AFFILIATIONS

ABSTRACT

I. INTRODUCTION
Multi-scale turbulence interaction, especially mixed micro- scale turbulence phenomenon, which includes both ion and elec- tron scale turbulences, is of interest 1 in the high temperature plasma confinement study at present, and there are many the- oretical studies. 2–8 Simultaneous measurements of each electron scale turbulence and ion scale turbulence are required. However, the measurement of turbulence, especially on the electron scale, is state-of-the-art because this observation requires very high spa- tial and temporal resolutions. There are a few previous studies of this diagnostic in tokamaks such as NSTX, 9.10 DIII-D, 11 KSTAR, 12 MAST, 13 and NSTX-U. 14 We have developed and installed this electron scale turbulence diagnostic to the Large Helical Device (LHD 15 ) plasma, and this is the first report for the application to the helical device to the author's knowledge. In addition, LHD has sev- eral ion-scale turbulence diagnostics, such as CO 2 laser used phase constant imaging (PCI), 16 a microwave Doppler reflectometer, 17 and beam emission spectroscopy (BES). 18 The ion scale turbulence observations have been compared with the gyrokinetic simulation (GKV 19,20 ) results. 21–23 The introduction of this electron scale tur- bulence measurement will allow for a more detailed comparative study. In order to measure an electron-scale turbulence such as elec- tron temperature gradient (ETG) driven mode, which has a high wavenumber ( k 1 ρ s ~ 40 and k 1 ~ 40 cm − 1 ), a millimeter-wave back-scattering system is one of the suitable candidates, where k 1 is the fluctuation wavenumber perpendicular to the magnetic field and ρ s is the ion gyroradius at the electron temperature. When the electromagnetic wave is launched to the turbulent plasma, a scat- tered wave that satisfies the Bragg relationship k = 2k l sin( θ s /2) is generated. 24 Here, k 1 is the local wavenumber of the probing beam and θ s is the scattering angle. To measure higher wavenumbers of k 1 ~ 40 cm − 1 , one can choose either forward-scattering of terahertz waves or back-scattering of W-band millimeter waves, as shown in Fig. 1 . In general, there are two types of scattering conditions. One is collective, and the other is non-collective scattering. Con- sidering the current situation, the scattering parameter (so-called Salpeter parameter) α = (k 1 λ Dc ) − 1 is calculated under several plasma conditions of temperature and density, as shown in Fig. 2 . Here, λ De is the electron Debye length. The electron density is higher than 1 × 10 19 m − 3 in the usual LHD plasma experiments; thus, the diagnostic region is almost in α > 1. This means that the scatter- ing signal is collective, and the scattering signal originates from the correlated density fluctuation ñ c behavior as in the following equation: 12,24
where P s is the scattered power, r 0 is the classical electron radius, λ i is the probing wave's wavelength, L is the scattering length, and P 1 is the probing wave power. Considering the installation of a millimeter-wave scattering system on the LHD, W-band 90 GHz is suitable as a probing fre- quency. There is no electron cyclotron resonance layer in the plasma confinement region in the line of sight, as shown in Fig. 3 . When we use the ordinary mode (O-mode) propagation in the plasma, we can access the plasma core region. However, the plasma center is located ~3 m away from the vacuum window because of the complicated LHD vacuum chamber. We need the focusing optics to be precise for small scale turbulence observation. For this aim, we developed the in-vessel focusing antenna. In addition, the complex magnetic structure generates stray light, especially electron cyclotron emission (ECE), which plays an important role in the background noise. In this paper, we describe the in-vessel focusing antenna and the millimeter wave circuits of back-scattering system and its char- acteristics as follows.
II. METAL LENS RELAY ANTENNA
Since the turbulence structure is small and the observation position in the plasma core region is located ~3 m away from the vac- uum window, the probing wave beam must be focused. In addition, the limited space around the viewing window precludes the use of large focusing optics. Furthermore, beam steering capability is also required because of the requirement to measure the radial structure of the turbulence. Figure 4 shows the cross section of the observation line of sight of the back-scattering system. A possible method is the in-vessel focusing optics. For these aims, the metal lens antenna is applied as an in-vessel focusing antenna. This antenna is composed of a conical horn and two lenses arranged in a co-linear configura- tion, as shown in Fig. 5 . One lens is a bi-concave shaped lens with a curvature of 380 mm and a diameter of 200 mm with 2343 2 mm holes. Another lens is a plano-convex shaped lens with a curvature of 73 mm and a diameter of 72, and 253 2 mm holes. This relay lens is capable of focusing a beam width of ~38 mm. The beam width of the probing beam is measured on a test bench. Figure 6 shows the beam profile obtained with a sub-THz imaging camera (TeraSense T30, 64 × 64 pixel 2 ), where the beam width is less than 40 mm at the 3 m distance. In addition, remote beam steering is possible, and a scattering angle of 159° ± 6° can be realized, covering almost the entire plasma radius. FIG. 4. Three-dimensional LHD CAD design of an in-vessel antenna pair for the back-scattering system. Here, the plasma shape is illustrated by the magnetic surface layers (pink). FIG. 5. Drawing of the metal lens combination antenna (left) and the photograph of the installation in-vessel of LHD (right). (upper) and the profile sliced on the center line of left figure (bottom).
