Glenn Joyce

Statistical mechanics of “negative temperature” states

The dynamics of two‐dimensional interacting “line” vortices is identical to that of the two‐dimensional electrostatic guiding center plasma. Both are Hamiltonian systems and are therefore susceptible to statistical mechanical treatments. The predictions of the microcanonical ensemble are explored for this sytem. Interest focuses primarily on the regime in which the interaction energy is high enough to be above the Onsager “negative temperature” threshold. Calculations of the probability distribution for a component, by means of the central limit theorem, are carried out in the manner of Khinchin. The probability distribution of a component reduces to the usual Gibbs distribution in the regime of positive temperatures, and is still explicitly calculable for negative temperatures. The negative temperature states are neither quiescent nor spatially uniform. Expressions for the temperature are explicitly provided in terms of the total particle energy and particle number. A BBGKY hierarchy can be derived for b...

SHOCK-LIKE SOLUTIONS OF THE ELECTROSTATIC VLASOV EQUATION.

It is shown how to construct shock-like time independent solutions of the electrostatic Vlasov and Poisson Equations in one dimension. The positive ions are assumed to be at zero temperature. The electrostatic potential is assumed to increase monotonically through the shock from zero to a constant value. The most important feature of the solution is a population of trapped electrons in the shocked plasma. In contrast to time-independent solutions based upon fluid equations, there is no upper limit on the amplitude of the shock.

Numerical simulation of the plasma double layer

A one-dimensional particle-in-cell computer simulation is used to model the formation of an electrostatic double layer. The conditions for the onset of the layer formation are explored and a relation between the length of the layer and the electrostatic potential difference across is found.

Numerical simulation of plasma double layers

Numerical simulation results are presented for a plasma double layer, the computer model being a finite one-dimensional particle-in-cell plasma with specified potential difference across the system. A single pulse is formed which crosses the system with constant velocity; this is followed by the formation of a potential drop across a limited region of the plasma. An approximate expression relating the spatial extent of the double layer and the potential drop is presented. Electron and ion beams are generated which tend to lead to instabilities in the upstream and downstream regions.

NUMERICAL INTEGRATION METHODS OF THE VLASOV EQUATION.

Abstract The methods of integrating the nonlinear Vlasov equation are reviewed, compared and interrelations are investigated. Another method is given which allows a truncation of the resulting infinite matrix without causing numerical instabilities. Its application to the linear and nonlinear Vlasov equation is discussed. It is shown that the cause for numerical instability is based on approximating a continuous eigenvalue spectrum by a discrete spectrum.

Self-consistent modeling of equatorial dawn density depletions with SAMI3

[1] Large-scale, dawn density depletions in the equatorial ionosphere have been observed by instruments on the STPSat1 and CHAMP satellites. The Naval Research Laboratory (NRL) ionosphere model SAMI3 (Sami3 is Also a Model of the Ionosphere) is used to study this new phenomenon using a self-consistent electric field. Two empirical Horizontal Wind Models (HWM) are used in the simulation study: HWM93 and HWM07. Dawn density depletions are found using HWM07 but not with HWM93. The cause of the depletions is a post-midnight enhancement of the eastward electric field that generates an upward plasma drift. This drift lifts low density plasma to high altitudes (i.e., ~600 km). We compare our model results to remote sensing data and to in situ satellite data.

DISPERSION OF ION--ACOUSTIC WAVES.

The dispersion of ion‐acoustic waves in quiescent rare‐gas discharge plasmas has been investigated experimentally and theoretically. Experimentally, various grid systems were used to generate the waves which were studied using a time‐of‐flight technique. The experimental results show that two separate propagating phenomena appear. The slower propagating disturbance is the ion‐acoustic wave, obeying the theoretically predicted dispersion behavior. The faster propagating disturbance, though superficially resembling a wave, is composed of bursts of ions produced by the driving potentials placed on the grids and would appear to be related to the “free streaming” term found by Landau. Previous theoretical models of ion‐wave propagation have untilized either purely initial‐value or steady‐state, boundary‐value calculations. A model is presented which more nearly simulates the experimental time‐of‐flight studies of finite packets of ion waves generated by finite sine‐wave bursts.

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.

Magnetic field dependence of plasma relaxation times

A previously derived Fokker‐Planck collision integral for an electron plasma in a dc magnetic field is examined in the limit in which the Debye length is greater than the thermal gyroradius, which is in turn greater than the mean distance of closest approach. It is demonstrated that the collision integral can be satisfactorily approximated by the classical Landau value (which ignores the presence of a dc magnetic field) if the following replacement is made: In the Coulomb logarithm, the Debye length is replaced by the gyroradius. This induces a fundamental logarithmic dependence on magnetic field in the relaxation times. Numerical comparison of the asymptotic approximations with the previously derived exact results is made, and good agreement is found. The simplification this introduces into the description of collision processes in magnetized plasmas is considerable.

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.