Operator of pair electron-ion collisions in alternating electromagnetic fields

Collisions of electrons with ions in the presence of an alternating electromagnetic field are considered. Based on the first principles (the Liouville equations for N particles), a general expression for the collisional operator in the approximation of pair collisions at an arbitrary scattering potential, including that depending periodically on time, is derived. The problem of collisions in plasma in the presence of an electromagnetic field can be reduced to this case by introducing drift coordinates. It is shown that the method of test particles can be applied to the problem of particle collisions in an alternating electromagnetic field.     

Plasma heating in a variable magnetic field

The problem of particle acceleration in a periodically variable magnetic field that either takes a zero value or passes through zero is considered. It is shown that, each time the field [0]passes through zero, the particle energy increases abruptly. This process can be regarded as heating in the course of which plasma particles acquire significant energy within one field period. This mechanism of plasma heating takes place in the absence of collisions between plasma particles and is analogous to the mechanism of magnetic pumping in collisional plasma considered by Alfvén.     

Multiparticle nature of collisions in plasma and a unique feature of Coulomb interaction

It is shown that the lower limit in the Coulomb logarithm is governed by the collective behavior of a plasma rather than by binary collisions with small impact parameters. For this reason, under the assumption that the particle-to-particle momentum transfer is governed mainly by binary collision, the numerical coefficient in the second moment of the momentum transferred turns out to be overestimated by a factor of two. In other words, the multiparticle character of the lower limit in the Coulomb logarithm governs not only the logarithm itself but also the numerical coefficient in front of it. Correctly incorporating the fluctuation electric fields on spatial scales shorter than or close to the Debye radius (the multiparticle nature of collisions in a plasma) provides a new insight into the physics of Coulomb collisions and leads to the appearance of a new characteristic spatial scale (r _Dr_min)^1/2 in plasma theory. Hence, an almost ideal plasma possesses a unique feature: the existence of a spatial scale that is much shorter than the mean distance between the particles and has no analogues in the systems of particles in which the interaction potential is not of Coulomb origin. The problem is considered in the limit of infinitely large values of the Coulomb logarithm.     

Steady states of a diode with counterstreaming electron and positron beams

Steady states of a plasma layer with counterstreaming beams of oppositely charged particles moving without collisions in a self-consistent electric field are analyzed. The study is aimed at clarifying the mechanism of generation and reconstruction of pulsar radiation. Such a layer also models the processes occurring in Knudsen plasma diodes with counterstreaming electron and ion beams. The steady-state solutions are exhaustively classified. The existence of several solutions at the same external parameters is established.     

Kinetic study of the linear stage of thermocurrent instability in the framework of the Boltzmann equation for a model gas

The linear stage of thermocurrent instability is investigated for a model gas in which the integral of inelastic collisions of electrons with gas particles has a divergent form and the frequencies of elastic and inelastic collisions are independent of the electron velocity. The proposed approach consists in the reduction of the Boltzmann equation for electrons in an inhomogeneous plasma to a set of equations for the moments of the electron velocity distribution function. The instability growth rate and the wave phase velocity as functions of the perturbation wavenumber are calculated, the maximum growth rate and the corresponding wavenumber are determined, and the dependence of these quantities on the degree of plasma quasineutrality is examined. It is demonstrated that the model satisfactorily (both qualitatively and quantitatively) describes the linear stage of thermocurrent instability in helium.     

Splitting of the spectra of MHD waves and the structure of a satellite alfvén resonance in a cold plasma in a strong axial magnetic field and a weak helical field

The possibility is demonstrated of splitting the eigenfrequencies of MHD plasma waves in a stellarator with a weakly rippled helical confining magnetic field. The distribution of the fields of an Alfvén wave in the satellite Alfvén resonance region is investigated when the influence of the helical ripple in a confining magnetic field on the resonance structure is comparable with the effects of the finite ion Larmor radius, electron inertia, and collisions between plasma particles.     

Longitudinal fluctuations in a nonuniform collisional plasma with nonequilibrium particle distributions

The amplitudes of high-frequency longitudinal fluctuations excited by a nonequilibrium source in a nonuniform plasma are calculated. The results obtained are applicable to arbitrary nonequilibrium distributions of plasma particles in the absence of parametric instabilities. The spectra of probing waves scattered by fluctuations in a linear ionospheric plasma layer under conditions typical of experiments on incoherent radio wave scattering are found. The effects of electron-ion collisions and electron temperature anisotropy on the scattering intensity are demonstrated.     

Electron-Ion collisions in relativistically strong laser fields

Electron-ion collisions in relativistically strong electromagnetic fields are considered. Analytical and numerical analyses both show that all qualitative effects characteristic of collisions in nonrelativistic strong fields [1–3] occur at relativistic intensities of an electromagnetic wave as well. Expressions for Joule plasma heating and for the energy distributions of fast particles are derived from simple analytic considerations and are confirmed by numerical simulations. It is found, in particular, that, due to the relativistic increase in the mass of a scattered electron, Joule heating in ultrarelativistic fields becomes more intense as the field amplitude grows.     

