions in numerical description of much smaller scale fluctuations result in underestimation of the measured poloidal scale turbulent fluctuation amplitude by the ELMFIRE code.

CONCLUSIONS

Basing on the results of the paper one should conclude that the ELMFIRE code benchmarking against the FT-2 X-mode Doppler reflectometry experimental data utilising the fast linear and full-wave DR synthetic diagnostics have demonstrated a good agreement between the measured and computed DR frequency spectra. For all used incidence angles both the spectra frequency shift and width, and in many cases the spectra form, were similar. The mean fluctuation velocity was close in the DR measurements and in the synthetic diagnostics. The GAM characteristics provided by the measurements and by the synthetic DR appear to be close, as well. However the variation of the DR signal at growing incidence angles in experiment is slower than predicted by both synthetic diagnostics. This difference could be presumably attributed to the overestimation of the turbulence poloidal wavenumber spectrum decay rate with growing wavenumber due to incorrect modelling in the smallscale domain. The substantial difference was found also in the decay of the DR signal CCFs with growing frequency shift in the probing wave channels. The quick decrease of the RCDR coherence observed in the experiment and fullwave synthetic diagnostic compared to the fast synthetic RCDR is attributed to the phase modulation of the probing wave in the former two cases due to the long-scale density fluctuations, which is shown to be close to π/4 both in the specially performed measurements and in the GK modelling. In spite of the fact that this value indicates only the beginning of the transition to the fluctuation reflectometry nonlinear regime, which therefore is not influencing the DR spectra, it already has a strong influence on the RCDR performance. A comparatively low threshold (in density fluctuation RMS and probing trajectory length) of the X-mode DR transition to the regime nonlinear in the turbulence amplitude due to the probing wave strong dispersion should also be mentioned.

FIG. 1 .

 1 FIG.1. The discharge parameter profiles. Density -solid curve; electron temperature -squares; ion temperature -triangles.

fFIG. 3

 3 FIG.3 Comparison of DR spectra for different antenna vertical displacement. Circles -experiment; triangles -fast synthetic DR, squares -full-wave synthetic DR.

FIG. 4

 4 FIG. 4 Dependence of the DR signal frequency shift on the antenna vertical displacement y a. and fluctuation wavenumber. Circles -experiment; triangles -fast synthetic DR; squares full-wave synthetic DR. FIG. 5 Dependence of the DR signal frequency width (rms) on the antenna vertical displacement y a. Circles -experiment; triangles -synthetic DR.

Fig. 4

 4 allows us to obtain estimations for the fluctuation poloidal velocity in experiment and in the computation. The estimation of the mean fluctuation poloidal velocity in experiment is given by

FIG. 6

 6 FIG. 6 Poloidal velocity temporal behavior. Solid curvemeasured fluctuation velocity; dashed-dotted curvefluctuation velocity by synthetic diagnostics. FIG. 7 Power frequency spectra of oscillations shown in Fig.6. Solid curve -measured fluctuation velocity; dotted curve -fluctuation velocity by synthetic diagnostics.

FIG. 8

 8 FIG.8 Dependence of the backscattering power on the fluctuation poloidal wavenumber. Circles -experiment; triangles -fast synthetic DR; squares -full-wave synthetic DR.

FIG. 10a

 10a FIG. 10a Density fluctuations (at three different moments of time) and h-factor behavior along the ray trajectory.FIG.10bThe phase perturbation variation along the ray trajectory at three different moments of time.

  .11 by dashed curve demonstrates variation in the range approximately from -π/2 to +π/2, which corresponds to the DR signal substantial phase modulation indicating transition to the nonlinear regime.

FIG. 11

 11 FIG.11The DR signal phase temporal variation. Fast synthetic signal -dashed line (SD = 0.93); experiment -solid line (SD = 1.23).

ACKNOWLEDGEMENTS

The financial support of the Russian Science Foundation grant 17-12-01110 is acknowledged. The work has been supported by the Academy of Finland grants 278487 and 296853 and 318314. CSC -IT Center for Science is acknowledged for generous allocation of computational resources for this work. The FT-2 tokamak maintenance and M.A. Irzak participation were supported by Ioffe Institute.


J.-M Noterdaeme
email: noterdaeme@ipp.mpg.de

V Bobkov

Ye O Kazakov

A Kostic

R Ochoukov

I Shesterikov

W Tierens

M Usoltceva

W Zhang

D Aguiam

R Bilato

L Colas

K Crombé

H Faugel

J Faustin

H Fuenfgelder

S Heuraux

A Kappatou

R Maggiora

M Mantsinen

A Messiaen

D Milanesio

J Ongena

R Ragona

A Silva

G Suárez López

D Van Eester

M Weiland

Asdex Upgrade

Eurofusion Mst1

ION CYCLOTRON RANGE OF FREQUENCY POWER: Progress in Operation and Understanding for Experiments with Metallic Walls

Significant progress in applying ICRF power to ASDEX Upgrade (AUG) through improved power coupling and reduced impurity production has been associated with progress in understanding and modelling. First, the coupling of the fast wave was improved using outer mid-plane gas injection. The local edge density increase in front of the antenna shifts the fast wave cut-off position closer to the antenna by ~2cm, a result confirmed with new density measurements in front of the antenna. The ICRF coupling increases by 120% (only 25% for top gas puffing). The increased density and resulting improved coupling. was also numerically modelled. Second, the new 3-strap antennas in AUG demonstrated clearly that a proper antenna design can successfully mitigate ICRF-specific tungsten (W) sputtering. The reduction of the W sputtering was achieved by minimizing the RF currents on the antenna surfaces exposed to the scrape-off-layer (SOL) plasma. The local RF currents, rectified DC currents and the W sputtering yield at the antenna side limiters experience a clear minimum close to a phasing between the central and the outer straps of 180° and a power balance ratio Pcen/Pout of ~ 2. At this optimum, the local source of sputtered W at the limiters is reduced by a factor between 1.5 and 6, depending on the location. The experiments and modelling confirm the hypothesis of sheath rectification as the source of the sputtered W. Furthermore, the new 3-ion ICRF heating scenario, which can produce very energetic particles, has been successfully reproduced in AUG. The progress in operation, in understanding and modelling is strongly supported by improved ICRF diagnostic coverage including density measurements directly in front of the antenna by reflectometry, advanced RF coupling characterization, measurements of antenna limiter currents, B-dot probes, Ion Cyclotron Emission (ICE) measurements and by dedicated tests on the experimental device IShTAR (Ion cyclotron Sheath Test ARrangement).

1.

INTRODUCTION

ASDEX Upgrade (AUG) is a medium size divertor tokamak (R = 1.65m, a = 0.5m, b=0.8m, Bt < 3.1T, Ip < 1.2 MA) with three heating methods: two neutral beam injectors deliver a total of up to 20 MW in deuterium beams at energies of 60keV and 93 keV, electron cyclotron power is available with up to 8MW at 140 GHz or 6.4 MW at 105 GHz. Power in the ion cyclotron range of frequencies is delivered by four antennas, powered by 4 generators in an ELM-resilient configuration with a total power of originally 8 MW and a frequency range of 30 to 60 MHz (and with reduced power capability at higher frequencies). Up to 6 MW have been coupled at 30 MHz. Starting 2018, an additional generator will be available to increase the installed power capability to 9.5 MW.

