The effect of trapped electrons on large amplitude ion-acousticwaves in a plasma with an electron beam

The nonlinear wave structures of large amplitude ion-acoustic waves are investigated in an electron beam-plasma system with trapped electrons, by the pseudopotential method. The speed of the ion-acoustic wave increases as the effect of trapped electrons decreases and the beam temperature increases. The region of the existence of ion-acoustic waves is examined, showing that the condition of the existence sensitively depends on the parameters such as the effects of the electron beam density and temperature, electrostatic potential, and the effect of trapped electrons. It turns out that the region of existence spreads as the effect of trapped electrons decreases and beam temperature increases. New findings of large amplitude ion-acoustic waves in an electron beam-plasma system with trapped electrons are predicted     

Cherenkov instability of a magnetized beam-plasma system with allowance for a momentum spread of beam electrons

Cherenkov instability is considered in a completely magnetized homogeneous beam-plasma system featuring a thermal momentum spread of beam electrons. The thermal spread in the beam is described in the scope of both the hydrodynamic approach and the kinetic equation method by giving the electron momentum distribution function in the form of theMaxwellian and semi-Maxwellian distributions. It is shown that two beam-plasma instability regimes, the single-particle and collective Cherenkov effects (Compton and Raman regimes) differing by the physical mechanism and the increments, are possible in a system (waveguide) with homogeneous transverse beam and plasma density profiles. Solutions to dispersion equations for these and a more general regime are obtained and analyzed.     

Thermal effects in the dissipative instability of the electron beam-plasma systems

The effects of the thermal motion of the charged particles in the dissipative instability of the under and over-limiting currents of a relativistic electron beam in a fully magnetized beam-plasma waveguide is investigated. It is shown that by increasing the temperature of the plasma electrons, the resonant frequency of the waveguide slightly increases and the growth rates of the instability development decreases. In addition, an increase of the temperature of the plasma electron can change the dissipative hydrodynamic instability to the collisionless kinetic instability. Furthermore, the dissipative instability of the overlimiting electron beam is shown to be more sensitive with respect to the electron plasma temperature compared to the underlimiting electron beam case.     

Obliquely propagating quantum solitary waves in quantum‐magnetized plasma with ultra‐relativistic degenerate electrons and positrons

The oblique propagation of the quantum electrostatic solitary waves in magnetized relativistic quantum plasma is investigated using the quantum hydrodynamic equations. The plasma consists of dynamic relativistic degenerate electrons and positrons and a weakly relativistic ion beam. The Zakharov‐Kuznetsov equation is derived using the standard reductive perturbation technique that admits an obliquely propagating soliton solution. It is found that two types of quantum acoustic modes, that is, a slow acoustic mode and fast acoustic mode, could be propagated in our plasma model. The parameter that determines the nature of soliton, that is, compressive or rarefactive soliton, for slow mode is investigated. Our numerical results show that for the slow mode, the determining parameter is ion beam velocity in the case of relativistic degenerate electrons. We also have examined the effects of plasma parameters (like the beam velocity, the density ratio of positron to electron, the relativistic factor, and the propagation angle) on the characteristics of solitary waves.     

Nonlinear Theory of the Instability of a Modulated Electron Beam of Low Density in a Plasma IV. Excitation of Nonresonant Waves

A system of nonlinear equations derived in a previous paper which describes the evolution of nonresonant waves in beam-plasma systems is solved numerically. It is given a physical interpretation of essential features of the nonresonant beam-plasma instability. The significant influence of higher harmonics on the evolution of an electron beam in the plasma which is modulated on a nonresonant unstable frequency, is investigated. The interaction of unstable nonresonant and resonant waves in beam-plasma systems is examined. It is shown that the evolution of resonant waves can be essentially influenced by an initial modulation of the beam on an unstable non-resonant frequency. The role of an initial velocity modulation of the beam for the influence of the wave spectrum is demonstrated.     

Observations of nonlinear Landau damping in an electron beam-plasma system

The nonlinear Landau damping of space charge waves of an electron beam into Trivelpiece modes by nonlinear interaction with plasma electrons has been observed experimentally in an electron beam-plasma system.     

