Application of Poloidal Correlation Reflectometry to study turbulence at

ASDEX-Upgrade

D. Prisiazhniuk1,2, A. Krämer-Flecken3, G.D Conway1 ,T. Happel1, P. Manz1,2,

P. Simon1,4, M. Dunne, U. Stroth1,2 and the ASDEX Upgrade Team

1 Max-Planck-Institut für Plasmaphysik, 85748 Garching, Germany

2 Physik-Department E28, Technische Universität München, 85748 Garching, Germany

3 Institut für Energieforschung und Klimaforschung/Plasmaphysik, 52425 Jülich, Germany

4 Institut für Grenzflächenverfahrenstechnic und Plasmatechnologsie,, Stuttgart, Germany

1. Introduction

Progress in understanding and characterization of plasma turbulence is of great

importance for optimization of future fusion devices. A main challenge in these investigations

is the measurement of turbulence properties on both small time-scales (μs) and small spatial-

scales (mm). Beside probes and laser based diagnostics, microwave diagnostics are sensitive

enough to measure turbulence with high spatio-temporal resolution. Additionally they could

be applied on future devices such as ITER or DEMO, due to their insensitivity to radiation,

erosion and deposition. At ASDEX Upgrade (AUG), a microwave based and heterodyne

Poloidal Correlation Reflectometry (PCR) has been installed, which is able to measure key

properties of turbulence such as correlation length, decorrelation time, inclination of the

eddies, being a measure of the pitch angle of magnetic field lines, and propagation velocity. In

this work we demonstrate various applications of the PCR to study turbulence at AUG.

Measurements of the turbulent propagation velocity, the magnetic field pitch angle, quasi-

coherent (QC) structures and geodesic acoustic modes (GAMs) are presented. For validation a

comparison with other diagnostics has been performed, too.

2. Poloidal Correlation Reflectometry at ASDEX-

Upgrade

A Poloidal Correlation Reflectometer is based on

the simultaneous measurement of reflected microwave

signals by several antennae [1]. At ASDEX Upgrade a 5

antenna array with a single central transmitting and 4

adjacent receiving antennae (with defined poloidal and

toroidal separations) has been installed at the mid-plane

of the Low Field Side (LFS) (Fig. 1). All antennae have

square aperture horns with the dimension 55x55 mm2 to

allow both O-mode and X-mode measurements. Due to

limitation of space at AUG long waveguides (10 m per

single path) with the dimension 10x10 mm2 have been

used.

Figure 1. PCR antennae array at ASDEX-Upgrade. Rad (red) is radiative antenna. B,D,E,C (blue) are receiving antennae.

At present, the PCR at ASDEX Upgrade operates in Ka-band. A schematic the

radiating and one of the receiving channels is shown in Fig. 2. A dual channel low noise (-150

dBc/Hz wideband noise) microwave synthesizer (from BNC) operated in the range 3-5 GHz

is used as both transmitter and local oscillator source. The synthesizer is operating in the fast

hopping frequency mode with a transient time of < 60 μs. For heterodyne detection, the

transmitter and local oscillator have a fixed difference of 2.5 MHz. Active multipliers (X8)

and power amplifier launch frequencies in the Ka-band range (24-40 GHz) at a power level of

about 40 mW into the waveguide connected with the radiation antenna. The reflected signals

are down-converted to an intermediate frequency of 20 MHz by mixers, followed by

amplifiers and a IQ-detection section. The resulting complex signal ( )( ) i tA t e is digitized

with a 2 MHz ADC at 14 bit resolution. This scheme is repeated 4 times for the 4 receiving

antennae.

Ka-band PCR system shows best operation for frequencies 28-37 GHz, limited by the

sensitivity of mixers. For this frequencies we covers a density range from 0.97 to 1.7×1019

m-3 for O-mode polarization. The position of reflection

depends on the line averaged density and the shape of the

density profile. For low line averaged densities (1.5×1019

m-3) the system can cover a radial range from ρ = 0.5 to

0.85. However, operation with such low densities is

complicated to perform at AUG due to gas recycling from

the wall. At higher L-mode densities (3×1019 m-3) the

system covers the edge region from ρ = 0.95 to 0.99. In

the next campaign the recently installed U-band (40-60

GHz) will allow core measurements for high densities as

well.

To correlate signals from polloidally and

toroidally separated antennae, the position of the

reflection points need to be known. They are obtained

Figure 2. Scheme of radiating and one of receiving channel.

