J. Plasma Fusion Res. SERIES, Vol.4 (2001) 48-53

Doppler Reflectometry :Measuring the Propagation Velocity of Density Perturbations
HIRSCH Marthias*, HOLZHAUER Eberhardr, BALDZUHN Juergen and KURZAN Bernd
Max-Planck-Institut fir Plasmaphysik, EUMTOM-Ass., D-85748 Garching, Germany
Ilnstitut
Plasmaforschung, Universitrit Stuttgart, D-70569 Stuttgart, Germanyflir(Received: 5 December 2000 / Accepted: 14 September 2001)

Abstract
Doppler reflectometry is a radar measurement where a microwave signal probes the plasma with aline of sight which is non-perpendicular with respect to the reflecting layer. According to the Bragg
condition the diagnostic selects density perturbations with finite wavevector K1 in the reflecting layer.
From the Doppler shift of the returning microwave signal the propagation velocity v1 perpendicular to themagnetic field can be obtained whereas the signal intensity contains information about the perturbation
amplitude. The diagnostic capability of Doppler reflectomery is discussed and results from the W7-AS
stellarator are presented. During stationary phases the measured values vr(r) and their radial dependence
are in good agreement with the .E x B velocity of the plasma obtained from passive spectroscopy.
Transient states of the plasma can be followed with a temporal resolution of less than 50 ps. Therefore
Doppler reflectometry allows one to measure the interdependence of sheared flow and turbulence on thattimescale.

Keywords:
reflectometry, plasma rotation, shear flow, turbulence, .E x

1. Introduction
A mechanism which is believed to cause phasetransitions and bifurcations in a plasma is thetool for the localized measurement of v1(r) with atemporal resolution of less than 50 ps. Doppler
reflectometry [-4] probes the plasma by a microwave
signal with a line of sight which is non-perpendicularinterdependence between the wavenumber spectrum of
perturbations K1 and the shear of their propagation

with respect to the reflecting layer. Density
perturbations with finite wave number K1 in thevelocity perpendicular to the magnetic field v1.
However, diagnostic access to the relevant quantities isreflecting layer result in higher diffraction orders for the
returning microwave which are selected by the tilt angle

hard to obtain: most fluctuation diagnostics applicable tothe confinement region of the plasma lack sufficient
resolution either in space (like microwave scattering) orin time (like diagnostics applying correlation techniquessuch as beam emission spectroscopy and correlation
ECE). Besides, the temporal resolution of spectroscopic
methods, which measure the E x B velocity yE x B of theunderlying background plasma is not better than 1 ms.
In this paper we introduce Doppler reflectometry as a*

I velocity, ELMof the antenna Q11,. Thus the antenna corresponds to a
bandpass filter in Kr-space of the perturbations whereK1 can be varied by a scan of 41, and where thebandwidth AK1 depends on the antenna pattern. This isin contrast to conventional reflectometry dedicated tomeasure the stratified background density profile whichuses a line of sight perpendicular to the reflecting layer

Corresponding author's e-mail: matthias.hirsch@ ipp.mpg.de48@2001 by The Japan Society of Plasma
Science and Nuclear Fusion ResearchHirsch M. et al., Doppler Reflectometry : Measuring the Propagation Velocity of Density Perturbations

such that the antenna acts as a low-pass filter receiving

L@=-i.K

the 0'n order of reflection. For typical conditions in

microwave reflectometry the K-selectivity of the(2)level. Such Doppler reflectometry provides direct access

For density fluctuations in magnetically confinedplasmas it is usually assumed that KIB.It then follows
from the scalar product in eq. 2 that the Doppler shift
only results from the velocity component of theperturbations perpendicular to the magnetic field (i.e. in
the direction of vB ,6) independent of the (toroid al and/or poloidal) orientation of the antenna tilt gtirt!
It is important to point out the crucial role of an
optimised antenna plasma geometry for the feasibility ofthe diagnostic: (l) Any error in the knowledge of Q11,

to the interdependent properties of the propagation

directly enters the calculation of v1 since yr * Kr * Qitt.

velocity vr and the K1-spectrum of density turbulence.

