As the plasma beta (β) increases in high-performance tokamaks, electromagnetic turbulence becomes more significant, potentially constraining their operational range. To investigate this turbulence, a cross-polarization scattering (CPS) diagnostic system is being developed on the HL-3 tokamak for simultaneous measurements of density and magnetic fluctuations. In this work, a quasi-optical system has been designed and analyzed for the Q-band CPS diagnostic. The system includes a lens group for beam waist size optimization, a rotatable wire-grid polarizer for polarization adjustment, and a reflector group for measurement range regulation and system response enhancement. Laboratory tests demonstrated a beam radius of order 4 cm at the target measurement location (near the plasma pedestal), cross-polarization isolation exceeding 30 dB, and poloidal and toroidal angle adjustment ranges of ±40° and ±15°, respectively. These results verify the system’s feasibility through laboratory evaluations. The quasi-optical system has been installed on the HL-3 tokamak during the 2023 experimental campaign to support the development of CPS diagnostics.

The quasi-optical design for the cross-polarization scattering (CPS) diagnostic1 to measure electromagnetic turbulence on the HL-3 tokamak (formerly known as HL-2M) is presented in this paper. Theoretical and experimental results indicate that as the plasma β = 2μ0p/B2 (p is the plasma pressure and B is the magnetic field) increases, the intensity of electromagnetic turbulence in the plasma significantly increases, potentially constraining the operational range of high-performance tokamaks.1,2 Therefore, to directly measure local electromagnetic fluctuations in plasma, CPS has been developed in lots of magnetic fusion devices, such as Tore-Supra,1,3 Tokamak Fusion Test Reactor,4,5 GAMMA-10,6,7 FT-1,8 Mega Ampere Spherical Tokamak(MAST),9 MAST Upgrade,10 DIII-D,11–14 C-2W,15 Experimental Advanced Superconducting Tokamak,16 and HL-2A.17,18

The principle of CPS is that the shared probe microwave is scattered into two orthogonal polarizations by density fluctuations ñ and magnetic fluctuations B̃, respectively,1,14,19
J(2)=iε0ωpe2ωiñneEi+ωceε0ωpe2σσEi×(B̃/B),
(1)
××Es+ωic21σiε0ωiEs=iμ0J(2)t,
(2)
where ɛ0, ωpe, Ei, ωi, ne, σ, and B are the vacuum permittivity, the local plasma frequency, the electric field of the incident wave, the incident wave frequency, the local plasma density, the unperturbed conductivity tensor, and the local magnetic field, respectively. The first and second terms on the right side of Eq. (1) correspond to the Doppler backscattering (DBS, parallel to Ei, scattered by ñ) and CPS (orthogonal to Ei, scattered by B̃) processes, respectively. Notably, there is a clerical error in Refs. 1 and 18. The numerator of the second term should be ωce instead of ωi.

However, there are still some challenges in the application of CPS. First, the intensity of magnetic fluctuations B̃ is significantly smaller than that of density fluctuations ñ (B̃/B2/ñ/n2 is about −20 to −50 dB), which introduces inherent difficulties in signal extraction and interpretation.1,5,9,12 Another challenge is the polarization match, which is crucial to ensure DBS signals do not contaminate the CPS signals.9,14 In addition, the ray-tracing analysis confirms that strict accordance with the toroidal and poloidal launch angles of the probe microwave is indeed necessary to improve the received signal level.18 

Therefore, the quasi-optical system plays a key role in the CPS diagnostic. First, it allows for beam width control, which is essential for improving spatial and wavenumber resolution. Second, it assists in launch angle control, enabling flexible regulation of the measurement wavenumber and position range while also improving the received scattering power and thereby the signal-to-noise ratio. Finally, it enables precise control of polarization, a critical factor for differentiating magnetic from density fluctuations.

Following the introduction section, quasi-optical design, including the Keplerian beam expander lens groups, the ellipsoidal and plane mirror group, and the rotatable polarizer, is described in Sec. II. The results of laboratory tests are presented in Sec. III. Finally, a summary is given in Sec. IV.

The general geometry and layout of the quasi-optical components of the system are shown in Fig. 1.

FIG. 1.