Figure 3. Calculation of reflection points with Torbeam code. Blue curves shows propagating of waves starting from radiative antenna. Red dots are reflection positions.

from the beam tracing code Torbeam [2], which uses the real geometry of ASDEX Upgrade

together with experimental measured electron density, electron temperature and magnetic

equilibria profiles. We have calculated the wave propagation for different angles inside the

radiation pattern and selected those which are detected by the receiving antennae (Fig. 3). The

turning points of these rays (red dots) correspond to the positions of measurements. For

reflection at ρ ~ 0.98 and the typical plasma geometry, the poloidal separation from ray

tracing calculations yields [1.06, 2.12, 3.19, 4.25] cm and the toroidal separation is given by

[0, 2.12] cm.

3. First applications and quasi coherent structures

Results are obtained for L-mode discharges and O-

mode polarisation. Typical power spectra measured at 31

GHz and ρ = 0.75 is shown in Fig. 4a. The spectra of all

antennae are similar, broad and close to symmetric (only

positive frequencies are plotted). A comparison with another

fixed frequency reflectometry system [3] shows, mostly a

good similarity. The coherence spectra between two

separated antennae do not reproduce the shape of the original

power spectra of every antenna and they are not concentrated

around zero frequency (Fig. 4b). The coherence spectrum in

most measurements in L-mode are dominated by quasi

coherent (QC) structures, which are less pronounced in the

spectra of density fluctuations, but there are clearly

observable in the coherence spectra. It is interesting that QC

structures are always located around the knee position of the

power spectrum (Fig. 4a) corresponding to the injection scale.

In the absence of QC structures the coherence spectrum has

low amplitude, that very fast decrease with separation

between points (exceptions are narrow MHD modes, that

usually also are high coherence). But also in those cases the

power spectrum looks broad and shows little difference in

shape. A probable explanation for the low values of the

coherence spectrum is a short deccorelation time, when the

turbulence decorelates faster than it propagate between two detection volumes. The QC

structures are toroidally elongated, as observed by long range correlation analysis between

different reflectometry systems (1.5 m toroidal separation, 0.3m poloidal separation) and

aligned with the magnetic field.

QC modes have been reported to be trapped electron modes (TEMs) [4]. According to

this prediction the QC structures should exist in the core region when the plasma is in the

Figure 4. a) Power spectrum of all antennae at ρ=0.75 measured in the LOC regime. b) Coherence spectrum between D and E antennae. QC structures clearly observed from coherence spectrum.

linear ohmic confinemet (LOC) regime while they should disappear at higher collisionallity

when the plasma is in saturated ohmic confiment (SOC, ion temperature gradient dominated

turbulence (ITG)). To check this hypothesis, measurements at the same reflection layer in

both LOC and SOC regimes should be performed. Unfortunately the frequency range of the

existing Ka-band is not large enough and in the

SOC regime the cutoff is shifted to the plasma

edge. However, we clearly observe similar

structures not only in the core of LOC plasma of

AUG, but independently of the regime

(LOC/SOC) also within the edge region of the

plasma. In order to address the origin of this

phenomena we compared properties of QC

structures in the core of LOC with those at the

edge of SOC plasmas. Edge QC structures have

broad spectral peaks with a full-width

comparable to half of the mean frequency.

About 40 shots have been analyzed and it has

been found that the mean frequency of the edge QC structure has values ranging from 60 to

150 kHz. With additional measurements of the propagation velocity [section 4] we find that

the mean frequency of the QC structure scales with velocity (Fig. 5), so that 2 / s sk V

always stays roughly in the range 0.25 0.45 sk . These values correspond to the maximal

growth rate of ITG and TEM instabilities [5]. The change in phase velocities for case of QC

structures have been measured by comparison with Doppler reflectometry (DR measured at

1~ 10 cm

k and PCR at 1~ 1 cm

k ) which yielded a value of ~ 1 km/s in the electron

diamagnetic direction [Section 4]. That is less than expected for the change in phase velocity

of drift wave turbulence [6], which is expected to be in the range of 3-7 km/s at these k

differences. Decorrelation times (4-14 μs) of the QC structures have been measured with the

PCR from the reduction of correlation during propagation which found to scale as

~ / d eT V dependence. The described properties are very close to QC structures observed

for the core of LOC [4] which could indicate their similar origin.

