E. Z. Gusakov

Low threshold parametric decay instabilities in ECRH experiments at toroidal devices

The experimental conditions leading to substantial reduction of backscattering decay instability threshold in ECRH experiments in toroidal devices are analyzed. It is shown that drastic decrease of threshold is provided by non monotonic behaviour of plasma density, which is often observed due to so-called density-pump-out effect or presence of magnetic islands, and by poloidal magnetic field inhomogeniety making possible localization of ion Bernstein decay waves. The corresponding ion Bernstein wave gain and the parametric decay instability pump power threshold is calculated. The possible experimental consequences of easy backscattering decay instability excitation are discussed.Experimental conditions leading to a substantial reduction in the backscattering decay instability threshold in electron cyclotron resonance heating (ECRH) experiments in toroidal devices are analysed. It is shown that the drastic decrease in threshold due to suppression of convective losses is provided by the nonmonotonic behaviour of plasma density, which is often observed due to the so-called density-pump-out effect or the presence of magnetic islands, and by poloidal magnetic field inhomogeneity making localization of ion Bernstein decay waves possible. The corresponding ion Bernstein wave gain and the convective parametric decay instability pump power threshold are calculated. The possible experimental consequences of easy backscattering decay instability excitation are discussed.

Strong Bragg backscattering in reflectometry

The reflection of the probing microwave occurring in the vicinity of the backscattering Bragg resonance point (far from the cut-off) at a high enough density fluctuation level and leading to a large jump of the reflected wave phase and a corresponding time delay is described analytically using a 1D model. Explicit expressions for the reflection and transmission coefficients are derived and compared against results of numerical modelling. The criteria for transition to the nonlinear regime of strong Bragg backscattering (BBS) is obtained for both O-mode and X-mode reflectometry. It is shown that a strong nonlinear regime of BBS may occur in ITER at the 0.5–2% relative density perturbation level both for the ordinary and extraordinary mode probing. The possibility of probing wave trapping leading to strong enhancement of the electric field and associated high phase variation of the reflected wave due to BBS is demonstrated.

Theory of anomalous backscattering in second harmonic X-mode ECRH experiments

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 daugh...

Induced backscattering in an inhomogeneous plasma at the upper hybrid resonance

A theoretical study of the parametric decay instability as occurring in electron Bernstein wave heating experiments and leading to anomalous reflection is performed. The threshold power is calculated for the fundamental instability mode which is proven to have a lower value. It is demonstrated that for the MAST experimental conditions the backscattering parametric decay instability can arise only if the pump power exceeds 80 kW in any microwave beam. It results that the threshold power is roughly inversely proportional to the square of the pump wave frequency. Hence, to increase the instability threshold lowering the pump frequency is suggested.

Spatial and wavenumber resolution of Doppler reflectometry

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

A Numerical Study of Forward- and Backscattering Signatures on Doppler-Reflectometry Signals

In Doppler reflectometry, two scattering processes may be involved, Bragg backscattering and forward scattering. In this paper, a numerical study of both processes is undertaken using a finite-difference time-domain full-wave code with plasma parameters compatible with Tore Supra or Asdex Upgrade Doppler reflectometers. The spectra modeling the plasma turbulence were chosen to isolate forward- and backscattering events, allowing the segregation of the two different signatures and bring forth the different mechanisms intervening in each of the cases. Some numerical precautions needed for this type of simulations are presented. The results obtained are compared with the theoretical models.

Transition into diffusive regime of propagation of probing electromagnetic waves in a turburlent inhomogeneous plasma and limitations for microwave reflectometry in reactor scale devices

A propagation of probing waves in plasma in the presence of broad wavenumber spectrum density turbulence is examined in one-dimensional geometry in this paper. It is shown that multiple Bragg scattering leads to a transition into diffusive regime of the wave propagation obstructing the plasma density profile measurement, if the turbulence level exceeds a threshold value. The criteria determining the threshold plasma density fluctuation level are derived both in the one-dimensional model and accounting for the two-dimensional side-scattering effects. The corresponding thresholds are evaluated for different modifications of reflectometry diagnostics planed for ITER.

Observation of turbulence exponential wave number spectra at ion sub-Larmor scales in FT-2 tokamak

Implementation of the correlative enhanced scattering technique in the FT-2 tokamak has resulted in measurements of both frequency and wave number spectra of a small-scale microturbulence. It is found that during the dynamic current ramp-up discharge the turbulence possesses a wide wave number spectrum which could be described by universal exponential dependence in the range of 3–4 orders of amplitude characterized by two parameters—the turbulence level and scale length. Both parameters are found to decrease substantially when the shear of the poloidal plasma rotation estimated from Doppler frequency shift of the enhanced scattering signal increases at plasma periphery. Simultaneously transition to an improved confinement resulting in the suppression of anomalous electron transport and decrease in the electron energy confinement time is observed in the experiment.

Multiple scattering effect in Doppler reflectometry

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.

Evolution of ETG mode scale turbulence and anomalous electron transport in dynamic tokamak experiments

Experimental study of ion sub-Larmor-scale turbulence by microwave scattering diagnostics developed at FT-2, DIII-D and NSTX tokamaks is reviewed. Peculiarities of electron temperature gradient (ETG) turbulence identification in dynamical experiments at these machines are discussed. The FT-2 experimental results concerning the role of the small-scale turbulence in the anomalous electron transport are compared with those published by DIII-D and NSTX teams. Possibilities of small-scale turbulence control by plasma rotation shear are discussed for marginal ETG turbulence in NSTX and FT-2.