Preamble

Frequency modulated continuous wave reflectometry for density profile measurement in front of ICRH antenna in Wendelstein 7-X Haoming Xiang , Andreas Krämer-Flecken , Xiang Han , Jia Huang , Matthias Hirsch , Gavin Weir , Dirk Hartmann , Peter Kallmeyer , Jozef Ongena Guntram. Czymek , Matthias Stern , Timo Schröder , Andreas Dinklage Alexander Knieps , Olaf Neubauer , Kristel Crombé , Norbert Sandri , Vecsei Miklós , Sandor Zoletnik , Gábor Anda , Daniel Dunai , Dávid Nagy , Dániel Imre Réfy , Matthias Otte , David-Antonio Castaño Bardawil , Rainer Schick Dirk Nicolai , Marc Beurskens , Shuai Xu , Jie Huang , Jianqing Cai , Tao Zhang , Xiao-dong Lin , Xiang Gao , Yun-feng Liang , and W7-X team 1 Shenzhen Institute of Research and Innovation, University of Hong Kong, Shenzhen 518172, China Forschungszentrum Jülich GmbH, IFN-1–Plasma Physics, D-52425 Jülich, Germany University of Wisconsin, Madison, 53705, WI, US Institute of Plasma Physics, Chinese Academy of Sciences, 230031 Hefei, Anhui, People’s Republic China Max-Planck-Institut für Plasmaphysik, 17491 Greifswald, Germany College of Physics and Optoelectronic Engineering, Shenzhen University, Shenzhen 518060, People’s Republic of China Koninklijke Militaire School-Ecole Royale Militaire, Brussels, Belgium Centre for Energy Research, H-1525 Budapest, Hungary

Abstract

A Frequency Modulated Continues Wave (FMCW) reflectometry with heterodyne detec- tion regime is developed for measuring the electron density profile in front of the ICRH antenna in Wendelstein 7-X (W7-X). The dual-band set up consists of the one at E-band (60GHz- 90GHz) and another at W-band (75GHz-110GHz), enabling to measure the local density at two different poloidal positions. The system is polarized in extraordinary mode (X-mode), corresponding to a measurable density of n at a central magnetic field of T. The transmission line consists of an oversized wave guide in Ka-band (WR-28) in the vacuum, and is tapered to the fundamental wave guide, respectively. Two pairs of sectoral horn antenna are mounted between the ICRH antenna straps. The horn mouth is designed to keep the E-plane at the Ka-band dimension whereas the elongated H-plane is customized for a sufficient gain and directivity. In this paper the layout of the front-end and the design of electronic module are presented. Furthermore, the evaluated density profiles from the exper- iments demonstrate a good agreement with profiles measured by other diagnostic, e.g. Akali metal beam. And the density profile inside the magnetic island is presented as well. The diagnostic will be operated routinely for density profile measurement and will contribute to related physical study on W7-X.

Keywords

Microwave reflectometry; ICRH antenna; density profile; magnetic island; W7-X stellarator

1 Introduction

The stellarator with its intrinsic advantages of steady state operation and absence of disruptions has attracted considerable attention in magnetic confinement fusion research . W7-X is the largest Haoming Xiang, E-mail address:

stellarator in the world and is highly optimized regarding the neoclassical transport.

One of the principal objective of W7-X is to demonstrate the confinement of fast ions at finite plasma . For the generation of fast particles an ion cyclotron resonance heating (ICRH) system is designed and implemented . The heating efficiency depends on the distance of ICRH antenna to the plasma. The ICRH antenna module consists of two parallel straps, which surfaces are slightly shifted in between to adapt to the 3D shape of the Last Closed Flux Surface (LCFS) of the standard magnetic configuration , allowing an RF power up to