Geometry and layout of the quasi-optical system, which includes the orthomode transducer (OMT) based dual polarized antennas, the transmitting lens group, the rotatable polarizer, and the reflector group. The OMT-based antennas have both vertical and horizontal ports, allowing them to receive or transmit waveforms in varying polarizations.

FIG. 1.

Geometry and layout of the quasi-optical system, which includes the orthomode transducer (OMT) based dual polarized antennas, the transmitting lens group, the rotatable polarizer, and the reflector group. The OMT-based antennas have both vertical and horizontal ports, allowing them to receive or transmit waveforms in varying polarizations.

Close modal

The overall design goal is to form a Gaussian beam at the edge of HL-3 plasmas for Q-band frequency operation, with the ability to control beam width, launch angle, and polarization. The quasi-optical system consists of the orthomode transducer (OMT) based dual polarized antennas, the transmitting lens group, the rotatable polarizer, and the reflector group.

The OMT-based antennas have both vertical and horizontal ports, allowing them to receive or transmit waveforms in varying polarizations. In Fig. 1, antennas 1 and 2 serve as the respective receive and transmit antennas.

As illustrated in Fig. 2, the transmitting lens group is designed for beam width optimization. In terms of wavenumber resolution, Δk=22w1+w2k0ρeff2, an optimal beam spot radius w04 exists.20 This radius is typically moderate, ranging around 2.5–3.5 cm. Straying from this optimal range could result in less accurate wavenumber measurements. Finally, the beam spot radius w04 also affects the spectral resolution: R=σfD=Δuu+Δkk. It influences Δk, which in turn affects the broadening of the Doppler shift peaks.21 Hence, controlling the beam spot radius is crucial for accurate spectral measurements.

FIG. 2.

Diagram of the transmitting lens group and reflector group. di denotes the component distances, and wj represents the beam waists at different positions. f1,2,3 correspond to the focal lengths of lenses 1, 2, and the elliptical mirror. R1 and R2 indicate the wavefront curvature radii of incoming and outgoing microwaves at the elliptical mirror.

FIG. 2.

Diagram of the transmitting lens group and reflector group. di denotes the component distances, and wj represents the beam waists at different positions. f1,2,3 correspond to the focal lengths of lenses 1, 2, and the elliptical mirror. R1 and R2 indicate the wavefront curvature radii of incoming and outgoing microwaves at the elliptical mirror.

Close modal
The transmitting lens group consists of three high-density polyethylene (HDPE) lenses (Fig. 1), forming two pairs of Keplerian beam expanders (Fig. 2). The Keplerian beam expander system, with two converging lenses at a distance equal to the sum of their focal lengths, enables frequency-independent Gaussian beam transformation.22 The relationship between the focal length (f), the radius of curvature (r1, r2), the refractive index (n), and the thickness (d) of the thick lens is given by the Lensmaker’s equation,23 
1f=(n1)1r11r2+(n1)dnr1r2.
(3)

The refractive index of HDPE, ∼1.52,24–26 was estimated by the free space measurement method, which comprises a vector network analyzer (VNA) and two antennae facing each other.27–29 The phase of the transmitted signal-beams was recorded under two conditions for a 10 mm thick HDPE sample: (a) sample in place and (b) sample removed. The refractive index n was then computed from the observed phase shift using the formula n = Δϕλ0/d + 1, where λ0 is the free-space wavelength, d is the thickness of the sample, and Δϕ is the measured phase shift in radians. Figure 3 presents the results of refractive index estimation within the frequency range of 30–40 GHz. The variations observed in the refractive index are possibly attributed to the multiple-reflection Fabry–Perot phenomenon.27 

FIG. 3.

(a) Free space measurement setup for the refractive index estimation. (b) Results of HDPE refractive index estimation. The blue and red lines depict two separate estimation results, while the black dashed line represents the theoretical value of 1.52 as a reference. The variations are possibly attributed to the multiple-reflection Fabry–Perot phenomena.

FIG. 3.

(a) Free space measurement setup for the refractive index estimation. (b) Results of HDPE refractive index estimation. The blue and red lines depict two separate estimation results, while the black dashed line represents the theoretical value of 1.52 as a reference. The variations are possibly attributed to the multiple-reflection Fabry–Perot phenomena.

