International audienceKinetic models and numerical simulations of E×B plasma discharges predict microfluctuations at the scales of the electron cyclotron drift radius and the ion plasma frequency. With the help of a specially designed collective scattering device, the first experimental observations of small-scale electron density fluctuations inside the plasma volume are obtained, and observed in the expected ranges of spatial and time scales. The anisotropy, dispersion relations, form factor, amplitude, and spatial distribution of these electron density fluctuations are described and compared to theoretical expectations

Microturbulence has been implicated in anomalous transport at the exit of the Hall thruster, and recent simulations have shown the presence of an azimuthal wave which is believed to contribute to the electron axial mobility. In this paper, the 3D dispersion relation of this E Â B electron drift instability is numerically solved. The mode is found to resemble an ion acoustic mode for low values of the magnetic field, as long as a non-vanishing component of the wave vector along the magnetic field is considered, and as long as the drift velocity is small compared to the electron thermal velocity. In these conditions, an analytical model of the dispersion relation for the instability is obtained and is shown to adequately describe the mode obtained numerically. This model is then fitted on the experimental dispersion relation obtained from the plasma of a Hall thruster by the collective light scattering diagnostic. The observed frequency-wave vector dependences are found to be similar to the dispersion relation of linear theory, and the fit provides a non-invasive measurement of the electron temperature and density. V C 2013 AIP Publishing LLC.

This paper presents recent efforts to better understand and quantify charged particle transport in Hall effect thrusters (HETs). Particle-in-cell (PIC) models, hybrid models, laser induced fluorescence (LIF) measurements and collective scattering (CS) experiments are combined to get a better insight into anomalous electron transport in HETs and to increase the predictive capabilities of simulation codes.PIC models have demonstrated that plasma turbulence associated with the development of a high frequency, short wavelength azimuthal instability can be responsible for anomalous transport. Scaling laws for anomalous electron mobility have not yet been derived and hybrid models, which are more practical than PIC models for parametric studies, must use empirical, adjustable transport coefficients that can be inferred from PIC results or LIF measurements of the ion velocity distribution function. CS experiments are aimed at validating the PIC model predictions of the azimuthal instability. The CS results show the first direct experimental evidence of the azimuthal instability predicted by the PIC code. The paper illustrates the synergy between experiments and models toward a complete and quantitative understanding of the physics of HETs.

A collective laser light scattering diagnostic ALTAIR (a french acronym for local analysis of anomalous transport using infrared light), using a CO2 laser beam (λ=10.6 μm) has been realized to measure plasma density fluctuations in the TORE SUPRA tokamak. This article describes in detail the optical setup, the signal processing, acquisition, and control systems required for this experiment. As the density fluctuations propagating in tokamaks have small wave numbers and require small scattering angles, such scattering experiments are considered as having no resolution along the beam. However, taking advantage of the pitch angle variation of the magnetic field lines around the magnetic axis along a vertical chord, it has been possible to obtain partial spatial localization of the scattering volume by rotating the direction of the analyzed wave vector in a horizontal plane. Heterodyne detection is used to determine the fluctuations propagation direction. The experiment has been tested on acoustic waves and the first results obtained on TORE SUPRA indeed show the existence of a spatial resolution.

Collective scattering measurements have been conducted on the plasma of a Hall thruster, in which the electron density fluctuations are fully characterized by the dynamic form factor. The dynamic form factor amplitude distribution has been measured depending on the k-vector spatial and frequency components at different locations. Fluctuations are seen as propagating waves. The largest amplitude mode propagates nearly along the cross-field direction but at a phase velocity that is much smaller than the Ē ϫ B drift velocity. Refined directional analysis of this largest amplitude mode shows a thin angular emission diagram with a mean direction that is not strictly along the Ē ϫ B direction but at small angles near it. The deviation is oriented toward the anode in the ͑Ē , Ē ϫ B ͒ plane and toward the exterior of the thruster channel in the ͑B , Ē ϫ B ͒ plane. The density fluctuation rate is on the order of 1%. These experimentally determined directional fluctuation characteristics are discussed with regard to the linear kinetic theory model and particle-in-cell simulation results.

For the first time, the internal magnetic turbulence is measured by a new cross polarization scattering diagnostic in the Tore Supra tokamak. The principle of this experiment is presented. It is based on the polarization change or mode conversion of the electromagnetic wave scattered by magnetic fluctuations.A strong correlation between the internal magnetic fluctuation and the additional heating is observed, contrary to the edge fluctuations.The observed fluctuations increase linearly with the poloidal beta number P~i n the L-mode confinement regime.PACS numbers: 52.70. Gw, 52.25.Sw, 52.35.Ra The electron thermal diffusivity measured in tokamaks is much larger than that predicted by neoclassical theory. In the standard models for this anomalous transport, the loss mechanism for particles and energy in the plasma is attributed to microturbulence [1]. Experimentally, the electrostatic turbulence or density fluctuations n have been intensively studied in tokamaks (edge and core), and the results were not always consistent to show that the electrostatic turbulence determines the internal energy confinement [2]. The magnetic turbulence B is at present measured only at the edge by magnetic coils [3], or indirectly by the analysis of the runaway electron transport [4]. The internal measurement of B is then indispensable for the clarification of its role in the anomalous heat transport. In this Letter, we present a new diagnosticthe cross polarization scattering diagnostic, which is the first attempt to measure the internal B. The cross polarization scattering has been intensively investigated by different authors [5 -8]. A simple qualitative description is given here. From an eletromagnetic wave E; of frequency~;, the scattered field E, . resulting from n, , 8 is given by -Vx(V&CKj+( ')(1 -)E, g J(2) =i p.o,where cr is the unperturbed conductivity tensor. Using a simple nonlinear Quid model, the induced current Ji2i for the cold plasma limit is given by l8 M J('i = ' -E; + ',~[ (~E;) X (B/B)], Cu i n. e g 0 CO (2)where cu", is the plasma frequency and 8 the static magnetic field. The first term on the right-hand side of Eq. (2), describing the interaction between n and E;, and being parallel to E;, gives a scattered wave of the same polarization. This is the usual scattering process for n.The second term, describing the interaction between 8 and E;, has a polarization perpendicular to E; due to the vectorial product between E; and 8, and can generate a scattered wave of cross polarization. This phenomenon, called the cross polarization scattering (CPS), is used to measure the magnetic fluctuation in our experiment.Two eigenmodes exist in tokamaks for wave propagation perpendicular to B: the ordinary mode (0) with polarization parallel to B, and the extraordinary mode (X)with polarization perpendicular to B. The scattering processes described above can be schematically described as follows: 0; + n~O"O; + 8~X, for an incident 0 wave, and symmetrically X; + n~X"X; + B~0, for an incident X wave. In tokamaks, due to the ...

