New Aspects of Plasma Physics

FOREWORD.

CONTENTS.

We present simulation studies of the formation and dynamics of dark solitons and vortices, and of nonlinear interactions between intense circularly polarized electromagnetic (CPEM) waves and electron plasma oscillations (EPOs) dense in quantum electron plasmas. The electron dynamics in the latter is governed by a pair of equations comprising the nonlinear Schrödinger and Poisson system of equations, which conserves electrons and their momentum and energy. Nonlinear fluid simulations are carried out to investigate the properties of fully developed two-dimensional (2D) electron fluid turbulence in a dense Fermi (quantum) plasma. We report several distinguished features that have resulted from our 2D computer simulations of the nonlinear equations which govern the dynamics of nonlinearly interacting electron plasma oscillations (EPOs) in the Fermi plasma. We find that a 2D quantum electron plasma exhibits dual cascades, in which the electron number density cascades towards smaller turbulent scales, while the electrostatic potential forms larger scale eddies. The characteristic turbulent spectrum associated with the nonlinear electron plasma oscillations determined critically by quantum tunneling effect. The turbulent transport corresponding to the large-scale potential distribution is predominant in comparison with the small-scale electron number density variation, a result that is consistent with the classical diffusion theory. The dynamics of the CPEM waves is also governed by a nonlinear schrödinger equation, which is nonlinearly coupled with the nonlinear Schrödinger equation of the EPOs via the relativistic ponderomotive force, the relativistic electron mass increase in the CPEM field, and the electron density fluctuations. The present governing equations in one spatial dimension admit stationary solutions in the form a dark envelope soliton. The dynamics of the latter reveals its robustness. Furthermore, we numerically demonstrate the existence of cylindrically symmetric two-dimensional quantum electron vortices, which survive during collisions. The nonlinear equations admit the modulational instability of an intense CPEM pump wave against EPOs, leading to the formation and trapping of localized CPEM wave pipes in the electron density hole that is associated with a positive potential distribution in our dense plasma.

Plasmas are usually described using classical equations. While this is often a good approximation, where are situations when a quantum description is motivated. In this paper we will include several quantum effects, ranging from particle dispersion, which give raise to the so called Bohm potential, to spin effects, and to quantum electrodynamical effects. The later effects appears when the field strength approaches the Schwinger critical field, which may occur in for example astrophysical systems. Examples of how to model such quantum effects will be presented, and the phenomena resulting from these models will be discussed.

Quantum plasmas is a rapidly expanding field of research, with applications ranging from nanoelectronics, nanoscale devices and ultracold plasmas, to inertial confinement fusion and astrophysics. Here we give a short systematic overview of quantum plasmas. In particular, we analyze the collective effects due to spin using fluid models. The introduction of an intrinsic magnetization due to the plasma electron (or positron) spin properties in the magnetohydrodynamic limit is discussed. Finally, a discussion of the theory and examples of applications is given.

There are important areas within which conventional electromagnetic theory and its combination with quantum mechanics does not provide fully adequate descriptions of physical reality. These difficulties are not removed by and are not directly associated with quantum mechanics. Instead electromagnetic field theory is a far from completed area of research, and modified forms of it have been elaborated by several investigators during the recent decades. The investigation to be described here has the form of a Lorentz and gauge invariant theory which is based on a nonzero electric field divergence in the vacuum state. It aims beyond Maxwell's equations and leads to new solutions of a number of fundamental problems. The applications include a model of the electron with its point-charge-like nature, the associated self-energy problem, the radial force balance, and a quantized minimum of the elementary electronic charge. There are further applications on the individual photon and on light beams, in respect to the angular momentum (spin), the spatially limited geometry, the associated needle radiation, and the particle-wave nature, such as in the photoelectric effect and in two-slit experiments at low light intensities.

The quantum methodologies useful for describing in a unified way several problems of nonlinear and collective dynamics of fluids, plasmas and beams are presented. In particular, the pictures given by the Madelung fluid and the Moyal-Ville-Wigner phase-space quasidistribution, including the related quantum tools such as marginal distributions for the tomographic representations, are described. Some relevant applications to soliton and modulational instability theories are presented.

