S. Heuraux

Status and prospects for mm-wave reflectometry in ITER

Reflectometry with wavelengths in the centimetre to millimetre-wave range will be used in ITER to measure the density profile in the main plasma and divertor regions and to measure the plasma position and shape in order to provide a reference for the magnetic diagnostics in long pulses. In addition, it is expected to provide key information for the measurement of density fluctuations. A set of reflectometers to meet the relevant ITER measurement requirements has been included in its present outline as part of the ITER design since 2001 and is being adapted to the present ITER baseline and to accommodate progress with reflectometry techniques and measurement capabilities. It comprises low and high field side (HFS and LFS, respectively) ordinary (O-) mode systems for the measurement of the density profile in the gradient regions, a LFS extraordinary (X-) mode system for the detailed study of the edge profile, an HFS X-mode system operating in the left hand cutoff to measure the core profile, a dedicated O-mode system for plasma-wall gap measurement and a multi-band, multiple line of sight O-mode system to measure divertor density profiles. This paper describes the evolution of the design, in particular some recent improvements in the engineering implementation and improvements aimed at enhancing the measurement capability. It concludes with a brief assessment of the likely measurement performance against the ITER measurement requirements for the parameters of interest and the overall confidence that the technique will be implanted on ITER.

Self consistent radio-frequency wave propagation and peripheral direct current plasma biasing: Simplified three dimensional non-linear treatment in the “wide sheath” asymptotic regime

A minimal two-field fluid approach is followed to describe the radio-frequency (RF) wave propagation in the bounded scrape-off layer plasma of magnetic fusion devices self-consistently with direct current (DC) biasing of this plasma. The RF and DC parts are coupled by non-linear RF and DC sheath boundary conditions at both ends of open magnetic field lines. The physical model is studied within a simplified framework featuring slow wave (SW) only and lateral walls normal to the straight confinement magnetic field. The possibility is however kept to excite the system by any realistic 2D RF field map imposed at the outer boundary of the simulation domain. The self-consistent RF + DC system is solved explicitly in the asymptotic limit when the width of the sheaths gets very large, for several configurations of the RF excitation and of the target plasma. In the case of 3D parallelepipedic geometry, semi-analytical results are proposed in terms of asymptotic waveguide eigenmodes that can easily be implemented n...

Recent results on turbulence and MHD activity achieved by reflectometry

Over the last years, owing to hardware progress and the development of new methods, reflectometry has become a common diagnostic on plasma fusion devices. This paper presents some results obtained with reflectometry on transport, turbulence and magnetohydrodynamic (MHD). The emphasis is put on some new results from Tore-Supra. Combining the density profile and fluctuation measurement, it was shown on Tore-Supra that the particle pinch inside the q = 1 surface is close to the neoclassical value in ohmic plasma, while the observed small diffusion is in agreement with a very low level of density fluctuations inside the q = 1 surface. In β scaling experiments, no change in the fluctuation levels was found on Tore-Supra, in agreement with the observation of weak confinement degradation with increasing β. Zonal flows have been detected by Doppler reflectometry in ASDEX-U and with correlation reflectometry in T-10. On Tore-Supra, a fast decrease in the density fluctuation level at high poloidal wavenumbers was measured with Doppler reflectometry, suggesting a minor role of electron temperature gradient driven modes. Various forms of Alfven eigenmodes (toroidal Alfven eigenmodes, Alfven cascades and possibly beta Alfven eigenmodes) have been detected with reflectometry in TFTR, JET and Tore-Supra. The density fluctuations induced by the mode were found to be higher on the high-field side.

X-mode heterodyne reflectometer for edge density profile measurements on Tore Supra

A new broadband reflectometer operating in the frequency range 50–75 GHz in extraordinary mode polarization has been developed and tested on Tore Supra to measure edge density profiles. Using solid state source and active frequency multipliers, it performs routine measurements in 20 μs. Modulation of the source frequency is the clue to heterodyne detection in order to ensure a high dynamic sensitivity without any phase locking system. The reflectometer can achieve a repetition rate of 5 μs between sweeps, so the dynamic behavior of fast plasma events can be followed. The profile is reconstructed fully automatically from raw data and initialization is given by detection of the first cutoff. The profiles are part of the public database of Tore Supra. High reliability of the measurements for various plasma conditions makes this diagnostic an ideal tool to study the plasma–surface interaction physics and rf antenna coupling processes.

