Radial Correlation Reflectometry Research Articles

Reconstruction of turbulence characteristics from fluctuation reflectometry measurements in the nonlinear regime

The nonlinear theory of radial correlation reflectometry (RCR) predicts that the cross correlation function of a signal follows a Gaussian distribution with a cutoff separation, where the correlation length is determined by both the turbulence amplitude and its radial correlation length. In contrast, phase spectrum analysis provides information solely on the turbulence amplitude. This work describes the possibility of applying both signal analysis methods and demonstrates that turbulence amplitude and radial correlation length can be simultaneously measured using RCR diagnostics in the nonlinear regime.

Density fluctuation correlation measurements in ASDEX Upgrade using poloidal and radial correlation reflectometry

The poloidal correlation reflectometry diagnostic operated in ordinary mode with additional radial correlation channel is applied in this paper to investigate the correlation of the turbulent density fluctuations. The perpendicular and radial correlation lengths, l⊥ and lr, the perpendicular velocity v⊥ and the dissipation (mutation) time τd are measured simultaneously from the outer core to edge in the L-mode plasmas of ASDEX Upgrade. It is shown that in the outer core region (0.6 < ρpol < 0.9) the measured correlation lengths scale with the drift wave length, l⊥ ≈ 5ρs and lr ≈ 10ρs, while the dissipation time is inversely correlated with the velocity τd ≈ 40/v⊥(τd is in μs and v⊥ in km s–1). In the pedestal region (0.925 < ρpol < 0.98), where the E × B shear flows are present, a loss of measured correlation is observed which can be explained by a combination of small propagation velocity and an additional reduction of τd. In the Er well region (ρpol ≈ 0.99), the measured perpendicular correlation length increases and the radial correlation length decreases lr ≈ 4ρs compared to the outer core values. The correlation measurements are interpreted in the frame of the linear regime of reflectometry (applied only to ρpol < 0.9). Using the Born approximation we show that the finite wavenumber sensitivity of the reflectometer increases the measured l⊥and lr, but does not affect the measured τd. By the including diagnostic correction the real correlation lengths l⊥ ≈ lr ≈ 3ρs are estimated.

Radial and poloidal correlation reflectometry on Experimental Advanced Superconducting Tokamak.

An X-mode polarized V band (50 GHz-75 GHz) radial and poloidal correlation reflectometry is designed and installed on Experimental Advanced Superconducting Tokamak (EAST). Two frequency synthesizers (12 GHz-19 GHz) are used as sources. Signals from the sources are up-converted to V band using active quadruplers and then coupled together for launching through one single pyramidal antenna. Two poloidally separated antennae are installed to receive the reflected waves from plasma. This reflectometry system can be used for radial and poloidal correlation measurement of the electron density fluctuation. In ohmically heated plasma, the radial correlation length is about 1.5 cm measured by the system. The poloidal correlation analysis provides a means to estimate the fluctuation velocity perpendicular to the main magnetic field. In the present paper, the distance between two poloidal probing points is calculated with ray-tracing code and the propagation time is deduced from cross-phase spectrum. Fluctuation velocity perpendicular to the main magnetic field in the core of ohmically heated plasma is about from -1 km/s to -3 km/s.

2D modeling of turbulence wave number spectra reconstruction from radial correlation reflectometry data

Computational analysis of radial correlation reflectometry in the framework of a model accounting for 2D probing wave propagation and scattering is performed. The procedure of the turbulence wavenumber spectra reconstruction from radial correlation reflectometry data previously proposed in the case of normal incidence of probing wave onto the 1D plasma is justified for the real geometry of a reflectometry experiment at large and modest scale fusion plasmas.

Radial correlation reflectometry at oblique probing wave incidence (linear scattering theory predictions)

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.

Two-dimensional full-wave simulations of radial correlation Doppler reflectometry in linear and non-linear regimes

The technique of radial correlation reflectometry both conventional and Doppler is studied using a two-dimensional full-wave code in extraordinary mode of propagation. Linear and non-linear regimes are considered for a wide range of antenna tilt angles and radial correlation lengths. The radial correlation length Lr computed from the amplitude, the complex amplitude and the complex phase signals are shown for each particular case. The numerical results show that the measurement of the turbulence radial correlation length with microwave reflectometry is challenging. It is shown that in most cases the radial correlation length as measured by microwave reflectometry is different from the turbulence radial correlation length. In the linear regime the results show that conventional reflectometry overestimates the radial correlation length in agreement with theory. It is shown that Doppler reflectometry provides a good estimation for Lr if the antenna tilt angle θ is properly scanned. In the non-linear regime both conventional and Doppler reflectometry provide similar Lr values regardless of the antenna tilt angle, but these values are shorter than the turbulence radial correlation length.

Numerical modelling of tokamak plasma micro turbulence wave number spectrum reconstruction using radial correlation reflectometry data

Radial correlation reflectometry (RCR) is used technique providing information on the tokamak plasma micro turbulence. The data interpretation in this technique using for probing simultaneously different frequencies is based on the hypothesis of high measurements localization. In essence, it is similar to that used in probe correlation method where the signal cross-correlation function (CCF) is identified with the turbulence CCF. Unfortunately according to a strict theoretical analysis, both numerical and analytical, this assumption is incorrect; nevertheless the analytical theory proposed here shows that it is possible to reconstruct the turbulence radial wave number spectra using the RCR experimental data. It is also demonstrated that the turbulence CCF is reconstructed more precisely than spectra. It is illustrated by numerical computations for FT-2 (Russian Federation) and Tore Supra (France) tokamaks. Capabilities of spatial inhomogeneous micro turbulence spectra reconstruction is investigated as the transport barrier characterization for example. Information is also reported on the limitations of this method.