Magnetic fluctuations (radial size ≈ 5 mm) are measured by a cross polarization scattering (CPS) diagnostic in Tore Supra. In the scenario O + B̃ → X, only the poloidal component of the magnetic fluctuations is measured, while both the radial and the poloidal component are measured in the scenario X + B̃ → O. These fluctuations are investigated quantitatively in the ohmic and low confinement regimes over a wide range of plasma currents, densities and additional heating powers. At the same time, the electron heat diffusivities expected from these fluctuations are compared with those obtained by profile analysis. Three main results are obtained: (a) The radial profile of the poloidal magnetic fluctuations in the gradient region (0.3 < r/a < 0.7) is established from these measurements. The magnetic fluctuation levels are found to increase towards the plasma edge, and this feature is compatible with that of electron heat diffusivity. (b) A strong correlation between the measured magnetic turbulence and the local temperature gradient is observed during the additional heating. (c) The local electron heat diffusivity induced by magnetic fluctuations is estimated using the non-collisional quasi-linear formula χmage = πqRvth(δBr/B)2, where the radial component of the magnetic turbulence is assumed to be of the same order as the poloidal component. Both the order of magnitude and the parametric dependence of χmage show similarities with electron diffusivities determined by transport analysis. In particular, a threshold is observed for the dependence of fluctuation induced heat fluxes on the local temperature gradient, which is close to the critical gradient observed for the measured heat fluxes.

The effects of an ion beam injected into a plasma have received an increasing interest in the recent years. Domains for instabilities have been predicted by linear kinetic theory, 1 whereas experiments have mainly been done on nonlinear effects. The occurrence of beam-generated noise has been observed, and the diffusion of ions in velocity space was reported in magnetized 2 and unmagnetized 3 * 4 plasmas. The parametric decay of a beam mode, 5 stationary waves in cylindrical geometry, 6 and large-amplitude waves 7 ' 8 have also been observed. All of these nonlinear effects depend on extensions of linear normal-mode theory. However, except for time-of-flight experiments 3 * 4 observations of the linear dispersion relation in the ion-beam-plasma system have not yet been reported. We thus wish first to state the predictions of linear theory, and then to evidence where a = n b /n e is the ion-beam relative density, Q-TjTp is the plasma-ion temperature ratio, 0 b = T e /T b is the beam-ion temperature ratio, V b ~v b /c s is the beam mean velocity, and R~mjm i is the mass ratio.In the long-wavelength limit, and in the absence of a beam (a=0), the principal root of Eq. (1) is the stable plasma ion-acoustic mode, with phase velocity close to 1 (or -1) 0 In the absence of ions at rest (a~l), these two ion-acoustic solutions are simply Doppler shifted, to a fast ion-5 G. C. Pomraning, The Equations of Radiation Hydrodynamics (Pergamon, New York, 1973), p 0 51. G H. Mayer, LASL Report No 0 LA-647, 1947 (unpublished) . 7 B 0 Kivel and H. Mayer, J" Quant 0 Spectrosc Radiat 0 Transfer 15, 13 (1965). 8 T 0 Leonard and F" Mayer, private communication,, the experimental existence of such predicted, simultaneous modes.When an ion beam of density n b , with a drifting Maxwellian distribution (mean velocity v b and temperature T b ), is introduced into a plasma with stationary ions (density n p , temperature T p ) and electrons (n e = n b + n p , T e ), the kinetic dispersion relation 1 can be written l-K" 2 fdV{V-Wy 1 BF/dV=0.(1)Equation (1) relates the wave phase velocity to the wave number K. The normalizing factors are the ion-sound speed c s = {T e /m { ) 1/2 for the phase velocity W= w/kc s , and the Debye length *D= ( € 0 T e /n e e 2 ) 1/2 for the wave number K=k\ v . F(V) is the total distribution function, comprised of plasma ions, beam ions, and electrons. In consistent units, it is written beam mode (velocity V b + 1) and a slow ion-beam mode (velocity V b -1).All these modes are still expected to exist for intermediate values of a, and provide the starting points for iteratively solving Eq. (1).The real part of the phase velocity of these principal modes is shown in Fig. 1, as a function of beam velocity. The full lines are the theoretical results for a = 0.1 and equal temperature ratios 6 = 0 b = 20 (all velocities normalized to c s ).Two types of dispersion relations are experimentally shown to exist in an ion-beamplasma system. For beam velocities close to the ion-sound speed, two normal modes, one unstable, are see...