Over the years, AUG has evolved from a carbon (C) machine to machine where all first wall components are made of tungsten (W) or are W coated. Major results obtained consist of the achievement of H-mode [START_REF] Noterdaeme | AIP Conf. Proc[END_REF], the development of an ELM-resilient coupling system [START_REF] Noterdaeme | 16 th IAEA Conf. on Fusion Energy[END_REF], the use of 3 He as minority [START_REF] Noterdaeme | [END_REF], the test of an antenna without Faraday screen [START_REF] Noterdaeme | AIP Conf. Proc[END_REF], application of the central ICRF to avoid impurity accumulation in various scenarios including the ITER baseline [START_REF] Th | The ITER baseline scenario investigated at ASDEX Upgrade[END_REF], generation of MHD modes by the ICRF-accelerated ions [START_REF] Garcia-Munoz | [END_REF], application of the Ion Cyclotron Wall Cleaning (ICWC) techniques [7]. Since the change to an all W machine, the need to understand the plasma-antenna interactions and to eliminate the increased impurity production due to the ICRF power has grown in importance. Whereas the antennas were originally 4 identical 2-strap antennas [8], they now consist of a pair of 2-strap antennas, with boron (B) coated limiters and a pair of 3-strap antennas with W coated limiters.

In addition to the experimental programme, understanding was improved by using theoretical modelling, assisted by data from sepcific diagnostics [START_REF] Faugel | An overview of the in-vessel ICRFdiagnostics in the ASDEX Upgrade tokamak[END_REF] and a supporting programme on a test stand (IShTAR) [START_REF] Crombé | AIP Conf. Proc[END_REF].

We report here on the recent advances that allowed experimentally to suppress significantly (and often completely) the ICRF-specific impurity production; these advances were accompanied by code developments. The density in front of the antenna plays a large role in the power coupling. With the help of a new edge reflectometer diagnostic, we have shown experimentally and confirmed theoretically that the edge density profile in front of the antenna can be modified to increase the antenna coupling. We have also modelled and confirmed experimentally that, in case the 3-strap antennas do not operate in their optimized configuration, convective cells can develop in front of the antennas. A new 3-ion ICRF scenario, theoretically predicted [START_REF] Ye | [END_REF]12], and experimentally tested on Alcator C-mod and JET [13], has further been investigated on AUG. In section 5, we give an overview of the recent developments of dedicated diagnostics, and in the last section, the accompanying programme on IShTAR is presented.

OPTIMIZATION OF THE ANTENNA GEOMETRY

After the AUG ICRF antenna limiters were replaced by the W-coated ones, the ICRF power from the original 2-strap antennas led to a strong increase of the plasma W content and high radiated power, negatively affecting the performance [14]. Spectroscopic measurements of the W erosion at the antenna limiters [15] confirmed that the W influx correlated strongly with the ICRF power. The ways to improve the antenna design and experimental conditions were at first assessed [16] by using RF near-field calculation. Further development of the theoretical description of the mechanisms driving the RF sheaths deemed responsible for the W sputtering, has been improved significantly in the recent years [17], partially due to more experimental data becoming available.

Experimental results

First experiments tested a 2-strap antenna in which shields covered the antenna corners where magnetic field lines pass only in front of one strap. These locations were initially considered as candidates to explain the appearance of the RF sheaths leading to the W sputtering. However, more advanced calculations, confirmed by experiments indicated that this modification does not lead to significant change of the W sputtering pattern [16]. This demonstrated that the RF fields at the Faraday Screen have a limited contribution to the limiter W erosion, and rather that the fields at the antenna frame (including the limiters) need to be reduced to reduce W sputtering.

For the second experimental step, one original 2-strap antenna was modified by introducing narrower straps and broader antenna limiters, in order to reduce the RF image current density at the limiters that drives the local RF electric fields including the parallel component E||. The latter had been assumed to be the most probable candidate to explain the mechanism driving the RF sheaths and thus the elevated plasma potentials which lead to ion acceleration and W sputtering. Indeed, the experiments showed a reduction of up to 40% of the sputtering yield measured at the limiters of the modified antenna, consistent with the core W content which was similarly smaller when the modified antenna was operated [18]. The third and most significant step was to build and install new 3-strap antennas [19] which were designed to minimize the RF image current in the antenna frame and the electric fields (including E||) at the lateral antenna limiters. The accompanying upgrade of the circuit feeding the antenna allowed the experimental characterization of the formation of the RF sheaths and W sputtering (Fig. 1) with the power balance parameter Pcen/Pout (ratio of the power launched by the central strap to that by both outer straps) and phase deviation from dipole DF as variables. Figure 1 presents the RF current, rectified DC current and the sputtering yield measured at one of the limiter tiles, as well as the ICRF specific increment of the W concentration in the plasma (see [START_REF] Bobkov | Impact of ICRF on the scrape-off layer and on plasma wall interactions: from present experiments to fusion reactor[END_REF] for details). Depending on antenna location, the W sources decrease by a factor of 1.5 to 6 for the optimized configuration [21]. Compared to the W-coated 2-strap antennas, the 3-strap antennas [22] showed a drastic decrease of the ICRF-specific W content, provided these were operated close to the optimal configuration (dipole phasing and Pcen/Pout » 2). The impurity performance was at the same level or better than the 2-strap antenna with B-coated limiters.

Development of codes

The observed minima of the RF current and E|| at the limiters can be well reproduced by near-field calculations using a simplified description with a vacuum layer between the antenna and the plasma [21,22]. More sophisticated analyses with RAPLICASOL and SSWICH codes [23], which take into account more realistic wave propagation in the scrape-off-layer, confirmed that for the 3-strap antenna minima are observed both for E|| and for the rectified potential at the limiters for the proper power ratio and phasing. The RAPLICASOL code [24,[START_REF] Jacquot | AIP Conference Proceedings[END_REF], used to model ICRF wave propagation and power coupling near the antenna, is now able to handle curved geometries, complete with corresponding curved Perfectly Matched Layers [START_REF] Colas | Perfectly Matched Layers for timeharmonic electromagnetic wave propagation in curved gyrotropic media[END_REF], and to import not only an arbitrary 3D density profile from experiments and EMC3-Eirene simulations, but also an arbitrary 3D vector field for the confining magnetic field. Great progress has also been made in the validation of RAPLICASOL against other ICRF codes such as TOPICA [24]. We found that RAPLICASOL and TOPICA predict similar reflection coefficients (to within ~2%). Other quantities of experimental interest which depend on the reflection coefficients, such as the coupled power, coupling resistance, and optimal matching settings, were also found to be in good agreement between both codes. TOPICA itself was in agreement with extensive experimental comparisons [27].