2 MHz

that can be delivered by a resonant ion population at the frequency of

5 MHz

pulse with maximum of duration every 5 min The knowledge of the density profile ( ) in front of the ICRH antenna is one of the critical issues for evaluating and optimizing the RF power coupling of the antenna to the plasma. The reflectometer diagnostic is advanced in its non-invasive approach and flexible access footprint for the horn and wave guide routing, and has been applied for the ne profile and the associated fluctuation measurements in many tokamaks and stellarators In ASDEX Upgrade a multichannel reflectometer is successfully installed at different poloidal locations on the ICRH antenna means of which, the ICRH power coupling, edge density profile evolution in front of the ICRH antenna have been studied . In the ICRH system of ITER, a frequency sweeping X-mode bistatic reflectometry is designed at four positions of the ICRH antenna, the

150 GHz

cut-off frequency range is calculated to cover the full and half magnetic field tokamak operation . On W7- X, considering the accessibility in the ICRH antenna module, the reflectometer system is designed for the profile measurement in front of the ICRH antenna, since it requires only a small amount of space for embedding the transmission line (TL) and front-end module. Furthermore, due to the 3D structure of magnetic topology, the density measurement from multiple sight lines would be preferable to reveal the 3D geometry of density profile in the edge area, especially configured with a island chain in the plasma edge.

Therefore two poloidally separated antenna pairs are mounted on the ICRH antenna to enable simultaneous measurement through different views plasma boundary. In this paper, the reflectometer set up is presented in section II, including the the design of the front-end, the TL module and the electronic schematic. The experimental results concerning the density profile evaluated during the plasma operation are illustrated in section III.

Finally the summary and future plan in IV.

2 Reflectometer set up

2.1 Requirement of reflectometer measurement An electromagnetic wave with a specific frequency is reflected by the plasma when the refractive index goes to zero. A complete density profile starts at zero requires the design of reflectometer system in an X-mode polarization. Here the X-mode cutoff frequency is calculated as:

f cutoff = �

where the indicates the upper (+) and lower (-) cutoff frequency respectively, is the electron cyclotron frequency, and

2.2 Transmission line and front-end modules The ICRH antenna is installed in the equatorial plane of module No.3 at the AEE31 port, low field side of W7-X (toroidal angle ). Two TL are assigned for the reflectometer, as shown in with the lower one used for E-band and the other for the W-band . The TL consists of an oversized waveguide in Ka-band (WR28) in the vacuum, which feeds through the ICRH brace along the path. The wave guide is inserted in the pipe that is used for the electrical cables. Leaving the support pipe, the transition to air is done with a thick Mica window. Outside this window the waveguide is tapered to the fundamental waveguide ( E-band or W-band) and connected to the reflectometer. In order to avoid any conflict with the ICRH system, the routing of the waveguide in the vacuum has to be bent by four times. To minimize the excitation of higher order modes in the waveguide and hence to reduce the transmission loss, the bends have been manufactured in the hyperbolic shape with an increasing curvature to decrease mode conversion . The vacuum window, a mica disk of thickness, is sandwiched between the O-ring of two flanges on each TL branch for sustaining the vacuum atmosphere. The fundamental wave guide connects the vacuum window to the reflectometer that positioned on the trolley of the ICRH system. The total length of the TL is /path in the upper branch and /path in the lower one. Two sectoral horn pairs are designed to realize a multiple sights line measurement in front of the ICRH antenna. The location of the two antenna pairs is a compromise of space availability within the ICRH antenna and the requirement to measure a density profile at the position of interest for the ICRH. The detailed structure, as well as its location with respect to the ICRF straps are shown in the fig.3. Each horn pair is mounted 117 mm behind the ICRH straps. The horn pair is made stainless steel with an aperture of dimensions of The antenna block is longer with the length of , because it contains a part of the band wave guide as shown in . The beam width of the main lobe can penetrate between the ICRH straps yet the side lobes are minimized to prevent the reflection from the straps. The length of E-plane is fixed at the Ka-band whereas the H-plane is elongated and tilted by in order to match the magnetic field pitch angle of W7-X. The fig.3(d) shows the estimation of the radiation pattern angle at -3 dB power for the operational frequency range. Here the pattern angle is empirically calculated to be where a is the length of the H-plane and is the wavelength of the beam . It is seen that the pattern angle decreases as increasing the probing frequency. The opening angle of the horn is resulting in a beam angle for the pattern well below the opening angle . With this horn geometry, the gain of the horn is estimated to linearly increase 6 dBi