Close modal
Gaussian beam transformation by a thin lens can be mathematically described using the following equations:30 
doutf=1+din/f1din/f12+ZR,in/f2,
(4)
wout2win2=1din/f12+ZR,in/f2.
(5)
In these equations, the parameters din and dout represent the distances from the lens to the input beam waist win and the output beam waist wout, respectively. The focal length of the thin lens is represented by f. In addition, zR=πω02λ denotes the Rayleigh distance or Rayleigh range, and w0 signifies the beam waist.
Referring to Fig. 2, the beam waist of the emitted microwave by the horn antenna can be carefully positioned at the desired location, which corresponds to one focal length of lens 1 (i.e., d1 = f1). Then get
w02=λf1πw01,
(6)
w03=λf2πw02=f2f1w01.
(7)

Therefore, the Keplerian beam expander system enables frequency-independent Gaussian beam transformation. The beam waist at the output, represented by w03, is determined by the ratio of the focal lengths of lens 2 to lens 1 and is proportional to the initial beam waist w01.

As shown in Fig. 2, the reflector group includes an ellipsoidal mirror and a plane mirror. The reflective nature of the ellipsoidal mirror enables beam direction manipulation, providing convenience for subsequent angle adjustments. In this design, the tilt angle of the ellipsoidal mirror is specifically chosen to ensure a 90° angle between the outgoing and incoming beams.

It is important to note that the beam waist of the microwave emitted by the horn antenna varies with the frequency. Therefore, additional adjustments are necessary when utilizing a Keplerian beam expander system. An effective approach is to incorporate an ellipsoidal mirror, which serves as the equivalent of a converging lens, providing a similar focusing effect as expressed in Eq. (5).

Theoretical calculations indicate that the beam waist of the antenna is proportional to the wavelength (w0 = kantλ). The half-power beam width (HPBW) of the Gaussian beam’s intensity profile, denoted as HPBW(z) or θHPBW, can be expressed as
HPBW(z)=2ln2w(z),
(8)
tanθHPBW2=limzHPBW(z)2z.
(9)
Then,
tanθHPBW2=ln22limzw(z)z=ln22λπw0.
(10)
The proportionality coefficient kant can be calculated as
kant=1πtanθHPBW2ln22.
(11)
By utilizing the ellipsoidal mirror and positioning it at a distance away from the input beam waist equal to the focal length (din = f), similar to the concept in Eq. (6), the frequency-dependent characteristics introduced by the antenna can be effectively mitigated,
w03=f2f1w01=f2f1kantλ,
(12)
w04=λf3πw03=f1f3f2πkant.
(13)
The distance away from the output beam waist is set to be equal to the distance away from the input beam waist, which is equal to the focal length, i.e., dout = din = f. The beam waist size w04 is then set to the desired value, determined by the required wavenumber resolution. The specific distance dout is determined by the relative position of the measured location and the ellipsoidal mirror. With these parameters, the radius of curvature Rout can be calculated by Eq. (14). Using Eq. (15), the radius of curvature Rin can then be computed
R(z)=z1+zRz2,
(14)
1f=1Rin+1Rout.
(15)

However, Rout and Rin are related to wavelength λ. For the center wavelength λm within the frequency range, we can calculate the corresponding values of Rout,m and Rin,m to determine the parameters of the ellipsoidal mirror.

Based on the aforementioned constraints and calculations, the parameters of the ellipsoidal mirror are determined to be a major axis (a) of 1272.1 mm, a minor axis (b) of 625.2 mm, and a tilt angle of 37.55°.

The ray-tracing code BORAY31 is utilized to estimate the scattering location and wavenumbers of the density and magnetic fluctuations at various launch angles. Results show that the toroidal and poloidal launch angles should cover the range of 5°–25° and 11°–40°, respectively.18 In addition, it is important to note that in order to improve the received scattering power and, hence, the signal-to-noise ratio, the toroidal launch angles should align with the poloidal launch angles.18,32,33

Therefore, the plane mirror is utilized to select the wavenumber by adjusting the poloidal launch angle and to reduce mismatch attenuation by modifying the toroidal launch angle. It receives the reflected microwave beam from the ellipsoidal mirror and directs it toward the plasma. It is specifically designed to rotate in two orthogonal directions, enabling simultaneous adjustment of both the toroidal (±15°) and poloidal (±40°) launch angles in order to facilitate the desired adjustments.

