J.-M. Rax

Plasma transport under neutral gas depletion conditions

It was previously shown that plasma transport is enhanced by neutral gas depletion when the plasma pressure is not negligible compared with the neutral gas pressure. Consequently, the plasma flux leaving the discharge is not a linear function of the central plasma density. The latest theoretical treatments of this problem have assumed isothermal fluids in pressure balance, discarding neutral gas heating. We present a model that incorporates the effects of neutral gas heating on the plasma transport enhancement. This model shows that (i) neutral gas depletion is more pronounced than previously calculated due to gas heating and (ii) as a consequence the plasma transport is further enhanced and the non-linearity of the plasma flux leaving the discharge is more pronounced.

Inductive heating and E to H transitions in high frequency capacitive discharges

Capacitive discharges have classically been operated in the electrostatic regime, for which the excitation wavelength λ is much greater than the electrode radius and the plasma skin depth δ is much greater than the electrode spacing. However, contemporary reactors are larger and excited at a higher frequency so that electromagnetic effects become significant. A self-consistent transmission line model valid in the entire range of λ and δ of practical interest is solved. The model is the electromagnetic generalization of the lumped-element circuit model classically used for capacitive discharges. We find that the plasma may either be sustained by the usual capacitive (E) field or by an inductive (H) field and that the discharge experiences E to H transitions as the voltage between the electrodes is raised. The transitions are global at low pressure and local at high pressure. In the latter case, the plasma parameters (e.g. the ion flux to the electrodes) are radially non-uniform, due to the non-uniformities of the rf voltage and current, leading to serious industrial issues.

Steady-state isothermal bounded plasma with neutral dynamics

The Tonks-Langmuir, Godyak, and Schottky steady-state isothermal models are extended when the dynamics of the neutral gas is taken into account. Exact analytic quadratures for the electron temperature, densities, and potential profiles are obtained for these three models within the plasma approximation. It is shown that, contrary to the uniform neutral pressure case, the particle and the power balance are both necessary to determine the electron temperature when neutral dynamics is included. When neutral dynamics is governed by collisions with ions, the neutral density that results from ionization is predicted to have a minimum at the center of the discharge, as indeed is observed in experiment. It is found that even a small amount of ionization can result in a rather strong neutral depletion. However, when the drag on neutrals due to collisions with ions is negligible, the predicted profile of the neutral density that results from intense ionization is reversed and exhibits an unexpected maximum at the center of the discharge.

Suppression of the standing wave effect in high frequency capacitive discharges using a shaped electrode and a dielectric lens: Self-consistent approach

The standing wave effect causes nonuniform plasma excitation in high frequencies capacitive discharges when the electrode size is not considerably smaller than the excitation wavelength. A shaped electrode was proposed by Sansonnens and Schmitt [Appl. Phys. Lett. 82, 182 (2003)] to suppress this unwanted effect. The shape of the electrode was calculated in the vacuum approximation (no plasma was present between the electrodes), and was found to be Gaussian. The authors postulated that the presence of plasma would not significantly modify the solution. However, it was shown [Chabert et al., Phys. Plasmas 11, 1775 (2004)] using a self-consistent nonlinear transmission line model that the presence of plasma significantly shortens the wavelength for a system composed of two parallel plate electrodes. It was therefore legitimate to expect the optimized shape of the electrode and lens to be different when a plasma is present. Here it is shown that to suppress the standing wave effect the current flowing in the ...

Autoresonant ion cyclotron isotope separation

A new isotope separation process based on selective cyclotron resonant interaction between ions and a tapered helicoidal magnetic structure is identified, analyzed, and evaluated. On the basis of a Hamiltonian analysis, the existence of a class of tapered magnetic modulation that provide a full conversion of linear momentum into angular momentum is discovered. The characteristics and parameters of this field configuration are analyzed and described. The dynamic of the nonresonant isotope is investigated in order to set up a separation criterion. This autoresonant ion cyclotron isotope separation mechanism provides an efficient alternative to other niches of enrichment process.

