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Notes: In the limit of a small Debye length (λD→0) the plasma boundary layer in front of a negative absorbing wall is split up into a collision-free planar space charge sheath and a quasineutral presheath, where the ions are accelerated to fulfill the Bohm criterion. Apart from ion inertia, the mechanism of the presheath depends on an additional effect controlling the ion field acceleration. The present paper considers a stationary presheath dominated by the deflection of the ion orbits in a magnetic field parallel to the wall. The ion transport is provided by charge exchange collisions with cold neutrals. The potential profiles and ion distributions resulting from the self-consistent kinetic analysis are compared with expectations based on a previous hydrodynamic model. The transition from "closed'' to "open'' ion orbits results in typical deviations near the sheath edge. The kinetic Bohm criterion is found to be fulfilled marginally. © 1996 American Institute of Physics.

Notes: One-dimensional particle simulations are performed to study the influence of a strong magnetic field on the plasma boundary layer in front of a completely absorbing wall. The magnetic field lines are parallel to the wall, and the ion transport is provided by charge exchange collisions with cold neutrals. The Debye length is small compared with the ion gyroradius and the electrons are Boltzmann distributed. A modified Particle-in-Cell Monte-Carlo-Collision (PIC-MCC) code is developed to avoid the problem of different time scales of electrons and ions. The self-consistent steady-state simulation is performed for a system with one spatial coordinate and two velocity components (1d, 2v). The results are compared with corresponding results of a self-consistent stationary solution of the ion Boltzmann equation. Although the potential and density profiles are essentially confirmed, the ion velocity distribution functions disagree with analytic solutions in certain singular regions unless certain pertubations in the electric field are suppressed. It is shown that this is due to a microscopic instability of the stationary solution. © 1998 American Institute of Physics.

Notes: A kinetic analysis is presented to study the influence of a strong oblique magnetic field on the plasma boundary layer in front of an absorbing wall. The ion transport is provided by (a) magnetic field lines intersecting the wall and (b) by charge exchange collisions with neutrals. The Debye length λD is small compared with the ion gyroradius ρi and the electrons are Boltzmann distributed. For the limiting case λD→0 and cold neutrals, an efficient method is developed to calculate the self-consistent stationary solution of the ion Boltzmann equation. The resulting ion distribution functions exhibit an involved structure. The kinetic Bohm-criterion is found to be fulfilled marginally. To investigate the stability of the solution, the analysis is supplemented by a particle simulation. It is shown that the involved structure of the stationary ion velocity distribution is smeared out (a) by an ion cyclotron instability (cold gas) and (b) by a finite gas temperature. The potential profiles and ion distributions resulting from the self-consistent kinetic analysis are compared with expectations based on a previous hydrodynamic model. © 1999 American Institute of Physics.

Notes: The temporal evolution of a collisionless ion matrix sheath in front of an electrode biased to a pulsed high negative voltage is investigated analytically and numerically. In the relaxation process a matrix extraction phase and a subsequent sheath expansion phase can be distinguished. For the matrix extraction phase we present an analytical model that is based on special solutions of the ion fluid equations and that is free of artificial assumptions. The model results in an explicit formula for the ion current to the electrode. The results are compared with numerical solutions of the ion fluid equations and show excellent agreement. By a simple parameter ansatz the model is extended to describe the sheath expansion phase. © 1999 American Institute of Physics.

Notes: The sheath and presheath relaxation in front of an electrode biased to high negative voltage pulses is investigated on the basis of ion fluid equations as well as of a particle-in-cell/Monte Carlo simulation. The electrons are assumed to be Boltzmann distributed and the ions are governed by charge exchange collisions. The electron Debye length is small compared to the ion mean free path. Switching on a high negative voltage, three phases on different time scales may be distinguished: the matrix extraction phase, the sheath expansion phase, and the presheath relaxation initiated by a rarefaction wave. Correspondingly, switching off a high negative voltage results in a fillup process followed by a sheath constriction and by a compression wave rearranging the presheath. All these phenomena are mixed if voltage pulses of finite duration are applied. We present numerical results exhibiting typical relaxation phenomena for single pulses as well as for periodic pulses with various frequencies and pulse forms. Results for the particularly important matrix extraction phase are compared with an analytic step model of the homogeneous matrix sheath [K.-U. Riemann and Th. Daube, J. Appl. Phy. 86, 1202 (1999)]. © 2002 American Institute of Physics.

Notes: Natural convection in a differentially heated horizontal cylinder is investigated numerically and analytically. Particular attention is paid to the structure of steady convection, the nature of the transients and the onset of unsteadiness for a range of Prandtl numbers extending from 0.7 to infinity. The numerical algorithm integrates the 2-D Navier-Stokes equations in velocity-pressure formulation with a Chebyshev-Fourier spatial approximation. A gradual shift from the conduction to the boundary layer regime is observed for increasing Rayleigh number and the steady flow structure becomes rapidly independent of Pr. Whereas classical scalings are obtained for the azimuthal velocity and the thermal boundary layer thickness, the dynamic boundary layer thickness is found to be independent of the Prandtl number. A simplified semi-analytical model derived from projecting the governing equations on the lowest Fourier modes is proposed, which explains this property. Its solutions are in good quantitative agreement with the full nonlinear solutions in particular for large Prandtl numbers. For large enough Rayleigh values, the transients are found to be dominated by internal waves and the approach to steady state is achieved in an oscillatory manner by decay of internal wave motion. In the steady boundary layer regime, the average Nusselt number classically scales like Ra1/4 and a correlation valid over the range of Prandtl numbers considered is 0.28Ra1/4. The onset of unsteadiness is investigated either by direct numerical integration or by linear stability analysis which combines Newton's iterations to determine the unstable steady states and Arnoldi's method to compute the eigenvalues of largest real part of the linearized evolution operator about a steady state. It is thus found that the steady state solution undergoes a Hopf bifurcation and that depending on the Prandtl number the most unstable eigenvector may break or keep the symmetry of the base flow. The critical Rayleigh number is found to achieve an asymptotic value for large enough Prandtl number. The location of the hottest point is also shown to have a very large effect on the critical value. Finally, time integration of the unsteady nonlinear equations indicates that the Hopf bifurcation seems of supercritical type for values of the Prandtl number up to 9 and possibly subcritical for larger Pr values. © 1997 American Institute of Physics.