The distance between the plane mirror and the ellipsoidal mirror is designed to be adjustable based on the size of the window and the optical aperture, allowing for flexible installation.

Polarization control is crucial for distinguishing the scattered signals from density fluctuations (ñ) and magnetic fluctuations (B̃). The relative fluctuation level B̃/B2/ñ/n2 is reported to be ∼−20 to −50 dB.1,5,9,12 Hence, a minimum polarization isolation exceeding 20 dB is necessary. The beam is focused between the two lenses of the Keplerian beam expander system, which facilitates enhanced polarization control. Considering the diminished diameter of the required polarizer, the integration of a higher speed rotatable polarizer at the beam’s focal point can significantly improve the temporal precision of polarization control. Therefore, a 150 mm hollow-core motorized rotary stage along with a wire grid polarizer is utilized to achieve the desired polarization control. The wire grid polarizer, composed of tungsten wires with a diameter of 10 μm and a wire spacing of 25 μm, provides excellent polarization isolation.17 In addition, the motorized rotary stage allows for precise adjustment of the polarizer angle, as shown in Fig. 1.

As shown in Fig. 4, antenna 1 is oriented with its H-plane (H1) aligned along the x-direction and its E-plane (E1) aligned along the y-direction. Antenna 2 is symmetric to antenna 1 with respect to the polarizer plane, but its polarization deviates from antenna 1 by an angle of γ due to the installation error.

FIG. 4.

Geometric relationship between the polarizer angle (θgrid), the polarization angle (θ), the pitch angle (α), the polarizer orientation angle (β), the installation error angle (γ), and the mismatch angle (δ). The x and y directions correspond to the toroidal and poloidal directions of the plasma, respectively.

FIG. 4.

Geometric relationship between the polarizer angle (θgrid), the polarization angle (θ), the pitch angle (α), the polarizer orientation angle (β), the installation error angle (γ), and the mismatch angle (δ). The x and y directions correspond to the toroidal and poloidal directions of the plasma, respectively.

Close modal

The wire grid polarizer is installed at an angle of β = 45° between the normal and the optical axes. By rotating the polarizer, the orientation of the beam’s polarization can be adjusted. In Fig. 4, the blue arrow represents the wire direction, and its projection on the x–y plane is denoted by the red vector Hin. An electric field vector parallel and perpendicular to the Hin is reflected and transmitted, respectively. Ein represents the transmitted electric field vector, which is perpendicular to Hin. It is important to note that the polarizer angle, denoted as θgrid, should not be confused with the polarization angle, denoted as θ. The relationship between the two angles is described by the equation tan(90 − θ) = cos(β)tan(90 − θgrid).

B0 represents the direction of the magnetic field lines at the edge of the plasma, with the direction perpendicular to B0 being the pure X-mode electric field direction. The angle α represents the orientation of the magnetic field B0 with respect to the x-axis, and δ represents the mismatch angle between the X-mode and Ein. It is important to note that α = θ + δ,
E1,xE1,y=RT(θ)ηt,00ηt,RT(αθ)SooSxoSoxSxx×R(αθ)ηt,00ηt,R(θ)ExEy,
(16)
E2,xE2,y=RT(α+γ)ηr,00ηr,RT(αθ)SooSxoSoxSxx×R(αθ)ηt,00ηt,R(θ)ExEy.
(17)

Moreover, the impact of polarization on signal extraction can be described by Eqs. (16) and (17).

The microwave beam emitted from antenna 1 undergoes polarization selection as it passes through the polarizer. Before entering the plasma, the incident microwave beam can be decomposed into two orthogonal modes (O mode and X mode) based on the relationship between its electric field and the background magnetic field. Inside the plasma, both the O-mode and X-mode waves interact with turbulents, leading to DBS and CPS scattering simultaneously. The scattering efficiencies for these four processes are denoted as polarization scattering matrix S = [Soo, SoxSxx, Sxo].34 The scattered microwaves propagate through the plasma and return to the polarizer. A portion of the scattered waves transmits through the polarizer and re-enters antenna 1, while another portion is reflected by the polarizer and enters antenna 2.