"To get rid of changes in 0,11, which may result fromdischarge conditions a differential measurement can be
performed with two Doppler reflectometry systems andantenna is insufficient to suppress the respective
unwanted order completely. Additional filtering in thefrequency spectrum becomes possible if the spectralfeatures can be separated by a sufficient Doppler shift ofthe diffraction orders. Vice versa this Doppler shift
displays the propagation velocity v1. Simultaneously,
the microwave power received in the respective -l'tdiffraction order is a fast monitor for the turbulence

2. Principles and Gonstraints of Doppler
Reflectometry

two antennas viewing the same spot with tilt +4nt."

The principle of Doppler reflectometry is explainedin Fig. I using the model of a moving reflection grating(2) In addition the selected wavenumbers Kun, depend on
the orientation of the antenna tilt with respect to thegrating. Changes in the direction of the magnetic field(i.e. of the local pitch angle) may result in a tilt direction
which is not oriented perpendicular to the fieldlines.
However, these effects are small since v1 * Kr = Kunt 'cos(d) = Kun, where a is the angle between antenna tilt

in vacuum with small sinusoidal corrugation
characterized by a wave number KL = 2Ell\L. For the-1" order of the diffraction pattern to return to theantenna the Bragg condition requires(l)

Kt=2. ko . sin(0,,,,)

direction and magnetic field orientation. (3) The

where fte is the wavevector of the microwave. By avariation of 4tr, the K1-spectrum of the density
perturbations can be scanned. If the reflection grating
propagates with a velocity v1 the returning microwave isbandwidth AK of the antenna filter is ideally determinedby the width of the antenna pattern alone. However, in
realistic cases AK is increased by both non-ideal beams i.e. non-parallel wavefronts - and/or by a finite curvatureof the reflecting layer within the beam spot. In W7-AS
the optimum spot diameter turned out to be limited inmodulated by the periodic structure and the frequency of
the wave diffracted in -l't order is Doppler shifted bysize by the poloidal curvature of the reflecting layer
originating from the rather small minor radius. For theexperiments Gaussian beams E q exp(-x2lwo2) are usedwith the beam waist lr0 close to the reflecting layer
which minimizes the effects of beam divergence. Inaddition Gaussian characteristics ideally have no sidelobes, which is of importance if the K1-spectrum of thedensity fluctuations has pronounced maxima outside theselected spectral range. Such a maximum could
significantly contribute to the received signal if it falls
into a side lobe ofthe antenna.
The diagnostic potential of Doppler reflectometry
depends on how accurately the local quantities v1(r) andKr(r) can be derived in a realistic plasma, i.e. in thepresence of (l) a background density profile with finite
gradient and (2) in the presence ofdensity perturbations
along the signal path. (l) : Analytical and numericalanalysis [5] show that refractive effects due to thebackground profiles in the plasma do not perturb thevlFig. 1 Principle of Doppler reflectometry illustrated by areflection grating in vacuum and a single antennaarrangement.
49

Hirsch M. et al., Doppler Reflectometry : Measuring the Propagation Velocity of Density Perturbations-20

measurement significantly and the probed wave vectors

K1(r) and thus the v1(r) can be obtained directly fromthe geometrical antenna tilt and the wavelength invacuum. In analogy to conventional reflectometry theswelling of the electric field close to cutoff results in an
enhanced sensitivity to density perturbations in a narrowlayer close to the nominal cutoff position. This layer isshifted radially outward if a finite Q1, is used. An
analytic solution for this radial shift is given by------y={ft6/g
LIJ-30backwallE-Y=21-b -40
o=o-50ooo

1_ Ig -60oL

Ginzburg [6]: the effective cutoff layer shifts to aposition where the index of refraction becomes pt =sin(Qr',). As a consequence the radial shift is reduced
and the measurement is generally more localized if x-'L.1,\-70-80

mode polarization is used instead of o-mode. (2): strong
density perturbations resulting in multiple scattering andscattering into higher diffraction orders can disturb the-4-2024
frequencY shift / MHZ

Fig. 2 Two examples of Doppler reflectometry spectra
obtained with the heterodyne reflectometer andan antenna tilt of Q',, = 3o. For both spectra theprobed position is reff = 14.2 cm,3 cm within thelocalization of the measurement both in real space andin K-space. In particular an estimate of the turbulence
level, i.e. the absolute power ofthe density perturbations
K1(r) from a measurement of the absolute microwave
power received in the -l't diffraction order, is possible

plasma boundary defined by a limiter. The

spectrum resulting from reflection at the torus
backwall is given for comparison. Note theonly with a priori assumptions about the turbulence
properties. However, the received microwave power canbe used as a fast but uncalibrated monitor for thelogarithmic scale of the vertical axis.

