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ABSTRACT: 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.
Plasma Physics and Controlled Fusion 02/2012; 54(3):035008. · 2.42 Impact Factor
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ABSTRACT: A new scheme of reflectometry diagnostic based on the enhanced scattering effect invented by the late Professor A D Piliya is proposed and analyzed in this paper. It is shown that due to wave trapping, a strong coherent density perturbation in a reflectometry experiment can cause a giant cross-section enhancement for scattering occurring between it and cut-off. The theoretical approach is based on the method developed by Piliya for the treatment of a three-wave interaction in inhomogeneous media. Similar values of the scattering enhancement factor are obtained both numerically and analytically.
Physica Scripta 09/2011; 84(4):045504. · 1.20 Impact Factor
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ABSTRACT: Reflectometry profile measurement requires an accurate determination of the plasma reflected signal. Along with a good resolution and a high signal to noise ratio of the phase measurement, adequate data analysis is required. A new data processing based on time-frequency tomographic representation is used. It provides a clearer separation between multiple components and improves isolation of the relevant signals. In this paper, this data processing technique is applied to two sets of signals coming from two different reflectometer devices used on the Tore Supra tokamak. For the standard density profile reflectometry, it improves the initialization process and its reliability, providing a more accurate profile determination in the far scrape-off layer with density measurements as low as 10(16) m(-1). For a second reflectometer, which provides measurements in front of a lower hybrid launcher, this method improves the separation of the relevant plasma signal from multi-reflection processes due to the proximity of the plasma.
The Review of scientific instruments 08/2011; 82(8):083502. · 1.52 Impact Factor
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C. Bourdelle,
T. Gerbaud,
L. Vermare,
A. Casati,
T. Aniel,
J.F. Artaud,
V. Basiuk,
J. Bucalossi,
F. Clairet,
Y. Corre, [......],
G.T. Hoang,
F. Imbeaux,
L. Manenc,
P. Monier-Garbet,
P. Moreau,
R. Sabot,
J.-L. Ségui,
A. Sirinelli,
D. Villegas,
the Tore Supra Team
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ABSTRACT: A collisionality scaling experiment associating a confinement analysis, turbulence measurements across the whole plasma and gyrokinetic modelling is reported. In Tore Supra L-mode plasmas, mid-radius dimensionless collisionality ν* has been varied performing a four-points scan from 0.1 to 0.7. The normalized confinement time exhibits a dependence with respect to collisionality: BτE ∝ ν*−0.3±0.3 which is strongly modified when accounting for the confinement dependence on the normalized Larmor radius, ρ*, and normalized pressure, β, since one obtains BτE ∝ ν*0.0±0.7. This weak dependence is consistent with ITER L mode scaling laws and dedicated experiments elsewhere (Luce 2008 Plasma Phys. Control. Fusion 50 043001). The global analysis is confirmed by normalized effective heat transport coefficients which do not vary outside their error bars in a limited radial range of reliability. The analysis is completed by density fluctuation δne/ne measurements across the whole plasmas. For normalized radius r/a < 0.7, δne/ne does not depart from its error bars and the radial wave-vector spectra are not modified. These observations are well reproduced by non-linear gyrokinetic simulations, where, despite high ν* values, no zonal flow damping mechanism is at play. At the plasma edge (r/a > 0.7), the lowest poloidal wave-vector measured by the Doppler reflectometer exhibits a decrease in δne/ne with increasing ν*, while the other turbulence measurements remain unaffected.