In practical applications, by rotating the polarizer to θ = α, the rotation matrix R(αθ) becomes the identity matrix I, effectively decoupling the scattering matrix. Considering the reflection and transmission efficiency (η) of the polarizer, for high polarization isolation, we have ηt,‖ → 1, ηt,⊥ → 0 and ηr,⊥ → 1, ηr,‖ → 0. In addition, by rotating antenna 1 to α = 0, we have R(α) = I. Similarly, rotating antenna 2 to γ = 0, results in R(γ) = I. With these considerations, Sxo and Soo could be distinguished,
E1,y=ηt,Sxxηt,Ey,
(18)
E2,x=ηr,Sxoηt,Ey.
(19)

A full-scale quasi-optical system has been implemented for laboratory testing. A series of tests were conducted to verify the design performance before the final installation of HL-3.

As illustrated in Fig. 5(a), a three-dimensional displacement platform was utilized to facilitate precise control over the movement of the receiving antenna in the x, y, and z directions. The typical parameters of the receiving antenna include a 20 dBi gain and a 3 dB beamwidth of 10°. In the measurement setup, the x-axis represents the horizontal direction, the y-axis represents the vertical direction, and the z-axis corresponds to the optical axis direction.

FIG. 5.

Test platform (a) and its calibration results (b). The receiving antenna (20 dBi, θHPBW = 10°) is capable of three-dimensional movement, allowing for the measurement of spatial power distributions. The voltage output of the logarithmic detector (Vout) is plotted as a function of the power entering the receive antenna (Pin) for three different frequencies: 34 GHz (black), 40 GHz (blue), and 48 GHz (red).

FIG. 5.

Test platform (a) and its calibration results (b). The receiving antenna (20 dBi, θHPBW = 10°) is capable of three-dimensional movement, allowing for the measurement of spatial power distributions. The voltage output of the logarithmic detector (Vout) is plotted as a function of the power entering the receive antenna (Pin) for three different frequencies: 34 GHz (black), 40 GHz (blue), and 48 GHz (red).

Close modal

The received microwave signal (with power Pin) from the movable antenna was transmitted into the radio frequency (RF) port of the mixer through a 4 m coaxial line, then mixed with the local oscillator (LO) signal and down converted to an intermediate frequency (IF) signal. The LO chain is configured as an active ×4 frequency multiplier with a frequency tunable synthesizer to provide sufficient drive power and cover the entire Q band. A logarithmic detector with a dynamic range exceeding 50 dB is employed to measure the power of the IF signal, providing a low frequency (DC) output (Vout) that is logarithmically (“linear in dB”) related to Pin level.35 

Then calibration was performed, and the results are depicted in Fig. 5(b). The power entering the receive antenna (Pin) was systematically increased from −60 to 0 dBm in 1 dBm increments for three different frequencies: 34 GHz (black), 40 GHz (blue), and 48 GHz (red). In addition, the voltage output of the logarithmic detector (Vout) is plotted as a function of the power entering the receive antenna (Pin) in Fig. 5(b). As one can see, the calibration results indicate that the power response of the test platform can be categorized into three regions: linear response region (−35–0 dBm), nonlinear response region (−50 to −35 dBm), and saturation region (<−50 dBm).

Gaussian beam radius measurements were conducted for three representative frequencies in the band of interest (34, 40, and 48 GHz). The receiving antenna was scanned in the x–y, y–z, and x–z planes to measure the power at various distances from the quasi-optical system.

The output voltage matrix Vout(x, y, z) obtained from the measurements was interpolated using the calibration results shown in Fig. 5(b) to derive the power distribution [Pin(x, y, z)] in units of dBm. Then, it was converted to power distribution in units of mW using the formula PmW=10(PdBm/10). For each z value, representing the distance from the quasi-optical system, the horizontal and vertical power distributions [Pin(x) and Pin(y)] were fitted using a Gaussian function to determine the half-power beam width [HPBWH(z) and HPBWV(z)]. The beam radius [w(z)] was then calculated using Eq. (8). Note that the input power for the transmitting antenna was set to 10 dBm to ensure that the testing was conducted within the linear response region of the test platform.