DENSITY PROFILE IN FRONT OF THE ANTENNA

The density profile directly in front of the antenna plays a significant role in the antenna coupling. New diagnostic capabilities (reflectometry directly in front of the antenna) and new modelling capabilities allowed significant advances in the calculation of the modifications of this density profile, which then could be confirmed by the experimental data.

Increase in coupling through gas puffing

The coupling of ICRF power to the plasma depends sensitively on the plasma density in front of the antennas since the launched fast wave is evanescent below the cut-off density (usually of the order of 10 18 m -3 for typical frequencies and antenna spectra in present day tokamak). The local density in front of the antenna and thus the ICRF coupling can be increased with local gas puffing/fuelling. In recent AUG experiments [28], midplane gas puffing close to the ICRF antenna was found to increase the ICRF power coupling most significantly (~120%) while top gas puffing increases it to a much smaller level (~25%) in typical H-mode plasmas with a moderate gas rate of 1.2 x 10 22 el/s. In parallel with experiments, the 3D edge plasma fluid and neutral particle transport code EMC3-EIRENE [29] is used to calculate the SOL density profiles for different gas puffing scenarios; the calculated profiles are then used in the antenna codes such as FELICE [30] and RAPLICASOL [START_REF] Jacquot | AIP Conference Proceedings[END_REF] to calculate the coupling resistances. The simulation results are in good agreement with the experimental results [31,32]. They indicate that midplane gas puffing increases the SOL density very significantly at locations locally close to the gas valve, and this increase decays exponentially as a function of geometrical distance between the gas valve and antenna. Top gas puffing increases the SOL density almost toroidally homogeneously but at a smaller level, and this increase is independent of the toroidal positions of the gas valves. The effects of local gas puffing on local plasma density are attributed to the localized high neutral density (gas cloud), magnetic field line connections to the gas cloud and the local decrease of the temperature [32][33][34].

Further EMC3-EIRENE simulations have been carried out for ITER [START_REF] Zhang | Scrape-off layer density tailoring with local gas puffing to maximize ICRF power coupling in ITER[END_REF] and DEMO [START_REF] Zhang | EMC3-EIRENE modelling of edge plasma to improve the ICRF coupling with local gas puffing in DEMO[END_REF]. The results suggest that in order to maximize ICRF coupling in these future machines, gas should be injected as close as possible to the ICRF antenna locations while keeping the gas cloud covering the antenna as much as possible. In ITER, midplane gas puffing close to the antenna could increase the coupling resistance by ~150%-200% for typical Hmode with standard density profiles.

Convective cells

While the antenna is designed to launch the fast wave, the slow wave is generated parasitically. The nonlinear interaction between the slow wave and sheath results in enhanced inhomogeneous sheath potentials and formation of E×B convective cells in the SOL, leading to density modifications in the SOL. To understand the ICRF induced SOL modifications, two methods have been developed: 1) EMC3-EIRENE simulations based on the experimental data (using the potential measured with a RFA probe) [37], and 2) self-consistent simulations by running the EMC3-EIRENE, RAPLICASOL and SSWICH [38] codes in an iterative way [39]. The calculated density convection can then be compared with the density measurements, obtained from the reflectometers embedded in the antenna [40]. Good qualitative agreement between simulation and measured density convection has been obtained. Our results indicate that the largest sheath potential, convective cells and thus density convection are located on the top and bottom of the antenna. Density depletions are seen inside the convective cells while density accumulations are developed where the convective cells interact with the wall. The 3-strap antenna with optimized antenna feeding configuration (dipole phasing, power ratio between central and outer straps=2:1) leads to the lowest the sheath potential and density convection among the studied cases.

The RF convective cells can also influence the turbulence transport and further modify the SOL density. Recent progress has been achieved on understanding the interaction between the turbulence and RF convective cells [START_REF] Zhang | Blob distortion by radio-frequency convective cells[END_REF]. It is shown that RF convective cells can distort and even break up the big blobs into small ones in the SOL. Self-consistent simulations by running the BOUT ++ [42], RAPLICASOL and SSWICH codes are expected to further address the underlying physics.

NEW 3-ION ICRF HEATING SCENARIO

The novel three-ion species ICRH scheme has been recently demonstrated as an efficient technique for heating various mixed ions plasmas [13], also holding promises for future ITER operations [43]. Following JET and Alcator C-Mod experiments, minority heating of 3 He ions in H-D plasmas has been successfully demonstrated on AUG.

The experiments were carried out in H-D mixed plasmas with H/(H+D) ≈ 0.7-0.8 at a magnetic field of 3T and 2.8T, and a plasma current of 800kA. Up to 2.6MW of ICRF power was coupled into the plasma at f = 30MHz. This choice of RF frequency and magnetic field places the cyclotron resonance of the 3 He minority ions in the plasma core for discharges at 3T and at the high-magnetic field side (HFS) at ρpol ≈ 0.3 for discharges at 2.8T. Hydrogen neutral beams (up to 8MW) were applied for plasma pre-heating and charge exchange recombination spectroscopy (CXRS) measurements. In the absence of a real-time control scheme for the 3 He concentration, a series of short (50ms) 3 He puffs from a gas valve at the mid-plane were applied. The 3 He puff rate ([2-18]×10 20 el/s) and the inter-puff interval were varied from shot to shot in order to assess the sensitivity of the heating scenario 3 He concentration in the core and to optimize the scenario performance on AUG. According to numerical computations, conditions of efficient double-pass wave absorption for this scenario can be achieved on AUG for 3 He concentrations in the range X[ 3 He] = n( 3 He)/ne ≈ 0.2-1.5%. At higher 3 He concentrations, a mode conversion heating regime is reached, characterized by a fairly low double-pass absorption efficiency (~10-30%).

Controlling the 3 He concentration is a key factor in determining the performance of this ICRF scenario on AUG. Operation at relatively high 3 He concentrations of ~3-5% resulted in low heating performance and increased W content, in line with modelling results predicting low double-pass wave absorption under these conditions. Figure 2(a) shows an evolution of plasma parameters for AUG discharge #34697 with on-axis 3 He resonance. High 3 He puff rates of 18×10 20 el/s and 17×10 20 el/s were applied for the first (t = 1.35-1.40s) and second (t = 2.35-2.40s) puffs, respectively.

The second panel of Fig. 2(a) shows the temporal evolution of the total helium concentration ( 3 He and 4 He) in the plasma, as measured by the CXRS system. Most of the measured helium content comes from 3 He, and the 3 He concentration increases rapidly after each 3 He puff and then decays.

