# Физика плазмы

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### Simulation of a Magnetically Isolated Vircator with an Under-Limit Electron Beam

Fri, 05/01/2020 - 00:00
Abstract

A method is proposed for producing microwave generation in a relativistic magnetically insulated vircator in the under-limit mode of an electron beam. The method is implemented if the repeated or multiple passage of the electron beam of the drift tube is organized. In this case, a virtual cathode is formed in the vircator and the powerful microwave generation occurs. Using the particle-in-cell (PiC) simulation, the microwave producing characteristics of the radiation are calculated upon the re-introduction of the beam into the drift tube and the nonlinear dynamics of the electron beam is studied.

### On the Calculation of the Electrical Conductivity of Hot Dense Nonideal Plasmas

Fri, 05/01/2020 - 00:00
Abstract—

Factors affecting the calculation of the electrical conductivity of hot dense nonideal plasma systems are revisited and scrutinized. Essential features relevant to truncation of the internal partition function, Coulomb strong coupling, electronic excited states, in addition to high ionization boundary and Coulomb logarithm, are thoroughly investigated and assessed. Particular interest has been given to the study of the frequently occurring problem of producing intersecting conductivity isotherms at high densities. An improved model for the prediction of the electrical conductivity of hot dense matter is developed and used to calculate the electrical conductivity of partially ionized and partially degenerate matter at high energy density. Compared to results from competitive models in the literature, predictions from the present model have shown better physical behavior in avoiding the problem of producing intersecting isotherms at high densities.

### Experimental Studies of the High-Frequency Oscillation Structure in the Discharge Channel of a Hall Thruster in Two Stable Discharge Modes

Fri, 05/01/2020 - 00:00
Abstract

The structure of high-frequency oscillations in the plasma of a Hall thruster (HT) is studied experimentally in two different stable discharge modes: the “jet” mode and the “bell” mode. The discharge modes under study differ in the geometrical shape of the plasma plume and in the main integral characteristics of the thruster, such as the anode efficiency, driving force, and the specific momentum and thermal conditions of the construction achieved at almost identical input parameters. The studies are mainly performed in the frequency range of 5 to 150 MHz. It is shown that, in this frequency range, the oscillations represent the set of the azimuthal wave harmonics that propagate in the direction coinciding with the electron drift direction and obey the almost linear dispersion relation. An explicit correlation is found between the spectral composition of the waves and the type of the discharge mode.

### Generation of a Beam of Fast Electrons, Plasma Bremsstrahlung, and Characteristic Radiation in a High-Current Z-Pinch

Fri, 05/01/2020 - 00:00
Abstract—

The generation of accelerated electron beams in a high-current Z-pinch formed by the implosion of wire cylindrical tungsten arrays on an Angara-5-1 facility is studied. The most intense characteristic and bremsstrahlung X-ray radiation of fast electrons is recorded from the central region of the pinch at the pin-ching stage. The transverse size of the radiation source in the characteristic tungsten radiation Lα is ~1.5‒1.8 mm, which is close to the transverse size of the radiation source in the soft X-ray emission (1‒1.5 mm). The current of accelerated electrons generated during the implosion of the wire array and the formation of a pinch is on the order of the Alfvén current (IA). This result is consistent with the estimate of the current of accelerated electrons made from the measured characteristic radiation intensity Lα of tungsten under the assumption that the mean free path of fast electrons in a pinch is on the order of its length.

### Effects of Nonextensive Ions (Heavier and Lighter) on Ion Acoustic Solitary Waves in a Magnetized Five Component Cometary Plasma with Kappa Described Electrons

Fri, 05/01/2020 - 00:00
Abstract

We have investigated the propagation characteristics of Ion-Acoustic Solitary Waves (IASWs) in a magnetized, cometary plasma consisting of hydrogen ions, positively and negatively charged oxygen ions, kappa described hot solar electrons, and slightly colder cometary electrons. The effects of q-nonextensive distributions, on both lighter and heavier ions have been studied by deriving the Zakharov–Kuznetsov (ZK) equation. The basic features of IASWs such as amplitude, width, and phase speed have been extensively studied by a numerical analysis of the ZK equation. It is found that superthermality of the electrons and nonextensivity of ions significantly modify the characteristics of the solitary waves. The amplitudes of the solitary waves seem to be well correlated to the presence of water molecules in a cometary plasma and the associated photoionization processes.