Electron heating in multiple-frequency capacitive discharges

Contemporary capacitive discharges are often driven by a combination of at least two frequencies to achieve independent control of the ion flux and the ion energy impacting the electrodes. This multiple frequency excitation leads to new electron heating mechanisms that are discussed in this paper. Firstly, we show that electron heating in the sheath is greatly enhanced by the combination of two frequencies, i.e. the heating produced is much larger than the sum of the two single contributions. Secondly, we show that when the higher frequency is such that the corresponding wavelength becomes comparable to the electrode size, electromagnetic effects become important and a significant amount of heating is provided by the inductive field. The discharge experiences a capacitive-to-inductive transition when the high frequency voltage amplitude is raised.

Efficiency of wave-driven rigid body rotation toroidal confinement

The compensation of vertical drifts in toroidal magnetic fields through a wave-driven poloidal rotation is compared with compensation through the wave driven toroidal current generation to support the classical magnetic rotational transform. The advantages and drawbacks associated with the sustainment of a radial electric field are compared with those associated with the sustainment of a poloidal magnetic field both in terms of energy content and power dissipation. The energy content of a radial electric field is found to be smaller than the energy content of a poloidal magnetic field for a similar set of orbits. The wave driven radial electric field generation efficiency is similarly shown, at least in the limit of large aspect ratio, to be larger than the efficiency of wave-driven toroidal current generation. Published by AIP Publishing.

A narrow-band, variable energy ion source derived from a wire plasma source

A low pressure wire-induced plasma source (WIPS) operated in its high-pressure mode (~10?2?mbar) exhibits a narrow ion energy distribution function peaked at an energy corresponding to the discharge voltage. In order to take advantage of this peculiar feature, we design an electrode geometry enabling the acceleration of ions extracted from a WIPS. Probing of the obtained ion plume by means of a retarding potential analyser (RPA) demonstrates the capability of such an ion source to generate narrow-band (full width at half maximum of about 20?eV), variable energy (1 to 5?keV) ion beams. Comparison with particle-in-cell simulations of the WIPS shows that the energy spread of these ion beams is actually about 10?eV, the slight broadening being mainly the effect of the limited planar RPA energy resolution. The ion beam spot size measured at 6?cm of the ion source exit is about 3?mm for a 10??A He+ beam at 2?keV, with a divergence of about one degree. Operating the WIPS in argon and xenon leads to similar properties for Ar+ and Xe+ beams, and in principle other species could also be used.

Fast electron energy deposition in a magnetized plasma: Kinetic theory and particle-in-cell simulation

The collisional dynamics of a relativistic electron jet in a magnetized plasma are investigated within the framework of kinetic theory. The relativistic Fokker–Planck equation describing slowing down, pitch angle scattering, and cyclotron rotation is derived and solved. Based on the solution of this Fokker–Planck equation, an analytical formula for the root mean square spot size transverse to the magnetic field is derived and this result predicts a reduction in radial transport. Some comparisons with particle-in-cell simulation are made and confirm striking agreement between the theory and the simulation. For fast electron with 1 MeV typical kinetic energy interacting with a solid density hydrogen plasma, the energy deposition density in the transverse direction increases by a factor 2 for magnetic field of the order of 1 T. Along the magnetic field, the energy deposition profile is unaltered compared with the field-free case.

Theory of unfolded cyclotron accelerator

An acceleration process based on the interaction between an ion, a tapered periodic magnetic structure, and a circularly polarized oscillating electric field is identified and analyzed, and its potential is evaluated. A Hamiltonian analysis is developed in order to describe the interplay between the cyclotron motion, the electric acceleration, and the magnetic modulation. The parameters of this universal class of magnetic modulation leading to continuous acceleration without Larmor radius increase are expressed analytically. Thus, this study provides the basic scaling of what appears as a compact unfolded cyclotron accelerator.