Strongly radially peaked ion temperature profiles with Ti(0) up to 4.3 keV were observed during the ICRF+NBI phase of the discharge after the first 3 He puff, when the He concentration decayed from ~4% to ~1.3-2%. For comparison, the core ion temperature during the NBI-only phase reached Ti(0) ≈ 1.9keV. Unfortunately, Te(0) data is not available for AUG discharges at 2.8-3T, making the analysis of the peakedness of the Te profile and comparison of Te and Ti profiles difficult to assess. We note that for #34697 with relatively high 3 He concentration, Te at ρpol ≈ 0.2 closely matched the corresponding Ti value.

Interestingly, similar to the Ti profile, the plasma toroidal rotation velocity also had a peaked profile, increasing from 100 km/s during the NBI-only phase to 230 km/s during the ICRF+NBI phase. These observations are quite similar to the ones reported for 3 He minority heating scenario in deuterium plasmas on AUG [START_REF] Mantsinen | AIP Conf. Proc[END_REF]. Whether this effect is due to ICRF fast-ion and heating physics, or is caused by the changes in the transport properties of the plasma (e.g. due to increased central radiation) needs further analysis.

With on-axis heated ICRF discharges, an efficient generation of energetic 3 He ions was observed, confirmed by the excitation of Alfvén modes (fAE ≈ 160-190 kHz), the appearance of fishbones and measurements with the fast-ion loss detector (FILD). Backward-orbit tracing of ions measured by FILD infers an acceleration of 3 He ions to the energies of at least ~1.7 MeV for the ICRF resonance at the center. In a few discharges, no 3 He was injected into the plasma and the heating scenario relied on the residual 3 He left from the previous discharges. Although Alfvén modes were observed in such plasmas, heating AUG plasmas with the three-ion scenario at extremely low 3 He concentrations did not show such clear signs as on JET, for which 3 He concentrations as low as ~0.2% were successfully used for plasma heating [START_REF] Ye | [END_REF].

In contrast to JET, medium-size AUG plasmas cannot confine multi-MeV energetic ions, which are generated with this ICRF scenario at extremely low 3 He concentrations. In order to improve the confinement of the RFheated 3 He ions on AUG and heating of the background plasma with ICRF, the magnetic field was reduced to 2.8T in pulse #34704, which resulted in shifting the 3 He cyclotron resonance off-axis to the HFS at ρpol ≈ 0.3 and reducing 3 He fast-ion energies. 3 He puffs with a puff rate of 2.3x10 20 el/s were applied every 0.5s, resulting in a 3 He concentration of ~0.5-1%. The ICRF power was increased in steps: 0.9MW, 1.9MW and 2.5MW, see Fig. 2(b). Consequently, the plasma stored energy increased from ~0.3MJ during the NBI-only phase (PNBI = 8MW) to ~0.4MJ during the ICRF+NBI phase.

We also note a gradual increase of Te measured at ρpol ≈ 0.2, which is consistent with the dominant collisional electron heating from energetic 3 He ions at such low 3 He concentrations. Furthermore, lower W levels were observed in this off-axis discharge when compared to on-axis discharges from this series of shots. CXRS measurements of energetic 3 He ions in this discharge were analyzed in [START_REF] Kappatou | [END_REF] and the measured spectra were shown to agree well with the modelled spectra using the 3 He distribution functions predicted by the TORIC-SSFPQL modelling, yielding the 3 He effective temperatures T⊥ ≈ 500 keV and T|| ≈ 15 keV at ρpol ≈ 0.3.

An interesting observation is the appearance of ~90-100 kHz MHD modes in the last phase of the discharge with ICRF heating only. The so developed HFS off-axis 3 He heating with the three-ion species scenario on AUG is highly relevant for H-mode studies in non-active ITER plasmas, for which an option is an equivalent 3 He minority heating in H- 4 He mixed plasmas as has been recently suggested [46].

IMPROVED DIAGNOSTIC CONVERAGE

The progress achieved in understanding the interactions between ICRF waves and magnetized plasmas has been substantially supported by new diagnostics.

These include the already mentioned density measurement by x-mode reflectometry embedded in the antenna [40], RF probes to characterize the radiation spectrum of the ICRF-antennas during plasma discharges and the ICE [47], shunts for measurements of RF-and DC-currents to the antenna limiters [START_REF] Faugel | An overview of the in-vessel ICRFdiagnostics in the ASDEX Upgrade tokamak[END_REF], additional spectroscopic lines of sight measuring WIline emission and RF current probes in the 3-strap ICRF antennas to provide information on the phasing between central and outer straps [START_REF] Faugel | An overview of the in-vessel ICRFdiagnostics in the ASDEX Upgrade tokamak[END_REF].

The RF probes consist of inductors that directly detect the magnetic field component of the ICRF wave field and provide information on the wave amplitude, wavenumber, and polarization. The probe coverage inside the ASDEX Upgrade torus is extensive (Fig. 3) and includes locations on the high-and the low-field side. A field-aligned probe array is installed to measure the parallel wavenumber of the ICRF wave [47]. An additional probe pair is available for radial scans on the low-field side manipulator [48]. The probes' outputs are sampled by logarithmic RF detectors [START_REF] Faugel | An overview of the in-vessel ICRFdiagnostics in the ASDEX Upgrade tokamak[END_REF] that measure both the amplitude and the phase difference between a pair of probes. A fast data acquisition system is used to measure wave frequency spectra for ion cyclotron emission studies [49].

DEVELOPMENTS ON IShTAR

IShTAR is a device to investigate antenna-plasma interactions [START_REF] Crombé | AIP Conf. Proc[END_REF]. It consists of a main vacuum vessel (1m diameter, 1m lengh) encircled by two big magnetic field coils in a Helmholz type configuration and containing an ICRF antenna. This vessel is connected to a helicon plasma source (0.4 m diameter, 1m length) with 5 smaller magnetic field coils.

The machine performance was improved to achieve the high density and radially uniform plasma in front of the ICRF antenna needed for the sheath studies. The magnetic field topology and its strength determines the plasma flow from the helicon source towards the ICRF antenna. Optimisation consisted in varying the currents in the big and small set of coils. From magnetic mapping one would expect that compression of magnetic field lines in the main vacuum vessel, as it shown in Fig. 4 (a) -(c), should lead to a narrower plasma density profile with higher central plasma density in the big vessel. The results indeed show a systematic peaking in density when the magnetic topology changes from Fig. 4(a) to (c), as shown in Fig. 5. This suggest that a magnetic field topology with Ismall = 1000 A and Ibig = 2500-3000 A, is favourable for the ICRF antenna operation as it presents a compromise with its relatively broad profile but still dense plasma in front of the ICRF antenna. The position of the antenna is indicated in the figure with an orange dashed line. To benchmark the theoretical tools for the studies of the ICRF antenna-plasma interaction a diagnostic is being developed to directly measure the electric fields in the sheath near the antenna structures. The development of a dedicated diagnostic technique for such a specific problem requires easy access and sufficient operational time, which IShTAR provides. The geometry is simplified but nevertheless mimics the physics phenomena of interest. The diagnostic is based on the Stark effect which modifies the emission spectra of the atoms when exposed to external electric fields. The effect is more evident for hydrogen and helium atoms. The relative shift of the spectral line from its unperturbed wavelength, allows us to extract the amplitude and direction of the electric field that excited helium atoms are submitted to.

