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.     

Electron energy balance and ionization in the channel of a stationary plasma thruster

The paper presents results of numerical simulations of the electron dynamics in the field of the azimuthal and longitudinal waves excited in the channel of a stationary plasma thruster (SPT). The simulations are based on the experimentally determined wave characteristics. The simulation results show that the azimuthal wave displayed as ionization instability enhances electron transport along the thruster channel. It is established that the electron transport rate in the azimuthal wave increases as compared to the rate of diffusion caused by electron scattering from neutral atoms in proportion to the ratio between the times of electron? neutral collisions responsible for ionization and elastic electron scattering, respectively. An expression governing the plasma conductivity is derived with allowance for electron interaction with the azimuthal wave. The Hall parameter, the electron component of the discharge current, and the electron heating power in the thruster channel are calculated for two model SPTs operating with krypton and xenon. The simulation results agree well with the results of experimental studies of these two SPTs.     

Modulational excitation of low-frequency dust acoustic waves in the Earth’s lower ionosphere

During the observation of Perseid, Leonid, Gemenid, and Orionid meteor showers, stable low-frequency lines in the frequency range of 20–60 Hz were recorded against the radio-frequency noise background. A physical mechanism for this effect is proposed, and it is established that the effect itself is related to the modulational interaction between electromagnetic and dust acoustic waves. The dynamics of the components of a complex (dusty) ionospheric plasma with dust produced from the evolution of meteoric material is described. The conditions for the existence of dust acoustic waves in the ionosphere are considered, and the waves are shown to dissipate energy mainly in collisions of neutral particles with charged dust grains. The modulational instability of electromagnetic waves in a complex (dusty) ionospheric plasma is analyzed and is found to be driven by the nonlinear Joule heating, the ponderomotive force, and the processes governing dust charging and dynamics. The conditions for the onset of the modulational instability of electromagnetic waves, as well as its growth rate and threshold, are determined for both daytime and nighttime. It is shown that low-frequency perturbations generated in the modulational interaction are related to dust acoustic waves.     

Unsteady beam-plasma discharge: II. Nonlinear theory

The mathematical model constructed in the first part of our paper is used to numerically investigate the development of the beam-plasma instability in a traveling-wave tube amplifier in the presence of a residual neutral gas. It is shown that the self-generation of ion acoustic waves in a plasma-filled amplifier can give rise to a modulation regime with a rigid excitation threshold. The dependence of the threshold for the self-modulation instability on the amplifier parameters is determined. The effect of self-modulation on the spectral and energy characteristics of the amplifier is analyzed.     

Unsteady beam-plasma discharge: I. Mathematical model and linear theory

A mathematical model is constructed that describes the development of the beam-plasma instability in a traveling-wave tube amplifier in the presence of a neutral gas. Steady solutions are derived for conditions of microwave discharges in a magnetized plasma-filled traveling-wave tube amplifier, and their stability is investigated. It is shown that the steady-state amplification regime may become unstable and change to the self-modulation regime. The relationships between the amplifier parameters at the instability threshold are obtained, and the frequencies of the excited ion acoustic waves are determined. The results of numerical modeling are found to agree well with the analytical results.     

Large-amplitude ion acoustic solitons in a bi-ion plasma

A gas-dynamic model is used to study the conditions for the existence of large-amplitude ion acoustic solitons in a plasma with negative ions. It is shown that the limiting Mach number—the upper boundary of the region of existence of compression solitons—depends nonmonotonically on the temperature of the positive ions. The result is that, for certain fixed densities of the negative ions, there are one or two temperature boundaries between the regions where solitons can and cannot exist. It is found that, for rarefaction solitons, it is fundamentally important to take into account electron inertia and that the Mach number of such solitary waves is restricted not by the complete decompression of electrons within the wave (as thought previously), but by the fact that the electrons at the center of the wave reach the acoustic speed, above which the thermal-pressure-induced action cannot be transferred back to the electron flow and smooth continuous solutions are impossible.     