### Full-Wave Modeling of Doppler Backscattering from Filaments

Fri, 05/01/2020 - 00:00
Abstract—

It is recognized that the filaments have a significant effect on the anomalous energy and particle transport in the tokamak periphery. They are actively investigated using various diagnostics in this regard. Recently studies of filaments using the Doppler backscattering method have been performed in the Globus-M and the ASDEX-Upgrade tokamaks. Backscattering from filaments manifests itself as a burst of quasi-coherent fluctuations of the signals of detectors. Such signals are easy to describe in the Born approximation using the diagnostic weighting function. However, the filaments in tokamaks differ noticeably in their size and intensity. With an increase in the amplitude of the filaments, it is necessary to consider the transition from linear scattering to nonlinear one and further up to the transition from backscattering to reflection from a moving filament. This problem can be solved only using a full wave code. Our simulation was carried out using the finite-difference time-domain code IPF-FD3D in slab geometry. We did not resort to using well-known non-linear MHD codes to determine filament parameters. In the simulation artificial filament-like perturbations were used, the parameters of which varied over a wide range. Modeling Doppler backscattering signal was focused on the identification of the influence of the amplitude of the filament and its size on the shape and the size of the Doppler backscattering output signal. The results obtained largely explain the similarity of the IQ detector data registered in different tokamaks.

### Dusty Plasma at the Moon. Challenges of Modeling and Measurements

Fri, 05/01/2020 - 00:00
Abstract

A brief review is given of the dusty plasma near the surface of the Moon. Electrostatic processes represent an important factor of formation of such plasma. Problems related to theoretical and numerical modeling of the plasma–dust system near the Moon, its experimental investigation, and interpretation of data on near-lunar dusty plasma are formulated.

### The Effect of Material and Roughness of the Probe Surface on Probe Characteristics

Fri, 05/01/2020 - 00:00
Abstract—

In the region of the surface of the probe introduced into the plasma, there are emission flows that introduce changes in the determination of its parameters. Despite the significant development of the theory of probes, when calculating plasma parameters for experimentally obtained current–voltage characteristics, electron emission is not taken into account, largely due to the serious complication of the mathematical apparatus. The authors calculated the probability of electron emission from a rough surface without collisions. Characteristics of probes from various materials (nickel, wolfram, molybdenum) in a glow discharge in helium are presented. The analysis of the chemical composition of the probe materials is carried out. It has been experimentally shown that the material of the probes and the state of their surface (degree of roughness) affect the results of probe measurements.

### Comparison of Plasma Heating at First and Second Electron Cyclotron Harmonics in the T-10 Tokamak

Fri, 05/01/2020 - 00:00
Abstract

In the T-10 tokamak, the results of plasma heating at the first and second electron cyclotron (EC) harmonics differ substantially. However, the problem is multi-parametric, so it is impossible to estimate the heating quality by sight. In this work, the analysis of heating at both harmonics is provided with two transport models, which were constructed separately for simulation in each mode. For the heating on the second harmonic, we solve the inverse problem of determining the profile of the absorbed power from the experimental electron temperature profile. In this mode, we are able to determine both the deposited power profile and the ratio of absorbed to deposited power. It is shown that at low plasma densities, this ratio is small, which, apparently, is a consequence of the low absorption of the heating waves during their single pass though the plasma. During the heating at the second harmonic, the absorbed power profile is much flatter than predicted by ray tracing calculations of EC waves. Multi-pass wave absorption with random reflections from the corrugated chamber wall leads to such absorption profiles. At high plasma densities, the absorbed power is close to the input power. However, in this case, the results at the second harmonic are worse than the results obtained at the first harmonic due to the flatter absorbed density profile.

### Anomalous Electron Transport in One-Dimensional Electron Cyclotron Drift Turbulence

Fri, 05/01/2020 - 00:00
Abstract

The transverse electron current due to the crossed electric and magnetic fields results in the robust instability driven by the electron $${\mathbf{E}} \times {\mathbf{B}}$$ drift. In the regime of interest for electric propulsion applications, this instability leads to the excitation of quasicoherent nonlinear wave resulting in the anomalous electron transport. We investigate the nonlinear stage of the instability and resulting anomalous electron current using nonlinear Particle-in-Cell simulations. It is found that the anomalous current is proportional to the applied electric field thus demonstrating constant anomalous mobility. Moreover, the scaling of the current density follows the dependence of the dominant resonance wavelength on the electric and magnetic field strength thus clearly demonstrating the cyclotron nature of the instability.