Nuclear Fusion 05/2011; 51(6):063037. · 4.09 Impact Factor
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ABSTRACT: The knowledge of turbulent transport is the key issue for the future of fusion plasma devices. A first step towards this goal rests in obtaining measurements concerning turbulence characteristics or transient events, which are required for the understanding of the transport phenomena. A possible way to obtain density fluctuations parameters is to use microwaves to probe fusion plasmas. However the interpretation of the received signals requires a model for reaching the accurate evaluation of the wanted parameters. Simulations of electromagnetic wave propagation in fluctuating plasmas permit to identify the signature of expected events and to model them. In the present work, it is shown how simulations have permitted to exhibit the role of the resonances of the probing wave induced by turbulence and to explain part of the origin of phase jumps seen during reflectometer measurements. Multi-scattering phenomena, taking into account wave trapping, can be simulated and show that the probing wave can continue to reach in average the cut-off layer as it is the case for a quiet plasma. These results suggest that it is possible to extract information on the turbulence at density fluctuations levels higher than allowed by usual methods using the framework of Born approximation. The software developed for reflectometry simulations is also used to compute and explain the frequency spectrum associated to Alfven's cascades seen with fixed frequency reflectometers working without a cut-off layer in the probed tokamak plasma. To finish, possible ways to extract the properties of a turbulent wavefront and its dynamics are explored for the ultra-fast frequency sweep reflectometer and for a reflectometer working as a backscattering diagnostics at fixed frequency. The physical aspects and the technical requirements are presented for each studied case (© 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)
Beiträge aus der Plasmaphysik 02/2011; 51(2‐3):126 - 130.
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ABSTRACT: In order to study the temporal dynamics of turbulence, the sweep time of our reflectometry has been shortened from 20 to 2 μ s with 1 μ s dead time. Detailed technical aspects of the upgrade are given, namely, about the stability of the ramp generation, the detection setup, and the fast acquisition module. A review of studies (velocity measurement of the turbulence, modifications of the wavenumber spectrum, radial mapping of correlation time, etc.) offered by such improvements is presented.
Review of Scientific Instruments 11/2010; · 1.37 Impact Factor
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ABSTRACT: Experimental reflectometry signals obtained in the absence of a cutoff layer, with the possibility of interferometric operation excluded, show a coherent and recurrent frequency spectrum signature similar to an Alfvén cascade signature. A possible explanation resides in the modulation of a resonant Bragg backscattering response by an Alfvén mode structure located at the center of the plasma whose frequency of oscillation modulates the backscattered signal in a conformable way. This situation is modeled and simulated using an O-mode full-wave Maxwell finite-difference time-domain code and the resulting signatures are discussed.
Review of Scientific Instruments 11/2010; · 1.37 Impact Factor
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ABSTRACT: Experimental reflectometry signals obtained in the absence of a cutoff layer, with the possibility of interferometric operation excluded, show a coherent and recurrent frequency spectrum signature similar to an Alfvén cascade signature. A possible explanation resides in the modulation of a resonant Bragg backscattering response by an Alfvén mode structure located at the center of the plasma whose frequency of oscillation modulates the backscattered signal in a conformable way. This situation is modeled and simulated using an O-mode full-wave Maxwell finite-difference time-domain code and the resulting signatures are discussed.
The Review of scientific instruments 10/2010; 81(10):10D927. · 1.52 Impact Factor
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ABSTRACT: 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.
IEEE Transactions on Plasma Science 10/2010; · 1.17 Impact Factor
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ABSTRACT: In fusion plasmas for energy, turbulence is clearly associated to the anomalous transport of energy and particles. Diagnostics using electromagnetic waves is usually used to measure the plasma parameters and the turbulence characteristics. One of the diagnostics is reflectometry, which is based on the radar principle and can be used to reach these different goals: density profile, turbulence characterization, plasma positioning, etc. During the plasma probing, fast phase variations called phase jumps have been measured, and part of them can be explained by a local enhancement of the probing field. Using an analytical model to compute the probing electric field amplification, a new expression for the phase variations has been written, taking into account the amplification of the probing electric field. This formula exhibits a good agreement with the full-wave computations. A possible improvement of the reflectometer sensitivity can be done using the local enhancement of the probing electric field induced by Bragg resonant density perturbations, which build resonant cavities. The computed cases show that it is possible to improve the reflectometry measurements when the local enhancement of the probing electric field exists. To illustrate the possible improvements, simulations of the radial wavenumber spectrum reconstruction have been done, and they confirm the possibility to increase the sensitivity and the spatial resolution for a given range of wavenumber.
