Description
Quantitative measurements of the wavenumber spectrum of electron-density fluctuations are important for extrapolating from current devices to future reactors. In this work, we made such measurements using Doppler backscattering (DBS). The measured wavenumber was varied by moving limited circular DIII-D plasmas vertically up and down within a single shot, which we call a bouncing ball plasma. We studied two such shots with similar parameters: L-mode, core electron density of $2.0 \times10^{19} m^{-3}$, plasma current of 1 MA, and toroidal field of 2 T. The DBS [1] settings are kept the same during the shot. We found that the plasma remains otherwise unchanged, as it is translated up and down. We assume density fluctuations of the form given in previous work [2], characterised by five fitting parameters. Instrumentation effects are accounted for using the Scotty beam-tracing code [3] to predict the backscattered power for a given set of parameters. By solving the inverse problem, we determine the fitting parameters that best reproduce the measured backscattered power. Using eight DBS channels, we determined the turbulence spectra at different radial locations (normalised radial coordinate $\rho$ between 0.5 and 0.9) over a range of wavenumbers: 2.0 $cm^{-1}$ < $k_\perp$ < 15.0 $cm^{-1}$, or 0.6 < $k_\perp\rho_s$ < 2.9. Here $k_\perp$ is the wavenumber of the turbulent density fluctuations and $\rho_s$ is the ion sound gyroradius. We found that for higher $k_\perp$, the density fluctuation level varies like ~$k_\perp^{-\gamma}$. We present the exponent, $\gamma$, evaluated at each radial location along with the associated error for two bouncing ball shots.
[1] W.A. Peebles, T.L. Rhodes, J.C. Hillesheim, et al. (2010). RSI, 81(10), 10D902.
[2] J. Ruiz Ruiz, F.I. Parra, V.H. Hall-Chen, et al. (2022). PPCF, 64(5), 055019.
[3] V.H. Hall-Chen, F.I. Parra, J.C. Hillesheim (2022). PPCF, 64(9), 095002.