On turbulence-correlation analysis based on correlation reflectometry

Drift wave micro-turbulence is the main source of anomalous transport in a tokamak. Correlation reflectometry is a powerful diagnostic tool which provides information on plasma turbulence and subsequently on underlying instability. In this paper, theoretical expressions for the analysis of radial correlation reflectometry (RCR) data are derived. Integral kernels, which convert the correlation function of two microwave reflectometry signals into a correlation function of plasma turbulence and inverse, are discussed. The analytical expression and the method of combining the RCR diagnostic and another local density fluctuation (e.g. Doppler enhanced scattering or heavy ion beam probe) is proposed. The correlation between reflectometry signals and those from other local fluctuation measurements is analysed. The long-range tail of the correlation decays much more gradually than the turbulence correlation, however, it decays faster than that of two microwave reflectometry signals. The way to calculate turbulence wave number spectrum for this case is also proposed.

Numerical modeling of micro turbulence wave number spectra reconstruction using radial correlation reflectometry: I. O-mode reflectometry at the linear plasma density profile

Based on the one-dimensional analytical theory of radial correlation reflectometry (RCR), numerical models of RCR experiments have been built. Computations are carried out for O-mode at a simple linear plasma density profile under conditions relevant to experiments. The turbulence spectrum and cross correlation function reconstruction procedure is applied and its feasibility is demonstrated while the assumptions of the model are fulfilled. The limitations of the method are discussed. The numerical models of the RCR experiments, targeted at the reconstruction of the turbulence spectrum in tokamaks where the plasma density profile can be approximated by a linear density profile, are performed and show in most of the cases that the wave number spectra can be extracted. The RCR capabilities and dependences on the main experimental parameters are also studied.

Fluctuation reflectometry theory and the possibility of turbulence wave number spectrum reconstruction using the radial correlation reflectometry data

One-dimensional linear theory of radial correlation reflectometry (RCR) is developed. The dependence of scattering signal on the fluctuation wave number is carefully examined in the case of linear and arbitrary plasma density profiles. The behaviour of scattering efficiency is analysed and singularity saturation at a scale much lesser than the Airy scale is demonstrated. The expression for the RCR cross correlation function is derived and the possibility of turbulence wave number spectrum reconstruction based on the RCR data is shown.

A Ka-band tunable direct-conversion correlation reflectometer for NSTX

The recent availability of broadband microwave quadrature mixers in the Ka-band (28-40 GHz) of frequencies has allowed the fabrication of low-cost direct-conversion detection circuits for use in the variable-frequency correlation reflectometer on the National Spherical Torus eXperiment (NSTX). The quadrature receiver in this case can be implemented as a simple homodyne circuit, without the complication of a single-sideband modulator or a feedforward tracking circuit present in more typical designs. A pair of direct-conversion receivers is coupled with broadband microwave voltage-controlled oscillators to construct a flexible dual-channel radar system with a fast frequency settling time of ∼160 μs. A detailed description of the design and a full characterization of the hardware are provided. Examples of turbulence measurements from radial and poloidal correlation reflectometry on NSTX using a poloidal array of antennas (oriented normal to the magnetic flux surfaces for conventional reflectometry) are presented.

Systematic and routine analysis of radial correlation reflectometry data in JET

This paper discusses a tool specially developed for the analysis of radial correlation reflectometry data in JET. The tool, which calculates the correlation length and coherent reflection from the raw data, has been designed for offline analysis and to assist diagnostic operators. After being verified in controlled tests using theoretical signals, the tool is validated by means of a study of ITB plasmas in JET.

X -mode reflectometry measurements in the JET plasma core region

The X-mode radial correlation reflectometry diagnostic on JET has long suffered from strong signal attenuation in the original transmission lines. To reach higher performances, new low-attenuation corrugated circular waveguides and a new cluster of six antennas have been successfully installed in Autumn 2005. The increase of the signal-to-noise ratio using these new transmission lines is found to be on the order of magnitude of 20 dB, thus enabling good quality of reflectometry measurement. With the benefit of this improvement, first X-mode reflectometry measurements of density fluctuations in the core region of the JET plasma are reported in this article.

Full-wave test of the radial correlation reflectometry analytical theory in linear and nonlinear regimes

Full-wave 1D simulations of fluctuation reflectometry are compared with the nonlinear theory recently published (Gusakov et al 2002 Plasma Phys. Control. Fusion 44 2327), for the case of time-independent turbulence, as well as for the case of space-time turbulence. Homogeneous and inhomogeneous turbulence models are considered. The simulations confirm quantitatively predictions of both linear and nonlinear theory for the correlation time and correlation length of the signal. The localization properties of the signal in the nonlinear regime are also found to be in good agreement with theory. Whereas the correlation time of the signal depends on the turbulence all over the plasma, its correlation length is essentially driven by the turbulence in the close vicinity of the cut-off. It turns out that theory gives a value of the correlation length within a factor of 2 even for turbulence levels as high as 20%, well beyond its validity domain.

Two-dimensional non-linear theory of radial correlation reflectometry

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.

Two-dimensional linear theory of radial correlation reflectometry diagnostics

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.

Non-linear theory of fluctuation reflectometry

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.