Hypothesis on acoustic receptive fields

A hypothesis of acoustic receptive fields is studied, which is based on the fact that the cochlea of the internal ear is a wave guide with traveling waves and the resonance in the critical layer. When a harmonic sound influences the ear, the traveling wave reaches the critical layer for the corresponding frequency and generates there a train of decaying waves about 25 periods in duration, which form a steep slope of the envelope. The funnel-shaped convergence of all neurones innervating the acoustic receptors of the Corti organ along the slope of the envelope gives rise to acoustic receptive fields. The hypothesis is consistent with some other experimental data. Such an acoustic receptive field makes it possible to use the whole train of waves in the critical layer to measure the frequency of the acting sinusoidal sound with the greatest possible accuracy. Similarly, a high accuracy of recognition of short-time sound pulses is provided, which could not be explained earlier.     

Process of commutation of a vacuum electric-discharge gap by laser plasma

The temporal parameters of a process of vacuum gap commutation under exposure to a nanosecond pulse of laser radiation incident on the cathode has been studied depending on the radiation energy. Based on the experiment data, it is suggested that a glow discharge is initially ignited in electrode erosion products under exposure to the laser pulse, which due to development of the ionization-overheating instability undergoes the contraction of current channel and transits to an arc discharge. With the radiation energy exceeding a threshold value, the radiation (incident on the cathode) accelerates directly the instability development and the glow discharge transition to the arc discharge due to the radiation absorption in the discharge plasma.     

Generation of auroral kilometric radiation by a finite-size source in a dipole magnetic field

Generation, amplification, and propagation of auroral kilometric radiation in a narrow three-dimensional plasma cavity in which a weakly relativistic electron beam propagates is studied in the geometrical optics approximation. It is shown that the waves that start with a group velocity directed earthward and have optimal relation between the wave vector components determining the linear growth rate and the wave residence time inside the amplification region undergo the largest amplification. Taking into account the longitudinal velocity of fast electrons results in the shift of the instability domain toward wave vectors directed to the Earth and leads to a change in the dispersion relation, due to which favorable conditions are created for the generation of waves with frequencies above the cutoff frequency for the cold background plasma at the wave generation altitude. The amplification factor for these waves is lower than for waves that have the same wave vectors but are excited by the electron beams with lower velocities along the magnetic field. For waves excited at frequencies below the cutoff frequency of the background plasma at the generation altitude, the amplification factor increases with increasing longitudinal electron velocity, because these waves reside for a longer time in the amplification region.     

Nonlinear Right-Hand Polarized Wave in Plasma in the Electron Cyclotron Resonance Region

The propagation of a nonlinear right-hand polarized wave along an external magnetic field in subcritical plasma in the electron cyclotron resonance region is studied using numerical simulations. It is shown that a small-amplitude plasma wave excited in low-density plasma is unstable against modulation instability with a modulation period equal to the wavelength of the excited wave. The modulation amplitude in this case increases with decreasing detuning from the resonance frequency. The simulations have shown that, for large-amplitude waves of the laser frequency range propagating in plasma in a superstrong magnetic field, the maximum amplitude of the excited longitudinal electric field increases with the increasing external magnetic field and can reach 30% of the initial amplitude of the electric field in the laser wave. In this case, the energy of plasma electrons begins to substantially increase already at magnetic fields significantly lower than the resonance value. The laser energy transferred to plasma electrons in a strong external magnetic field is found to increase severalfold compared to that in isotropic plasma. It is shown that this mechanism of laser radiation absorption depends only slightly on the electron temperature.     

