Bulletin of the American Physical Society
61st Annual Gaseous Electronics Conference
Volume 53, Number 10
Monday–Friday, October 13–17, 2008; Dallas, Texas
Session VF3: Plasma Boundaries |
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Chair: Raoul Franklin, The Open University, UK Room: Addison Room |
Friday, October 17, 2008 8:00AM - 8:15AM |
VF3.00001: Improvement of a multi-fluid plasma model for the near-cathode region in thermal plasmas$^*$ Frank Scharf, Ralf Peter Brinkmann To model and simulate High Intensity Discharge lamps, a proper model for the near-cathode region of thermal plasmas is necessary. Two such models have been presented by the groups around Benilov and Mentel, respectively.$^{1,2,3}$ Both models yield good results for some conditions (defined mainly by differing collision rates), but also non-physical or no results for other conditions. A prominent indicator of the second case is the appearance of super-sonic neutrals. In this contribution a multi-fluid approach incorporating elements from both previous models is presented. In particular, the new model allows for both three body recombination and heavy particle inertia. It thus promises more accurate results over a wider range of physical parameters. Additionally, the new model features a new way to implement the physical boundary conditions numerically. Applying linearization techniques allows a direct, consistent implementation without having to resort to time-consuming shooting methods.\\[.5ex] $^1$M. S. Benilov et al., {\it Proc. GEC2004}, MT1.002\\ $^2$N. A. Almeida et al., {\it J. Phys. D: Appl. Phys.} {\bf 37} (2004) 3107\\ $^3$S. Lichtenberg et al., {\it J. Phys. D: Appl. Phys.} {\bf 38} (2005) 3112\\[.5ex] $^*$Supported by the DFG within Graduiertenkolleg 1051 [Preview Abstract] |
Friday, October 17, 2008 8:15AM - 8:30AM |
VF3.00002: Presheaths are a useful concept; their role in establishing anisotropy at the sheath edge Noah Hershkowitz, Greg Severn Presheaths provide ion acceleration to the Bohm velocity. Presheaths are a useful concept for collisionless and weakly collisional plasmas, but their nature and their affects on ions depend on the neutral pressure and the mechanisms of ion production. Presheaths depend on chamber geometry and ion-neutral collisions as the neutral pressure is increased, and cease to be interesting when the collision lengths become comparable to the sheath thickness. They are certainly complicated by the presence of more than one ion species, positive or negative; the question is by how much. At the lowest pressures they affect the spread in the parallel ion velocity distribution function (IVDF), which can be interpreted as the ion ``temperature''. At higher pressures ion-neutral collisions determine the perpendicular ion temperature as well. This talk will consider modifications to the parallel and perpendicular IVDFs (measured with respect to the normal to wafer surfaces) associated with the presence of presheaths, and will try to make sense of out of lots of apparently contradictory experimental results. [Preview Abstract] |
Friday, October 17, 2008 8:30AM - 8:45AM |
VF3.00003: Experimental studies of transverse metastable ion velocity distribution functions in the presheath of a weakly collisional argon plasma Greg Severn, Dongsoo Lee, Noah Hershkowitz Laser-induced fluorescence (LIF) measurements made with a diode laser have measured the transverse metastable ion velocity distribution function profile near a negatively biased plate in a low temperature $(T_e < 1 eV)$, low pressure $(p_0 < 1 mTorr)$ dc multidipole argon discharge plasma. The metastable argon ions in the $3s^23p^4(3P)3d\:^4F_{7/2}$ state are found to be characterized by a Maxwellian temperature transverse to the direction normal to the plate. For a neutral pressure of 0.3mTorr, the transverse temperature increases along the presheath from 0.026 eV in the bulk plasma to 0.058 eV at the presheath sheath boundary. This result is compared with PIC code simulations\footnote{A. Meige, {\em et al.}, Phys. Plasmas, 14, 032104 (2007)} and experimental results\footnote{N. Claire, {\em et al.}, Phys. Plasmas, 13, 062103 (2006)} found in the literature. [Preview Abstract] |
Friday, October 17, 2008 8:45AM - 9:00AM |