IEEE Transactions on Plasma Science 10/2010; · 1.17 Impact Factor
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ABSTRACT: Measurements show that the vicinity of powered ion cyclotron range of frequency (ICRF) antennae is biased positively with respect to its environment [
J. Gunn et al., Proc. 22nd IAEA Fusion Energy Conference, Geneva 2008, EX/P6-32
]. This is attributed to radio-frequency (rf) sheath rectification. The radial penetration of these direct current (dc) potentials from ICRF launchers into the tokamak scrape-off layer (SOL) determines the power deposition on the walls and especially on the antenna structure, which is a key point for long time clean discharges. Within independent flux tube models of rf sheath rectification the radial penetration of dc potentials is determined by the skin depth x0 = c/ωpe for the slow wave. When self-consistent exchange of transverse rf current is allowed between neighboring flux tubes, such a structure can be broadened radially up to a characteristic transverse length L. Broadening arises as soon as L>x0. A linear modeling of the process gives a first evaluation of the theoretical length L = (L∥ρci/2)1/2. Within the “flute assumption,” it scales with the length L∥ of open flux tubes and the ion Larmor radius Ωci. This trend has been confirmed by nonlinear fluid simulations using the SEM code taking into account nonlinearities of the sheath dynamics. Parametric regimes are outlined where broadening or nonlinearity arise. Langmuir probe measurements on Tore Supra suggest that the observed broadening is lower than predicted by the code. This suggests that actual rf current exchanges probably do not occur over the whole length of magnetic field lines but only on a fraction of it. This “effective parallel magnetic connection length” L∥eff is estimated from the measurements. The model is finally applied to several potential maps generated by an ITER antenna, with different plasma parameters depending on possible SOL scenarios in ITER, and “reasonable assumptions” about L∥eff. It comes out that L ranges between 1 and 10 cm depending on local L∥eff and on typical ITER plasma parameters.
Physics of Plasmas 04/2010; 17(4):042503-042503-12. · 2.15 Impact Factor
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ABSTRACT: 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.
Plasma Physics and Controlled Fusion 05/2009; 51(6):065018. · 2.42 Impact Factor
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A Casati,
T Gerbaud,
P Hennequin,
C Bourdelle,
J Candy,
F Clairet,
X Garbet,
V Grandgirard,
O D Gürcan, S Heuraux,
G T Hoang,
C Honoré,
F Imbeaux,
R Sabot,
Y Sarazin,
L Vermare,
R E Waltz
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ABSTRACT: Turbulence measurements in TORE SUPRA tokamak plasmas have been quantitatively compared to predictions by nonlinear gyrokinetic simulations. For the first time, numerical results simultaneously match within experimental uncertainty (a) the magnitude of effective heat diffusivity, (b) rms values of density fluctuations, and (c) wave-number spectra in both the directions perpendicular to the magnetic field. Moreover, the nonlinear simulations help to revise as an instrumental effect the apparent experimental evidence of strong turbulence anisotropy at spatial scales of the order of ion-sound Larmor radius.
Physical Review Letters 05/2009; 102(16):165005. · 7.37 Impact Factor
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ABSTRACT: The EU will supply the plasma position reflectometer for ITER. The system will have channels located at different poloidal positions, some of them obliquely viewing a plasma which has a poloidal density divergence and curvature, both adverse conditions for profile measurements. To understand the impact of such topology in the reconstruction of density profiles a full-wave two-dimensional finite-difference time domain O-mode code with the capability for frequency sweep was used. Simulations show that the reconstructed density profiles still meet the ITER radial accuracy specifications for plasma position (1 cm), except for the highest densities. Other adverse effects such as multireflections induced by the blanket, density fluctuations, and MHD activity were considered and a first understanding on their impact obtained.