Absorption of zero Lamb waves in an elastic layer by mechanical resonators with friction

The propagation of zero Lamb waves in a plate with mechanical resonators attached to its surfaces is studied. It is shown that, in a plate that is single-mode for symmetric (antisymmetric) waves, the zero symmetric (antisymmetric) Lamb wave can be absorbed by mechanical resonators with a certain friction. The single-mode (for symmetric or antisymmetric waves) plate can be not thin compared to the wavelength of the transverse wave.     

Excitation of an Additional Region of Short-Wavelength Plasma Oscillations in Ionospheric Heating Experiments

We discuss transfer of plasma waves, excited by a powerful radio wave due to its scattering on artificial ionospheric irregularities, into an additional region of very short plasma oscillations polarized almost perpendicular to the magnetic field. Such a region can exist in the magnetized ionospheric plasma due to the strong spatial dispersion. We take into account the plasma-wave diffusion over the spectrum caused by multiple scattering on irregularities, as well as the nonlinear process of plasma-wave interaction due to induced scattering by ions. The latter process leads to the transfer of primary plasma waves into the additional region. The induced scattering is considered in the differential approximation valid for sufficiently smooth plasma-wave spectra. The numerical calculations are performed for a Maxwellian plasma in which suprathermal electrons are absent. It is shown that in this case, the additional region of plasma waves is excited if the pump frequency is close to but slightly less than the fourth electron gyroharmonic, so that the absorption of primarily excited plasma waves becomes sufficiently strong. Application of our calculations to the results of ionospheric experiments is discussed.     

Nonlinear Theory of the Instability of a Modulated Electron Beam of Low Density in a Plasma. II. Energetic Analysis of Certain Types of Monoenergetic Beam-Plasma Interactions Based on the Čerenkov Resonance Condition

The energy and momentum balance equations for a potential wave in a monoenergetic electron beam-plasma system are considered in the linear approximation, when the wave is in ?erenkov resonance with the beam particles. An energetic analysis of certain types of beam-plasma instabilities is given. It is shown that the energy and momentum balance equations are consistent with the dispersion relation for all unstable waves. From this fact follows that the energy and momentum densities of all linear unstable waves in reactive beam-plasma systems are equal to zero. An interpretation and a possible classification of beam-plasma instabilities are given.     

Resonant Wave-Particle Interaction in an Explosively Unstable Beam-Plasma System II. Investigation of the Relaxation Behaviour of the Electron Beam

Three typical saturation mechanisms of the explosive instability (EI) in a beam-plasma system are investigated. It is shown that the maximum values of the electric field strengths of the explosively unstable plasma waves can be of the same order as the maximum wave amplitude of the linearly unstable waves. Some conclusions with regard to the role played by the EI in the evolution of a real beam-plasma system are presented. The relaxation of a strongly modulated electron beam by the explosive wave coupling mechanism is examined in an appendix. A qualitative interpretation of the diversity of the EI saturation mechanisms found in this investigation is given.     

Peculiarities of electron-beam interaction with waves in partially plasma-filled corrugated waveguide

It is shown when the cross-section of a waveguide is partially filled by magnetized plasma, slow and fast E-waves can exist simultaneously at the same frequency, which is lower than the plasma frequency. In the case of spatially periodic corrugation of the waveguide wall, the waves can be coupled, forming new waves with hybrid properties in a certain frequency range. The interaction of an electron beam with the hybrid waves differs from the interaction with a slow plasma wave in a waveguide with smooth walls or with the wave in an evacuated corrugated waveguide. For example, when two waves traveling in the same direction are coupled, the increments of the hybrid waves have values on the order of but somewhat smaller than those of the increment of a slow plasma wave in a smooth waveguide.Moscow Radio-Engineering Institute, Academy of Sciences of the USSR. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 34, No. 7, pp. 825–836, July, 1991.     

