Session NR3: Plasma Sheaths and Boundary Layers

The interaction of the near-field plasma with antennas used in magnetic fusion research

Plasma heating and current drive using antennas in the Ion Cyclotron Range of Frequencies (ICRF) are important elements for the success of magnetic fusion. The antennas must operate in a harsh environment, where local plasma densities can be \textgreater\ 10$^{18}$/m$^{3}$, magnetic fields can range from 0.2-5 Tesla, and antenna operating voltages can be \textgreater\ 40 kV. This environment creates operational issues due to the interaction of the near-field of the antenna with the local plasma. In addition to parasitic losses in this plasma region, voltage and current distributions on the antenna structure lead to the formation of high electric fields and RF plasma sheaths, which can lead to enhanced particle and energy fluxes on the antenna and on surfaces intersected by magnetic field lines connected to or passing near the antenna. These issues are being studied using a simple electrode structure and a single-strap antenna on the Prototype Materials Plasma EXperiment (Proto-MPEX) at ORNL, which is a linear plasma device that uses an electron Bernstein wave heated helicon plasma source to create a high-density plasma suitable for use in a plasma-material interaction test stand. Several diagnostics are being used to characterize the near-field interactions, including double-Langmuir probes, a retarding field energy analyzer, and optical emission spectroscopy. The RF electric field is being studied utilizing Dynamic Stark Effect spectroscopy and Doppler-Free Saturation Spectroscopy. Recent experimental results and future plans will be presented.   

Ion velocities in an electronegative presheath

Under certain conditions in radio-frequency (rf) discharges, features in ion energy distributions (IEDs) measured at an electrode depend very sensitively on ion velocities far upstream, in the presheath. By measuring such distributions together with sheath voltage waveforms, presheath ion velocities can be determined and long-standing controversies regarding presheath transport can be resolved. For rf-biased, inductively coupled plasmas in CF$_4$ gas, we determined the presheath velocities of all significant positive ions. Velocities were significantly lower than those predicted by electropositive models. These results contradict the claim that negative ions are confined to a core electronegative plasma surrounded by an electropositive peripheral plasma and presheath. Also, they indicate that models that neglect the effect of negative ions in presheaths will under certain conditions yield dramatically inaccurate predictions for IEDs, average ion energy, and rf bias power.   

Bulk plasma effects of the electron sheath

Electron sheaths are commonly found around relatively small, positively biased boundaries. Conventional analysis treats these structures as local phenomena with little impact on the bulk plasma. We present a theoretical treatment of the electron sheath that suggests an extensive presheath region, many times larger than that of an analagous ion sheath. We also find that the electrons must flow into the electron sheath with a minimum flow speed, which can be considered an electron sheath equivalent of the Bohm criterion. Two-dimensional particle-in-cell simulations are presented, demonstrating the existence of this electron presheath and a global flow of electrons to the positive boundary. Velocity distributions reveal that electron flux across the sheath edge is not random thermal flux, but a Maxwellian electron distribution flow-shifted to meet the minimum flow speed at the sheath edge. Qualitative agreement is found between the density distribution of electrons in simulations when compared to LCIF measurements of a thermionic plasma.   

The characteristics of RF modulated plasma boundary sheaths: An analysis of the standard sheath model

The characteristics of radio frequency (RF) modulated plasma boundary sheaths are studied on the basis of the so-called ``standard sheath model.'' This model assumes that the applied radio frequency $\omega_{\rm RF}$ is larger than the plasma frequency of the ions but smaller than that of the electrons. It comprises a phase-averaged ion model -- consisting of an equation of continuity (with ionization neglected) and an equation of motion (with collisional ion-neutral interaction taken into account) -- a phase-resolved electron model -- consisting of an equation of continuity and the assumption of Boltzmann equilibrium --, and Poisson's equation for the electrical field. Previous investigations have studied the standard sheath model under additional approximations, most notably the assumption of a step-like electron front [1]. This contribution presents an investigation and parameter study of the standard sheath model which avoids any further assumptions. The resulting density profiles and overall charge-voltage characteristics are compared with those of the step-model based theories. \\[4pt] [1] V.A.~Godyak and Z.K.~Ghanna, \emph{Sov.~J.~Plasma Phys.} \textbf{6}, 372 (1979)   

Theory of the Electron Sheath and Presheath

Electron sheaths are commonly found near Langmuir probes collecting the electron saturation current. The common assumption is that the probe collects the random flux of electrons incident on the sheath, which tacitly implies that there is no electron presheath and that the flux collected is due to a velocity space truncation of the velocity distribution function (VDF). This work provides a dedicated theory of electron sheaths, which suggests that electron sheaths are not so simple. Motivated by VDFs observed in recent Particle-In-Cell (PIC) simulations, we develop a 1D model for the electron sheath and presheath. In the model, under low temperature plasma conditions, an electron pressure gradient accelerates electrons in the presheath to a flow velocity that exceeds the electron thermal speed at the sheath edge. This pressure gradient allows the generation of large flows compared to those that would be generated by the electric field alone. It is due to this pressure gradient that the electron presheath extends much further into the plasma (nominally by a factor of $\sqrt{m_i/m_e}$) than an analogous ion presheath. Results of the model are compared with PIC simulations.   

Virtual Cathodes near small electrodes biased near the plasma potential and its effects on Langmuir probes

Movable small (3cm x 3.8cm) plates biased near the plasma potential are immersed in a filament discharge in a multi-dipole chamber. The plates are small (A$_{plate}$/A$_{chamber}$ \textless\ (m$_{e}$/M$_{i})^{1/2})$ [1] such that an electron sheath is possible. Plasma potential and IVDF's near the plate are measured, and virtual cathodes, a double layer consists of an ion sheath and an electron sheath, was found to form. Ion velocities are determined by Laser-Induced Florescence, the electron temperature and electron density are measured by a planar Langmuir probe and the plasma potential is measured by an emissive probe. Effects of the virtual cathode on Langmuir probe I-V characteristics were predicted through estimating the current collection of an electrode in the presence of the virtual cathode, and was experimentally investigated by comparing I-V characteristics of the small plate and a 0.6cm diameter Langmuir probe. \\[4pt] [1] S. D. Baalrud, N. Hershkowitz and B. Longmier, Phys. Plasmas 14, 042109 (2007)