VF3.00004: How is the Bohm criterion satisfied in plasmas with several positive ions Miles M. Turner, Derek D. Monahan Under most conditions, ions entering the sheath at the edge of a plasma satisfy the Bohm criterion. When there are several ions present, the Bohm criterion fails to uniquely determine the speeds with which the ions enter the sheath. Instead it prescribes a locus of possible solutions, and in general, we do not know which solution will be realized. In a generalization of the Tonks-Langmuir model, and in other cases where essentially all ions have the same mean free path, it has been shown that the realized solution is that each ion leaves the plasma with its own Bohm speed, which is to say, with the same kinetic energy. This seems intuitively reasonable, because in such cases one may assert that all the ions reaching the sheath edge have traversed the same potential drop. In this paper, we consider a model in which the ion elastic collision frequency is large compared with the ionization frequency. With this assumption, there is a region adjacent to the sheath where the ion fluxes approaching the sheath may be assumed to be constant, and in this region an analytical solution to the transport equations can be found in which the ion motion is mobility limited. For two ion species, this analytical solution is characterized by two dimensionless physical parameters, which are essentially the ratio of the ion fluxes and the ratio of the mean free paths. In this model, the sheath solution must match this bulk transport solution, and this requirement uniquely determines the manner in which the Bohm criterion is satisfied. In fact, one can realize any and every solution of the Bohm criterion by an appropriate choice of the dimensionless parameters. [Preview Abstract] |
Friday, October 17, 2008 9:00AM - 9:15AM |
VF3.00005: Analytical expression for Child-Langmuir sheath edge around a corner T.E. Sheridan An expression for the position of the sheath edge around a two-dimensional corner cathode with included angle $\theta_{c}$ has been discovered. This expression is valid in the Child-Langmuir approximation, i.e., $\phi_{c}\gg kT_{e}/e$, where $-\phi_{c}<0$ is the cathode bias and $T_{e}$ is the electron temperature. In polar coordinates $\left(r,\theta\right)$, the sheath edge is given by $\left(r/s_{0}\right)\sin\left[\pi\theta/\left(2\pi-\theta_{c}\right)\right]=\left[\pi/\left(2\pi-\theta_{c}\right)\right] $ where $s_{0}$ is the planar sheath width far from the corner. This result is verified by comparison with numerical solutions of Watterson [J. Phys. D: Appl. Phys. 22, 1300 (1989)] for a knife edge ($\theta_{c}=0$) and a convex square corner ($\theta_{c}=\pi/2$). The observed agreement suggests that this expression is correct for all corner angles, both convex and concave. [Preview Abstract] |
Friday, October 17, 2008 9:15AM - 9:30AM |
VF3.00006: Langmuir's paradox, wave-particle scattering, and the presheath Scott Baalrud, James Callen, Chris Hegna Langmuir's paradox, perhaps the oldest unsolved mystery of gas discharge physics, is a measurement of anomalous electron scattering near plasma boundaries. In particular, a Maxwellian was reportedly measured much closer to the boundary than the mean free path for electron scattering in a stable plasma; here one should expect truncation of the distribution function corresponding to the sheath potential energy. In this paper we theoretically analyze the presheath region that is present in Langmuir paradox-relevant plasmas ($T_e \gg T_i$). It is shown that the ion-acoustic instability is present throughout the presheath causing amplification of the thermal fluctuations. A collision operator for the plasma kinetic equation including instabilities in a finite space-time domain is derived which shows that the electron collision frequency is dominated by wave-particle interactions in the presheath by up to 3 orders of magnitude. The collision operator satisfies the Boltzmann $\mathcal{H}$-theorem, so the only equilibrium is a Maxwellian which is achieved at a rate depending on collisionality. Wave-particle scattering shrinks the electron mean free path to within $\sim$cm for these discharges showing that one should expect a Maxwellian at the location of the previously reported measurements. [Preview Abstract] |
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