A Doppler backscattering diagnostic for the EXL-50U spherical tokamak: plasma considerations and preliminary quasioptical design

TL;DR

This paper develops a Doppler backscattering (DBS) diagnostic design for the EXL-50U spherical tokamak to measure turbulence-driven transport across ion- to electron-scale wavenumbers. It combines SCOTTY-based beam tracing with synthetic DBS to map cutoff locations and accessible turbulence wavenumbers via the Bragg condition $k_\perp = -2K$, and to design a U-band ($40$–$60$ GHz) quasioptical system that accommodates the device's large magnetic pitch angle. The results show that DBS can access scattering locations in the range $0.15 < \rho < 1$ with $k_\perp$ spanning roughly $0.24$–$0.95$ mm$^{-1}$ (and probing up to $k_\perp\rho_s \sim 10$, with potential reach toward $k_\perp\rho_s \sim 30$ for electron-scale). The proposed implementation emphasizes toroidal steering and tunable frequencies to minimize mismatch attenuation, delivering edge-to-core coverage in H-mode plasmas and enabling measurements of cross-scale turbulence relevant to proton-boron fusion in spherical tokamaks.

Abstract

The EXL-50U spherical tokamak was built by Energy iNNovation to develop technologies for proton-boron fusion in spherical tokamaks (Liu et al., Phys. Plasmas 2024). We present a conceptual design of the Doppler backscattering (DBS) diagnostic for the EXL-50U spherical tokamak. DBS is a diagnostic capable of measuring plasma turbulence, which is especially important for transport in tokamaks. Starting from a set of physical design constraints, such as port window availability and in-vessel space, we used SCOTTY (Hall-Chen et al., PPCF 2022), an in-house beam tracing code, to predict the location of the cutoffs and the corresponding scattering wavenumbers for several EXL-50U plasma scenarios. We find that we are able to measure scattering locations of 0.15 $<$ $ρ$ $<$ 1, with corresponding turbulent wavenumbers of 2.47 cm$^{-1}$$<$ $k_{\perp}$ $<$ 9.49 cm$^{-1}$. Here, $ρ$ is the normalised radial coordinate of the scattering location, and $k_{\perp}$ is the corresponding turbulent wavenumber. We then determine the optimal toroidal launch angles to ensure that the probe beam's wavevector is perpendicular to the magnetic field at the cutoff location, thereby maximising the backscattered signal. This matching is crucial due to the EXL-50U's high magnetic pitch angle, $\sim35^{\circ}$ at the outboard midplane. Given our results, we propose the use of toroidal steering and tunable frequency channels to ensure beams are well-matched with the magnetic pitch angle. We propose a quasioptical system that covers the U-band range (40--60 GHz).

Figures (17)

• Figure 1: Schematic of Doppler backscattering. (a) An antenna emits a microwave probe beam into the plasma and receives the backscattered signal from turbulent density fluctuations. According to the Bragg condition, the turbulence wavenumber is double that of the probe beam's wavenumber, $k_{\perp}$ = $-2K$. Here $k_{\perp}$, $K$ and $K_s$ are the wavenumbers of the turbulence, probe beam, and scattered electric field, respectively, and $\mathbf{B_p}$ and $\mathbf{B_T}$ are poloidal and toroidal components of the magnetic field, respectively. Note that backscattering occurs along path of the probe beam, but as the signal is dominated by scattering from the cutoff location hallbeamtrace, in this paper we assume that the backscattered signal only comes from the cutoff. (b) Scattering when the probe beam is not in the plane perpendicular to the magnetic field, that is, if it is mismatched. We define the angle between the normal of the magnetic field and the probe beam's wavevector and the plane perpendicular to the magnetic field to be the mismatch angle, $\theta_m$, such that sin$\left(\theta_m\right)$ = $\mathbf{\hat{K}} \cdot \mathbf{\hat{b}}$, where $\mathbf{\hat{K}}$ and $\mathbf{\hat{b}}$ are unit vectors of the probe beam's wavevector and magnetic field $\mathbf{B}$, respectively.
• Figure 2: Electron density (a)--(c) and temperature (d)--(f) profiles, as functions of the normalised radial coordinate, $\rho$, for the three scenarios used in this paper. These scenarios include the self-consistently modelled H-mode (A), shown in (a) and (d), the lower-density H-mode (B), shown in (b) and (e), and an L-mode, shown in (c) and (f). H-mode (A) has an internal transport barrier due to neutral beam injection. To reach zero density outside the last-closed flux surface, the electron density profiles (orange points) were extrapolated (blue lines) in (a) and (b).
• Figure 3: Magnetic field profile in the EXL-50U. Here $B_R$, $B_T$, and $B_Z$ are the radial (a), toroidal (b), and $Z$ (c) components of the magnetic field, respectively. The black contour lines show the last closed flux surface and the black crosses in (a)--(c) denote the magnetic axis. The magnetic pitch angle plot on the midplane, $Z=0$, is large and changes significantly with position (d).
• Figure 4: Cutoff frequencies along the midplane in the EXL-50U for (a): H-mode (A), (b): H-mode (B), and (c): L-mode. Here $f_{ce}$ is the fundamental harmonic electron cyclotron frequency, $f_{pe}$ is the plasma frequency, and $f_r$ is the X-mode cutoff frequency. The red dashed lines are the frequencies used, with the black circles and red crosses representing the O-mode cutoffs and the X-mode cutoffs, respectively. In (b), $f_{r}$ is slightly lower than 60 GHz, so a point is not plotted for 60 GHz. A 20 GHz frequency range allows for core to edge coverage.
• Figure 5: Poloidal section of the EXL-50U containing the plasma (depicted in pink). The launch position is set at $R = 1.9$ m, $Z = -1.0$ m. Microwave probe beam must be launched at appropriate angles to avoid it from being incident on PF14, a coil that goes toroidally around EXL-50U. Note that the plasma shape here differs from that shown in Fig. \ref{['fig:Bfield']} as scenario development has yet to be completed. Moreover, the vessel wall is not toroidally symmetric, so we will not consider the vessel wall in our analysis.