Dynamics of beam instability in a finite plasma volume: Numerical experiment

Results are presented from numerical simulations of the dynamics of beam instability in a finite plasma volume (plasma-filled cavity) in a weak magnetic field. It is shown that, in such a system, the low group velocity of the plasma waves excited by an electron beam can result in the generation and amplification of an electric field; strong electron heating in the axial region; and, as a consequence, the generation of a high potential at the axis. The quasistatic radial electric field so produced accelerates ions toward the periphery of the plasma column, forming a directed ion beam with an energy much higher than the thermal energy of the bulk plasma electrons.     

Relaxation of an electron beam during the onset of the electromagnetic filamentation instability

Results are presented from three-dimensional particle-in-cell simulations of relaxation of an electron beam in a plasma. When penetrating into the plasma, the electron beam generates the return current carried by the plasma electrons. In a collisionless plasma, the relaxation mechanism is related to the onset of an electromagnetic filamentation instability. The instability leads to the generation of a quasistatic magnetic field, which decays due to the magnetic field reconnection in the final stage of the system evolution.     

Study of the mechanism for fast ion heating in the GOL-3 multimirror magnetic confinement system

Results are presented from experimental studies of ion heating in the GOL-3 device. The experiments were carried out in a multimirror configuration with a local magnetic well. It was found that, during the injection of a relativistic electron beam, a decrease in the local density of the beam in a magnetic well, which is proportional to the decrease in the strength of the longitudinal magnetic field, results in the formation of a short plasma region with a low electron temperature. The measured longitudinal gradient of the plasma pressure corresponds to an electron temperature gradient of ～2–3 keV/m. Axially nonuniform heating of the plasma electrons gives rise to the macroscopic motion of the plasma along the magnetic field in each cell of the multimirror confinement system. The mixing of the counterpropagating plasma flows inside each cell leads to fast ion heating. Under the given experimental conditions, the efficiency of this heating mechanism is higher than that due to binary electron-ion collisions. The collision and mixing of the counterpropagating plasma flows is accompanied by a neutron and γ-ray burst. The measured ratio of the plasma pressure to the vacuum magnetic field pressure in these experiments reaches 0.2.     

Effect of the external magnetic field on the critical current for the onset of a virtual cathode in an electron beam

The critical current at which an unsteady oscillating virtual cathode forms in an electron beam is studied as a function of the external magnetic field guiding the beam electrons. It is shown that the critical beam current decreases with external magnetic field and that there is an optimum magnetic induction at which the critical current for the onset of an oscillating virtual cathode in the beam is minimum. For a strong guiding magnetic field, the critical beam current is described by relationships derived under the assumption that the motion of the beam electrons is one-dimensional. Such behavior is explained by the characteristic features of the dynamics of the beam electrons in longitudinal and radial directions in the interaction space at different inductions of the external magnetic field.     

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.     

Mechanism for ion acceleration along the normal to the axis of a beam-plasma discharge in a weak magnetic field

The mechanism responsible for the previously discovered phenomenon of acceleration of an ion flow along the normal to the axis of a beam-plasma discharge in a weak magnetic field is investigated. It is suggested that the ions are accelerated in the field of a helicon wave excited in the discharge plasma column. It is shown theoretically that, under actual experimental conditions, a helicon wave can be excited at the expense of the energy of an electron beam. The spectral parameters and spatial structure of the waves excited in a beam-plasma discharge in the frequency ranges of Langmuir and helicon waves are studied experimentally and are shown to be related to the parameters of the ion flow. Theoretical estimates are found to agree well with the experimental results.     

Experimental study of electron vortex structures in an electrostatic plasma lens

Results are presented from experimental studies of electron vortex bunches in a cold ion-beam plasma consisting of strongly magnetized electrons and a beam of almost free positive ions. The existence of electron vortex bunches was detected from local minima of the electric potential on surfaces perpendicular to the magnetic field lines. It is found that the vortices have the form of magnetic-field-aligned filaments, in which electrons rotate with a velocity significantly exceeding both the velocity of the vortex as a whole and the electron velocity in the ambient plasma. It is shown that, in a sufficiently strong magnetic field, the accumulation of electrons in the vortices terminates when the condition for the longitudinal confinement of electrons by the electric field fails to hold.     

