Landau Damping and Debye Shielding
Landau damping in collisionless plasma - Debye shielding of electrostatic plasma perturbation
ELECTROSTATIC SHIELDING↗
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Debye shielding in stark broadening of isolated helium I lines
Debye shielding in stark broadening of isolated helium I lines
STARK EFFECT↗
Classical path broadening functions for a Debye shielded interaction
Procedure to replace electron correlation effects with Debye shielded interaction including classical path broadening functions for Stark effects
Cooper, J.↗
On the generalized formulation of Debye shielding in plasmas
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G. Livadiotis↗
Generalized slab universal instability and its appearance in pair plasma
In this work, a generalized linear dispersion relation of electromagnetic slab universal modes is derived, taking into account arbitrary ion charge state, electron finite Larmor radius (FLR) effects, and Debye shielding effects. As a consequence, it provides more accurate predictions and is applicable to a wider range of plasmas. We find that electron FLR effects have a weakly stabilizing effect on the slab universal instability in electron–ion plasma, while Debye shielding strongly stabilizes this instability when λ D approaches ρ i (λ D is the Debye length and ρi is the ion gyroradius). In particular, we examine the stability criterion for this instability in electron–positron pair plasmas and find that the instability persists in this simplest plasma system as long as the pair plasma number density exceeds the critical value n c = B 2 /(8πm e c 2 ).
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Fast correlation heating in moderately coupled electron–ion plasmas
If the electrons in a plasma are suddenly heated, the resulting change in Debye shielding causes the ion kinetic energy to quickly increase. For the first time, this correlation heating , which is much faster than collisional energy exchange, is rigorously derived for a moderately coupled, electron–ion plasma. The electron–ion mass ratio is taken to be the smallest parameter in the Bogoliubov–Born–Green–Kirkwood–Yvon hierarchy, smaller even than the reciprocal of the plasma parameter. This ordering differs from conventional kinetic theory by making the electron collision rates faster than the ion plasma frequency, which allows stronger coupling and makes the ion heating a function only of the total energy supplied to the electrons. The calculation uses known formulae for correlations in a two-temperature plasma, for which a new, elementary derivation is presented. Suprathermal ions may be created more rapidly by this mechanism than by ion–electron Coulomb collisions. This means that the use of a femtosecond laser pulse could potentially help to achieve ignition in certain fast ignition approaches to inertial confinement fusion.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Fractional Laplacian spectral approach to turbulence in a dusty plasma monolayer
This work presents an analytical investigation of anomalous diffusion and turbulence in a dusty plasma monolayer, where energy transport across scales leads to the spontaneous formation of spatially disordered patterns. Many-body simulations of 10,000-particle dusty plasma monolayers are used to demonstrate how the global dynamics depend on the statistical properties of the dust assembly for realistic laboratory conditions. We find that disorder due to variations in the dust size distribution and charge-driven nonlocal interactions resulting in anomalous dust diffusion are key factors for the onset of instabilities. The resulting dynamics exhibit features of inertial turbulence over slightly more than half a decade of scales proportional or smaller than the Debye shielding length. These processes are examined analytically using a recently developed Fractional Laplacian Spectral (FLS) technique, which identifies the active energy channels as a function of scale, disorder concentration, and features of the nonlocal-interactions. The predictions from the theoretical (spectral) analysis demonstrate agreement with the results from the many-body (kinetic) simulations, thus providing a powerful tool for the study of active turbulence.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
On the theory of Stark broadening of spectral lines in a plasma
Stark broadening of spectral lines in argon plasma and need to include Debye shielding effects
Oertel, G. K.↗
Turbulent shear flow of continuum plasma.
The turbulence structure of weakly ionized, continuum plasma is analyzed with emphasis on the turbulent fluctuation and the transport properties of the ionized species. The mean gradients of the velocity and ionized-species concentrations are considered to be uniform. It is assumed that the turbulence Reynolds number is small and that the turbulence field is homogeneous in order to close the dynamic equations of turbulence. It was found that the ratio of the Debye shielding length to the local integral scale of turbulence must be sufficiently small in order for the detailed quasi-neutrality to prevail. The condition of the detailed quasi-neutrality is necessary, in addition to the equal mean concentrations of electrons and ions, in order for the turbulence properties involving the electrons to be the same as those involving the ions.
