Measurement of high-k density fluctuation wavenumber spectrum in MAST and Doppler backscattering for spherical tokamaks

The high-k ($7\lesssim k_{\mathrm{\perp }}{\rho }_i\lesssim 11$) wavenumber spectrum of density fluctuations has been measured for the first time in MAST [B. Lloyd et al, Nucl. Fusion 43, 1665 (2003)]. This was accomplished with the first implementation of Doppler backscattering (DBS) for core measurements in a spherical tokamak. DBS has become a well-established and versatile diagnostic technique for the measurement of intermediate-k ($k_{\mathrm{\perp }}{\rho }_i\sim 1$, and higher) density fluctuations and flows in magnetically confined fusion experiments. A novel implementation with 2D steering was necessary to enable DBS measurements in MAST, where the large magnetic field pitch angle presents a challenge. We report on the scattering considerations and ray tracing calculations used to optimize the design and present data demonstrating measurement capabilities. Initial results confirm the applicability of the design and implementation approaches, showing the strong dependence of scattering alignment on toroidal launch angle. We also present comparisons of DBS plasma velocity measurements with charge exchange recombination and beam emission spectroscopy measurements, which show reasonable agreement over most of the minor radius, but imply large poloidal flows approaching the magnetic axis in a discharge with an internal transport barrier. The 2D steering is shown to enable high-k measurements with DBS, at $k_{\bot}>20
$\mathrm{c}\mathrm{m}$^{-1}$($k_{\bot} \rho_i>10$) for launch frequencies less than 75 GHz; this capability is used to measure the wavenumber spectrum of turbulence and we find $\mathrm{\mid }n(k_{\mathrm{\perp }}){\mathrm{\mid }}^2\propto k_{\mathrm{\perp }}^{-4.7\pm 0.2}$ for $k_{\bot} \rho_i \approx 7-11$, which is similar to the expectation for the turbulent kinetic cascade of $\mathrm{\mid }n(k_{\mathrm{\perp }}){\mathrm{\mid }}^2\propto k_{\mathrm{\perp }}^{-13\mathrm{/}3}$.