### Propagation of a Plasma Flow Generated in a Plasma-Focus Discharge in the Background Plasma

Fri, 05/01/2020 - 00:00
Abstract

The results of studying the propagation of plasma flows in the surrounding medium performed on the PF-3 plasma focus facility in the laboratory simulation of astrophysical jets from young stellar objects are presented. The modes with the plasma formations which retain their compactness when propagated over significant distances are obtained. The decrement of the flow’s deceleration as a result of its interaction with the background gas is determined. A technique is developed for estimating the plasma temperature by the ratio of radiation intensities from various parts of the spectrum. It is shown that the background gas is heated by the flow radiation, which leads to a change in its ionization state. Thus, the plasma flow propagates not in a neutral gas but in a weakly ionized plasma.

### Formation Rate and Energy Yield of Hydroxyl Radicals in Water under the Action of Gas-Discharge Plasma

Wed, 04/01/2020 - 00:00
Abstract—

The kinetics of hydroxyl radical formation in water under the action of a pulsed discharge in vapor-gas bubbles formed near the surface of a graphite electrode immersed into water is studied. The reaction of potassium hexacyanoferrate(II) oxidation is used to determine the concentration and formation rate of OH radicals in the liquid phase. The power dissipated in the discharge is estimated from measurements of the time dependences of the current through the discharge cell, the voltage applied to the electrodes, and the integrated intensity of the discharge radiation. The yields of OH radicals per 100 eV of the energy applied to the plasma are calculated. It is found that, with an increase in power from 13 to 100 W, the rate of radical generation increases within the range of (2.8–34.8) × 10–7 mol/(L s). The radical yield weakly depends on power and is equal to 0.12 ± 0.03 particles/100 eV.

### Three-Dimensional Isothermal Ion Acoustic Shock Waves in Ultra-Relativistic Degenerate Electron–Positron–Ion Magnetoplasmas

Wed, 04/01/2020 - 00:00
Abstract

The modifications, which arise from ultra-relativistic and degenerate effects of electrons and positrons as well as the chemical potentials in the basic features of three-dimensional isothermal ion acoustic shock waves (IIASWs) propagating in magnetized electron–positron–ion (e–p–i) plasmas are studied. The cold ions are considered to be magnetized and inertial, while the small particles (i.e., electrons and positrons) are taken to obey the Fermi–Dirac statistics. The well-known reductive perturbation analysis is applied to obtain the nonlinear Zakharov–Kuznetsov–Burgers equation (NZKBE). The analytical shock wave solution is obtained by employing the tanh technique. Furthermore, the asymptotic behavior and the stability of the shock structures are discussed. In the current model, the disturbances of nonlinear isothermal ion acoustic waves are found to exhibit only monotonic IIASWs. The consequences of the chemical potential, the presence of ultra-relativistic degenerate electrons and positrons, and magnetic field on the essential properties of three-dimensional IIASWs are numerically examined. The numerical investigations give rise to significant high lights on the propagation and the dynamic behavior of IIASWs. It is found that the amplitudes of the monotonic IIASWs decrease with chemical potentials of ultra-relativistic degenerate electrons and positrons increase.

### EM-Wave Diffraction by a Finite Plate with Neumann Conditions Immersed in Cold Plasma

Wed, 04/01/2020 - 00:00
Abstract

The present research article presents the investigation of diffraction phenomenon of EM-plane wave by a non-symmetric plate of finite length under the influence of cold plasma. The Wiener–Hopf equation is formulated by boundary value problem related to this model and Fourier transform. The standard way of Wiener–Hopf procedure is used to tackle the resulting equation. Asymptotic expansion and modified stationary phase method are used to find the result for the diffracted wave by finite plate under the assumption of Neumann boundary conditions in an anisotropic medium. The case of an isotropic medium has been obtained by assigning the particular values to elements of permittivity tensor. The high-frequency signal can be assumed only when very large operating frequency is taken into account as compared to the cyclotron frequency. Various physical parameters for isotropic and anisotropic medium are discussed graphically.

### Generation and Diagnostics of Pulse Plasma Flows

Wed, 04/01/2020 - 00:00
Abstract

Pulsed plasma accelerators are widely used for the production of high-temperature pulsed plasma flows for fundamental and practical applications. The basic parameters of pulsed plasma accelerators are the characteristics of the external electric and magnetic circuits, as well as the structural and energy properties of the plasma flow. This work aims to characterize an IPU-30 pulsed plasma accelerator. The triple Langmuir probe method, calorimetric plasma energy density measurements, Rogowski coil, and high-speed visible imaging with a Phantom VEO710S fast camera are used to diagnose the pulsed plasma obtained in the IPU-30. The local plasma parameters such as electron temperature and density, the energy density of the pulsed plasma flow, pulsed plasma current, and also discharge current are experimentally obtained at different discharge voltages and air pressure in the chamber. The typical waveforms of the triple probe and Rogowski coil are presented in the form of oscillograms. The images of plasma formation in the discharge gap are obtained and the velocity of a pulsed plasma flow is measured.