One way of applying Stark spectroscopy is on the passive optical emission spectra recorded with a single fibre coupled to a high-resolution spectrometer (the spectral resolution is 0.0023 nm per pixel). With this technique we have collected the emitted light from the sheath around the leading edge of IShTAR's ICRF antenna box. Since the ICRF antenna was employed in the discharge scenario, the unperturbed spectra were recorded from a helium calibration lamp [Fig. 6]. With the maximum power delivered to the ICRF antenna, which was of the order of 1 kW, the relative shift of the spectral line profile detected was corresponding to electric field of E = 3.4 ± 0.3 kV cm -1 [50] Even though the described effect is localized to the regions where the electric fields are present and sufficiently strong, the measurements are time-averaged and volume integrated. To improve the method, a newly designed optical head with a fibre-bundle instead of a single fibre in combination of a local helium gas-puff will provide spatially resolved electric field distribution in the sheath.

As a next step, we are implementing a laser-aided spectroscopy, as it is superior to the passive optical emission, in terms of spectral, spatial and temporal resolution of the recorded spectra. Doppler-free saturation spectroscopy is such a technique currently in the implementation phase in IShTAR. Spectra recorded in this way will allow us to obtain electric field measurements with higher accuracy and better sensitivity. [51,52,53].

Another approach to obtain RF sheath electric field of the ICRF antenna is a combined experimental-numerical method. In the experimental part, the ICRF magnetic field components were measured in front of the antenna with an array of B-dot probes driven on a manipulator. The resulting experimental profiles are compared to calculations performed in COMSOL software [54], from which the E fields can then also be derived.

IShTAR's ICRF antenna is modelled with high geometrical precision (± 0.1 mm). Good qualitative agreement of numerical and experimental results allows us to consider the model reliable and to trust electric field values retrieved from the simulation. A vacuum approximation of the parallel electric field distribution is obtained from the COMSOL model and used as an input to test a code that calculates DC voltages in the sheath. Work on plasma implementation into the IShTAR model is being carried out. The presence of a Lower Hybrid (LH) resonance complicates numerical calculations. A common method of avoiding this resonance by replacing part of the low density plasma with a vacuum layer is however not adequate for IShTAR, since the whole plasma volume in the device is low density SOL-like plasma. Further analysis thus is needed to achieve reliable numerical results.

Local density measurements at the very edge of the plasma near the antenna limiters and even in the limiters shadow (~ 1x10 15 m -3 ) have been performed with RF compensated planar Langmuir probes. The probes dimensions had to be big enough (1 mm thick, 5 mm radius) to obtain tolerable signal-to-noise ratio and at the same time small enough not to perturb plasma too much when measuring very close (~ 2 cm) to metallic antenna structures. [50]

FIG. 1 .

 1 FIG. 1. RF feeding diagrams using the strap power balance Pcen/Pout and phase deviation from dipole DF as variables in a discharge with PICRF=1MW; local measurements at a single antenna limiter tile of (a) the toroidal RF current, (b) the DC current circulation and (c) of the increment of the W sputtering yield; (d) increment of the W content in plasma at Te»1.5 keV.

FIG 2 :

 2 FIG 2: Overview of plasma parameters for AUG discharge #34697 with a central 3 He ICRF resonance (3T, f = 30MHz) and discharge #34704 with a HFS off-axis 3 He resonance (2.8T, f = 30MHz). Ti and Te were measured with the CXRS and Thomson Scattering systems, respectively. The displayed data is averaged over the time interval of 100 ms.

FIG. 3 :

 3 FIG. 3: (a) top and (b) poloidal cross-sectional views of the AUG. The positions of the low-field side (LFS) and the high-field side (HFS) B-dot probes is shown. The HFS probes are positioned radially opposite to the ICRF antennas.

Fig. 4 .

 4 Fig. 4.(a) -(c) Change of magnetic field topology and strength in the main vessel of IShTAR experiment as a function of the current in the big set of coils (Ibig). The current in the small set of coils is kept constant at 1000 A.

FIG. 5 .

 5 FIG. 5. Radial profile of the plasma density in the main vacuum vessel as a function of the magnetic field in the center of the main vessel. The range of magnetic fields Bbig corresponds to the change of current in the set of big coils Ibig inFig.4. (a)-(c).

ACKNOWLEDGEMENTS

This work has been carried out within the framework of the EUROfusion Consortium and has received funding from the Euratom research and training programme 2014-2018 under grant agreement No 633053. The views and opinions expressed herein do not necessarily reflect those of the European Commission.


C Silva
email: csilva@ipfn.tecnico.ulisboa.pt

D Aguiam

M Bernert

G D Conway

L Gil

B Gonçalves

L Guimarais

T Happel

Stéphane Heuraux

P Manz

M E Manso

V Nikolaeva

J Santos

E Seliunin

A Silva

F Da Silva

U Stroth

J Vicente

E Wolfrum

The Asdex Upgrade

Eurofusion Mst1 Team

IST Contributions to the ASDEX Upgrade Edge and Divertor Physics Using Microwave Reflectometry

des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

INTRODUCTION

Information of the plasma density is essential for the study and operation of magnetically confined fusion devices. Microwave reflectometry appears as an attractive diagnostic due to its high temporal and spatial resolution and its application to profile as well as fluctuation density measurements.

The microwave reflectometry systems developed by IST for ASDEX Upgrade (AUG) consist of: (i) a multi-band frequency modulated continuous wave (FM-CW) O-mode reflectometer with the unique capability of providing profile and fluctuations density measurements on the high-field side (HFS) and low-field side (LFS) simultaneously, making it a relevant diagnostic for poloidal asymmetry studies; (ii) a fast frequency hopping Omode reflectometer used to obtain more detailed information on density fluctuations at the LFS; and (iii) a multichannel X-mode reflectometry diagnostic recently installed to measure the edge density profile in front of the ICRF antenna. This contribution presents an overview of the scientific results obtained with the different reflectometry systems used in a complementary way in order to address some of the key issues under investigation at AUG.

INFLUENCE OF THE HIGH-FIELD SIDE DENSITY FRONT ON THE MIDPLANE DENSITY PROFILES

The separatrix density and the scrape-off layer (SOL) conditions have a significant impact on the pedestal stability and hence on plasma confinement. However, the physics mechanisms responsible for the changes in confinement with fuelling, input power and impurity seeding have not yet been fully identified. Our main goal is to clarify the impact of the region of high density in the inner divertor (HFSHD) on the H-mode midplane profiles following a previous work for L-mode plasmas [1].