The representative spatial power distributions in the vertical y–z plane are depicted in Figs. 6(a), 6(c), and 6(e), providing insight into the beam patterns at 34, 40, and 48 GHz. Furthermore, the beam profiles at three different z positions (z = 30, 35, and 40 cm) are displayed in Figs. 6(b), 6(d), and 6(f), demonstrating a close resemblance to a Gaussian distribution. These profiles offer a detailed view of the beam intensity distribution at different distances from the plane mirror. For instance, at a distance of 30 cm (black lines) from the plane mirror, the peak power for the 34 GHz beam is ∼0.05 mW (−13 dBm), with a gradual decrease as the distance increases. The spatial power distributions in the horizontal x–z plane are similar to those in the y–z plane. Note that the power at the Gaussian beam width is reduced by 8.68 dB relative to the peak power, as 86.5% of the total energy is contained within the Gaussian beam width.36 

FIG. 6.

Representative beam patterns for (a) 34 GHz, (c) 40 GHz, and (e) 48 GHz. Corresponding beam profiles at z = 30 cm (black), z = 35 cm (blue), and z = 40 cm (red) are displayed in (b), (d), and (f). All of these profiles exhibit a close resemblance to a Gaussian distribution.

FIG. 6.

Representative beam patterns for (a) 34 GHz, (c) 40 GHz, and (e) 48 GHz. Corresponding beam profiles at z = 30 cm (black), z = 35 cm (blue), and z = 40 cm (red) are displayed in (b), (d), and (f). All of these profiles exhibit a close resemblance to a Gaussian distribution.

Close modal

The calculated Gaussian beam width w(z) is shown in Fig. 7. The beam widths for the 34 GHz (black square) and 40 GHz (blue triangle) emission frequencies exhibit similarity in the z = 20–40 cm range, but the 40 GHz beam width is narrower for z > 40 cm. Moreover, the beam width for 48 GHz (red circle) is lower than the other two frequencies across the entire measurement range. Within the target measurement area in the plasma (z = 30–40 cm, corresponding to R = 2.35–2.45 m, covering from the plasma edge to the pedestal top), the radial beam widths are of order 4 cm. In addition, the fluctuation in beam width with a change in distance might be attributed to multipath effects, specifically the constructive or destructive interference between signals from direct and reflected paths.37 This interference might affect power distribution and potentially influence the calculated beam width.

FIG. 7.

Test results of Gaussian beam radii for three probe frequencies: 34 GHz (black square), 40 GHz (blue triangle), and 48 GHz (red circle). The locations of various plasma radii are indicated at the top.

FIG. 7.

Test results of Gaussian beam radii for three probe frequencies: 34 GHz (black square), 40 GHz (blue triangle), and 48 GHz (red circle). The locations of various plasma radii are indicated at the top.

Close modal

In summary, the quasi-optical microwave system achieves a beam width of 3–4 cm. However, there is still frequency dependence in the beam width, which suggests further optimization in future studies.

The polarization isolation of the rotating polarizer was tested using the above test platform, with the receiving antenna fixed at a distance of z = 20 cm from the wire grid polarizer. During the test, the wire grid polarizer was rotated at a constant speed of 200° per second, and the corresponding changes in received power were measured.

The solid lines in Fig. 8 illustrate the test results of polarization isolation. Figures 8(a) and 8(b) show the normalized outputs from the receiving antenna for transmission and reflection, respectively. These plots illustrate how the outputs change with the angle of the wire grid polarizer, θgrid, at a launching frequency of 34 GHz.

FIG. 8.

Polarization isolation test results. Normalized outputs from the receiving antenna for transmission (a) and reflection (b) as functions of the wire grid polarizer angle θgrid at a launching frequency of 34 GHz. PIOMT and PIgrid represent the polarization isolation of the OMT antenna and the rotating wire grid polarizer, respectively.

FIG. 8.

Polarization isolation test results. Normalized outputs from the receiving antenna for transmission (a) and reflection (b) as functions of the wire grid polarizer angle θgrid at a launching frequency of 34 GHz. PIOMT and PIgrid represent the polarization isolation of the OMT antenna and the rotating wire grid polarizer, respectively.