III. MILLIMETER WAVE CIRCUIT
The millimeter wave circuit for the back-scattering measure- ments is shown in Fig. 7 . Since precise density fluctuation measure- ments require the low-noise source for probing beam, a dielectric resonator oscillator with a synchronized quartz oscillator is used as a source. Probing 90 GHz millimeter wave is generated by ×6 multi- pliers. A part of the probe 15.0 GHz wave is led to the mixer (mixer 1) and mixed with the local 15.15 GHz wave to generate the intermedi- ate frequency (IF) component for heterodyne phase measurements. In the W-band mixer (mixer 2), the received 90 GHz wave and the local 90.9 GHz wave are mixed to generate another IF signal com- ponent. Each IF signal is used for quadrature signal detection, and the output of in/quadrature (IQ) detection is led to the analog to digital convertors (National Instruments PXI-6115) with a sampling rate of 2.5 MHz. The LABCOM data acquisition system collects the acquired signal in real-time and also controls the acquisition setting via their web site. 25 In addition, the above millimeter wave circuits are located in the diagnostic room, which is separated from the LHD experiment room. Because of the need to connect the 60 m distance with low transmission loss, 1.5 and 3.0 in. corrugated waveguides are used to connect to the LHD viewing port. The measured transmis- sion loss is shown in Fig. 8 . The total transmission loss is ~8 dB at 90 GHz. This value includes the losses due to two quartz windows and 12 miter bends. In the current configuration, the main noise is considered to be ECE radiation. In order to estimate the noise level during the FIG. 8. In situ transmission loss measurement of 1.5-in. corrugated wavequide. Note that this result includes two quartz windows and 12 bends. FIG. 9. Complex frequency power spectrum of the scattering signal from the plasma (red). The "w/o RF" line (gray) indicates the system noise level, and the "w/o RF" line (orange) shows the background plasma noise, which is considered to be mainly radiated ECE. plasma discharge, the system is modified to modulate the power of a probe wave with a single pole single throw (SPST) switch. When the SPST switch is off, the probe beam does not launch to the plasma and only ECE radiation noise can be detected. Figure 9 shows the observed frequency spectrum. ECE radiation noise, which has broad frequency components, is detected, but the scattered signal is found to be large enough to allow the fluctuation measurements. In addition, the case of the spectrum of "w/o plasma" shows the small intensity. This means the reflected wave components from the opposite wall, that is, multi-reflection components, are small. Currently, during normal plasma measurements, SPST operates at a ratio of 98 (on): 2 (off) to estimate the background noise. There- fore, the high wavenumber turbulence is routinely observed by this back-scattering system. In the current antenna setup ( Fig. 4 ), the radial component of the perpendicular wavenumber is dominant. Theoretically, the large poloidal wavenumber is of more interest for ETG studies. However, we think both radial and poloidal components are not independent and the radial wavenumber measurement is meaningful. Simula- tions involving both components allow for comparison study to be made. Since it is important to know this wavevector informa- tion, scattering position, and beam bending effects, the LHDGauss ray tracing code 2627 on the AutoAna system 28 is used to analyze the experimental conditions immediately after each LHD plasma discharge.
ACKNOWLEDGMENTS
The authors would like to thank the technical staff of LHD for their support. The authors also would like to thank Mrs. K. Takehara and T. Ito for their support of metallic lens pro- duction. This work was partially supported, in part, by KAK- ENHI (Grant Nos. 19H01880, 17K18773, 17H01368, 15H02335, and 15H02336), by a budgetary grant-in-aid from the NIFS LHD project under the auspices of the NIFS Collaboration Research Pro- gram (Grant Nos. ULPP027 and KLPH024), by the NINS program for cross-disciplinary study (Grant Nos. 01311802 and 01311903), and by the collaboration programs of the RIAM of Kyushu University and FIR-UF of Fukui University. Additional support was provided by Japan/U.S. Cooperation in Fusion Research and Development.
DATA AVAILABILITY
The data that support the findings of this study are available from the corresponding author upon reasonable request.