4. Measurement of the velocity and the magnetic field pitch angle

The QC structures discussed in the previous section show a significant level of

coherence between different antennae combinations. Apart from the investigation and

identification of these structures we use the coherence for the measurement of the

perpendicular velocity ( ExB phV V V ) and the pitch angle of the magnetic field lines. Time-

delay analyses from cross-correlation functions (CCFs) between different antennae

combinations have been used. The normalized CCF is defined as

Figure 5. Frequency scaling of edge QC

structures.

where X(t) and Y(t) are complex signals from

different antennae. In figure 6 shows CCFs for shot

#31384. The time delay is observed which increases

with distance between correlated points. However, as

shown in ref. [1] the time delay of the CCF is not

only related to a propagation, but also to the

inclination of the magnetic field line. In zeroth order

it is assumed that QC structures are aligned with the

magnetic field lines. To decouple pitch angle and

velocity, instead of a regularly used two-point

analysis we use a multipoint analysis of all possible

combinations with bayesian-approach. The main idea

of the method is the estimation of the probability to

have some specific pitch angle and specific from the

measured time delays and its errors. The Bayesian probability is defined as

with velocity V , pitch angle , time delay of i combination i

, and its errors

i ,

respectively. The prior probability p( , )V

assumed equally distributed and the probability

of measurement ({ , }) iip does not depend on

and V , and therefore can be used as

normalisation factor. The likehood

probability ({ , } | , ) iip V 2 2exp( ( ( , )) / )

ii V

describes the probability to measure a time delay

i if the real velocity is V and real pitch angle is

. The analytic function ( , ) V is obtained from

geometry of measured points. The strength of the

method is the possibility to include systematic

errors. Error bars of measured pitch angle and

velocity are estimated from the 1/e level of the

probability function in V and direction,

accordingly.

We have performed a set of measurements to deduce the velocity in the edge region

Figure 6. CCFs between different antennae combinations. Time-delay increase with distance in perpendicular to magnetic field direction.

2 2

( ) ( )

( ) [1]

( ) ( )

i i

iXY

i i

i i

X t Y t

X t Y t

({ , } | , ) p( , )( , |{ , }) [2]

({ , })

i

i

i

i

i

i i

p V Vp V

p

Figure 7. Comparison of the velocity

measured by PCR with DR flow

measurements. The offset of 1 km/s in ED

direction are observed.

for different plasma parameters. For time windows of 5 ms an error bar of 0.5 km/s is

achieved. However, the error bar estimation does not take into account uncertainties in the

estimation of the reflected position. We have compared velocity measurements from this

method with Doppler reflectometry (DR) measurements. DR at AUG measures the

perpendicular plasma velocity from the Doppler shift of a backscattered signal from turbulent

fluctuations with some specific wavelength [7]. The comparison yields similar velocities

which show the same trend (Fig. 7). However, there is a 1 km/s offset between PCR and DR

velocities. This offset does not depend on the value of the velocity, as might be expected if

the positions from ray tracing are misaligned. Another explanation for the offset is that DR

measures at higher k-value ( 1~ 10 cm

k ) compared to PCR ( 1~ 1 cm

k ). In this case change

in phase velocity of ~ 1 km/s in the electron diamagnetic direction has to be assumed. Note

that a PCR measurement of the velocity is possible in cases where DR shows no

backscattered signal due to a low level of turbulence, which generally is the case of plasma

core or in the H-mode pedestal.

The possibility to measure the pitch angle from the inclination of QC structures has

been studied as well. The expected change of sign of measured pitch angle due to inversion of

magnetic field or plasma current has been observed. Additionally, we have analyzed shots

with different current and magnetic field values.

The expected increase of the measured angle

with increased current, as well as a decrease of

the measured angle with increased magnetic

field, has been observed. Typical error bars that

we manage to achieve for the edge plasma

region are of the order of 0.5-1.5 degrees. The

calculated angles have been compared with the

magnetic equilibrium reconstruction code

CLISTE. CLISTE provides space distributed

components of the magnetic field {Bx, By, Bz}

from which the angle 2 2arctan( / )x z yB B B

can be extracted. A comparison of the calculated

angle from PCR with those from the

reconstruction code (Fig. 8) shows good

similarity. However, some deviations have been found, which cannot be explained by the

error bars of the measurements. One possible candidate is that CLISTE produces an

axisymmetric reconstruction, while the PCR angle are local measurements. Thereby we might

use measurement of angle by PCR as an additional parameter for a better CLISTE

reconstruction.

Figure 8. Comparison of the pitch angle

measured by PCR with angle deduced

from magnetic equilibrium reconstruction

code CLISTE.

5. Envelope techniques for GAM detection

Another application of the PCR are

measurements related to geodesic acoustic modes

(GAMs) using only single channel phase fluctuation

data. Here, we use the fact that high frequency

density turbulence is expected to be modulated by

the GAM as proposed by Nagashima who used the

envelope of high frequency density oscillations from

electrostatic probes for the detection of GAMs [9].