The Review of scientific instruments 11/2008; 79(10):10F104. · 1.52 Impact Factor
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R Sabot,
F Clairet,
G D Conway,
L Cupido,
X Garbet,
G Falchetto,
T Gerbaud,
S Hacquin,
P Hennequin, S Heuraux,
C Honoré,
G Leclert,
L Meneses,
A Sirinelli,
L Vermare,
A Truc
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ABSTRACT: 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 Alfvén eigenmodes (toroidal Alfvén eigenmodes, Alfvén cascades and possibly beta Alfvén 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.
Plasma Physics and Controlled Fusion 11/2006; 48(12B):B421. · 2.42 Impact Factor
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ABSTRACT: Simulations of spectra generated in thin velocity shear layers having homogeneous turbulence with realistic wavenumber spectra and radial distribution were made with a 2D full-wave O-mode code. With a Doppler setup good localization of the velocity layer can be reached by changing the frequency at fixed oblique incidence. The poloidal velocity range existing in the shear layer is also accessed. Advantages and limitations of simulations are also discussed.
Nuclear Fusion 08/2006; 46(9):S816. · 4.09 Impact Factor
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ABSTRACT: 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.
Nuclear Fusion 08/2006; 46(9):S743. · 4.09 Impact Factor
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ABSTRACT: 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.
Plasma Physics and Controlled Fusion 08/2006; 48(9):1389. · 2.42 Impact Factor
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L. Colas,
V. Basiuk,
B. Beaumont,
A. Bécoulet,
G. Bosia,
S. Brémond,
M. Chantant,
F. Clairet,
A. Ekedahl,
E. Faudot,
A. Géraud,
M. Goniche, S. Heuraux,
G.T. Hoang,
G. Lombard,
L. Millon,
R. Mitteau,
P. Mollard,
K. Vulliez,
the Tore Supra team
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ABSTRACT: Long pulse operation on the Tore Supra tokamak has entered a new phase, characterized by the use of heating power level in excess of 10 MW, during pulses lasting several tens of resistive times. This has been made possible by the use of ion cyclotron range of frequency (ICRF) heating (9 MW coupled to the plasma at 57 MHz), combined with lower hybrid current drive (LHCD: 3 MW at 3.7 GHz) and efficient fuelling techniques (supersonic gas injection, pellets). This paper addresses key technological, operational and physics issues related to the long pulse operation of the Tore Supra ICRF system and required for a reactor: R&D on the ICRF plant, real-time control and safety procedures, integration with other tokamak subsystems, experimental investigation and theoretical modelling of the edge ICRF physics (wave coupling, heat loads on antenna front faces). As far as possible lessons are drawn from the experience gained on Tore Supra for the design and operation of a next-step device.
Nuclear Fusion 06/2006; 46(7):S500. · 4.09 Impact Factor
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ABSTRACT: For the first time, a two-dimensional (2D) fluid model and an analytical expression for the rectified potential with respect to the transverse polarization current are established and verified by a 2D PIC (particle in cell) code over the validity domain of our model. Then the model is extended to the overall ion cyclotron frequency range used in different heating and current drive scenarios. First, the models demonstrate that these transverse polarization currents add some inertia in the temporal dynamic. Due to the nonlinear behavior of the I-V sheath characteristic, the time average amplitude (dc potential) of the rectified potential structure is increased compared to the time average rf potential. Second, they induce only a slight widening of the potential structure. Such modifications are quantified using a “test map” initially characterized by a Gaussian shape. The map is assumed to remain Gaussian near its summit. The time behavior of the peak can be estimated analytically in the presence of polarization current as a function of its width r0 and amplitude ϕ0 (normalized to local temperature and to a characteristic length for transverse transport). A potential peaking criterion has been built to determine the peaking zone of the dc potential structure induced by the rf field. Computations made for typical parameters of the edge plasma in front of the antenna of the Tokamak Tore Supra show that the dc rectified potential is up to 50% higher than the previous computations neglecting polarization current effects. The weak diffused and high dc potential structures computed can explain the hot spot formation induced by convective cells associated to high energetic ion fluxes on the corners of the Ion Cyclotron Resonance Heating antenna.
Physics of Plasmas 04/2006; 13(4):042512-042512-16. · 2.15 Impact Factor