### Description of Large-Scale Processes in the Near-Earth Space Plasma

Wed, 04/01/2020 - 00:00
Abstract

We suggest a solution of the problem of the description of magnetic and electric fields occurring during large-scale nonradiative processes in the collisionless space plasma. The key idea is that the quasi-neutrality condition and the field-aligned force equilibrium of electrons should be taken into account. Equations describing the plasma are divided into two parts, namely, a system of transport equations which describes the plasma motion, and a system of equations for fields. The fields are defined in the instantaneous action approximation via the current spatial distributions of hydrodynamic plasma parameters and boundary conditions obtained from the system of elliptic equations containing no partial time derivatives. Three forms of the generalized Ohm’s law corresponding to different levels of plasma magnetization are considered. It is shown that, depending on the form of a system of transport equations derived for each plasma component, five key variants of the equation system describing the plasma can be obtained from the three forms of the Ohm’s law. The first form of the generalized Ohm’s law refers to the general case in which all plasma components unmagnetized and the system of transport equations represents the Vlasov equations for each plasma component. The second form of the Ohm’s law corresponds to the case of unmagnetized ionic plasma components, while electrons are magnetized and their pressure tensor is expressed through their longitudinal and transverse pressures as well as through the magnetic field. In the latter case two variants of the system of transport equations are possible, and the ions are described by Vlasov equations in both of them. In the first variant, the electrons are described by the Vlasov equation in the drift approximation. In the second variant, the electrons are described by the system of Chew–Goldberger–Low equations of magnetogasdynamics. The third variant of Ohm’s law corresponds to the case in which all plasma components are magnetized, and the pressure tensor of each component is replaced by its expression through the longitudinal and transverse pressure, as well as through the magnetic field. In this case, two variants of the transport equation system are also possible. In the first variant, each component is described by the Vlasov equation in the drift approximation. In the second variant, each component is described by the system of the Chew–Goldberger–Low equations of magnetogasdynamics.

### Energy Confinement in Self-Organized Tokamak Plasma (without Transport Barriers)

Wed, 04/01/2020 - 00:00
Abstract—

The phenomenon of improved energy confinement during radiative cooling at the plasma edge was studied experimentally in the T-10 tokamak. It was shown that the effect is independent on the kind of radiating gas. No substantial differences were observed using Ne, which radiates at two-thirds of the plasma radius, or He, which radiates at the very edge. This phenomenon is explained in frames of nonequilibrium thermodynamics. In a self-organized plasma, the energy balance is described by a Smoluchowski-type equation, where the plasma thermal conductivity and its functional dependence on the intensity of the heat flux, perturbing the pressure profile, is determined from experiment.

### Stability of a Planar Plasma Crystal

Wed, 04/01/2020 - 00:00
Abstract

The stability of a planar plasma crystal in an external confining force field is investigated. Particles are assumed to be located in the plasma with Maxwellian electrons and with a directed flow of cold ions. It is shown that, together with the coupled wave instability, four more types of aperiodic instabilities arise, which lead to the formation of different structures. A region of the crystal stability in the space of external parameters is constructed.

### Spatial Structure and Dynamics of a Pulsed Arc Discharge in Vacuum

Wed, 04/01/2020 - 00:00
Abstract

The process of switching a short vacuum gap using an auxiliary discharge over the surface of a dielectric is studied by the high-speed recording of images of the plasma in the optical spectral range. Based on the analysis of the obtained experimental data, it is suggested that the cathode spot and cathode flame in the ultraviolet spectral range play a significant in the formation of current channel in the discharge.

### Fast-Scale Perturbations of Electromagnetic Fields upon Development of Arc Discharges at an Early Stage of Disruption in the T-10 Tokamak Plasma

Wed, 04/01/2020 - 00:00
Abstract

The conditions leading to the development of fast-scale (  f ~ 0.2–1.5 MHz) electromagnetic oscillations in the periphery regions of plasma at an early stage of disruption in the T-10 tokamak are analyzed. Spatial and temporal characteristics of fast-scale oscillations are investigated by moving magnetic and electric probes mounted inside the tokamak vacuum chamber. Analysis reveals that initiation of the fast-scale oscillations can be related to the development of arc discharges in plasma near the T-10 tokamak limiters. The transition to a major disruption and collapse of the plasma current is accompanied by a sharp increase in the amplitude of the fast-scale electromagnetic oscillations. Monitoring the fast-scale electromagnetic oscillations at the plasma periphery can be an important trigger for systems to safely quench the discharge in a to-kamak.

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