Estimation of the electron density and radiative energy losses in a calcium plasma source based on an electron cyclotron resonance discharge

The parameters of a calcium plasma source based on an electron cyclotron resonance (ECR) discharge were calculated. The analysis was performed as applied to an ion cyclotron resonance system designed for separation of calcium isotopes. The plasma electrons in the source were heated by gyrotron microwave radiation in the zone of the inhomogeneous magnetic field. It was assumed that, in such a combined trap, the energy of the extraordinary microwave propagating from the high-field side was initially transferred to a small group of resonance electrons. As a result, two electron components with different transverse temperatures—the hot resonance component and the cold nonresonance component—were created in the plasma. The longitudinal temperatures of both components were assumed to be equal. The entire discharge space was divided into a narrow ECR zone, where resonance electrons acquired transverse energy, and the region of the discharge itself, where the gas was ionized. The transverse energy of resonance electrons was calculated by solving the equations for electron motion in an inhomogeneous magnetic field. Using the law of energy conservation and the balance condition for the number of hot electrons entering the discharge zone and cooled due to ionization and elastic collisions, the density of hot electrons was estimated and the dependence of the longitudinal temperature T _e∥ of the main (cold) electron component on the energy fraction β lost for radiation was obtained.     

Nonlinear regimes of Farley-Buneman instability

The dynamic suppression of the instability of a quasi-monochromatic wave by nonlinear wave-wave interaction is considered. It is shown that, near the threshold of linear instability, the process of decay into two strongly damped waves leads to the onset of a quasi-periodic or a stochastic nonlinear stabilization regime involving a small number of modes. A case study is made of the Farley-Buneman instability in an isothermal magnetized current-carrying plasma in which particle collisions play an important role. Typical characteristic features of different stabilization regimes are analyzed as functions of current and other plasma parameters.     

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...     

Diffuse and constricted modes of a dc discharge in neon: Simulation of the hysteresis transition

Results are presented from theoretical studies of high-pressure (～100 Torr) dc discharges in neon. The diffuse and constricted discharge modes are studied using a model including the equation of balance for charged and excited particles, heat conduction equations for the neutral gas and plasma electrons, and Poisson’s equation for the radial electric field at a fixed total discharge current. A specific feature of the constricted mode in the investigated range of low fields and high degrees of ionization is that the excitation and ionization rates in the center of the discharge tube and at the periphery differ by several orders of magnitude. This implies that, in the constricted mode, the region where the electron energy distribution function is Maxwellian due to electron-electron collisions may adjoin the region (beyond the constriction zone) where the high-energy part of the distribution function is depleted. The hysteresis transition between the diffuse and constricted modes is analyzed. A transition from the constricted to the diffuse mode can be regarded as a manifestation of the nonlocal character of the formation of the electron distribution function, specifically, the diffusion of high-energy electrons capable of producing gas ionization from the central (constricted) region toward the periphery. The nonlocal formation of the distribution function is described by a nonlocal kinetic equation accounting for electron-electron collisions and electron transport along the radius of the discharge tube. Since only high-energy electrons produce gas ionization, the effect of the nonlocal formation of the electron distribution function is taken into account by introducing the effective temperature of the high-energy part of the distribution function and solving the equation for the radial profile of the high-energy part of the distribution function. This approach allows one to approximately take into account the nonlocal character of the electron distribution function without substantial expenditure of computer resources. The nonlocal model makes it possible to numerically simulate the hysteresis transition between the diffuse and constricted modes, which is impossible in the local approximation.     

Control for the parameters of a low-pressure glow discharge in argon by means of acoustic flows

The possibility to control the parameters of a low-pressure glow discharge in argon by means acoustic flows is demonstrated by numerical simulations. It is shown that such flows result in an increase in the densities of charged and excited particles in the axial region of the discharge and contraction of the positive column, while stability of the discharge is preserved.     

Role of Collisions with Neutrals in the Process of Modulational Excitation of Dust Acoustic Perturbations in Dusty Ionosphere

Plasma Physics Reports - The role of inelastic collisions of electrons and ions with neutrals during the development of modulational instability involving dust acoustic perturbations in dusty...     

