Bulletin of the American Physical Society
65th Annual Gaseous Electronics Conference
Volume 57, Number 8
Monday–Friday, October 22–26, 2012; Austin, Texas
Session HW1: Plasma Sheaths II |
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Chair: Ralf Peter Brinkmann, Ruhr-Universit\"at Bochum Room: Amphitheatre 204 |
Wednesday, October 24, 2012 8:00AM - 8:30AM |
HW1.00001: Plasma-Sheath Model Invited Speaker: Karl-Ulrich Riemann In typical gas discharges a quasineutral plasma is shielded from a negativ absorbing wall by a thin positive sheath that is nearly planar and collision-free. The subdivision of ``plasma'' and ``sheath'' was introduced by Langmuir and is based on a small ratio of the electron Debye lenghth $\lambda_D$ to the dominant competing characteristic plasma length $\ell$. Depending on the special conditions, $\ell$ may represent, e.g., the plasma extension, the ionization length, the ion mean free path, the ion gyro radius, or a geometric length. Strictly speaking, this subdivion is possible only in the asymptotic limit $\lambda_D/\ell\to 0$. The asymptotic analysis results in singularities at the ``sheath edge'' closely related to the ``Bohm criterion.'' Due to these singularities a direct smooth matching of the separate plasma and sheath soltions is not possible. To obtain a consistent smooth transition, the singular sheath edge must be bridged by an additinal narrow ``intermediate'' model zone accounting both for plasma processes (e.g., collisions) and for the first build up of space charge. Due to this complexity and to different interpretations of the ``classical'' papers by Langmuir and Bohm, the asymptotic plasma-sheath concept and the definition of the sheath edge were questioned and resulted in controversies during the last two decades. We discuss attempts to re-define the sheath edge, to account for finite values of $\lambda_D/\ell$ in the Bohm criterion, and demonstrate the consistent matching of plasma and sheath. The investigations of the plasma-sheath transition discussed so far are based on a simplified fluid analysis that cannot account for the essential inhomogeneity of the boundary layer and for the dominant role of slow ions in space charge formation. Therefore we give special emphasis to the kinetic theory of the plasma-sheath transition. Unfortunately this approach results in an additional mathematical difficulty caused by ions with zero velocity. We discuss attempts to avoid this singularity by a modification of the kinetic Bohm criterion and investigate the influence of slow ions on the structure of the plasma-sheath transition. The most important conclusions are illustrated with selected examples. [Preview Abstract] |
Wednesday, October 24, 2012 8:30AM - 8:45AM |
HW1.00002: Accuracy of the step sheath approximation Mark Sobolewski In modeling plasma sheaths, it is useful to approximate the electron density profile by a sharp, step-like drop between a quasineutral region and an electron-free region. This approximation allows rapid and efficient numerical calculations of sheath properties and, when combined with other assumptions, allows predictions for sheath properties to be calculated analytically. Nevertheless, the approximation must result in some loss of accuracy. Here, the accuracy of the step approximation was investigated by comparisons with exact solutions for Poisson's equation in the sheath and with experimental measurements of current and voltage waveforms and ion energy distributions. In general, the errors introduced by the step approximation are small but not negligible. The resulting errors in current and voltage are noticeable during the part of the rf cycle when the sheath is nearly collapsed. The effects on the ion energy distribution are most noticeable in the amplitude of the low-energy peak, which is sensitive to the choice of boundary conditions on the plasma side of the step. Using the exact Poisson solution in place of the step approximation results in a modest improvement in the agreement with experiment. [Preview Abstract] |
Wednesday, October 24, 2012 8:45AM - 9:00AM |
