Design of a Doppler backscattering diagnostic for the Wisconsin HTS Axisymmetric Mirror (WHAM)
The Wisconsin HTS Axisymmetric Mirror (WHAM) is a compact high-field magnetic mirror. In such magnetic mirrors, cross-field transport is dominated by the flute instability (Endrizzi et al., 2023). To investigate density fluctuations associated with the flute instability, we designed a Doppler backscattering (DBS) diagnostic for WHAM, to be installed at the midplane port window. The diagnostic uses a two-channel tunable Ka-band (26.5--40 GHz) source and X-mode polarization. The azimuthal launch angle is set mechanically by rotating the external quasioptical assembly. As such, the system is reconfigurable during dedicated setup periods. Using the \textit{Scotty} beam-tracing code (Hall-Chen et al., 2022), we show that the proposed DBS system can measure density fluctuations with perpendicular wavenumbers $1 \leq k_\perp \leq 3~\mathrm{cm}^{-1}$ over radial locations $0.7 \leq \rho \leq 0.9$, where $\rho$ is the normalized radial coordinate. This is achieved with probe frequencies between 28 and 38.5 GHz, an elevation launch angle of $0^\circ$, and azimuthal launch angles in the range $1^\circ$--$3^\circ$. The selected configurations have low mismatch angle at cutoff, $|\theta_{m,c}|<1^\circ$. The quasioptical system uses a Ka-band horn and a biconvex ultra-high molecular weight polyethylene lens, and satisfies the port-access constraints in WHAM. The planned microwave system has a monostatic, homodyne architecture based on two phase-coupled Ka-band microwave channels. These two channels will be for the transmitted signal and coherent local oscillator (LO) for IQ downconversion, respectively. As the two phase-coupled channels can be independently tuned or swept with a controlled frequency offset, the same microwave chain can also support profile-reflectometry measurements using cutoff-delay information.