65 GHz

5 dBi

110 GHz

. Fig.4 depicts the Poincaré figure at the ICRH antenna cross section in the so-called standard (EJM) and low-iota (DBM) configuration, where an island chain structure exists in the open field line region. The two red dashed lines indicate the line of sight (LoS) of the reflectometer at the poloidally separated positions.

In the EJM configuration, the upper LoS penetrates through the O-point of the island toward the plasma core and the lower one passes through the X-point of the island. In the DBM configuration, the lower LoS intersects with the O-point of island. With the two LoS, a radial coverage of density profile measurement spans from the scrape-off-layer to the plasma edge region including the island region in EJM configuration. It enables us to measure the ne profile at the O- and X-points of the island simultaneously once the corresponding cutoff layer is located in the island region.

2.3 Reflectometer architecture

The two sub-system are independently assembled but utilize a similar electronic design. It uses a mature scheme that has been developed in the EAST and Tore Supra reflectometer systems.

The schematic of the microwave reflectometer on W7-X can be seen in fig. . A arbitrary waveform generator (AWG) based on the Mokulab platform generates the VCO control signal with a voltage resolution of . The generated signal is pre-calibrated to realize a linear frequency sweep after linear amplified to a range of

15 V

to meet the turning voltage requirement of VCO. The carrier output from VCO is modulated by a

100 MHz

signal of Quartz oscillator to achieve heterodyne detection. A single side band modulator(SSBM) with a band suppression level better than 20 dB is applied to ensure a good signal to noise ratio. The modulated beam is amplified afterward and then fed into the active multiplier accordingly to reach the E- or W-band frequency range. However, the minimum probing frequency of E-band branch is

2 GHz

instead of

60 GHz

, which is because the initial VCO frequency of

4 GHz

to the E-band multiplier, while for the W-band probing frequency starts from

81 GHz

, due to the initial VCO frequency is

5 GHz

for the same reason. The transmitted beam is feed through the TL to the plasma. A coaxial delay line with a transmission loss of 5 dB m is used to compensate the

time delay relative to the launching arm. After being multiplied, this reference signal is mixed with the received plasma signal in a balanced mixer to generate the intermediate frequency (IF) signal.

The I/Q demodulator separates the IF signal into the in-phase (I) and quadrature (Q) parts via a reference signal of

600 MHz

individually, which allows ones to distinguish the absolute phase and amplitude of the beat signal that is required for the profile inversion process. In order to ensure a better input power lever in RF part of I/Q detector, a Low Noise Amplifier (LNA) with a gain of 20 dB is used after the mixer. A low-pass filter at

110 GHz

is installed in the receiver part to prevent the stray radiation from the ECRH.

The microwave components, DC power module, and the Mokulab are integrated into a cm metallic case as shown in fig.2, excluding coaxial delay lines and the date acquisition module (DAQ). Typically the probing frequency is swept within in both of the two microwave bands. Totally 6 channels are fed into the DAQ, including both VCO voltages and two sets of I and Q signals. The DAQ module has 8 channels with a 14-bit resolution. A memory of

512 M

insufficient to cope with a normal plasma operation of pulse length of on W7-X at a sampling rate of MSamples/s. A digitize cycle with an interval of 100 ms to streaming data in real time for a measurement at a time window of is proposed in the normal operation so that to cover a long time plasma pulse.

