Measuring long wavelength plasma density fluctuations by CO2 laser scattering (abstract)
Authors: Evans D. E. 
Published: July 2002

Long wavelength density fluctuations can be observed by scattering even with a probe beam of much shorter wavelength provided the scattering angle is small enough. This paper is concerned with experiments in which the scattering angle is comparable with the probe beam divergence so the scattered and incident radiation never achieve spatial separation. Under these circumstances, the role of diffraction is preeminent and Fourier optics methods are used to describe the propagation of the beam, which is taken to be TEM00 mode Gaussian. Interaction between the probe beam and the plasma disturbance is described by refraction and no appeal is made to explicit scattering theory. Analysis of the effect of a monochromatic wave disturbance confined to a plane perpendicular to the probe beam (a plane grating in effect) reveals oscillations at the wave frequency induced on the probe with an intensity varying over the beam profile in a regular pattern symmetric about the beam axis. Detail of the pattern depends on the wavelength of the disturbance, its direction, and its axial position relative to a local beam waist. These oscillations are readily identified as due to radiation scattered by the plasma wave into diffraction orders, beating with the unperturbed part of the beam. Indeed, it can be shown1 that Fourier optics plus refraction produce almost the same result as conventional scattering theory,2 the small discrepancy being traceable to the neglect in the latter of incident beam wavefront curvature. The results of the two approaches coincide in the Fraunhofer limit. Computations of this sort have been confirmed by experiments using transducer-driven waves in air3 and by plasma experiments where the same regular patterns are observed from spontaneous plasma waves.4,5 Calculation suggests and experiments have demonstrated6 that additional information, such as the absolute direction of wave propagation, can be deduced from phase, measured with a multichannel detector array.
Asymmetric profiles are frequently encountered in far forward scattering experiments in plasma, and they are attributed either to (1) the volume effect, that is, the finite width of a plasma wave, or (2) a pair of counter-propagating waves, such as poloidal waves in a torus met twice by a probe beam traversing a minor diameter. The first explanation rests on the difference between the multiple order scattering of a two-dimensional grating (Raman–Nath) and the single-order scattering of a three-dimensional crystal (Bragg). In a regime intermediate between these extremes, both +1 and −1 orders are present, but of unequal intensity, therefore giving rise to asymmetry in the beam profile. The Fourier optics treatment can be extended to describe a wave of arbitrary interaction length L, and a controlling parameter Q=κ2L/k (κ and k being wave numbers of the plasma wave and the probe radiation, respectively) which is ≪1 for Raman–Nath and ≫1 for Bragg, determines the precise regime that prevails.7 Calculations describing the counter-propagating waves model have been performed and verified experimentally, again using transducer-driven waves in air.8 Profiles based on this model are currently providing best fits to data recently recorded from tokamak plasmas in TOSCA. A preliminary inspection of the results of these measurements reveals, from the orientation of the beam profile pattern, predominantly poloidal waves. Their maximum intensity is near 100 kHz and they fall away towards higher frequencies as ν−2.5. Evidence for coherent gross modes at lower frequencies is also seen. Wave numbers are in the range 1 cm−1&lt;κ⊥&lt;30 cm−1, bracketing the neighborhood where κ⊥ρi∼1. The strength of the relative density fluctuation ñe/n̄e of a few per cent is consistent with diffusion coefficients D⊥∼104 cm2 s−1, and there is evidence for inverse correlation between ñe/n̄e and confinement time τE.