Martin Lampe

Interactions between dust grains in a dusty plasma

Dust grains in plasma acquire a large negative charge, and can constitute a strongly coupled system. If the plasma is stationary, the plasma-mediated electrostatic potential around a single grain can be calculated by orbital-motion-limited (OML) theory, including ion absorption at the grain surface. This potential is repulsive at all ranges, and falls off as r−2 at long range. Nonlinear modifications occur when there are several grains, but the interaction is still repulsive. If the plasma is streaming by the grains, each grain generates a wake field potential which can be calculated via linear response theory, and which attracts other grains to stationary points behind the grain. There is in addition an attractive force between grains, due to ion-impact momentum deposition. In certain parameter regimes, this “shadowing” force can yield a weak net attraction at long range. Trapped-ion effects are significant at high plasma density, but have not yet been calculated.

Trapped ion effect on shielding, current flow, and charging of a small object in a plasma

The problem of electrostatic shielding around a small spherical collector immersed in nonflowing plasma, and the related problem of electron and ion flow to the collector, date to the origins of plasma physics. Calculations have typically neglected collisions, on the grounds that the mean free path is long compared to the Debye length. However, it has long been suspected that negative-energy trapped ions, created by occasional collisions, could be important. This paper presents self-consistent analytic calculations of the density and distribution function of trapped and untrapped ions, the potential profile, the ion and electron current to the collector, and the floating potential and charge of the collector. Under typical conditions for dust grains immersed in a discharge plasma, trapped ions are found to dominate the shielding near the grain, substantially increase the ion current to the grain, and suppress the floating potential and grain charge, even when the mean free path is much greater than the Debye length.

Interaction of electromagnetic waves with a moving ionization front

The problem of an electromagnetic wave packet, incident on a relativistically moving plane ionization or recombination front in a stationary gas, is considered. The frequency of the reflected wave packet is found to obey the usual double Doppler shift relation. However, the reflection coefficients and the physics can differ significantly from the case of reflection from moving material objects. In the unmagnetized case, the ratio of the energy in the reflected wave packet to that in the incident wave packet is found to be er*/ei*=ωi*/ωr* for an oncoming overdense ionization front, for which ωi*<ωr* (where ωi* and ωr* are the incident and reflected wave frequencies in the laboratory frame). For an oncoming ionization front in the presence of an applied magnetic field normal to the front, er*/ei* can considerably exceed ωi*/ωr*. For a retreating recombination front (ωi*≳ωr*), in the overdense unmagnetized case, er*/ei*=ωr*/ωi*. These results have important implications for the production of sub‐millimeter w...

Theory and Simulation of the Beam Cyclotron Instability

A detailed theory in conjunction with the results of computer simulation experiments is presented for the beam cyclotron instability. The main results are (1) After a period of exponential quasilinear development, turbulent wave‐particle interactions cause cross‐field diffusion of the electrons which smears out the electron gyroresonances. This occurs at a level of turbulence which scales as Σκ(| Eκ |2/4πN0Te)∼(Ωe/ωe)2(Ωe/kve), where Ωe and ωe are the electron cyclotron and plasma frequencies, and results in a transition to ordinary ion sound modes that would occur in an unmagnetized plasma. The magnetic field serves to reduce the effects of electron trapping. (2) This level of turbulence appears to have virtually no effect on long wavelength fluid modes. (3) At this level the instability stabilizes if ordinary ion sound is stable due to ion Landau damping. For cold ions it continues to develop at the slower ion acoustic growth rate until the fields become strong enough to trap the ions. After the fields ...

Theoretical overview of the large-area plasma processing system (LAPPS)

A large-area plasma processing system (LAPPS) is under development at the Naval Research Laboratory. In the LAPPS, the plasma is generated by a sheet electron beam with voltages and current densities of the order of kilovolts and tens of milliamps per cm2. The plasma dimensions are a metre square by a few centimetres thick. The beam is guided by a magnetic field of 50-300?G. Since an electron beam of this type efficiently ionizes any gas, high electron densities of n~1012-1013?cm-3 are easily generated at 30-100?mTorr background pressure. In addition to large area and high electron density, the LAPPS has advantages for plasma processing. These include independent control of ion and free radical fluxes to the surface, very high uniformity, very low electron temperature (Te, {<}1?eV, but can be controllably increased to a desired value) and a geometry that is well suited for many applications. This paper sketches an initial theoretical overview of issues in the LAPPS and compares aspects of the theory to a preliminary experiment.