2.4 Experimental results

2.5 Commissioning of reflectometer-vacuum test After having complete the installation of reflectometer on W7-X, the performance of the system is assessed by monitoring the behaviour of beat frequency. The beat signal describes the phase variation ( ), and the corresponding group delay of the beam ( ) at the given sweep rate ( given by

f beat = dϕ

dt = 1

df df dt = τ g df dt (2)

where the is group delay. The group delay consists of the delay time in the system, the delay time in the coaxial line and the delay time that beam needs to travel from the transmitter to the receiver after the reflection. As deduced from equ.2, a given constant sweep rate , the be modified by varying the distance between the transmission and receiving antenna pairs. The distance variation is realized by moving the ICRH antenna trolley (flexible for moving backward or forward within cm). The test is carried out in the vacuum case without plasma, during the test, the sweep rate of VCO is set in 25 kHz and a delay time of is applied between two consecutive voltage sweeps. The E-band system working properly and has commissioned in the experimental operation. In the later sections of the paper, the test and experimental results are focused on E-band only. Fig.6(a)-fig.6(c) show the variation of beat frequency spectrum of E-band system when the ICRH antenna trolley moving backward towards the vessel wall, i.e. from a position of 293 mm the color in each spectrum indicates the power of beat frequency with the unit of log scale . Two clear frequency strips are observed, which the value varies with the probing frequency in the spectrum of each figure. The bending of beat frequency strips are attributed to the dispersion effect in the TL. Moreover, the beat frequency value of lower branch keeps constant with the ICRH antenna trolley moving backward, which means the beat frequency induced in this branch is due to a fixed reflection in front of reflectometer antenna.

This lower branch is result from reflection at the ICRH antenna straps due to the side lobes of the antenna pattern.

It is noted that the beat frequency of upper branch increase with the ICRH antenna trolley moving backward, which fits well with the first wall reflection when consider the group delay variation according to equ.2. Considering the variation of beat frequency value for the three different trolley positions of ICRH antenna, the absolutely distance difference measured by reflectometer can be inferred from the equation of , where is the group delay difference between two moving cases and is the speed of light.

During the calculation, the sweep rate of E band is constant as

6265 GHz

. It is seen in fig.2(d) that the distance difference deduced from reflectometer matches well with the calculation of ICRH antenna trolley moving, which demonstrates that the system performs well.

2.7 Profiles verification

After the commissioning of the system, the reflectometer operated routinely during the recent experimental campaign. Since the whole system of reflectometer is installed on the ICRH module.

It is essential to figure out the influence of ICRH application on the measurement of reflectometer. , with the front two time slices without ICRH, and later two with

6 MW

ICRH power) corresponding to a different density level are selected for comparison. Fig.8 shows the beat frequency spectrum calculated at four different time slices, respectively, the color in each spectrum indicates the power of beat frequency with the unit of log scale . The branch which is interested for density profile evaluate are indicated in black points with dashed line in each figure.

It is clearly seen that the beat frequency value decreases when compared to the case with back wall reflection (the beat frequency with back wall is not shown here and in this discharge its value located around

0 MHz

due to adjust the length of delay line). Moreover, an weak indication of ICRH strap reflection is seen in each spectrum due to relative increase of amplitude for the branch of plasma reflection. It is seen in fig.8(c) and fig .8(d) that the main branch interested in density profile evaluation are clearly detected and no clear deformation of beat frequency and other interference is seen in the spectrum after applying of ICRH power.

