Small-angle scattering theory revisited: Photocurrent and spatial localization

In this paper theory on collective scattering measurements of electron density fluctuations in fusion plasmas is revisited. We present the first full derivation of the expression for the photocurrent beginning at the basic scattering concepts. Thereafter we derive detailed expressions for the auto- and crosspower spectra obtained from measurements. These are discussed and simple simulations made to elucidate the physical meaning of the findings. In this context, the known methods of obtaining spatial localization are discussed and appraised. Where actual numbers are applied, we utilize quantities from two collective scattering instruments: The ALTAIR diagnostic on the Tore Supra tokamak [A. Truc et al., "ALTAIR: An infrared laser scattering diagnostic on the Tore Supra tokamak," Rev. Sci. Instrum. 63, 3716-3724 (1992)]. and the LOTUS diagnostic on the Wendelstein 7-AS stellarator [M. Saffman et al., "CO2 laser based two-volume collective scattering instrument for spatially localized turbulence measurements,"Rev. Sci. Instrum. 72, 2579-2592 (2001)].