One-dimensional nonlinear self-organized structures in dusty plasmas

Dusty plasmas, which are open systems, can form stable one-dimensional self-organized structures. Absorption of plasma by dust particles results in the plasma flux from the plasma regions where the dust is absent. It is found that, in a one-dimensional dust layer, this flux is completely determined by the number of dust particles per unit area of the layer surface. This number determines all of the other parameters of the steady-state dust structure; in particular, it determines the spatial distributions of the dust density, dust charge, electron and ion densities, and ion drift velocity. In these structures, a force and electrostatic balance is established that ensures the necessary conditions for confining the dust and plasma particles in the structure. The equilibrium structures exist only for subthermal ion flow velocities. This criterion determines the maximum possible number of dust particles per unit area in the steady-state structure. The structures have a universal thickness, and the dust density changes sharply at the edge of the structure. The structures with a size either less than or larger than the ion mean free path with respect to ion-neutral collisions, quasi-neutral and charged structures, and soliton-and anti-soliton-like structures are investigated. Laboratory experiments and observations in extraterrestrial plasma formation are discussed in relation to dust structures.     

Ionization instability and dusty plasma structurization

In the presence of ionization processes, a homogeneous equilibrium dust distribution often appears as a balance between plasma generation by ionization and plasma absorption by dust particles. It is shown that such equilibrium, often present in laboratory plasmas, is generally unstable against the formation of dust clumps separated by dust-free regions (dust voids). The driving force that separates an initially homogeneous dusty plasma into dust clumps and dust voids is the drag force produced by ions flowing out from the regions with reduced dust density. The lower the dust density, the lower the electron absorption by dust particles and the larger the ionization rate proportional to the electron density. An increase in the ion drag force leads to a further decrease in the dust density and, thus, drives the instability. In the nonlinear stage, the instability creates structures—dust clouds separated by dust voids. The dependence of the instability growth rate on the wavenumber (or, in other words, on the size of the dust-free and dust-containing regions) is investigated. It is shown that, for sufficiently small wavenumbers, a homogeneous distribution is always unstable. An analogy with a gravitational-like instability related to shadowing of the plasma flux by dust particles is pointed out. This effect, which is due to collective shadowing of the plasma flux, dominates the shadowing by individual dust particles discussed previously. Similar to the usual gravitational instability, perturbations with the largest scales are always unstable. Contrary to the usual gravitational instability, the largest growth rate corresponds not to the largest possible scale but to the size close to the mean free path of plasma particles colliding with dust particles. A special investigation is undertaken to determine the influence of the ion-neutral collisions on the growth rate of the instability.     

Incoherent Scattering of Electromagnetic Waves by Langmuir Fluctuations Trapped in a Plasma Density Well

Incoherent scattering of a probing wave by Langmuir fluctuations trapped and enhanced near a local minimum of the electron density (plasma density well) in plasma with a parabolic density profile is considered. Steady-state amplitudes of fluctuations are calculated for arbitrary velocity distribution functions of plasma particles with allowance for electron collisions. It is shown that quasi-periodic oscillations with two characteristic scales can be present in the spectrum of the plasma line. The smaller scale is due to the wellknown effect of discretization of the spectrum of Langmuir fluctuations in a plasma density well. The larger scale is associated with the generation of scattered waves in two spatial regions and subsequent interference of these waves at the exit from the density well. Oscillations with this scale are more stable under unsteady plasma conditions and can be more often observed in experiments. The results of this work can be used to experimentally determine the plasma parameters, such as the electron collision frequency and the size and lifetime of the plasma density well.     

Heat transfer in dust structures in an RF discharge plasma

Results are presented from experimental studies of heat transfer in liquid-like plasma-dust structures. The experiments were performed with aluminum oxide grains ～3–5 μm in size in an RF discharge plasma. The heat capacity of the dust grains in plasma is measured. The thermal conductivity and thermal diffusivity of liquid-like plasma-dust structures are deduced under the assumption that the observed temperature gradients and the propagation of a thermal perturbation in a dusty plasma are related to heat conduction within the dust component. The measured temperature dependences of the thermal conductivity and thermal diffusivity are in qualitative agreement with the results of numerical simulations performed in the model of a simple single-atom liquid. It is shown that quantitative discrepancy between the experimental and numerical results is related to the energy loss of dust grains in their collisions with the neutral particles of the ambient gas.     

Three-body collisions in a plasma in a strong laser field

Electron-ion collisions in a high-density plasma in strong electromagnetic fields are considered. The applicability condition for the approximate model of pair collisions in strong fields are determined. It is shown that this condition is identical to the condition for the plasma to be transparent. Investigations were carried out by the test particle method generalized to the case of several scattering centers. An accurate calculation of short-range collisions is provided by a “jump” method that is based on the exact solution to the problem of the motion of a particle in a Coulomb potential. This method can also be applied in other approaches to simulating a collisional plasma (such as particle-in-cell and molecular dynamics methods).     

