Interpreting Radial Correlation Doppler Reflectometry using Gyrokinetic Simulations

TL;DR

This paper uses gyrokinetic simulations to interpret radial correlation Doppler reflectometry, revealing that measurements depend on the binormal wavenumber and turbulence spectrum, and proposing a method to characterize turbulence eddy shapes.

Contribution

It introduces a nonlinear gyrokinetic model showing the turbulence spectrum's influence on RCDR measurements and highlights the importance of the binormal wavenumber dependence.

Findings

Radial correlation length scales inversely with binormal wavenumber, matching experimental observations.

Turbulence exhibits a non-separable power law spectrum in wavenumber space.

Measurement of radial correlation length is limited by radial resolution, especially at electron scales.

Abstract

A linear response, local model for the DBS amplitude applied to gyrokinetic simulations shows that radial correlation Doppler reflectometry measurements (RCDR, Schirmer et al., Plasma Phys. Control. Fusion 49 1019 (2007)) are not sensitive to the average turbulence radial correlation length, but to a correlation length that depends on the binormal wavenumber $k_\perp$ selected by the Doppler backscattering (DBS) signal. Nonlinear gyrokinetic simulations show that the turbulence naturally exhibits a non-separable power law spectrum in wavenumber space, leading to a power law dependence of the radial correlation length with binormal wavenumber $l_r \sim C k_\perp^{-\alpha} (\alpha \approx 1)$ which agrees with the inverse proportionality relationship between the measured $l_r$ and $k_\perp $ in experiments (Fernandez-Marina et al., Nucl. Fusion 54 072001 (2014)). This offers the possibility of characterizing the eddy aspect ratio in the perpendicular plane to the magnetic field and motivates future use of a non-separable turbulent spectrum to quantitatively interpret RCDR and potentially other turbulence diagnostics. The radial correlation length is only measurable when the radial resolution at the cutoff location $W_n$ satisfies $W_n \ll l_r$, while the measurement becomes dominated by $W_n$ for $W_n \gg l_r$. This suggests that $l_r$ is likely inaccessible for electron-scale DBS measurements ($k_\perp\rho_s > 1$). The effect of $W_n$ on ion-scale radial correlation lengths could be non-negligible.