Session JW3: Basic Plasma Physics Phenomena in Low-temperature Plasmas

A new equilibrium theory for rf discharges

Two problems often encountered in RF discharges are 1) anomalous skin depth and 2) anomalous electron diffusion across magnetic fields B. Both effects can be explained if the discharges are not unusually long or short. The Simon short-circuit effect\footnote{A. Simon, Phys. Rev. 98, 317 (1955).} then allows the electrons to follow the Boltzmann relation even across B. Once Maxwellian electrons are assumed, a remarkable result can be obtained for radial profiles of density, potential, and ion drift velocity toward the cylindrical wall. In suitably normalized units, these profiles take on a universal shape for all discharges, regardless of B. The velocity profile naturally reaches the Bohm velocity at the wall (= sheath edge). Our code EQM solves for the radial profiles of plasma and neutral density including neutral depletion. All radial dependences are taken into account exactly, and no assumption of a presheath is necessary. To get the profile of $T_{e}$ requires energy balance in the specific discharge. We have done this for helicon discharges described by the HELIC code.\footnote{D. Arnush, Phys. Plasmas 7, 3042 (2000).} Iteration between EQM and HELIC yields all profiles and also the absolute density for given RF power.   

Study of the EEDF and electronic temperature through various magnetic field barriers

The Electron Energy Distribution Function (EEDF) is investigated in a planar ICP source at 4~MHz, for a pressure from 1 to 100~mTorr and a discharge power from 50 to 200~W. A DC magnetic field is generated by permanent magnets. The effect of various magnetic field configurations from constant to sharp barriers are studied using spatially resolved cylindrical Langmuir probes. In all magnetic field configurations, the density decreases with the distance to the coil. The electronic temperature varies differently depending on the field configurations: i) without magnetic field, Te decreases linearly away from the coil (about 1~eV within 12~cm), ii) with a constant magnetic field, Te decreases rapidly near the antenna (about 0.5~eV within the first 1-2~cm) and remains constant when moving further away, iii) with a sharp magnetic field barrier located in the middle of the chamber body, Te decreases within the steep magnetic field gradient. These experiments show that to decrease rapidly the electron temperature, it is required to generate a strong gradient of magnetic field.   

PIC-MCC simulation of plasma transport across a magnetic filter

A magnetic filter is used in the ICP negative ion source for the ITER neutral beam injector to limit the flux of extracted electrons and to prevent negative ion destruction by fast electrons. Plasma transport across the filter from the ICP driver to the extraction grids is however poorly understood and the design of the magnetic filter is empirical. Simulations with a PIC MCC (Particle-In-Cell Monte Carlo Collisions) model have been performed under 1D, 2D periodic, and 2D bounded conditions, with the B field perpendicular to the simulation domain. Results show that : (1) in the 1D simulation only a very small fraction of the electrons can cross the filter, (2) in the 2D periodic simulation the fraction of electrons crossing the filter is still very small in spite of the formation of large amplitude and low frequency drift wave instabilities in the direction perpendicular to the B field, (3) in the 2D bounded simulation the presence of the side walls redirects the electron flow toward the extraction grids, leading to a much larger and non uniform electron flow to the grids that scales as 1/B. These results are consistent with those from a fluid model (G. Hagelaar et al., these proceedings).   

Enhanced metastable population through evaporation cooling and recombination in the argon afterglow

Measurements, modelling and numerical simulations performed in a pulsed inductively coupled argon plasma at low pressures (1---5 Pa) show that very low electron temperatures are achieved on a characteristic time scale of a few tens of micro seconds through evaporation cooling. This allows for recombination resulting in the observed increase of the metastable density in the afterglow phase. The previously observed super-linear scaling with the electron density of the electron decay time is well reproduced analytically by assuming that microfield limited electron-stabilized three-body recombination into highly excited Rydberg states takes place. This hypothesis is strongly supported by experimental results from various diagnostic techniques.   

Development of Ion Energy Distributions Through the Pre-sheath and Sheath in Dual-Frequency Capacitively Coupled Plasmas

Ion properties in the sheath and pre-sheath, and ion energy and angular distribution functions (IEADs) to surfaces, are of critical interest to plasma etching. In single frequency capacitively coupled plasmas, the narrowing in angle and spread in energy of ions as they cross the sheath are well definable functions of frequency, sheath width and mean free path. When using multiple frequency biases, the development of the IEAD is significantly more complex. In this paper, we report on a computational investigation of the development of IEADs in low pressure plasmas having multi-frequency substrate biases as the ions transition from the bulk plasma, through the presheath and sheath, and strike the substrate. The simulations were performed with an ion Monte Carlo Simulation embedded within the Hybrid Plasma Equipment Model. IEADs are tracked as a function of height above the substrate and phase in the rf cycle. Computed results are compared to laser-induced fluorescence experiments of ion velocities in an inductively coupled plasma with a multi-frequency substrate bias. Gas pressures are a few to 10s of mTorr, in Ar and Ar/O$_{2}$ mixtures.   