To explore the effect of fuelling and input power a discharge with steps in these quantities is analysed. Fig. 1 displays the evolution of the LFS separatrix density, ne,sep, and HFS density just in front of the inner wall, ne,wall, both estimated from reflectometry, together with that of the main discharge parameters. At the LFS, the edge density at the midplane is observed to respond clearly to the increase in the fuel rate leading to an outward shift of the density profile. This is mainly seen by the increase in LFS separatrix density. On the contrary, the input power has a minor impact on the density profile at the LFS with no changes observed in ne,sep when the power is stepped-up. At the HFS, an HFSHD is observed to exist at the midplane from early in the discharge (t < 1.5 s) as consequence of the relatively high input power and line-averaged density. The density measured by reflectometry just in front of the inner vessel wall, follows closely the temporal evolution of the HFSHD in the divertor region. The density gets stronger when the gas input is raised at t = 2.5 s and augments strongly when the input power is stepped up, close to t = 4 s. The effect of the input power is therefore clearly different at LFS and HFS, as it strongly increases the HFS density while the LFS profiles are not significantly modified.

Plasma confinement is also differently influenced by the variation in input power and fuelling (see Fig. 1). The normalized confinement time is observed to improve slightly (5 -10%) when the power is stepped up and to degrade when the fuel rate is increased, corresponding to a different dependence on the plasma parameters than that observed for the HFSHD, which increases with both input power and fuelling. Results presented here confirm the existence of a relationship between plasma confinement, the shift in the midplane LFS density profile and the presence of the HFSHD with respect to changes in fuelling as previously reported [2]. However, the detrimental effect of the HFSHD on confinement was not visible in the discharges analyzed here with variations in the heating power. This suggests that more is at play with respect to the effect of the HFSHD in confinement. The presence of the HFSHD may be responsible for the relative shift of temperature and density profiles, causing a reduction in MHD stability. However, this detrimental effect is probably overcompensated by the positive effect of increasing the heating power on energy confinement.

The link between the HFSHD, divertor conditions and midplane density profiles is further explored by analysing the neutral pressure data measured by baratrons below the inner and outer divertor, Fig. 1. As the deuterium fuelling is raised, both the outer divertor neutral pressure and the LFS separatrix density increase confirming previous observations [3]. On the contrary, when the input power is raised neither the divertor neutral pressure in the outer target nor the midplane LFS separatrix density are significantly modified. Concerning the inner divertor, when deuterium fuelling is raised both the inner divertor neutral pressure and the SOL density at the HFS midplane increase, similarly to the observation at the LFS. However, when the input power is raised both the inner divertor neutral pressure and the SOL density at the HFS midplane increase contrary to the observed at the LFS. The evolution of the inner divertor neutral pressure is consistent with that of the HFSHD as both are seen to increase with fuelling and input power. Neutral pressure data gives further evidence that the LFS density profile is mainly influenced by the outer divertor target. An increase in the input power leads to a strong increase of the neutral pressure at the inner target and to a strengthening of the HFSHD but has a modest influence at the LFS (both at the midplane and outer divertor). In summary, our results indicate that the separatrix density at the LFS is better correlated with the neutral pressure at the outer target while the HFS SOL density follows the neutral pressure at the inner divertor.

HFS/LFS EDGE TURBULENCE IN DIFFERENT STATES OF DIVERTOR DETACHMENT

Transport in the SOL depends on the state of the divertor detachment. It is also widely accepted that SOL/edge properties are not poloidally symmetric and therefore data from the under-diagnosed HFS is essential to improve the understanding of SOL transport and its link to the divertor conditions. To fill that gap, density fluctuations were measured simultaneously at the LFS and the HFS with the AUG FM-CW reflectometry system operating in fixed frequency in plasmas where the state of divertor detachment evolves from attached to completely detached along density ramp L-mode discharges. Fluctuations are probed at three fixed density plasma layers that vary in radial position along the discharge following the dynamics of the plasma density profile. Density profiles at both the HFS and the LFS were also measured in paired discharges with the same FM-CW diagnostic operating in swept frequency enabling to localize the density layers where fluctuations are being measured at each probed time interval along the discharge.

The radial profiles of the density fluctuations level (ne/ne) at the HFS and the LFS are displayed in Fig. In the last part of the discharge, during the complete detachment state, the reflected signals reveal that the increase of density fluctuation levels results mainly from an increase of the low frequency components (< 15 kHz), which is also observed in the Langmuir probe data. This is in agreement with the generally accepted view that radial transport at the LFS SOL is dominated by filamentary activity. Experimental results are in line with an enhanced convection of filaments that has been reported before [6] at the LFS at the beginning of the outer divertor detachment leading to a flatter edge/SOL density profile. Adapted from [4].

At the HFS a much lower level of fluctuations than at the LFS is observed at the midplane for all the divertor states, in agreement with ballooned transport. A strong increase of density fluctuations is seen at the far-SOL associated with filaments at the LFS becoming faster and less frequent. The increase of ne/ne at the HFS cannot be attributed to an increase of the local radial transport but rather to the presence of filaments that propagate parallel to the magnetic field lines from the LFS to the HFS. This study using HFS/LFS reflectometry measurements provides a consistent picture of the poloidal asymmetry in the density fluctuations and reveals that the divertor conditions influence significantly the midplane turbulence.

EDGE INSTABILITIES ACROSS THE L-H TRANSITION AND IN H-MODE

The L-H transition in AUG is often accompanied by the appearance of edge coherent modes (CMs) [7] or quasicoherent modes (QCMs) [START_REF] Graça | EPS Conference on Plasma Physics[END_REF] in density fluctuations. QCMs have also been detected in other devices [e.g. 9-10], including during ELM cycles. The underlying instabilities of these modes are mostly an open question, despite their relevance for understanding edge transport and pedestal physics.

Slow power ramp shots at different densities (𝑛 𝑒 ̅̅̅ 𝐿-𝐼 = 2.3, 4.0 and 4.6 ×10 19 m -3 ) have been conducted in AUG to study edge instabilities across the L-H transition and in H-mode, including the intermediate I-phase [10]. A lower single null configuration with B×∇B towards the X-point, constant deuterium gas puff and central ECRH power steps were used. Fig. 4 shows an overview of the medium density shot, in which the plasma undergoes an I-phase from 2.1 to 2.5 s with confinement improvement, as seen in the line-averaged electron density traces (Fig. 4(c)). Instabilities start to develop during this period and their amplitude grows and saturates when the plasma enters the ELM-free H-mode, as shown in the reflectometry phase (Fig. 4(a)) and radial magnetic field (Fig. 4(b)) spectrograms, which feature strong edge CMs with a multi-peak structure from 50 to 80 kHz. These have toroidal and poloidal mode numbers n = -(2-8) and m = 16-64, with propagation in the electron diamagnetic direction in the lab frame. Similar modes have been previously observed in AUG [START_REF] Graça | EPS Conference on Plasma Physics[END_REF] and they are also present in the low density shot, but not in the high density one. After a few ELMs with which the CMs disappear and reappear, the plasma enters a very long ELM-free phase without impurity accumulation, lasting from 3.3 to 4.1 s and appearing to approach stationarity (see Fig. 4(c)), being only interrupted by NBI. The CMs are not present, but a broader QCM is visible in the reflectometry spectrogram of Fig. 4(a), with a down-chirping frequency from 60 to 35 kHz. It also exists in the high density shot, but not in the low density one and it is not visible in any magnetic signal. The high density QCM has n = 20-23, being smaller and slower than the low density CMs.