Chung, P. M.↗
Surface density of accumulated electrons on walls in contact with a plasma
It is shown that the surface density of accumulated electrons on a wall in contact with a plasma can be expressed as a simple function of the Debye shielding distance in the plasma. The result may have applications to problems involving objects immersed in a space plasma.
De, B. R.↗
Collision integrals for the interaction of the ions of nitrogen and oxygen in a plasma at high temperatures and pressures
The corrections to the transport cross-sections and collision integrals for Coulomb interactions arising from the application of realistic interaction energies of the ions of nitrogen and oxygen are investigated. Accurate potential-energy curves from an ab initio electronic-structure calculation and a semiclassical description of the scattering are used to determine the difference between the cross-sections for the real interaction forces and a Coulomb force for large values of the Debye shielding parameter. Graphs of the correction to the diffusion and viscosity-collision integrals are presented for temperatures from about 10,000 K to 150,000 K. This correction can be combined with tabulations of the collision integrals for shielded Coulomb potentials to determine the contribution of N(+)-N(+), N(+)-O(+), and O(+)-O(+) interactions to the transport properties of high-temperature air. Analytical forms are fitted to the calculated results to assist this application.
Stallcop, James R.↗
Generation of Kappa Distributions in Solar Wind at 1 au
We examine the generation of kappa distributions in the solar wind plasma near 1 au. Several mechanisms are mentioned in the literature, each characterized by a specific relationship between the solar wind plasma features, the interplanetary magnetic field (IMF), and the kappa index-the parameter that governs the kappa distributions. This relationship serves as a signature condition that helps the identification of the mechanism in the plasma. In general, a mechanism that generates kappa distributions involves a single or a series of stochastic or physical processes that induces local correlations among particles. We identify three fundamental solar wind plasma conditions that can generate kappa distributions, noted as (i) Debye shielding, (ii) frozen IMF, and (iii) temperature fluctuations, each one prevailing in different scales of solar wind plasma and magnetic field properties. Moreover, our findings show that the kappa distributions, and thus, their generating mechanisms, vary significantly with solar wind features: (i) the kappa index has different dependence on the solar wind speed for slow and fast modes, i.e., slow wind is characterized by a quasi-constant kappa index, K (is) approx. 4.3 +/- 0.7, while fast wind exhibits kappa indices that increase with bulk speed; (ii) the dispersion of magnetosonic waves is more effective for lower kappa indices (i.e., further from thermal equilibrium); and (iii) the kappa and polytropic indices are positively correlated, as it was anticipated by the theory.
Livadiotis, G.↗
Collisional simulations of the modulator section in coherent electron cooling
The first section of any coherent electron cooling (CeC) system is the modulator, where the density of the electron beam is modulated by the copropagating ion beam. This density modulation is a result of Coulomb collisions between the individual particles of the two beams. The pairwise, stochastic part of the interactions impacts the overall performance of the CeC process. We present the first simulations of the density modulations of the electron beams from a collisional picture of the dynamics, considering the proof-of-principle CeC experiments at Brookhaven National Laboratory. These simulations were performed using PHAD, which is the first efficient, large-scale collisional numerical method in beam physics that we have previously developed and benchmarked. Realistic beam distributions and external fields have been optimized to provide strong modulation signals necessary for variations of coherent electron cooling systems. Cooling performance limits and potential collisionless simulation pitfalls are pointed out. Published by the American Physical Society 2024
43 PARTICLE ACCELERATORS↗
Lectures on statistical mechanics
Presented here is a transcription of the lecture notes from Professor Allan N. Kaufman’s graduate statistical mechanics course Physics 212A and 212B at the University of California Berkeley from the 1972–1973 academic year. 212A addressed equilibrium statistical mechanics with topics: fundamentals (micro-canonical and sub-canonical ensembles, adiabatic law and action conservation, fluctuations, pressure, and virial theorem), classical fluids and other systems (equation of state, deviations from ideality, virial coefficients and van der Waals potential, canonical ensemble and partition function, quasistatic evolution, grand-canonical ensemble and partition function, chemical potential, simple model of a phase transition, quantum virial expansion, numerical simulation of equations of state, and phase transition), chemical equilibrium (systems with multiple species and chemical reactions, law of mass action, Saha equation, chemical equilibrium including ionization and excited states), and long-range interactions (including Coulomb, dipole, and gravitational interactions, Debye–Hückel theory, and shielding). 212B addressed nonequilibrium statistical mechanics with topics: fundamentals (definitions: realizations, moments, characteristic function, and discrete variables), Brownian motion (Langevin equation, fluctuation–dissipation theorem, spatial diffusion, Boltzmann’s H-theorem), Liouville and Klimontovich equations, Landau equation (derivation, elaboration, and H-theorem, and irreversibility), Markov processes and Fokker–Planck equation (derivations of the Fokker–Planck equation and a master equation), linear response and transport theory (linear Boltzmann equation, linear response theory of Kubo and Mori, relation of entropy production to electrical conductivity, transport relations and coefficients, normal mode solutions of the transport equations, sketch of a generalized Langevin equation method for transport theory), and an introduction to nonequilibrium quantum statistical mechanics.