Furthermore, taking the 1/e power of beat frequency spectrum and its errorbar, approximately valued at

11 MHz

Considering , combine with equ.2, one can roughly estimate the spatial resolution of reflectometer as , as introduced in section 2.5, the sweep rate of E band is constant as

6265 GHz

, resulting a spatial resolution of However, there is no clear indication from each sub-figure in fig.8 of a sudden drop of beat frequency value and a large increase of the amplitude among whole bands (a well accepted judgment for the distinguish of probing initial density where a transition from back wall reflection to plasma reflection). This is due to the minimum probing frequency of E-band is above the so called initial density, and the whole band reflected by plasma. The minimum probing frequency(

2 GHz

of E-band system is very close to the zero probing frequency (

8 GHz

at a edge magnetic field

28 T

) for this case. The zero density layer can be detected by E-band system when the edge magnetic field is at

4 T

as seen from fig.1 in the further W7-X experiments. For the density profile evaluation, it is recovered from the phase variation according to the Bottollier algorithm The initial point is fixed by taken the electron cyclotron frequency for each density construction.

The radial position of this point also taken from the other edge profile diagnostic, such as Alkali beams (ABES) . Fig.9 shows the density profiles evaluated at four different time slices with the line integrated density ramp up. An out-shift of the profiles are clearly seen which match well with the increase of line integrated density, as indicated in fig 7 FIGURE:7. Furthermore, it is seen that the profile measurement is not perturbed by the ICRH application (up to

6 MW

), and a reasonable profiles at = 4 s in fig.9 are calculated.

The verification of the density profiles is based on a comparison of the evaluated density profile measured by the diagnostic of ABES and reflectometer. It is impossible to simply compare the profiles obtained by those two diagnostics since a 3-D structured magnetic topology on W7-X. A more efficient way is to trace the ABES ne profile ( , Module AEB21) from the equatorial plane to the reflectometer LoS ( , Module AEE31) via the field line tracer (FLT) the ABES measurements are traced along the magnetic field lines (pink lines, fig.10 (a)) from the bean-shaped cross-section ( = 331 , black points) to the reflectometer’s one ( , Module AEB21, red points). Secondly, the FLT is performed to obtain a Poincaré figure by means of the line-traced positions (green points) as start points, as seen zoom in the fig .10 (c). Then the inter- sections along the reflectometer LoS can be collected on each flux surface of the Poincaré figure, which are indicated by the blue-dots in the fig.10 (c). By assuming the density level constrains on the same flux surface in the Poincaré figure, one can obtain the mapped ne profile along the reflectometer LoS, as is shown in fig.11. It is noted that the obtained tracing points(red points) of ABES and the intersection points (blue points) in fig.10(c) are located in different phases of the island chain, in that case the mapped ne profile didn’t include those measurement inside the island. Fig.11 shows the density profiles at two time slices of program . It is seen that inside the LCFS, a well matched density profiles between two diagnostics demonstrate a convince and promising measurement of reflectometer. The comparison of density profile outside the LCFS is challenging in W7-X, an advanced mapping method is required and this is planned in the future work.

As illustrated in fig.4(a), the LoS of E-band system goes across the X-point of the magnetic island. The LoS could intersect the magnetic island by applying the control coils to adjust the island chain . The island divertor and its properties are key issue for W7-X. The 5/5-island chain is the island divertor in this case and it is interest to see the measurement inside the magnetic island.

Poincaré figure (obtained by FLT from ideal coils) and magnetic field line connection length contour

(obtained by FLT including ideal coils, control coils and trim coils). It is seen that the LoS of reflectometer intersects the island indicated by Poincaré figure. The beat frequency measured by reflectometer presents a jump in its value when the cutoffs those probing frequencies are located inside the magnetic island, as shown in fig.12(c).

The beat frequency should be a continuous evolution when probing a monotonous density profile. And an upward jump of beat frequency means an abrupt decrease of density gradient, therefore a flatten density profile is seen in fig .12(b). Furthermore, The width of flatten region in the density profile corresponding well with the width of magnetic island indicated by the Poincaré figure and connection length at LoS of reflectometer.