Fig. 4. Time traces from an L-H transition experiment: (a) spectrogram of reflectometry phase; (b) spectrogram of radial magnetic field coil; (c) line-averaged electron density; (d) heating and radiated power. The vertical dashed lines indicate the time instants of L-I-H transitions.

Between the phases with the CMs and QCM there is a period of alternation between the two modes (shaded region in Fig. 4), which is correlated with changes in several edge and divertor parameters. Whenever the QCM appears, temperature and density decrease in the edge and increase with a small time delay in the divertor. This suggests that the QCM causes an increase of transport in the pedestal, expelling plasma to the divertor. This may explain the absence of impurity accumulation and ELMs, as the increased transport could prevent the edge gradients from reaching the peeling-ballooning instability boundary. If so, these observations may open the door to an ELM-free regime at AUG which will be the subject of future experiments.

To sum up, edge instabilities with a complex time evolution after the L-I-H transition have been observed in AUG. Their type and behavior is different for the low and high density branches of the L-H power threshold and they may play an important role in the H-mode pedestal structure, stability and confinement.

UNDERSTANDING DENSITY PROFILES IN FRONT OF THE ICRH ANTENNA

A new multichannel reflectometer diagnostic was recently installed in an ICRF antenna, aiming mainly for ICRF coupling and operation studies [START_REF][END_REF]. The diagnostic has been implemented and successfully commissioned. One of the most challenging tasks of the diagnostic was the implementation of an automatic initialization of the Xmode upper cutoff measurement, which is the main source of error in X-mode density profile reconstruction. Two first fringe estimation algorithms were developed [START_REF][END_REF]: one based on amplitude and spectral information and another one using a neural network model to recognize the first fringe location from spectrogram data. The experimental density profile measurements were validated against other existing diagnostics on AUG. Based on the profile data, the high radial and poloidal sensitivity of the diagnostic has been demonstrated by tracking a vertical displacement of a circular plasma. The experimental density profiles were used to corroborate ICRH power coupling simulations under different gas puffing conditions and to observe poloidal convective transport during ICRH operation, taking advantage of the multichannel topology and its sensitivity to local plasma perturbations. RF sheaths formed during ICRF operation are believed to promote convective transport associated with the potential map in front of the ICRH antenna that influence power coupling as observed using the simultaneous reflectometry density profile measurements at the top, middle and bottom regions of the ICRF antenna [13].

This new reflectometry system opens up new research opportunities in the area of SOL physics by exploring the high temporal and spatial resolution of the diagnostic and by taking advantage of the three channels installed at different poloidal locations. In addition to the density profile measurements, the system is also being validated as a diagnostic tool for density fluctuations measurements [START_REF] Seliunin | EPS Conference on Plasma Physics[END_REF], particularly relevant in the far-SOL that is generally inaccessible to the FW-CW reflectometer. The electron density profiles measured by different diagnostics, such as Langmuir probes mounted on the midplane manipulator (MEM), the lithium beam diagnostic (LiB) and multichannel reflectometer diagnostic (RIC) are compared in Fig. 5 for discharge #34290. Two time periods with ne,core = 3.3×10 19 m -3 (left) and 5.0×10 19 m -3 (right) are presented. Solid lines correspond to mean density profiles while dashed lines correspond to 2 times the standard deviation (σ) of the fluctuations above and below the mean profiles. As illustrated in Fig. 5, both the averaged SOL density and the amplitude of the fluctuations increase with core density as expected. A good agreement is observed between the profiles from the RIC, probes and LiB for both periods. RIC median ± 2σ profiles fit reasonably well the upper and lower boundaries of MEM density profiles and may represent the impact of fluctuation activity in the plasma profiles. Differences in the amplitude of the fluctuations between the used diagnostics are most probably related with their different temporal resolutions, with larger fluctuations amplitudes naturally obtained for probes (2 MHz) and modest values obtained with LiB (10 kHz). As the density is increased, a flattening of the SOL plasma density profile is observed to occur above a Greenwald fraction of about fGW = 0.45-0 .5, in good agreement with previous results, suggesting an enhancement of the SOL radial transport [6].

SYNTHETIC REFLECTOMETRY DIAGNOSTIC

Aiming to improve the understanding and interpretation of experimental results from reflectometry, a synthetic reflectometry diagnostic has been developed employing full-wave simulations. By modelling reflectometry diagnostics together with sophisticated plasmas models, a true synergy can be developed between the experimental and numerical work to improve the reliability and interpretation of turbulence measurements.

The state-of-the-art full-wave code REFMUL is based on a finite-difference time-domain method [START_REF] Silva | [END_REF]. This twodimensional code allows setting up synthetic reflectometers by modelling features such as transmission waveguides, metallic horn antennae or in-phase I(t) = A(t)cos(φ(t)) and quadrature Q(t) = A(t)sin(φ(t)) detection schemes, similar to what is implemented experimentally. The probed medium, the plasma itself, can be modelled using analytical descriptions (for instance using well known turbulence models that can be found in literature) or employing numerical results obtained from more realistic gyro-fluid turbulence codes such as the GEMR [16].

Both approaches are used to study relevant phenomena in fusion plasmas such as coherent filament-like density structures [17] or broadband turbulence [18]. One illustrative example is shown in Fig. 6 where a background plasma density is displayed together with the electric field component of a probing wave at one given time iteration of a full-wave Doppler simulation. In this figure, it is possible to distinguish multiple effects in the reflected probing beam that occur in both Doppler and conventional set-up, such as the main reflection near the cut-off layer, Bragg backscattering, beam splitting and forward-scattering effects which are put in evidence using oblique injection. REFMUL has been used, in particular, to model O-mode reflectometry diagnostics under different conditions of turbulence and infer plasma turbulence characteristics, such as the turbulence level, from the actual measurements. The evolution of reflectometry phase fluctuations with the plasma turbulence level (δne/ne) is shown in Fig. 7 as an example. These results were obtained from simulations with Kolgomorov-like turbulence superimposed on a linear density profile. A linear relation between the phase and the turbulence level is observed only up to δne/ne ≈ 2-4% followed by non-linear behavior at higher turbulence levels. The saturated phase response above a given turbulence level corresponds to a slight decrease in the reflected power and to the existence of nonlinear physical phenomena in the plasma-wave interactions. The existence of non-linear response regimes of reflectometry stress the importance of numerical simulations in order to properly characterize the diagnostic response.

Fig. 7. Standard deviation of reflectometry φ(t) signals for turbulence level scans with 2 probing frequencies (33GHz and 49GHz

) and 2 density gradient scale lengths Ln. Published in [17].

7.