Close modal

The electromagnetic wave launched from the transmitting antenna is set to be vertically polarized. In Fig. 8, the black and red lines correspond to the vertically and horizontally polarized outputs of the receiving antenna, respectively. The maximum transmission of the polarizer occurs when there is alignment between the polarization of the receiving antenna and the rotatable polarizer, as indicated by the maximum vertically polarized outputs at θgrid = 0° or 180° in Fig. 8(a).

Any misalignment between the polarization of the receiving antenna and the polarizer results in polarization loss. At θgrid = 90°, the polarization of the receiving antenna and the rotatable polarizer are perpendicular, resulting in the minimum transmission [Fig. 8(a)] and maximum reflection [Fig. 8(b)]. The minimum transmission is 39 dB lower than the maximum, while the minimum reflection is 35 dB lower than the maximum. As a result, the polarization isolations for the transmission and reflection of the wire grid polarizer are 39 and 35 dB, respectively. Furthermore, the difference in the vertically and horizontally polarized outputs at θgrid = 180° for transmission and at θgrid = 90° for reflection indicates a polarization isolation exceeding 40 dB for the receiving antenna.

In particular, the shape differences of the black curves in Fig. 8(a) (narrow) and (b) (wide) can be attributed to the differences between the polarizer angle θgrid and the polarization angle θ.

Similar to Eqs. (16) and (17), the relationship between the received power (PE2) and the polarization angle is described by Eqs. (20) and (21), as illustrated by the dash lines in Fig. 8. The measured results align well with the calculated values across a wide range of angles,
E1,xE1,y=RT(θ+γ1)ηt,00ηt,R(θ)ExEy,
(20)
E2,xE2,y=RT(θ+γ2)ηr,00ηr,R(θ)ExEy,
(21)
where γ1 and γ2 represent the installation error angles between the transmitting and receiving antennas for transmission and reflection measurements, respectively.

The polarization isolations of two additional frequencies, 40 and 48 GHz, were also tested. The results indicate that the polarization isolations for the transmission and reflection of the wire grid polarizer are 35 and 30 dB at 40 GHz and 34 and 30.25 dB at 48 GHz, respectively.

In summary, the rotating wire grid polarizer achieves polarization isolation exceeding 30 dB throughout the Q-band frequency range, meeting our requirements.

In this work, the quasi-optical system of the CPS diagnosis, including the Keplerian beam expander lens group, the ellipsoidal and plane mirror groups, and the rotatable polarizer, has been designed for the HL-3 tokamak. The Keplerian beam expander lens group enables frequency-independent Gaussian beam transformation, while the ellipsoidal mirror compensates for the variation of the beam waist in the antenna with respect to frequency. The quasi-optical microwave system achieves a beam width of order 4 cm within the target measurement area in the plasma. Based on the previous simulation, the toroidal and poloidal launch angles are designed to have an adjustment range of ±15° and ±40°, respectively. The rotating wire grid polarizer achieves polarization isolation exceeding 30 dB throughout the Q-band frequency range, while the polarization isolation of the OMT antenna is higher than 40 dB. In summary, the designed quasi-optical system meets the requirements for simultaneous measurements of density and magnetic fluctuations. At present, the CPS diagnostic with this quasi-optical system has been installed on the HL-3 tokamak during the 2023 experimental campaign. Further tests and experimental results of CPS will be shown in the near future.

This work was supported by the National Natural Science Foundation of China (Grant Nos. 12105087, 12175113, and 12275096), the Joint Funds of the National Natural Science Foundation of China (Grant No. U21A20440), and the Sichuan Key R&D Project (Grant No. 2023YFG0139).

The authors have no conflicts to disclose.

Y. Zhou: Conceptualization (equal); Data curation (equal); Investigation (equal); Software (equal); Visualization (equal); Writing – original draft (equal). R. H. Tong: Writing – review & editing (lead). W. L. Zhong: Funding acquisition (equal); Project administration (equal); Supervision (equal); Writing – review & editing (equal). Y. Tan: Funding acquisition (equal); Supervision (equal). M. Jiang: Supervision (equal). Z. B. Shi: Writing – review & editing (equal). Z. C. Yang: Methodology (equal); Software (equal); Validation (equal). Y. Q. Shen: Methodology (equal); Software (equal); Validation (equal). J. Wen: Methodology (equal); Validation (equal). A. S. Liang: Methodology (equal); Validation (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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