Plasma current and conductivity effects on hose instability

Hose instability dispersion relations, which include a self‐consistent treatment of the spatial and temporal evolution of plasma conductivity and plasma current, are derived for a relativistic beam propagating in weakly ionized gas. A simplified conductivity model is used which neglects temperature dependence of the electron mobility. In some regimes the results are dramatically different from those found previously for a beam propagating in a fixed conductivity channel. For example, the hose growth rate is found to decrease with increasing current Ib for a beam propagating in initially neutral gas, even though the plasma return current fraction increases rapidly with Ib. As another example, it is found that an externally driven discharge current can completely eliminate hose instability in a fixed conductivity channel, but causes only a weak decrease in growth rate when the plasma conductivity is modeled self‐consistently. OFF

Structure and dynamics of dust in streaming plasma: dust molecules, strings, and Crystals

In a plasma with ions streaming at a uniform velocity /spl sim/c/sub s/, dust grains can be accurately modeled as particles interacting via the dynamically-screened Coulomb interaction, calculated from linear response theory for the plasma. This force is nonreciprocal, i.e., action does not equal reaction, which has remarkable dynamical consequences. We show that up to four grains can form a stable self-bound molecule, which propels itself upstream against the ion flow. Stable equilibria are also found for pairs of grains confined in harmonic or quartic external potentials. For two grains in an anharmonic potential, or for three or more grains in any potential, there is no conserved quantity and self-excited oscillations can occur. In general, there are multiple equilibria, hysteresis occurs as parameters are varied, and it is not possible to distinguish ground and excited states. We show how the organizational and dynamical principles that govern the behavior of few-grain and low-dimensional systems also elucidate the more complex dynamics of crystals.

Beam-generated plasmas for processing applications

The use of moderate energy electron beams (e-beams) to generate plasma can provide greater control and larger area than existing techniques for processing applications. Kilovolt energy electrons have the ability to efficiently ionize low pressure neutral gas nearly independent of composition. This results in a low-temperature, high-density plasma of nearly controllable composition generated in the beam channel. By confining the electron beam magnetically the plasma generation region can be designated independent of surrounding structures. Particle fluxes to surfaces can then be controlled by the beam and gas parameters, system geometry, and the externally applied rf bias. The Large Area Plasma Processing System (LAPPS) utilizes a 1–5 kV, 2–10 mA/cm2 sheet beam of electrons to generate a 1011–1012 cm−3 density, 1 eV electron temperature plasma. Plasma sheets of up to 60×60 cm2 area have been generated in a variety of molecular and atomic gases using both pulsed and cw e-beam sources. The theoretical basis ...

Quasi-neutral particle simulation of magnetized plasma discharges: general formalism and application to ECR discharges

We have developed an electrostatic particle-in-cell/Monte Carlo (PIC/MC) simulation method for magnetized discharges, in which both internal electric fields and sheath potentials are determined from the requirement of quasineutrality within the bulk plasma, rather than by solving Poissons equation. Thus the electric field is not sensitive to statistical noise which may occur in the small quantity n/sub e/-n/sub i/. Sheaths are treated self consistently as thin potential barriers, and the Bohm criterion for ion flux into the sheath is imposed as a boundary condition. Electron plasma oscillations do not appear in the model, and the debye length is essentially set to zero. Thus time steps and spatial gridding can be chosen to represent the characteristic macroscopic time and space scales of interest, which may be orders of magnitude larger than the plasma frequency/debye length scales. The simulation technique correctly represents kinetic features such as non-Maxwellian distributions and Landau damping and can be used for either collisional or collisionless plasmas. We present results from an axisymmetric simulation of an electron cyclotron resonance (ECR) discharge in low-pressure argon, which show that the discharge is strongly affected by cross-field ion flows, even when the vessel walls are insulators. We also present analytic calculations based on the model, which afford new insights into cross-field transport in a metallic vessel and show that the classic Simon diffusion can be strongly inhibited by the effect of sheath potentials.

Limits of validity for orbital-motion-limited theory for a small floating collector

The orbital-motion-limited (OML) theory has been widely used to calculate the ion response to a charged grain immersed in plasma. The theory assumes there are no potential barriers preventing plasma ions from reaching positive-energy points in phase space. However, Allen et al. [J. Plasma Phys.63, 299 (2000)] have recently shown that for any finite-size negatively charged dust grain in a Maxwellian plasma, there are always potential barriers sufficient to exclude some ions. We calculate the magnitude of the potential barriers, and determine which ions are subject to barriers. The OML theory is shown to become exact in the limit of small grain size, and to be very accurate in calculating ion current to the grain for typical conditions pertinent to dusty plasma. Thus OML theory is well justified in calculating the floating potential. However, we find that potential barriers can influence the shielding of the potential at r ∼ λD under some conditions, especially large grams, high plasma density, and small Ti/Te.