The transition from linear to non-linear regime of fluctuation reflectometry is followed within a one-dimensional WKB model. The general case of statistically inhomogeneous turbulence and arbitrary density profile is investigated analytically. It is shown that in spite of the fact that the signal frequency broadening in both regimes is determined by poor localized small angle scattering, in non-linear regime radial correlation reflectometry provides highly localized information on the turbulence characteristics.

A quantitative model explaining generation of the anomalous backscattering signal in the second harmonic X-mode electron cyclotron resonance heating (ECRH) experiments at TEXTOR tokamak as a secondary nonlinear process which accompanies a primary low-threshold parametric decay instability (PDI) leading to excitation of two—upper hybrid (UH)—plasmons trapped in plasma is developed. The primary absolute PDI enhancing the UH wave fluctuations from the thermal noise level is supposed to be saturated due to a cascade of secondary low-threshold decays of the daughter UH wave leading to excitation of the secondary UH waves down-shifted in frequency and the ion Bernstein wave. A set of equations describing the cascade is derived and solved numerically. The results of numerical modelling are shown to be in agreement with the analytical estimations of the growth rate of the initial and secondary parametric decays and the saturation level. The generation of backscattering signal is explained by coupling of the daughter UH waves. The fine details of the frequency spectrum of the anomalously reflected extraordinary wave and the absolute value of the observed backscattering signal in the second harmonic X-mode ECRH experiments at TEXTOR are reproduced.

As a result of the two-dimensional consideration, a general analytic approach to the non-linear regime of fluctuation reflectometry allowing determination of its spectral and correlation characteristics in explicit form is developed. The expressions for average signal and cross-correlation function of radial correlation reflectometry valid for arbitrary plasma density profile, turbulence spatial distribution and wave number spectra are derived. The analytical predictions are compared to the results of one-and two-dimensional numerical modelling.

A nonlinear theory of Doppler reflectometry is developed in the case of a high level of turbulent density perturbations, when the multiple forward scattering of the probing wave is dominant. It is shown that even in this regime the diagnostics is able to measure the plasma poloidal velocity with a spatial resolution that is, however, dependent on the plasma density profile and the turbulence distribution. The problem of diagnostics results interpretation is discussed.

The two-dimensional linear theory of radial correlation reflectometry applicable for the case of low turbulence level, when the probing line is observable in the spectrum of reflected wave, is developed. It is shown that the small angle scattering in the plasma volume makes a significant contribution to the fluctuation reflectometry signal complicating the turbulence correlation length measurements. The conditions under which the cut off backscattering plays the dominant role and the correlation length estimation is possible are discussed.

Doppler reflectometry spatial and wavenumber resolution is analyzed within the framework of the linear Born approximation in slab plasma model. Explicit expression for its signal backscattering spectrum is obtained in terms of wavenumber and frequency spectra of turbulence which is assumed to be radially statistically inhomogeneous. Scattering efficiency for both back and forward scattering (in radial direction) is introduced and shown to be inverse proportional to the square of radial wavenumber of the probing wave at the fluctuation location thus making the spatial resolution of diagnostics sensitive to density profile. It is shown that in case of forward scattering additional localization can be provided by the antenna diagram. It is demonstrated that in case of backscattering the spatial resolution can be better if the turbulence spectrum at high radial wavenumbers is suppressed. The improvement of Doppler reflectometry data localization by probing beam focusing onto the cutoff is proposed and described. The possibility of Doppler reflectometry data interpretation based on the obtained expressions is shown.

The effect of the X-mode parametric decay into two short wavelength upper hybrid (UH) plasmons propagating in opposite directions is analyzed. Due to the huge convective power loss of both the UH plasmons along the inhomogeneity direction, the power threshold of the convective parametric decay instability (PDI), which can be excited in the presence of a monotonous density profile is derived to exceed the gyrotron power range currently available. In the presence of the magnetic island possessing the local density maximum at its O-point the daughter UH plasmons can be trapped in the radial direction that suppresses their energy loss from the decay layer in full and makes the power threshold of the convective two-plasmon PDI drastically (three orders of magnitude) lower than in the previous case. The possibility of the absolute PDI being due to the finite size of the pump beam spot is demonstrated as well. The power threshold of the absolute instability is shown to be more than two orders of magnitude lower than the threshold of the convective instability at the monotonous density profile.

Turbulence radial correlation length measurements by making use of Doppler reflectometry are analysed in this paper assuming the linear (in density perturbation amplitude) regime of the probing wave scattering. Based on the Born approximation applicable in this case, we get a general integral representation of the scattering signal amplitude, which is then analysed in detail both analytically and numerically. Asymptotic analytical evaluation of the scattering signal amplitude gives a criterion on the incidence angle, exceeding which leads to suppression of the poor localized forward scattering contribution to the Doppler reflectometry signal. In the latter case, fast decay of correlation in the two frequency channels appears to be similar to that expected from the turbulence correlation function. The analytical estimations and predictions are confirmed by numerical evaluation of the scattering signal amplitude. The analysis performed proves the feasibility of the radial correlation Doppler reflectometry technique for measurements of the correlation length of a modest level turbulence at oblique launching of the probing wave beam.