HW1.00003: STUDENT AWARD FINALIST: A Kinetic Theory of Planar Plasma Sheaths Surrounding Electron Emitting Surfaces J.P. Sheehan, Igor Kaganovich, Noah Hershkowitz, Yevgeny Raitses It has long been known that electron emission from a surface significantly affects the sheath at that surface. Typical fluid theory of a planar sheath with emitted electrons assumes that the plasma electrons follow the Boltzmann relation and the emitted electrons are emitted with zero energy and predicts a potential drop of $1.03T_e$ across the sheath at a floating boundary. By removing the assumption that all plasma electrons entering the sheath are reflected back into the bulk plasma (i.e. the Boltzmann relation) and considering electrons lost to the wall, we find that the predicted sheath potential is reduced to $0.91T_e$. Using a kinetic description of the emitted electrons, assuming a half Maxwellian distribution with temperature $T_{ee}$, greatly affects the sheath potential. We show that kinetic theory predicts that the sheath potential significantly depends on the plasma to emitted electron temperature ratio. For example, we predict that an emissive probe ($T_{ee} = 0.2$ eV) in a plasma with $T_e = 1$eV will have a sheath potential of $0.51T_e$. Additionally, it is noted that the electron velocity distribution function in the sheath is unstable to the two-stream instability. [Preview Abstract] |
Wednesday, October 24, 2012 9:00AM - 9:15AM |
HW1.00004: Characteristics of Sheath and Presheath Recovery during Pulse Fall Time Jae-Myung Choe, Kyoung-Jae Chung, Y.S. Hwang, Gon-Ho Kim Recovery motion of sheath and presheath is investigated with various fall times of negative bias on the target. Experimental observation was carried out with the collisionless argon plasma and the various pulses with fast and slow fall times which are shorter and longer than the ion transition time scaled of 3/$\omega _{pi}(\omega _{pi}$=ion plasma frequency), respectively. Electrical probe was employed to measure the density distribution. Ion distribution and speed near the target are important factors in determining the position of sheath . For the slow fall time, sheath and presheath boundaries recover with the same speed. Child-Langmuir sheath continuously persists due to enough time to rearrange ions and electrons. For the fast fall time, ion matrix sheath, which is immediately responding to the target voltage, leads the recovery of sheath with supersonic speed. Presheath follows ion inertia that was formed at the plateau time and its speed does not follow the speed of the sheath. Voltage-responding electrons enhance the ion diffusion from the bulk plasma, resulting in the plasma filling in the depletion region. For the intermediate fall time ($\ga $3/$\omega _{pi})$, the transformation from ion matrix to Child-Langmuir sheath occurs after ion responds. Detailed results will be presented. [Preview Abstract] |
Wednesday, October 24, 2012 9:15AM - 9:30AM |
HW1.00005: Numerical simulation of pulsed plasma sheath dynamics in an oblique magnetic field Abolfazl Mahmoodpoor, Hamid Ghomi, Shahryar Mirpour During past several years many authors [1-2] have investigated plasma sheath structure in an oblique magnetic field, that called magnetized plasma sheath, and their work is mainly in steady state case. In this paper, the dynamic of magnetized pulsed plasma sheath are simulated. We applied an exponentially voltage to the cathode and investigate the temporal and spatial evolution of electric field, ion and electron density. For implement of our main motivation, we used two dimensional fluid model and solved numerically Poisson's equation, continuity and momentum transfer equations for ions by FDT method to determine electric potential, density and speed of ions. To complete our equations system, also assume that electron density identified by Boltzman equation. Therefore we consider a plasma sheath with two dimensions coordinate space and three dimensions of speed. It is shown that electric field of pre-sheath, ion and electron density fluctuate during pulse time and spatial length of electron density fluctuation increase with increasing of magnetic field magnitude. \\[4pt] [1] Zou X, Liu J-y, Gong Y, Wang Z-X, Liu Y, Wang X-G, \textit{Vacuum} \textbf{73}, 681-685 (2004).\\[0pt] [2] M. M. Hatami, A. R. Niknam and B. Shokri, \textit{Vacuum} \textbf{83}, (2009)231-234 [Preview Abstract] |
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