We discuss collective effects that can be relevant in cold atom physics. Similarities with plasma physics are emphasized. Both neutral and ionized atomic clouds are considered. We establish the basic frequencies and wave modes of a cloud of ultra-cold neutral atoms confined in a magneto-optical trap. The existence of a hybrid mode, Tonks-Dattner resonances and Mie oscillations are studied. Landau damping and resonant neutral atom-density wave interactions are also considered. Finally, free expansion and ambipolar diffusion regimes for a cold ionized cloud of atoms are discussed.

The nonlinear development of the nonrelativistic Rayleigh-Taylor instability of a fluid (plasma) system is investigated within the thin foil model (long wavelength approximation). Explicit solutions are obtained for two- and three-dimensional configurations with the help of various mathematical techniques that include Lagrange variables, complex variable representations, Lie Symmetry transformations and the Hodograph transformation.

The effective ion acceleration during the interaction of an ultra short and ultra intense laser pulse with matter is possibly one of most important results in the investigation of the interaction of multi-terawatt and petawatt power laser pulses with plasmas. At high laser intensities a very efficient acceleration regime has been predicted where the radiation pressure of the laser pulse plays a major role. The stability of this regime against the onset of the relativistic Rayleigh-Taylor instability is investigated.

A theoretical model for the generation of 'seed' magnetic field and plasma flow on galactic scales driven by externally given baro-clinic vectors is presented. The incompressible plasma fields can grow from zero values at initial time t = 0 from a non-equilibrium state T_e ≠ T_i (where T_e(T_i) are electron(ion) temperatures, respectively) due to pressure gradients. An exact analytical solution of the set of two fluid equations is obtained which is valid for both small and large plasma β-values. The magnetic field generated by this mechanism has three dimensional structure. Weaknesses of previous single fluid models for seed magnetic field generation are also pointed out. The estimate of the magnitude of the galactic seed magnetic field turns out to be 10^-15 G and may vary depending upon the scale lengths of the density and temperature gradients. The seed magnetic field may be amplified later by αω-dynamo (or by some other mechanism) to the present observed values of ~ (2 - 10)μG. The theory has been applied to laser-induced plasmas as well and the estimate of the magnetic field's magnitude is in agreement with the experimentally observed values.

A theory of finite-amplitude mirror type waves in non-Maxwellian space plasmas is developed. The collisionless kinetic theory in a guiding center approximation, modified for accounting the effects of the finite ion Larmor radius effects, is used as the starting point. The model equation governing the nonlinear dynamics of mirror waves near instability threshold is derived. In the linear approximation it describes the classical mirror instability with the linear growth rate expressed in terms of an arbitrary ion distribution function. In the nonlinear regime the mirror waves form solitary structures that have the shape of magnetic holes. The formation of such structures and their nonlinear dynamics has been analyzed both analytically and numerically. It is suggested that the main nonlinear mechanism responsible for mirror instability saturation is associated with modification (flattening) of the shape of the background ion distribution function in the region of small parallel particle velocities. The width of this region is of the order of the particle trapping zone in the mirror hole. Near the mirror instability threshold the saturation arises before its width reaches the ion thermal velocity. The nonlinear mode coupling effects in this approximation are smaller and unable to take control over evolution of the space profile of saturated mirror waves or lead to their magnetic collapse. This results in the appearance of quasi-stable solitary mirror structures having the form of deep magnetic depressions. The relevance of the theoretical results to recent satellite observations is stressed.

We briefly review recent asymptotic and phenomenological models, aimed to understand the formation of pressure-balanced mirror structures, in the form of magnetic holes and humps, observed in the solar wind and in planetary magnetosheaths, and also obtained by direct numerical simulations of the Vlasov-Maxwell equations.

Large amplitude Alfvén waves are frequently found in magnetized space and laboratory plasmas. Our objective here is to discuss the linear and nonlinear properties of dispersive Alfvén waves (DAWs) in a uniform magnetoplasma. We first consider the effects of finite frequency (ω/ω_ci) and ion gyroradius on inertial and kinetic Alfvén waves, where ω_ci is the ion gyrofrequency. Next, we focus on nonlinear effects caused by the dispersive Alfvén waves. Such effects include the plasma density enhancement and depression by the Alfvén wave ponderomotive force, nonlinear interactions among the DAWs, the generation of zonal flows by the DAWs, as well as the electron and ion heating due to wave-particle interactions. The relevance of our investigation to the appearance of nonlinear dispersive Alfvén waves in the Earth's auroral acceleration region, in the solar corona, and in the Large Plasma Device (LAPD) at UCLA is discussed.