REAL-TIME PLASMA POSITION CONTROL O-mode microwave reflectometry will be used on ITER and foreseeably on DEMO to complement the standard magnetic diagnostics for plasma position control. After a successful validation of the control scheme at the LFS in 2011 [19], the FMCW system at AUG continues to be used as a test ground for the development of this novel control technique, namely the real-time diagnostic infrastructure was upgraded to produce a demonstration at both HFS and LFS by generating the geometric plasma radius in real-time (RT). The system was successfully tested in standard regimes and also in plasmas developing an HFS density front were the validation assumptions of the technique are violated. Reflectometry's RT inner, Rin, and outer, Raus, separatrix positions were combined to produce an approximation of the geometric plasma radius, Rgeo = (Rin + Raus)/2, that was used to replace the corresponding magnetic measurement normally used as the position controller input signal. During the reflectometry control phase, the geometric radius of the plasma column was programmed to swing 1.5cm (non-symmetrically) around its original position. As can be seen the new controller maintained reflectometry's Rgeo within ≈ ±0.5 cm of the target trajectory. Reflectometry estimates for Rin, Raus, and Rgeo are coherent with their magnetic counterparts, demonstrating very good precision. Input Rgeo offsets were successfully handled by the position controller when switching to and from reflectometry input at t ≈ 2.6s and t ≈ 7.6s. From t ≈ 4.9s to t ≈ 8s a HFSHD front develops breaking the validity assumption of a constant density at flux-surfaces. During this period, the HFS separatrix position estimate is no longer valid and simply represents the position of a layer with a density similar to the one used to estimate the separatrix at the LFS. Reflectometry provided Rgeo becomes then the mid-point position of the inner and outermost layers with densities equal to the expected density at the separatrix. In this period, the controller is acting as a gap controller rather than a replacement of a standard magnetic controller. In all four control discharges (#33448, #33450, #33452 and #33453) the system operated flawlessly during the complete programmed reflectometry control phases. The uninterrupted stream of control Rgeo estimates, produced every 1 ms, reach the DCS with a total latency always < 350 μs proving that the developed system could be operated in much faster (3x) control cycles.

SUMMARY

Experimental results demonstrate that the IST reflectometry systems at AUG provide a valuable contribution to a better understanding of important physics issues such as pedestal instabilities, SOL turbulence, dynamics of the density profiles and the connection between midplane and divertor conditions. Different upgrades are under development, to improve the temporal resolution and to expand the measuring density range of the FM-CW system that will provide uniquely versatile diagnostics for combined profile and fluctuations measurements particularly relevant for edge instabilities and turbulence studies.

Fig. 1 .

 1 Fig. 1. Top: Evolution of the neutral pressure measured by the baratrons at the inner and outer divertor together with that of the LFS separatrix density, ne,sep, and HFS density just in front of the inner wall, ne,wall, both estimated from reflectometry. Bottom: Line-averaged core density, fuelling rate, NBI heating power and H98 for discharge #30733.

  2. Also displayed in the figure is the fluctuation amplitude obtained by Langmuir probes at the LFS midplane in similar experimental conditions. The density fluctuation levels from reflectometry increase radially at both the LFS and the HFS as it is typically observed in fusion plasmas. The values of ne/ne at the HFS SOL are lower than at the LFS (by a factor of ≈ 2), which is consistent with ballooned transport. Density fluctuations from reflectometry at the LFS far-SOL matches quite well the Langmuir probe results (taking into account that ne/ne by the reciprocating probe were estimated from the ion saturation current measurements ignoring the contribution of temperature fluctuations).

Fig. 2 .

 2 Fig. 2. Radial profiles of ne/ne at the LFS and the HFS obtained from FM-CW reflectometry in discharge #33484 with an edge line-averaged density of ne ≈ 1.3 10 19 m -3 . The value of ne/ne estimated from the Langmuir probe data at the LFS midplane in similar experimental conditions is also indicated. Published in [4].The relative density fluctuations at the LFS and HFS along different divertor states (in a density ramp discharge) are depicted in Fig.3revealing strong poloidal asymmetries of the SOL/edge midplane turbulence. Also it is seen that ne/ne changes differently along the discharge with radius. At the LFS, density fluctuations close to the separatrix (at ρpol =1.00-1.01 and ρpol=1.05), present a modest variation with increasing background density, also seen in the reciprocating Langmuir probe data (measuring around ρpol=1.05), while at ρpol≈1.04 density fluctuations increase along the density ramp. In the last part of the discharge, during the complete detachment state, the reflected signals reveal that the increase of density fluctuation levels results mainly from an increase of the low frequency components (< 15 kHz), which is also observed in the Langmuir probe data. This is in agreement with the generally accepted view that radial transport at the LFS SOL is dominated by filamentary activity. Experimental results are in line with an enhanced convection of filaments that has been reported before[6] at the LFS at the beginning of the outer divertor detachment leading to a flatter edge/SOL density profile.

Fig. 3 .

 3 Fig. 3. Radial profiles of ne/ne obtained from the homodyne signal of the FM-CW reflectometer at HFS (left) and LFS (right) for discharge #33484. Color of points corresponds to the different divertor states according to [5]: attached (blue), onset (red), fluctuating (green) and complete detachment state (purple). Symbols correspond to different probed densities: ne = 0.40 × 10 19 m -3 (circles), 0.84 × 10 19 m -3 (squares) and 1.61 × 10 19 m -3 (triangles). Adapted from [4].

Fig. 5 .

 5 Fig. 5. Electron density profiles averaged over 10ms for discharge #34290 at two time periods, corresponding to ne,core=3.3×10 19 m -3 (a) and ne,core=5.0×10 19 m -3 (b). Dashed curves indicate the median ± 2σ profiles.

Fig. 6 .

 6 Fig. 6. Snapshot of a Doppler simulation showing the electric field Ez. The probing beam suffers forward-scattering, becoming fragmented.

Fig. 8

 8 Fig. 8 shows the main time traces of one of the 4 control discharges performed during 2016 experimental campaign. The top plot shows the core line-averaged density (H1), deuterium fuelling (D), NBI and ECRH heating power and plasma current (Ip). During the flat-top phase of the ELMy H-mode discharge, position control is handed to the reflectometry based controller from t ≈ 2.6 s until t ≈ 7.6 s, when the magnetic controller recover the control to perform the plasma ramp down.

Fig. 8 .

 8 Fig. 8. Control of plasma position using Rgeo (target inject trajectory in black). Position controller using reflectometry Rgeo approximation switched on during t = [2.6 .. 7.6]s. From t=4.9s until t=8 s a HFSHD front appears.

ACKNOWLEDGEMENTS

This work has been carried out within the framework of the EUROfusion Consortium and has received funding from the Euratom research and training programme 2014-2018 under grant agreement No 633053. IST activities also received financial support from "Fundação para a Ciência e Tecnologia" through project UID/FIS/50010/2013. The views and opinions expressed herein do not necessarily reflect those of the European Commission.