by 1o < 41, < 15'is 3.5 cm-r < Kr < 9 cm-l. The lower

turbulence level.

boundary results from the finite width and Doppler shiftof the -l't order of diffraction which overlaps with theOth order of reflection for Q1x < 6o for this antenna
system and experimental conditions. The frequency shift

3. Doppler Reflectometry Experiments at
W7.AS :
Doppler reflectometry spectra obtained at the W7AS stellarator (R = 2.0 m, average minor radius a = 0.17m) with a heterodyne reflectometer are shown in Fig. 2.
The experimental setup and the geometry of the antenna
system are described in [4]. If the Doppler shift issufficiently high (continuous line) the * l" diffraction
orders can be well separated from the 0'n order ofin Fig. 3 varies almost linearly with Q", = sinQ",
indicating that the perturbations selected by the antenna
propagate with a common constant Doppler velocity= 2nLflLK.
The flux surface averaged velocity perpendicular to
the magnetic field v1 is calculated from the measured
yDoppler

Doppler velocity vpooo1.. taking into account the flux

reflection. The antenna alrangement is oriented such thatthe red-shifted feature indicates a poloidal propagationof the turbulence in electron diamagnetic direction. Dueto the tight focussing of this antenna (wo = l.) c.fir =compression of the magnetic surfaces. At the chosen
position in the W7-AS stellarator vnoppr". iS increased
with respect to v1 by about factor of 2 to 3.5 dependingon the magnetic configuration and the Shafranov shift.
An example for the radial profile of the propagation
velocities vr(r) is plotted in Fig. 4 together with v6 u (r)5.10) the K1-resolution is poor and also the +1't
diffraction order enters the receiver as can be seen by
the weak blue shifted spectral feature with same'frequency snlft ll/l .
With increasing 0,i1, the peak of the spectrum shifts
towards higher frequencies indicating that the antenna
selects K1 from a wave number spectrum which isconsiderably broader than the system resolution. A scan

as derived from active charge exchange recombinationof Q11, can be performed on a shot to shot basis andturbulence riding on the background plasma whichrotates with vs"s. Under steady state conditions and forthe ECRH discharses investieated so far the radialspectroscopy using He as a tracer impurity [7]. The
measured propagation velocity of the density
perturbations is the sum of two compoflgotS v1 ='y'zxa I
vturb where v,u.6 is the intrinsic phase velocity of theexamples for three timepoints of a discharge are givenin Fig. 3. The range of wavevectors that can be selected50

Hirsch M. et al., Doppler Reflectometry : Measuring the Propagation Velocity of Density Perturbations

o0rJ4J-E\-5.YE3E'6I -10oo)O^czo.E -rsfqg1oI -zo-25051015

00.05

0.1

0.15

0.2

effective radius / mtilt angle / deg

Fig. 4 Radial profile v,(r) compared with the profilev.,"(r) as obtained from active Charge Exchange

Fig. 3 Frequency shift of the -1st diffraction order as afunction of Q,,, for three different times of a

Recombination Spectroscopy (CXRS). Verticalbars indicate the -10dB width of the Doppler
shifted feature. As an example an ECRH heateddischarge with changes in the confinement
properties. The probed density (x-mode, f = 85

GHz, Q". = 2.5 T) is always = 2.101s m€, the radial
position of the nominal cutoff-layer is 2-3 cm

discharge is shown.

inside the limiter position. Vertical bars indicate
the -10d8 width of the Doppler shifted feature (forcomparison see Fig. 2). The resulting Doppler
velocities veqee161 ar€ also included.

itself is represented in Fig. 6d by the envelope ofmagnetic fluctuations measured with a Mirnov probe.
The ELM is characterized by a burst of fluctuations withprofile v1(r) is always identical within the error bars to

overall duration of 1 ms resulting in a decrease of edge
density and temperature gradients (not shown in thefigure) and a fast particle and power flux across the last

the profile of vs,r(r) evaluated from spectroscopy.
Therefrom we conclude that for these conditions thecontribution of the intrinsic phase velocity of theclosed flux surface (also not shown). During thequiescent H-mode interval preceding the ELM event (t <turbulence v6,6 must have been small.

