Session ET2: Sheaths and Fireballs

Electron Sheaths and Fireballs

Probes and electrodes are the most common method of manipulation and diagnosis of low temperature low pressure laboratory plasmas. The variety of behavior that a probe can induce locally and globally in the plasma is in part determined by the electrode size, geometry, and bias relative to the plasma potential. When biased above the plasma potential electrodes and probes have been observed to modify electron and ion velocity distribution functions, induce electron flows, generate ion flows that are determined by probe geometry and proximity to insulating surfaces, and induce secondary discharges called fireballs that are driven by electron-impact ionization. Until recently, the understanding of the basic positive electron sheath and presheath properties that lead to many of these phenomena went unrecognized and was not well understood [1]. In this talk, recent advances in the understanding of the behavior of positive electrodes are presented and our current line of research on positive probes is discussed.

[1] Interaction of biased electrodes and plasmas: sheaths, double layers, and fireballs, Scott D Baalrud, Brett Scheiner, Benjamin T Yee, Matthew M Hopkins and Edward Barnat, 2020 Plasma Sources Sci. Technol. 29 053001   

Author not Attending

The entry velocity of electrons into the electron sheath is a fundamental quantity that determines the electron saturation current into a Langmuir probe, and thus the respective calibration constant of a Langmuir probe’s plasma density measurement. Conventional wisdom believes that electrons enters the electron sheath at the random thermal flux speed v_e=(T_e/2πm_e)^1/2. A recent theory suggest that electrons enter electron sheaths at an electron Bohm velocity v_eB=(T_e/m_e)^1/2 instead of the electron thermal velocity as conventionally assumed. To test this theory, the flux density ratio Γ_e,se/Γ_i,se of electrons and ions entering their respective sheaths was directly measured in a multi-dipole confined hot cathode source via an almost continuous A_i/A_e area ratio scanning of an asymmetric double probe. Removing known perturbation to the experimental results, the measured value agrees the critical flux ratio of ~ (m_i/2.3m_e)^1/2 with the predictions assuming electrons entering the electron sheaths at their thermal velocity. The predictions associated with the electron Bohm criterion has not been found. If the predictions of such theories are true, the electron or ion presheath density drops will be very different from conventionally expected values.

    

Sheath expansion around Langmuir Probes: is it only about the probe bias potential?

It has recently been shown that  that Langmuir probes (LPs) measure an unphysically positive plasma potential in the presheath of low temperature plasma,  near conducting boundaries at which ion rich sheaths form [Li et al., Plasma Sources Sci. Technol. 29 (2020) 025015]. It has been argued heuristically that the difference between plasma potential profiles measured by LPs and emissive probes (EPs), in the presheath,  is related to ion flow caused by sheath formation. More recently we have shown that in the presheath, Langmuir probes also overestimate electron density rather dramatically, especially as the probe gets close to the sheath. We present experimental evidence that the two anomalies are interrelated, and that sheaths are distorted and expanded around a Langmuir probe where ion flow is present, even when the probe bias potential passes through the local plasma potential, in weakly collisional (λ_{mean-free-path} >> λ_D), low pressure (P_neutral ≤ 1 mTorr), low temperature (kT_e ~ (1-5) eV), single ion species plasma, where the feedstock gas is Ar or He or Xe or Kr.   

How sheath properties change with gas pressure: modeling and simulation

Here we test a 1D collisional sheath model using particle-in-cell simulations, which include charge-neutral collisions using the direct simulation Monte Carlo method. The model was created to predict how several important sheath properties change with gas pressure: the sheath edge values of the ion velocity, relative plasma density, electric field, potential, and sheath width. Currently, there are multiple models for each property, each lacking validation. We find that numerical solutions to our model and simulations agree over a large pressure range (0.01-10,000 mTorr). Both predict the ion velocity and relative density decrease with increasing pressure, while the potential and sheath width increase. The electric field is found to remain constant in both. However, the model doesn't account for kinetic effects, like non-Maxwellian features of the electron velocity distribution and temperature gradients. We find that the former leads to small differences between the model and simulations at low pressures (<100 mTorr) and that the difference can become significant at the highest pressures (>100 mTorr). Ultimately, we derive expressions for each quantity that depend only on the pressure and adjust the coefficients to best represent the simulation data with its kinetic effects.   

Plasma fireballs, their creation and behavior

Fireballs were first observed as localized discharge phenomena on positively biased small electrodes in plasmas. Many similar forms of bounded glow phenomena in low-pressure gas discharges are now also termed fireballs. The strong glow of a fireball is due to energetic electrons impacting with neutrals. The sharp boundary of the glow is evidence for a localized electric field such as a sheath or double layer. Fireballs mostly appear as spheres or cylinders attached to the electrode, but new forms have been observed with various geometries and/or in magnetic fields. We have undertaken many investigations of the creation and behavior of fireballs, in particular the instabilities that can be detected in the low frequency range, due to ion fluctuations, as well as in various high frequency ranges, due to electrons. The particle dynamics within the plasma space charge formations and the exchange between them have been investigated. Recently we have concentrated on the interaction between several separately created fireballs, showing also the influence of the fireballs on the background plasma parameters. The current oscillations show specific frequencies for the dynamic states of the fireballs, where periodic expulsion and backflow of ions occur near the surrounding double layer.   

Development of a Discontinuous Galerkin fluid solver for argon plasma-sheath

The understanding of plasma-sheath formation phenomenon is of vital importance for a great variety of engineering fields, that range from electric propulsion for space applications  to magnetically confined fusion devices, from development of thermal protection systems for hypersonic flows till the study of development of arcing in microelectronics. 

The aim of this work is to develop a fluid solver that will combine a reasonable computational cost with the high order spatial accuracy that the Discontinuous Galerkin discretization is able to achieve: in order to describe a mixture of argon plasma (electrons, single-charged ions, neutral atom) we are going to compare two different approaches, the multifluid and the multicomponent modeling, in order to assess their performance under different pressure conditions; the governing equations used in both cases remind of the Navier-Stokes equations (as they account for conservation of density, momentum and, eventually, energy) coupled to the Poisson equation, ensuring charge conservation throughout the entire domain. The intrinsic multiscale character of the problem (which is in large part due to the large disparity in mass between electrons and ions/neutrals, that reflects naturally in strong thermal nonequilibrium, i.e. the electron temperature is higher than the heavy temperature) is described and overcome by taylor-made ESDIRK time integration.

Results obtained are critically compared to well-known solution from literature providing the basis for future development towards more complex mixtures: the chosen high order framework allows to adequately resolve sharp gradients in the solution, typical of the plasma-sheath transition, and the implemented implicit time-discretization is able to overcome the strict  stability constraints for this models.

    

Author not Attending

A high density multi-dipole confined hot cathode discharge has been developed using a large area DC heated LaB₆ hot cathode. This device facilitates the investigation of a gradual transition of an unmagnetized discharge from a partial ionized discharge to a fully ionized discharge. Evolution of electron temperature, electron density, and optical emission characteristics with the discharge transition is measured and compared to the evolution of these parameters in abruptly transited helicon discharges. Due to the lack of coupling between the discharge characteristics (i.e. plasma conductivity) and the RF-power coupling mechanisms, this discharge is expected to provide a unique opportunity to investigate previous claims of known phenomena in helicon plasmas and other fully ionized discharges. These phenomena include neutral depletion, transition of optical emission characteristics, and temperature evolution. Preliminary of these investigations will be presented in this oral report. Issues in plasma diagnostics in these unmagnetized, high density discharges are also presented.