plasma dynamics↗
Collaborative Research: Unravelling the Physics Associated with the Production of Extremely Dense Plasma States of Microscale (Final Report) Nanosecond-pulsed Discharges
The aim of this project is to study and establish the physical mechanisms that contribute to the formation of anomalously dense plasmas in high-pressure nanosecond-pulsed discharges. These discharges have a broad range of applications such as plasma-assisted combustion, plasma flow actuators, biomedical sterilization and exotic materials synthesis. The structure and formation of these discharges, producing high plasma densities of ~10 14 -10 15 cm -3 , are well-studied and understood. Fast-pulsed microscale high-pressure discharges can be driven to even higher densities of > 10 19 cm -3 , approaching warm dense matter conditions. The mechanisms that generate these plasmas have not been understood. Analysis of the warm dense matter state under laboratory conditions is an expensive and non-trivial endeavor. For instance, dense plasmas can be generated by electrical explosions of metal foils and wires. Plasmas generated after the explosion have a short lifetime and often present difficult conditions for diagnostics. Generation of dense plasmas was also achieved during high-voltage nanosecond pulsed discharges when the so-called explosive electron emission is obtained. Unfortunately, this process is very difficult to control for the studies of warm dense matter. In our recent study, we have shown that additional heating of plasma by lasers can further increase the density of plasma and even lead to the fully ionized state. This method, potentially, allows better control of the plasma parameters. In this work, we studied a second stage laser-heated micro-discharge using a self-consistent one-dimensional particle-in-cell Monte Carlo-collision (1D PIC-MCC) model coupled with Maxwell’s equations. We predicted the generation of a fully ionized plasma on the picosecond time scale. However, this model considered the plasma as an ideal gas despite the high pressure and the nearly fully ionized state. The ideal plasma model assumes that the dilute gas approximation is valid, where the inter-particle interactions are negligible. For charged particles this assumption holds as long as the shielded Coulomb potential assumption is valid. For very high plasma densities, this concept breaks down since the Debye sphere surrounding each charged particle no longer contains enough electrons to statistically provide the shielding of the single particle Coulomb interaction potential. At such densities, the plasma can no longer be described as ideal and non-ideal coupling effects need to be considered. In this report, we elucidate our recent work of developing a PIC-MCC model with improvements for non-ideal plasma conditions due to Coulomb coupling at high densities. In particular, we study the interaction of green light radiation and a dense microplasma, and explore the non-ideal plasma effects in this interaction. In this computational model, we implement the two most important non-ideal effects: ionization potential depression (IPD) and enhanced collision cross sections. Our primary goal is to study the physics associated with electromagnetic (EM) wave heating, also called the second-stage wave-heating, and establish the role of plasma non-ideality in this phenomenon. Our secondary goal is to improve the chemistry mechanism of the 1D PIC-MCC model by including a more detailed excited species collision treatment. At high pressures, stepwise ionization from excited species might play an important role in the ionization process. Previously, this ionization mechanism was neglected due to the excitation collision cross section of xenon being smaller than that of ionization. However, a preliminary study showed that the excited species density in the initial microplasma was an order of magnitude higher than the electron density. Therefore, my aim is to determine the significance of this additional ionization pathway to the plasma generation.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Sheath constraints on turbulent magnetised plasmas