2.8 Summary and outlook

A frequency modulated continuous wave (FMCW) reflectometer with heterodyne detection has been developed for the density profile measurement in front of the ICRH antenna in W7-X. Two subsystems share a similar electronics schematic covering the frequency range of E-band (60GHz- 90GHz) and W-band (75GHz-110GHz), with X-mode polarization scheme corresponding to a mea- surable ne coverage up to . The E-band system offers a convinced density profile which is comparable with the measurements of line integrated density and ABES. The measure- ment of reflectometer is not influenced by application of ICRH system. Moreover, a density profile is obtained when the LoS of reflectometer goes across the magnetic island. The high spacial ) and temporal resolution (normally at ) allowing to tracking the fast event and plasma transport study. The reflectometer will be operated routinely for density profile measurement and contribute to the physical study of W7-X experiments. The W-band system will be commissioned in the upcoming experimental campaign. A combination of two sub-system at one position (either at X-point or O-point of island) will be carried out in the near future as well. The cross check of density profile with other edge diagnostic will be fulfilled.

Acknowledgemens This work has been carried out within the framework of the EUROfusion Consortium, funded by the European Union via the Euratom Research and Training Programme (Grant Agreement 101052200 EUROfusion). Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European Union or the European Commission.

Neither the European Union nor the European Commission can be held responsible for them. And this work was supported National Key Program of China No.2022YFE03050003 and No. 2022YFE03070004.

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The cutoff density distribution at different probing frequencies with the variation of magnetic field, the horizontal dashed line indicates a typical magnetic field of at magnetic axis 2.5T with edge magnetic field of 2.3T on W7-X, the blue vertical dashed lines denote the initial probing frequency at E-band and W-band respectively The reflectometer layout is emphasized by color, the ICRH transmission line is depicted in grey. The sectoral horn structure, vacuum window and the electronic box of reflectometer shown in detail in the individual figure.

(a) The photo of the ICRH straps and the sectoral horn pairs of reflectometer. (b) The dimension of horn, and (c) its inside cut shape. (d) Radiation pattern angle estimation for the -3 dB pattern. The colored lines indicate the operational frequency. The E-plane of the horn is fixed at 3.556 mm, the H-plane is scanned in the range of 25mm to 50 mm. The red dashed line is the opening angle of the horn and the vertical black dashed line is a = 40.3 mm of the H-plane. (a)Poincaré figure (in grey) for a standard configuration with 5/5 island chains at the toroidal angle . The launcher and receiver are labeled by the red triangles, and the lines of sight are indicated by the red lines.

The vessel and divertor modules are presented in the light blue. (b) Poincaré figure in the low-iota configuration (DBM).

Schematic of the FMCW reflectometer. System performance during the ICRH antenna trolley mov-ing, (a)-(c) beat frequency variation and (d) the distance difference comparison between the result deduced from reflectometer mea- surement and the ICRH antenna trolley moving.

W7-X plasma experiment of 20230330.040, time traces from (a)plasma heating with ECRH and ICRH, (b) diamagnetic en-ergy and (c) line-integrated density.

Beat frequency comparison between four different time slices with the line integrated density ramp up. With t=1s, 2s with-out the ICRH and t=3.2s, t=4s with 0.6kW of ICRH power. The beat frequency branch reflected by the plasma and reflected by the ICRH antenna straps are marked in black points and grey points, respec-tively.

Density profile evaluated at four different time slices with the line integrated density ramp up.

With t=1s, 2s without the ICRH and t=3.2s, t=4s with 0.6kW of ICRH power

Mapping the profile measurement form ABES diagnostic cross section to density profile reflectometer cross section via magnetic field line tracing. (a) shows the results of tracing. The detail of the two cross sections, with (b) the Alkali beams (ABES) cross section and (c) the profile reflectometer cross section Density profiles comparison between measurements of ABES and measurements of reflectome- ter after mapping from FLT. (a) t=2s, (b) t=3.5s

Density profile inside the magnetic island.(a) Poincar e fig-ure and connection length contour, the LoS of reflectometer indi-cated in blue points, (b) the density profile, and (c) is the beat fre-quency