Magnetoacoustic solitons in pair-ion fullerene plasma

ABSTRACT

The propagation of magnetoacoustic (fast magnetohydrodynamic) waves in pair-ion (PI) fullerene plasma is studied in the linear and nonlinear regimes. The pair-ion (PI) fullerene plasma is theorized as homogeneous, magnetized, warm and collisionless. Employing multi-fluid magnetohydrodynamic model, the dispersion relation is obtained and wave dispersion effects which appear through ion inertial length are discussed. Using reductive perturbation technique (RPT), the Korteweg–de Vries (KdV) equation is derived and its solution for small but finite amplitude magnetoacoustic solitons propagating in the direction perpendicular to the external magnetic field is presented. The compressive magnetoacoustic soliton (i.e. positive potential pulse) propagating with super Alfvénic speed is obtained in magnetized PI fullerene plasma. The variations in the amplitude and width of the magnetoacoustic soliton structures are also illustrated by using numerical values of the plasma parameters such as ions' density, temperature difference between fullerene ions and magnetic field intensity, which have been taken from the PI plasma experiments already published in the literature.     

Observation of transition from a reactive-medium instability to an inverse Landau damping in a beam-plasma system

The wave excited by a coaxial probe in a beam-plasma system usually propagates as two waves which are independent of each other, i.e., a damped Trivelpiece mode of the plasma and a growing space charge wave of the beam (referred to a reactive-medium instability). While, when the beam velocity is equal to or slightly larger than the phase velocity of the plasma wave, the inverse Landau damping of the wave is observed, instead of the damped Trivelpiece mode.     

Behavior of the fast cyclotron wave in a nonuniform magnetic field

The fast cyclotron wave becomes unstable and is excited in a spiral electron beam-plasma system when the perpendicular energy component of the beam is sufficiently large. When a nonuniform magnetic field is applied to the system, the cyclotron frequency as well as the parallel velocity component of the beam vary spatially. It is confirmed experimentally, that the variation affects the excited wave and results in a spatial variation of its wavenumber in the way predicted by the dispersion relation of the fast cyclotron wave.     

Obliquely propagating ion-acoustic solitary and shock waves in magnetized quantum degenerate multi-ions plasma in the presence of trapped electrons

The properties of obliquely propagating ion-acoustic waves have been investigated in multi-ions magnetized plasma comprising of inertial, positively and negatively charged ion fluids, trapped electrons, and negatively charged stationary heavy ions. The propagation of the waves is oblique to the ambient magnetic field which is along the z-direction. Only fast type of modes exists in the linear regime. The reductive perturbation method was adopted to derive the Korteweg– de Vries (KdV) and Burger equations, as well as the solitary and shock wave solutions of the evolved equations, have been used to analyze the properties of the small but finite amplitude waves. The effects of the constituent plasma parameters, namely, the trapping effect of electrons, the electron degenerate temperature and the viscosity coefficient on the dynamics of the small amplitude solitary and shock waves have been examined. The influence of the magnetic field and the obliquity parameter on the propagation characteristics of ion-acoustic waves are discussed.     

Symmetry boundary conditions

A simple approach to energy conserving boundary conditions using exact symmetries is described which is especially useful for numerical simulations using the finite difference method. Each field in the simulation is normally either symmetric (even) or antisymmetric (odd) with respect to the simulation boundary. Another possible boundary condition is an antisymmetric perturbation about a nonzero value. One of the most powerful aspects of this approach is that it can be easily implemented in curvilinear coordinates by making the scale factors of the coordinate transformation symmetric about the boundaries. The method is demonstrated for magnetohydrodynamics (MHD), reduced MHD, and a hybrid code with particle ions and fluid electrons. These boundary conditions yield exact energy conservation in the limit of infinite time and space resolution. Also discussed is the interpretation that the particle charge reverses sign at a conducting boundary with boundary normal perpendicular to the background magnetic field.     

Two‐dimensional magnetosonic shock wave propagation in dense electron–positron–ion plasmas

Two‐dimensional (2D) magnetosonic wave propagation in magnetized quantum dissipative plasmas is studied. The plasma system is comprised of inertial ions, inertia‐less electrons, and positrons. The multi‐fluid quantum hydrodynamic model is used, in which quantum statistical and quantum tunnelling effects of electrons and positrons are included. Reductive perturbation analysis is performed to derive the Zabolotskaya–Khokhlov equation for the 2D propagation of a magnetosonic shock wave in a magnetized qauntum plasma. The effects of varying the different plasma parameters such as positron density and magnetic field intensity on the propagation characteristics of magnetosonic shock waves are discussed with non‐relativistic degenerate plasma parameters in astrophysical plasma situations.