The stability is discussed of the drift-Alfvén wave which is driven by the equilibrium density gradient, in both unbounded and bounded, collisional plasmas, including the effects of both hot ions and a finite ion Larmor radius. The density gradient in combination with the electron collisions with heavier plasma species is the essential source of the instability of the electrostatic drift mode which is coupled to the dispersive Alfvén mode. In the analysis of modes in an unbounded plasma the exchange of identity between the electrostatic and electromagnetic modes is demonstrated. Due to this, the frequency of the electromagnetic part of the mode becomes very different compared to the case without the density gradient. In the case of a bounded plasma the dispersion properties of modes involve a discrete poloidal mode number, and eigen-functions in terms of Bessel functions with discrete zeros at the boundary. The results are applied to the solar plasma.

A physical background is presented and an analytical description is given for the electrostatic drift mode in partially ionized magnetized plasmas with inelastic collisions. In such plasmas the creation of plasma particles is balanced by a certain number of phenomena in which ions and electrons are lost. Dispersion equation is derived for the drift mode, with the appropriate instability conditions, indicating that inelastic collisions can make the mode unstable.

The physics of Alfvén waves in weakly ionized plasmas like the solar photosphere is discussed. The magnetization and the collision frequencies of the plasma constituents are quantitatively examined. It is shown that the ions and electrons in the photosphere are both un-magnetized, their collision frequency with neutrals is much larger than the gyro-frequency. This implies that eventual Alfvén-type electromagnetic perturbations must involve the neutrals as well. It follows that in the presence of perturbations the whole fluid (plasma + neutrals) moves, the Alfvén velocity includes the total (plasma + neutrals) density and is thus considerably smaller compared to the collision-less case, the perturbed velocity of a unit volume, which now includes both plasma and neutrals, becomes much smaller compared to the ideal (collision-less) case, and finally the corresponding wave energy flux for the given parameters becomes much smaller compared to the ideal case.

A fluid and kinetic analysis is presented of the ion sound mode in a weakly ionized collisional plasma in the regime when the ion collision frequency exceeds the ion gyro-frequency while the electrons remain magnetized. Under these conditions, an ion sound wave can propagate at arbitrary angles with respect to the direction of the magnetic field. In the presence of an electron flow along the magnetic lines the sound mode can grow. Due to the electron collisions the mode is unstable while ion collisions cause an angle dependent instability threshold which is such that the mode is most easily excited at very large angles. Hot ion effects in one part of the work are included by means of an effective viscosity which effectively describes the ion Landau damping effect. In the presence of an additional light ion specie, the mode frequency and increment in a certain parameter range are increased.

Several additional effects are discussed, including the electron-ion collisions, the perturbations of the neutral gas, and the electromagnetic perturbations. The electron-ion collisions are shown to modify the previously obtained angle dependent instability threshold for the driving electron flow. The inclusion of the neutral dynamics implies an additional neutral sound mode which couples to the current driven ion acoustic mode, and these two modes can interchange their identities in certain parameter regimes. The electromagnetic effects, which in the present model imply a bending of the magnetic field lines, result in a further destabilization of an already unstable ion acoustic wave.

In the case when the ion collision frequency is arbitrary the ion species is to be described by a collisional Boltzman kinetic equation. In the same time the electron collision frequency is high enough so that the fluid description is used for the electrons in the presence of an electron drift in the perpendicular direction. This results in the instability of accidentally excited ion sound oscillations, which turn out to be highly unstable for practically all physically acceptable values of the electron drift. In addition, the presence of a population of hotter electrons is shown to reduce the perpendicular electron drift and to increase the instability threshold.

After introducing the basic multifluid model equations, this review discusses three different methods to describe nonlinear plasma waves, by giving a rather general overview of the relevant methodology, followed by a specific and recent application. First, reductive perturbation analysis is applicable to waves that are not too strongly nonlinear, if their linear counterparts have an acoustic-like dispersion at low frequencies. It is discussed for electrostatic modes, with a brief application to dusty plasma waves. The typical paradigm for such problems is the well known KdV equation and its siblings. Stationary waves with larger amplitudes can be treated, i.a., via the fluid-dynamic approach pioneered by McKenzie, which focuses on essential insights into the limitations that restrict the range of available solitary electrostatic solutions. As an illustration, novel electrostatic solutions have been found in plasmas with two-temperature electron species that are relevant in understanding certain magnetospheric plasma observations. The older cousin of the large-amplitude technique is the Sagdeev pseudopotential description, to which the newer fluid-dynamic approach is essentially equivalent. Because the Sagdeev analysis has mostly been applied to electrostatic waves, some recent results are given for electromagnetic modes in pair plasmas, to show its versatility.