Abstract A solid target in contact with a plasma charges (negatively) to reflect the more mobile species (electrons) and thus keep the bulk plasma quasineutral. To shield the bulk plasma from the charged target, there is an oppositely (positively) charged sheath with a sharp electrostatic potential variation on the Debye length scale λ D . In magnetised plasmas where the magnetic field is inclined at an oblique angle α with the target, some of the sheath potential variation occurs also on the ion sound gyroradius length scale ρ S cos α , caused by finite ion gyro-orbit distortion and losses. We consider a collisionless and steady-state magnetised plasma sheath whose thickness l ms ∼ max ( λ D , ρ S cos α ) is smaller than the characteristic length scale L of spatial fluctuations in the bulk plasma, such that the limit l ms / L → 0 is appropriate. Spatial structures are assumed to be magnetic field-aligned. In the case of small magnetic field angle α ∼ δ ≡ ρ S / L ≪ 1 , electric fields tangential to the target transport ions towards the target via E × B drifts at a rate comparable to the one from parallel streaming. A generalised form of the kinetic Bohm–Chodura criterion at the sheath entrance is derived by requiring that the sheath electric field have a monotonic spatial decay far from the target. The criterion depends on tangential gradients of potential and ion distribution function, with additional nontrivial conditions.
kinetic Bohm–Chodura condition↗
The Diagnostics of the External Plasma for the Plasma Rocket
Three regions of plasma temperature/energy are being investigated to understand fully the behavior of the plasma created by the propulsion device and the operation of the RPA. Each type of plasma has a RPA associated with it; i.e. a thermal RPA, a collimated RPA, and a high temperature RPA. Through the process of developing the thermal and collimated RPAs, the proper knowledge and experience has been gained to not only design a high temperature RPA for the plasma rocket, but to understand its operation, results, and uncertainty. After completing a literature search for, reading published papers on, and discussing the operation of the RPA with electric propulsion researchers, I applied the knowledge gained to the development of a RPA for thermal plasma. A design of a thermal RPA was made which compensates for a large Debye length and low ionized plasma. From this design a thermal RPA was constructed. It consists of an outer stainless steel casing, a phenolic insulator (outgases slightly), and stainless steel mesh for the voltage screens. From the experience and knowledge gained in the development of the thermal RPA, a RPA for collimated plasma was developed. A collimated RPA has been designed and constructed. It compensate for a smaller Debye length and much higher ionization than that existing in the thermal plasma. It is 17% of the size of the thermal RPA. A stainless steel casing shields the detector from impinging electrons and ions. An insulating material, epoxy resin, was utilized which has a negligible outgassing. This material can be molded in styrofoam and machined quite nicely. It is capable of withstanding moderately high temperatures. Attached to this resin insulator are inconel screens attached by silver plated copper wire to a voltage supply. All the work on the RPAs and thermal ion source, I performed in the University of Alabama in Huntsville's (UAH) engineering machine shop.
Karr, Gerald R.↗
Dispersion of modified fumed silica in elastomeric nanocomposites
In polymer nanocomposites, surface modification of silica aggregates can shield Coulombic interactions that inhibit agglomeration and formation of a network of agglomerates. Surface modification is usually achieved with silane coupling agents although carbon-coating during pyrolytic silica production is also possible. Pyrogenic silica with varying surface carbon contents were dispersed in styrene-butadiene (SBR) rubber to explore the impact on hierarchical dispersion, the emergence of meso-scale structures, and the rheological response. Pristine pyrogenic silica aggregates at concentrations above a critical value (related to the Debye screening length) display correlated meso-scale structures and poor filler network formation in rubber nanocomposites due to the presence of silanol groups on the surface. Here, in the present study, flame synthesized silica with sufficient surface carbon monolayers can mitigate the charge repulsion thereby impacting network structural emergence. The impact of the surface carbon on the van der Waals enthalpic attraction, a * , is determined. The van der Waals model for polymer nanocomposites is drawn through an analogy between thermal energy, k B T, and the accumulated strain, γ. The rheological response of the emergent meso-scale structures depends on the surface density of both carbon and silanol groups.
36 MATERIALS SCIENCE↗