Spatial distribution of the RF power absorbed in a helicon plasma source

The spatial distributions of the RF power absorbed by plasma electrons in an ion source operating in the helicon mode (ω _ci < ω < ω _ce < ω _pe ) are studied numerically by using a simplified model of an RF plasma source in an external uniform magnetic field. The parameters of the source used in numerical simulations are determined by the necessity of the simultaneous excitation of two types of waves, helicons and Trivelpiece-Gould modes, for which the corresponding transparency diagrams are used. The numerical simulations are carried out for two values of the working gas (helium) pressure and two values of the discharge chamber length under the assumption that symmetric modes are excited. The parameters of the source correspond to those of the injector of the nuclear scanning microprobe operating at the Institute of Applied Physics, National Academy of Sciences of Ukraine. It is assumed that the mechanism of RF power absorption is based on the acceleration of plasma electrons in the field of a Trivelpiece-Gould mode, which is interrupted by pair collisions of plasma electrons with neutral atoms and ions of the working gas. The simulation results show that the total absorbed RF power at a fixed plasma density depends in a resonant manner on the magnetic field. The resonance is found to become smoother with increasing working gas pressure. The distributions of the absorbed RF power in the discharge chamber are presented. The achievable density of the extracted current is estimated using the Bohm criterion.     

Generation of auroral kilometric radiation by a finite-size source in a dipole magnetic field. Part II

Propagation and amplification of extraordinary electromagnetic waves in a dipole magnetic field in a narrow 3D plasma cavity in which a weakly relativistic electron beam propagates along the magnetic field in the direction of the gradient of the magnetic field strength is investigated. The domain of wave vectors at the starting point for which the wave amplification factors at the output of the density cavity reach their maximum values is found, and the amplification factor as a function of the wave frequency is determined. It is shown that the longitudinal velocity of fast electrons, which enables generation of waves in a broader frequency range, plays an important role in the formation of the spectrum of the auroral kilometric radiation (AKR). In this case, waves with the largest amplification factors at the output of the cavity have frequencies exceeding the cutoff frequency of the background plasma at the wave generation altitude. The global inhomogeneity of the magnetic field and plasma density, which governs the residence time of the waves in the amplification region, plays a key role in the formation of the AKR spectrum. It is shown that this time is the main factor determining the energy of the waves emerging from the source.     

Double layer in a cylindrical hollow-cathode discharge

A dc cylindrical coaxial glow discharge with an inner grid anode has been studied. The region between the two electrodes is seen dark, while a brightly glowing region forms inside the grid anode up to the center. The current-voltage characteristic of a dc cylindrical glow discharge in nitrogen is similar to that of a normal glow discharge, while the normal glow discharge voltage decreases with increasing pressure. The minimum plasma potentials are observed in the hollow cathode region due to the accumulation of electrons at the back of the grid anode. At the center, some of the passed electrons are converged, so their potential is decreased. These electrons have a sufficient time to be redistributed to form one group with a Maxwellian electron energy distribution function. The electron temperature measured by electric probes varies from 1.6 to 3.6 eV, while the plasma density varies from 3.9 × 10¹⁶ to 7 × 10¹³ m⁻³, depending on the discharge current and probe position. The plasma density increases as the electrons move radially from the grid toward the central region, while their temperature decreases.     

Evolution of the radial structure of a negative corona during its transformation into a glow discharge and a spark

With the proper stabilization of a negative corona, it is possible to increase the threshold current at which the corona discharge in the point-plane gap in air transforms into a spark. Then, in the current range corresponding to the transition region between the corona discharge and the spark, a new type of discharge arises—an atmospheric-pressure diffuse glow discharge. The transformation of the negative corona into a glow discharge and then into a spark is accompanied by the rearrangement of the discharge structure. The experiments show that, as the corona current increases, the radial current profile at the anode shrinks and the glow diameter near the anode increases. The radial profiles of the current and the corona glow during the transition to a glow discharge are measured. The longitudinal structure of the corona is computed using a 1.5-dimensional model that, unlike the other available models, includes gas ionization in the drift region of the corona. The experimental data are used to determine the effective cross section of the current channel at the anode. The radial glow profile near the anode is calculated using the measured current profile and assuming that the field profile is parabolic.