Double layer formation in the expanding region of an inductively coupled electronegative plasma

Double-layers (DLs) were observed in the expanding region of an inductively coupled plasma with $\text{Ar}/\text{SF}\_6$ gas mixtures. No DL was observed in pure argon or $\text{SF}\_6$ fractions below few percent. They exist over a wide range of power and pressure although they are only stable for a small window of electronegativity (typically between 8\% and 13\% of $\text{SF}\_6$ at 1mTorr), becoming unstable at higher electronegativity. They seem to be formed at the boundary between the source tube and the diffusion chamber and act as an internal boundary (the amplitude being roughly 1.5$\frac{kT\_e}{e}$)between a high electron density, high electron temperature, low electronegativity plasma upstream (in the source), and a low electron density, low electron temperature, high electronegativity plasma downstream

Experimental investigation of double layers in expanding plasmas

Double layers (DLs) have been observed in a plasma reactor composed of a source chamber attached to a larger expanding chamber. Positive ion beams generated across the DL were characterized in the low plasma potential region using retarding field energy analyzers. In electropositive gases, DLs were formed at very low pressures between 0.1 and 1 mTorr with the plasma expansion forced by a strongly diverging magnetic field. The DL remains static, robust to changes in boundary conditions, and its position is related to the magnetic field lines. The voltage drop across the DL increases with decreasing pressure, i.e., with increasing electron temperature around 20 V at 0.17 mTorr. DLs were also observed in electronegative gases without a magnetic field over a greater range of pressure 0.5 to 10 mTorr. The actual profile of the electronegative DL is very sensitive to external parameters and intrusive elements, and they propagate at high negative ion fraction. Electrostatic probes measurements and laser-induced photodetachment show discontinuities in all plasma parameters electron density, electron temperature, negative ion fraction at the DL position. The voltage drop across the electronegative DL is about 8 V, is independent of the gas pressure and therefore of the electron temperature

Experimental and numerical study of crack healing in a nuclear glass

International audiencea b s t r a c t An experimental study of thermally or water-induced crack healing in an inactive borosil-icate glass, chemically analogous to that used in France for the vitrification of nuclear waste was carried out. Partial welding of glass plates was observed after annealing in air at 425 °C (77 °C below T g) when at least 20 MPa compressive stress was applied, while annealing at 450 °C under 20 MPa led to a complete disappearance of the interface. Closure of indenta-tion-induced cracks was observed during annealing at 400 °C in an ESEM as a result of viscous relaxation of residual stresses but it did not constitute a sufficient proof of crack healing. DCDC specimens were thus pre-cracked in an ESEM and then either annealed at various temperatures (350–490 °C) in secondary vacuum or in air, or left in water at 70–90 °C, sometimes under a compressive stress normal to the crack face. The specimens were then reloaded in the ESEM and the crack opening displacements under a given load were compared to those measured during pre-cracking. The cracks were bridged by an alteration layer over a distance from the crack tip which decreased as loading increased. The restraining effect of these bridges on crack opening was assessed via finite element simulations, using interface elements. The tensile strength of the bridging layer was estimated as 27–39 MPa after vacuum annealing at 400 °C, 11–20 MPa after 15 days in water at 90 °C and 44–78 MPa after 11 days in water at 70 °C under 5 MPa normal compression. Partially healed cracks did not resume propagation from their former crack tip, but due to branch cracks re-initiated a few hundred microns behind it which grow avoiding the healed area. This behaviour was explained using finite element simulations

Periodic formation and propagation of double layers in the expanding chamber of an inductive discharge operating in Ar/SF₆ mixtures

It has previously been shown [Tuszewski et al., Plasma Sources Sci. Technol.12, 396 (2003)] that inductive discharges in electronegative gases are subject to two types of instability: the sourceinstability related to the E to H transition and a transport instability, occurring downstream when an expanding chamber is present. These two types of instability are observed in our “helicon” reactor operated without a static magnetic field in low-pressure Ar∕SF6 mixtures. Temporally and spatially resolved measurements show that, in our experiment, the downstream instability is a periodic formation and propagation of a double layer. The double layer is born at the end of the source tube and propagates slowly to the end of the expansion region with a velocity of 150ms⁻¹

Transition from unstable electrostatic confinement to stable magnetic confinement in a helicon reactor operating with Ar∕SF₆ gas mixtures