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.     

Investigation of the chaotic dynamics of an electron beam with a virtual cathode in an external magnetic field

The effect of the strength of the focusing magnetic field on chaotic dynamic processes occurring in an electron beam with a virtual cathode, as well as on the processes whereby the structures form in the beam and interact with each other, is studied by means of two-dimensional numerical simulations based on solving a self-consistent set of Vlasov-Maxwell equations. It is shown that, as the focusing magnetic field is decreased, the dynamics of an electron beam with a virtual cathode becomes more complicated due to the formation and interaction of spatiotemporal longitudinal and transverse structures in the interaction region of a vircator. The optimum efficiency of the interaction of an electron beam with the electromagnetic field of the vircator is achieved at a comparatively weak external magnetic field and is determined by the fundamentally two-dimensional nature of the motion of the beam electrons near the virtual cathode.     

Nonlinear ineraction of an annular electron beam with azimuthal surface waves

A nonlinear theory is developed that describes the interaction between an annular electron beam and an electromagnetic surface wave propagating strictly transverse to a constant external axial magnetic field in a cylindrical metal waveguide partially filled with a cold plasma. It is shown theoretically that surface waves with positive azimuthal mode numbers can be efficiently excited by an electron beam moving in the gap between the plasma column and the metal waveguide wall. Numerical simulations prove that, by applying a constant external electric field oriented along the waveguide radius, it is possible to increase the amplitude at which the surface waves saturate during the beam instability. The full set of equations consisting of the waveenvelope equation, the equation for the wave phase, and the equations of motion for the beam electrons is solved numerically in order to construct the phase diagrams of the beam electrons in momentum space and to determine their positions in coordinate space (in the radial variable-azimuthal angle plane).     

Amplification of surface waves in a plasma waveguide by a straight relativistic electron beam in a finite magnetic field

The problem of the excitation of electron waves in a thin-walled annular cold plasma in a cylindrical waveguide by a straight relativistic electron beam in a finite magnetic field is considered. The dispersion properties of a waveguide system with parameters close to the experimental ones are investigated. It is shown that the growth rate of the excited high-frequency plasma wave is comparable to that of the low-frequency wave, which is weakly sensitive to the strength of the longitudinal magnetic field.     

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.     

Kinetic theory of the positive column of a low-pressure discharge in a transverse magnetic field

The influence of a transverse magnetic field on the characteristics of the positive column of a planar low-pressure discharge is studied theoretically. The motion of magnetized electrons is described in the framework of a continuous-medium model, while the ion motion in the ambipolar electric field is described by means of a kinetic equation. Using mathematical transformations, the problem is reduced to a secondorder ordinary differential equation, from which the spatial distribution of the potential is found in an analytic form. The spatial distributions of the plasma density, mean plasma velocity, and electric potential are calculated, the ion velocity distribution function at the plasma boundary is found, and the electron energy as a function of the magnetic field is determined. It is shown that, as the magnetic field rises, the electron energy increases, the distributions of the plasma density and mean plasma velocity become asymmetric, the maximum of the plasma density is displaced in the direction of the Ampère force, and the ion flux in this direction becomes substantially larger than the counter-directed ion flux.     

Influence of the electrons reflected from the collector on the parameters of a high-current relativistic electron beam

In plasma microwave oscillators, electrons fall onto the surface of a graphite collector, which leads to the generation of secondary electrons. The influence of the electrons reflected from the collector on the parameters of a high-current relativistic electron beam propagating in a strong longitudinal magnetic field was studied experimentally and by numerical simulations. It is shown that the penetration of the reflected electrons into the drift space can lead to a substantial increase in the depth of the potential well in the drift space, a decrease in the velocity of the beam electrons, and a broadening of the electron energy distribution function.     