The occurrence of amplitude-modulated electrostatic and electromagnetic wavepackets in pair plasmas is investigated. A static additional charged background species is considered, accounting for dust defects or for heavy ion presence in the background. Relying on a two-fluid description, a nonlinear Schrödinger type evolution equation is obtained and analyzed, in terms of the slow dynamics of the wave amplitude. Exact envelope excitations are obtained, modelling envelope pulses or holes, and their characteristics are discussed.

We study two important classes [viz. dust-ion acoustic (DIA) and dust-acoustic (DA)] of electro-acoustic solitary waves in dusty plasmas. We employ the reductive perturbation method for small but finite amplitude solitary waves as well as the pseudo-potential approach for arbitrary amplitude ones. We analyze the effects of positive ions, nonplanar geometry and dust charge fluctuation on DIA solitary waves. On the other hand, we examine the effects of non-isothermal (vortex-like and nonthermal) ion distributions and positive dust on DA solitary waves. It has been reported that the effects, which are included in DIA (DA) solitary waves, do not only significantly modify the basic features of DIA (DA) solitary waves, but also introduce some important new features. The basic features and underlying physics of DIA and DA solitary waves, which are relevant to space and laboratory dusty plasmas, are briefly discussed.

Significant amount of dust will be produced in the next generation magnetic fusion devices due to plasma-wall interactions. The dust inventory must be controlled as it can pose a safety hazard and degrade performance. Safety concerns are due to tritium retention, dust radioactivity, toxicity, and flammability. Performance concerns include high-Z impurities carried by dust to the fusion core that can reduce plasma temperature and may even induce sudden termination of the plasma. Questions regarding dust in magnetic fusion devices therefore may be divided into dust safety, dust production, dust motion (dynamics), characteristics of dust, dust-plasma interactions, and most important of all, can dust be controlled in ways so that it will not become a severe problem for magnetic fusion energy production? The answer is not apparent at this time, which has motivated this work. Although dust safety and dust chemistry are important, our discussions primarily focus on dust physics. We describe theoretical frameworks, mostly due to dust research under a nonfusion context, that have already been established and can be used to answer many dust-related questions. We also describe dust measurements in fusion devices, numerical methods and results, and laboratory experiments related to the physics of fusion dust. Although qualitative understanding of dust in fusion has been or can be achieved, quantitative understanding of most dust physics in magnetic fusion is still needed. In order to find an effective way to deal with dust, future research activities include better dust diagnosis and monitoring, basic dusty plasma experiments emulating fusion conditions (for example, by using a mockup facility), numerical simulations bench-marked by experimental data, and development of a new generation of wall materials for fusion, which may include wall materials with engineered nanostructures.

A skin size (k_⊥ ≲ ω_pe/c) plasma mode characterized by a dispersion relation ω ≃ ck_⊥k_∥/k_De (k_De the electron Debye wavenumber), adiabatic ions, and ω≪ k_∥v_Te, in a uniform plasma is destabilized in the tokamak geometry by a modest electron temperature gradient η_e and ballooning parameter α_e. When unstable, a large electron thermal diffusivity emerges because of the cross-filed wavelength much longer than that of the conventional electron temperature gradient (ETG) mode.

Parallel and perpendicular plasma flow velocity shears are independently controlled and superimposed in fully-ionized collisionless magnetized plasmas using a modified plasma-synthesis method with concentrically three-segmented electron and ion emitters. The fluctuation amplitude of the drift wave which has an azimuthal mode number m = 3 is observed to increase with increasing the parallel shear strength in the absence of the perpendicular shear. When the perpendicular shear is superimposed on the parallel shear, the drift wave of m = 3 changes into that of m = 2. Furthermore, the parallel shear strength required for the excitation of the drift wave becomes large with a decrease in the azimuthal mode number. Introduction of hybrid ions, i.e., superposition of two kinds of positive ions, is found to cause unexpected stabilization of the drift wave.