Ordinary-mode reflectometry: modification of the scattering and cut-off responses due to the shape of localized density fluctuations

Ordinary wave reflectometry in a plasma containing a localized density perturbation is studied with a one-dimensional (1D) model. The phase response is studied as a function of the wavenumber and position of the perturbation. It is shown that it strongly depends upon the perturbation shape and size. For a small perturbation wavenumber, the response is due to the oscillation of the cut-off layer. For larger wavenumbers, two regimes of resonant Bragg scattering are found: for a broad perturbation, the phase response is an image of the perturbation itself; for a narrow perturbation, it is an image of the Fourier transform. These features are enhanced for a broadband perturbation (modulated square wave) and scattering can occur over the whole region up to the cut-off. Furthermore, in that case there is a specific behaviour at the cut-off due to the sharp boundary effects of this perturbation. Because of this peculiarity, the phase response obtained for a damped square perturbation reproduces the results of an earlier experiment (Rhodes et al, Rev. Sci. Instrum. 1992).

Radial wave number spectrum of density fluctuations deduced from reflectometry phase signals

A method to extract the radial wave-number spectrum of the density fluctuations from the reflectometry phase signal is proposed and the main points to interpret it are described. The method buildup is based on reflectometry studies devoted to phase or amplitude variations induced by coherent density perturbations. These previous analyses show that all the wave numbers up to the Bragg detection limit kf (fluctuation radial wave number) <2ko (incident wave number in vacuum) contribute to the phase fluctuations. Although the main part comes from the vicinity of the cutoff layer the entire probing zone contributes to the phase fluctuations. The phase fluctuations dependencies in kf and L (length of the density gradient) found in the literature for the O mode have been estimated for the X mode in the Bragg backscattering zone in the case of extensive density perturbations. The assumptions used to establish this diagnostic and its limitations are discussed. The numerical study with a FDTD code in two-dimensiona...

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.

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.

Density fluctuation measurements using X-mode fast sweep reflectometry on Tore Supra

The knowledge of the turbulence characteristics is a key point to build models able to predict the confinement time in a fusion reactor. A method to extract the radial profile of the density fluctuations from the fast swept reflectometry phase signal is proposed and tested on Tore Supra (TS). The relationship between the wavenumber spectrum of the set of phase perturbations obtained during a frequency sweep and the wavenumber spectrum of the turbulence itself is the aim of the method. This relationship can be derived analytically for the O-mode. For the X-mode it is established by full wave simulations. As a result, the radial profile of density fluctuations can be obtained from a mere integration of the wavenumber spectrum of the phase fluctuations. The assumptions used to establish this diagnostics and its limitations are discussed by using simulations. Then the method is applied to recover the radial profile of the density fluctuations in the cases of the TS fast swept reflectometer data. With this method, the expected density profile evolution as a function of the plasma current is clearly shown.

ICRF coupling and edge density profile on Tore Supra

In addition to the propagation and absorption of the waves into the plasma, a crucial point in ion cyclotron radiofrequency heating (ICRH) is to know how the energy is coupled to the plasma. The coupling efficiency is experimentally estimated through measurements of the antenna coupling resistance and it is of primary importance to precisely establish its dependence on the plasma parameters. The coupling resistance is highly connected to the density profile, which determines the cut-off positions of the magnetosonic waves for a given radiated wave number spectrum. For a large size tokamak like Tore Supra these cut-off densities range between 10 18 and 10 19 m -3 , corresponding to the plasma edge. In this study, the RF coupling is investigated with respect to the plasma edge density profile measured by X-mode reflectometry and a characteristic cut-off position of the magnetosonic wave. We show that the edge density is not only a function of the average density but also depends in a complex way, on various edge plasma regimes, the power deposition, or the kind of limiter materials or divertor perturbation used to control the edge. Over a large variety of plasma edge regimes, it is shown how the distance between a characteristic ICRH cut-off density layer and the antenna is the relevant parameter to address the problem of the RF coupling efficiency. Simulation of the coupling process with the three-dimensional antenna code Ion Cyclotron ANTenna compares well with RF measurements, provided that the experimental density profiles are used in the computations.