Drift-induced plasma transport across a magnetic field barrier

Various low-temperature plasma sources rely on a steady magnetic field for their operation. Most of these sources have an axisymmetric configuration where any magnetic drifts are closed along the azimuthal direction and therefore do not interfere with the overall plasma transport to the chamber walls. However, in non-axisymmetric sources the magnetic drift is bounded by the walls and tends to induce increased transport across the magnetic field. In this paper, we use self-consistent numerical simulations to demonstrate and analyze this bounded-drift effect for the magnetic filter in the negative ion source currently under development for the ITER neutral beam heating system. We show that the plasma in this source develops asymmetry in order to redirect the bounded electron drift across the magnetic filter toward the extraction grids. The resulting cross-field electron current collected by the grids scales as 1/B rather than the classical 1/B$^{2}$ scaling.   

Modeling High-Voltage Breakdown for Angled Dielectric Insulators

Angled dielectric-insulator breakdown is investigated using an improved 2D PIC model [1]. This work will develop the capability to predict and control breakdown thresholds by ordering various contributions to breakdown. Models emphasize secondary-emission [2], space-charge, dielectric-surface charge, and single- and multi-layer [3] angled-insulator configurations in DC fields. Effects of seed current, field emission, ambient and desorbed gas, and applied RF fields will also be studied. Key observations of single-layer multipactor DC breakdown [4] simulations with an imposed constant-current show: positive dielectric-surface charging, avalanche current developing in a few hundred ps, saturation by shortened secondary lifetimes, and absence of avalanche breakdown at large angles due to space-charge effects.\\[4pt] [1] Taverniers, S., et al., ICOPS 2009 Proc., 2009.\\[0pt] [2] Vaughan, J.R.M., IEEE TED, Vol. 36, No. 9, 1989, pp.1963- 1967.\\[0pt] [3] Leopold, J.G., et al., Proc. 2010 PMHVC.\\[0pt] [4] Jordan, N.M., et al., J. Appl. Phys., 102, 2007.   

Fast Nonequilibrium Plasma Thermalization in N$_{2}$-O$_{2}$ Mixtures at Different Pressures

Observations of a shock wave propagating through a decaying plasma in the afterglow of an impulse high-voltage nanosecond discharge and of a surface dielectric barrier discharge in the nanosecond range were analyzed to determine the electron power transferred into heat in air plasmas in high electric fields. It was shown that approximately half of the discharge power can go to heat for a short ($\sim $1 $\mu $s at atmospheric pressure) period of time when reduced electric fields are present at approximately 10$^{3}$ Td. A kinetic model was developed to describe the processes that contribute towards the fast transfer of electron energy into thermal energy under the conditions considered. Calculations based on the developed model agree qualitatively with analyses of high-voltage nanosecond discharge observations. Different gas pressures and N$_{2}$-O$_{2}$ mixture compositions were investigated.   

Analysis of the High Amplitude RF Electric Field Induced Plasma Using a Finite-Difference Time-Domain Simulation

A fast rise-time RF pulsed electric field of sufficient amplitude that is transmitted through a dielectric slab will induce dielectric surface flashover and cause a significant drop in transmitted power. A finite-difference time-domain code was developed to simulate the flashover plasma represented by its frequency-dependent permittivity; this is transformed to a discrete algorithm that computes electric field and plasma density from electric flux density and momentum transfer collision rate. Results for nitrogen, air, and argon are included. At the gas pressures of interest ($>$ 5 kPa), the collision rate reaches THz levels which, at 2.85~GHz frequency RF radiation, leads to a comparatively low plasma conductivity. As a result an absorption of 60{\%} of the incident power is calculated, consistent with the experimental observations. The results of the calculations are compared with experimental data of high power microwave induced surface flashover; the experimental apparatus uses a conditioned 50~ns rise-time 3~$\mu $s duration pulse at 2.5 MW peak power at 2.85 GHz to induce flashover across a polycarbonate window.   

Post-breakdown secondary discharges at the electrode/dielectric interface of a cylindrical barrier discharge

The electrical breakdown characteristics of a double-walled cylindrical dielectric barrier discharge (DBD) lamp with a neon buffer gas under pulsed voltage excitation have been investigated. Following the formation of plasma in the main discharge gap, we have observed secondary breakdown phenomena at the inner and outer mesh electrode/dielectric interfaces under specific operating conditions. Plasma formation at these interfaces is investigated by monitoring the Ozone production rate in controlled flows of ultra high purity oxygen together with the overall electrical voltage-charge characteristics of the lamp. The results show that this secondary breakdown only occurs after the main discharge plasma has been established, and that significant electrical power may be dissipated in generating these spurious secondary plasmas. The results are important with regards to optimising the design and identifying efficient operating regimes of DBD based devices that employ mesh-type or wire/strip electrodes.