An example for the capability of the Doppler

335.5 ms, (open circles in Fig. 5) the turbulence level isreflectometer to follow dynamic phenomena is given in

low and the spectral feature measured with Doppler
reflectometry barely exceeds the receiver noise by +5
dB. The average Doppler shift scatters around 1.5 MHz

Figs. 5, 6 which show Doppler reflectometry
measurements obtained with heterodyne detection
during a strong Edge Localized Mode (ELM)-like event[8]. The probed layer is located about 2 cm inside theseparatrix. The fast evolution of the signal is measured
by 6 Bandpass filters (Lf = 25O kHz) with a temporalresolution of (z > 20 ps). Their center frequencies arechosen to measure the red-shifted (corresponding tocorresponding an flux surface averaged vr = 20.5 krn/s.
With the onset of the ELM the total power received in
the -l't order increases by a factor of 8 dB within a timeinterval of less than 50 pts. For individual channels theincrease exceeds 15 dB. As the plasma remains
turbulent the Doppler shift and thus v1 decreases
continuously to about I MHz (Fig. 6c, and Fig. 5, filled

electron diamagnetic direction) radiation of theheterodyne reflectometer at six values in the frequency
interval -2.5 MHz < -fooppr", < -0.5 MHz. Examples ofspectra measured at four time slices are given in Fig. 5.

circles). A spin-up of v1 to its H-mode value is observed

In Fig. 6a the temporal evolution of the Doppler

over.

on a timescale of 300 ps about together with thedecrease of the turbulence level as the ELM event isreflectometry spectra is shown as a grey scale plot. The

4. Conclusion

total power received in -1't diffraction order and theDoppler shift ofthe spectral feature are obtained from a

Doppler reflectometry has been proven to be a
promising tool for the localized measurement ofpropagation velocity and wave number spectra offit to the six frequency channels and given in Figs. 6b, c
respectively. The temporal evolution of the ELM event5lHirsch M. et aI., Doppler Reflectometry : Measuring the Propagation Velocity of Density Perturbations

B
*-1.0

dl

:20

F',uaog'zo

Lo=o-810
oo3q)

ts6E38"s-3-2.0.6-1frequency shift / MHzN,-tr-lFig.5 Doppler reflectometry spectra measured via 6
bandpass filters at for different times during ans1.0ca

ELM-event in W7-AS (reflecting layer about 2 cm

t-2

inside the plasma boundary) The negativetDoppler shift corresponds to propagation inelectron diamagnetic direction. Note the log scale.

-2.5

The receiver background noise is included forcomparison as measured with a spectrum

ioanalyzer and reflection from the torus backwall.

oioo.

density perturbations. The measured Doppler shift isintrinsically linked to the propagation velocity v1 in the0.sdar€t s

direction perpendicular to the magnetic field

Fig. 6 Temporal evolution

independent on the poloidal and/or toroidal direction of
the antenna tilt. First Doppler reflectometry results atof Doppler reflectometry

signals measured during an Edge localized Mode(ELM) event in W7-AS via bandpass filters asshown in Fig. 5: (a) contour plot of the spectra, (b)total power received in the -1st diffraction order,(c) frequency shift. The temporal evolution of theevent is characterized in the lowest trace by thepower of magnetic fluctuations measured with aMirnov coil (d).

W7-AS with variable Q11, show a broad K-spectrum
within the accessible wavenumber range. The Doppler
shift varies linearly with Q1r,, i.e. the density
perturbations propagate with a common group velocity
v1. During stationary phases the measured v1(r) is equal

to v6,u(r) within the error bars, indicating that theintrinsic phase velocity of the perturbations riding on thebackground plasma is small. Transient states of theplasma can be followed with a temporal resolution of <t3l X.L. Zol et al., Proc. of the 4th Reflectomety
Workshop, Cadarche, March 2-24 1999, EURCEA-FC-1674, Proc. 26th EPS Conf. on Controlled
Fusion and Plasma Physics (Maastricht, 1999) 23,50 ps. Thus Doppler reflectometry is well suited toinvestigate the interdependence of the turbulence
spectrum and the propagation velocity respectively its1041.

t4l M. Hirsch et al., Rev. Sci. Instrum. 72 (l),324shear.

(2001).

t5l M. Hirsch et a1.,2001, submitted to Plasma Phys.
Control. Fusion.

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t2l M. Hirsch et al., Proc. of the 4th Reflectomety

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53