The envelope of high frequency reflectometry

fluctuations is given by 2 2( ) ( ) ( ( )) Env t x t H x t . Here x(t) is the high

frequency component (250-450 KHz) of the real part

of the complex signal and H(t) the Hilbert transform

of x(t).

The method was tested and the GAM

signature was found in the spectrum of the envelope

(Fig. 9a). Note, the oscillations are not visible in the

spectrum of the complex amplitude. Based on the

spectrum it is difficult to prove that this small peak

around 20 kHz is related to a GAM. However, to prove this we calculated the coherence

between 2 closely separated antennae (B and E) and found that the GAM is clearly visible

there (Fig. 9b). To show the global structure of the

GAM, we measured the coherence between 2 different

reflectometry systems (1.5 m toroidal and 0.3 m

poloidal separation). Both reflectometry systems show

an oscillation at the GAM frequency and the

calculation of the cross-phase shows that they are

perfectly in phase (Similar to an m=0 velocity

component). By varying the filter limits in steps of 50

kHz it is found that the GAM appear only for filter

frequencies above 200 kHz (knee position of power

spectrum). We compared this method with DR that is

traditionally used for investigation of GAMs at AUG

[10]. DR measures GAMs from the oscillation of

Doppler shifted frequency of backscattered signal. In

Fig. 10a depicts the coherence between the envelope of

PCR and the DR. A coherence of up to 40% is visible

Figure 9. a) Power spectrum of

envelope for antennae B and C. b)

Coherence between B and C

envelops. Clear coherence at GAM

frequency observed.

Figure 10. a) Coherence (a) and Cross-phase (b) between envelope of PCR and flow of Doppler reflectometry. Zero cross-phase between envelope and flow observed.

at the GAM frequency. The flow (DR) and the envelope modulation (PCR) are perfectly in

phase. This fact is in contradiction to the observation by Nagashima [8], that a cross-phase of

π/2 is between flow and envelope. Based on these facts we can conclude that for the case of

AUG we observe a modulation of the high frequency turbulence due to a modulation of the

turbulence frequency which is caused by an oscillation in the flow (assuming kV ), and

not due-to a real modulation of the turbulence energy.

6. Conclusion and discussion

The first application of PCR to study turbulence at AUG has been shown in this paper.

Coherence spectra of L-mode plasmas typically dominated by QC structures. Properties of

observed edge QC structures have been compared to core LOC QC structures reported earlier,

showing similar properties. The observation of fast decorrelation of other coherent features

suggest that, in order to better measure them, the measurement separation should be

decreased. Measurements of the velocity and magnetic pitch angle from time-delay analysis

of QC-structures have been shown. For the first time we have compared velocity

measurements with those of DR and magnetic field pitch angle with the results of equilibrium

reconstructions from CLISTE, both show similar trends, but some deviations have been

found. Measurements of the pitch angle are of particular interest because they present a

simple method for the estimation of q profiles. The investigation of bootstrap current effects

and the structure of magnetic islands appear to be possible and should be demonstrated.

Another interesting application of PCR is related to GAMs, where the envelope of high

frequency density turbulence found to be modulated by the GAM frequency. Analysis of the

properties of this modulation may suggest that, at the tokamak midplane, the turbulence

spectrum width is simply modulated in frequency due to advection with the GAM flow, rather

than an actual energy transfer.

We aimed to use the diagnostic for the documentation of turbulence properties for

different turbulence regimes. The newly installed U-band will give significantly increased

coverage of the diagnostics towards core. The change of turbulence properties in the transition

from TEM to ITG during the LOC-SOC transition will be studied. Zonal Flow structures and

energy transfer from turbulence by the envelope method will be studies as well.

The authors thank J. Friesen and Jülich team for the help with the installation of the

diagnostics. This work was partly performed in the framework of the Helmholtz Virtual

Institute on Plasma Dynamical Processes and Turbulence Studies using Advanced Microwave

Diagnostics (VH-VI- 526) and 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.

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[3] L. Cupido et al., Rev. Sci. Instrum. 77, 10E915 (2006)

[4] H. Arnichand et al., Nucl. Fusion 54, 123017 (2014)

[5] D. Told et al. Physics of Plasmas 20, 122312 (2013)

[6] B. Scott, IPP-Report 5/92 (2001)

[7] G.D. Conway et al., Plasma Phys. Control. Fusion 46, 951 (2004)

[8] K. Itoh et al., Plasma Phys. Control. Fusion 47, 451 (2005)

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