Excitation of plasma waves by nonlinear currents induced by a high-frequency electromagnetic pulse

Excitation of plasma waves by nonlinear currents induced by a high-frequency electromagnetic pulse is analyzed within the kinetic approach. It is shown that the most efficient source of plasma waves is the nonlinear current arising due to the gradient of the energy density of the high-frequency field. Generation of plasma waves by the drag current is usually less efficient but not negligibly small at relatively high frequencies of electron–ion collisions. The influence of electron collisions on the excitation of plasma waves by pulses of different duration is described quantitatively.     

Determination of plasma density from data on the ion current to cylindrical and planar probes

To improve probe methods of plasma diagnostics, special probe measurements were performed and numerical models describing ion transport to a probe with allowance for collisions were developed. The current–voltage characteristics of cylindrical and planar probes were measured in an RF capacitive discharge in argon at a frequency of 81 MHz and plasma densities of 10¹⁰–10¹¹ cm^–3, typical of modern RF reactors. 1D and 2D numerical models based on the particle-in-cell method with Monte Carlo collisions for simulating ion motion and the Boltzmann equilibrium for electrons are developed to describe current collection by a probe. The models were used to find the plasma density from the ion part of the current–voltage characteristic, study the effect of ion collisions, and verify simplified approaches to determining the plasma density. A 1D hydrodynamic model of the ion current to a cylindrical probe with allowance for ion collisions is proposed. For a planar probe, a method to determine the plasma density from the averaged numerical results is developed. A comparative analysis of different approaches to calculating the plasma density from the ion current to a probe is performed.     

Analysis of the differential cross sections for bremsstrahlung during collisions between two charged particles in a uniform electric field

Under the nonrelativistic Born approximation, differential cross sections are derived for elastic collisions between two point charged particles in an external constant uniform electric field and for bremsstrahlung during these collisions.An analysis of the cross sections obtained shows that, due to the interference of the wave functions of two colliding particles during their reflection from the potential barrier of an external electric field, the differential cross sections for elastic collisions and for unpolarized bremsstrahlung (i) are both oscillatory in character and (ii), instead of being linearly proportional to one another (as in the case without an externale electric field), are related in a more complicated manner.     

Differential Expansion of the Elastic Collision Integral of Electrons with Neutral Particles

Plasma Physics Reports - The differential expansion of the integral of elastic collisions of electrons with heavy neutral particles is derived under the assumption that the electron distribution...     

Theory of transverse surface electromagnetic waves propagating along a plasma-metal boundary with a finite radius of curvature in a magnetic field

The spectra of electromagnetic waves propagating perpendicular to the axis of a plasma-filled metal waveguide in a magnetic field are studied with allowance for the effects exerted upon the wave frequency by the radial plasma density variation and by the emission of waves through a narrow axial slit in a waveguide wall. The case of wave propagation along the boundary between a plasma and a cylindrical metal waveguide wall with a periodically varying radius of curvature is also considered. The electromagnetic properties of the plasma are described by a dielectric tensor in the hydrodynamic approximation. The spatial distribution of the wave field is determined by the method of successive approximations. Results are presented from both analytical and numerical investigations. Analytical expressions for the corrections to the wave frequency due to the emission of the wave energy from the waveguide and due to the slight corrugation of the waveguide wall are obtained. The rates of wave damping due to the emission of the wave energy through a narrow axial slit and due to collisions between the plasma particles are found. The correction to the frequency that comes from the periodic variation of the radius of curvature of the plasma surface is calculated to within terms proportional to the square of the small parameter describing the azimuthal corrugation of the waveguide wall. The effect of the radial plasma density variation on the dispersion of the surface modes is examined both analytically and numerically.     

Theory of Electromagnetic Surface Waves in Plasma with Smooth Boundaries

A theory of nonpotential surface waves in plasma with smooth boundaries is developed. The complex frequencies of surface waves for plasma systems of different geometries and different profiles of the plasma density are calculated. Expressions for the rates of collisionless damping of surface waves due to their resonance interaction with local plasma waves of continuous spectrum are obtained. The influence of collisions in plasma is also considered.     

A theory of Brownian coagulation in a bounded planar region

A method for calculating time-dependent probabilities and rates of coagulation is given for particles on a bounded two-dimensional region. Equations are derived and solved for the random variations of displacements between two particles which undergo independent Brownian motion and bind irreversibly upon collision. The solution is used to calculate expected times required for collisions of particles. Comparison with earlier models shows that revised boundary values and initial conditions predictably lengthen required collision times by about a factor of four. Applicatons of the methodology are discussed.