Two types of instabilities were previously identified in inductive discharges having an expanding chamber when negative ions are present: (i) the sourceinstability, occurring in the neighborhood of the capacitive-to-inductive (E to H) transition, and (ii) the downstream instability, which was shown to be the periodic formation and propagation of double layers. These unstable double layers were found over the entire parameter space (pressure/power) of interest, and they were born at the interface of the source and diffusion chambers. They acted as an internal electrostatic barrier separating a low-electronegativity, high-electron-density plasma upstream (in the source) and a high-electronegativity, low-electron-density plasma downstream. In this paper we have investigated the effect of adding a static axial magnetic field, classically used to increase the confinement and the plasma heating via helicon wave propagation. This had the following consequences: (i) the unstable double layers, and therefore the axial electrostatic confinement, were suppressed in a large part of the parameter space, and (ii) the magnetic confinement leads to a radially stratified plasma, the center being a low-electronegativity, high-density plasma and the edges being essentially an ion-ion plasma

Equilibrium model for two low-pressure electronegative plasmas connected by a double layer

Plihon et al. [J. Appl. Phys.98, 023306 (2005)] have recently shown that double layers usually form during the expansion of a low pressure electronegative plasma. These double layers act as permeable internal boundaries between the source (upstream) plasma and the downstream expanding plasma; positive ions flow from upstream to downstream whereas negative ions flow in the opposite direction. So far, the detailed physical mechanisms leading to their formation have not been identified. In this paper, we develop a model for the two plasma equilibria, upstream and downstream, assuming that the double layer exists and couples the two plasmas. At very low pressure, typically 0.5mTorr, the coupling is strong and acts both ways. The negative ions created downstream contributes to the upstream equilibrium as well as the upstream positive ions contribute to the downstream equilibrium. As the pressure increases, the situation becomes asymmetric. The sourceplasma is not affected by the negative ions flowing from downstream, whereas the positive ions coming from the source control the downstream plasma equilibrium, where local ionization is negligible.This work has been supported by the European Space Agency, under Ariadna Study Contract No. ACT-04-3101. One of the authors A.J.L. acknowledges the hospitality of the LPTP, where the collaboration was begun

Electron heating mechanisms in dual frequency capacitive discharges

We discuss electron heating mechanisms in the sheath regions of dual-frequency capacitive discharges, with the twin aims of identifying the dominant mechanisms and supplying closed-form expressions from which the heating power can be estimated. We show that the heating effect produced by either Ohmic or collisionless heating is much larger when the discharge is excited by a superposition of currents at two frequencies than if either current had acted alone. This coupling effect occurs because the lower frequency current, while not directly heating the electrons to any great extent, strongly affects the spatial structure of the discharge in the sheath regions

Conjunctions of Among Constraints

Many existing global constraints can be encoded as a conjunction of among constraints. An among constraint holds if the number of the variables in its scope whose value belongs to a prespecified set, which we call its range, is within some given bounds. It is known that domain filtering algorithms can benefit from reasoning about the interaction of among constraints so that values can be filtered out taking into consideration several among constraints simultaneously. The present pa- per embarks into a systematic investigation on the circumstances under which it is possible to obtain efficient and complete domain filtering algorithms for conjunctions of among constraints. We start by observing that restrictions on both the scope and the range of the among constraints are necessary to obtain meaningful results. Then, we derive a domain flow-based filtering algorithm and present several applications. In particular, it is shown that the algorithm unifies and generalizes several previous existing results.Comment: 15 pages plus appendi

Determination of set-membership identifiability sets

International audienceThis paper concerns the concept of set-membership identifiability introduced in \cite{jauberthie}. Given a model, a set-membership identifiable set is a connected set in the parameter domain of the model such that its corresponding trajectories are distinct to trajectories arising from its complementary. For obtaining the so-called set-membership identifiable sets, we propose an algorithm based on interval analysis tools. The proposed algorithm is decomposed into three parts namely {\it mincing}, {\it evaluating} and {\it regularization} (\cite{jaulin2}). The latter step has been modified in order to obtain guaranteed set-membership identifiable sets. Our algorithm will be tested on two examples

Simulations of electromagnetic effects in high frequency capacitively coupled discharges using the Darwin approximation

The Darwin approximation is investigated for its possible use in simulation of electromagnetic effects in large size, high frequency capacitively coupled discharges. The approximation is utilized within the framework of two different fluid models which are applied to typical cases showing pronounced standing wave and skin effects. With the first model it is demonstrated that Darwin approximation is valid for treatment of such effects in the range of parameters under consideration. The second approach, a reduced nonlinear Darwin approximation-based model, shows that the electromagnetic phenomena persist in a more realistic setting. The Darwin approximation offers a simple and efficient way of carrying out electromagnetic simulations as it removes the Courant condition plaguing explicit electromagnetic algorithms and can be implemented as a straightforward modification of electrostatic algorithms. The algorithm described here avoids iterative schemes needed for the divergence cleaning and represents a fast and efficient solver, which can be used in fluid and kinetic models for self-consistent description of technical plasmas exhibiting certain electromagnetic activity