Evolution of a Langmuir wave in a weakly inhomogeneous plasma in a longitudinal electric field

The spatial evolution of a Langmuir wave excited by external sources in a weakly inhomogeneous electron plasma in a longitudinal electrostatic field is considered. It is shown that, in a longitudinal electrostatic field, a Langmuir wave can only be amplified in an inhomogeneous plasma provided that the current of trapped electrons exceeds that of untrapped electrons. In this case, as the wave propagates through the inhomogeneous region where its phase velocity increases, some untrapped electrons become trapped in the wave potential wells. As a result, the current of trapped electrons increases and the wave is amplified. Moreover, in the regions where the bulk electrons are localized, the minima of the wave are amplified to a greater extent than its maxima.     

Experimental study of the dynamics of neutron emission from the GOL-3 multimirror trap

In experiments on the plasma heating and confinement in the GOL-3 multimirror trap, a deuterium plasma with a density of ～10¹⁵ cm^?3 and an ion temperature of 1–2 keV is confined for more than 1 ms. The plasma is heated by a relativistic electron beam. The ion temperature, which was measured by independent methods, reached 1.5–2 keV after the beginning of the beam injection. Since such a fast ion heating cannot be explained by the classical energy transfer from electrons to ions through binary collisions, a theoretical model of collective energy transfer was proposed. In order to verify this model, a new diagnostics was designed to study the dynamics of neutron emission from an individual mirror cell of the multimirror trap during electron beam injection. Intense neutron bursts predicted by this model were detected experimentally. Periodic neutron flux modulation caused by the macroscopic plasma flow along the solenoid was observed. The revealed mechanism of fast ion heating can be used to achieve fusion temperatures in the multimirror trap.     

Effect of the longitudinal momentum of electrons on their surfatron acceleration by an electromagnetic wave in space plasma

By numerically calculating the second-order nonlinear time-dependent equation for the wave phase on a particle trajectory, the effect of the longitudinal (with respect to the external magnetic field) momentum of electrons on the dynamics of their surfatron acceleration by an electromagnetic wave propagating across the external magnetic field in space plasma is analyzed. It is shown that, for strongly relativistic initial values of the longitudinal component of the electron momentum (the other parameters of the problem being fixed), the electrons are trapped into the ultrarelativistic regime of surfatron acceleration within a definite interval of the initial wave phase Ψ(0) on the particle trajectory. It was assumed in the calculations that Ψ(0) ≤ π. For the initial wave phases lying within the interval of 0 < Ψ(0) ≤ π, the electrons are immediately trapped by the wave, whereas at π ≤ Ψ(0) ≤ 0, no electron trapping is observed even at long computation times. This result substantially simplifies estimates of the wave damping caused by particle acceleration. The dynamics of the velocity components, momentum, and relativistic factor of electrons in the course of their ultrarelativistic acceleration are considered. The obtained results present interest for the development of modern concepts of the mechanisms for the generation of ultrarelativistic particles in space plasma, correct interpretation of experimental data on the flows of such particles, explanation of possible reasons for the deviation of the fast particle spectra observed in the heliosphere from the standard power-law scaling, and analysis of the relation between such deviations and the space weather.     

On the longitudinal distribution of electric field in the acceleration zones of plasma accelerators and thrusters with closed electron drift

The long-term experience in controlling the electric field distribution in the discharge gaps of plasma accelerators and thrusters with closed electron drift and the key ideas determining the concepts of these devices and tendencies of their development are analyzed. It is shown that an electrostatic mechanism of ion acceleration in plasma by an uncompensated space charge of the cloud of magnetized electrons “kept” to the magnetic field takes place in the acceleration zones and that the electric field distribution can be controlled by varying the magnetic field in the discharge gap. The role played by the space charge makes the mechanism of ion acceleration in this type of thrusters is fundamentally different from the acceleration mechanism operating in purely electrostatic thrusters.     

Nonlocal theory of the spectra of modified ion cyclotron oscillations in a charged plasma produced by gas ionization

The problem of the stability of a charged plasma cylinder in crossed longitudinal magnetic and radial electric fields is considered under the assumption that the plasma electrons are magnetized and distributed uniformly in space and that the plasma ions have a low density and move without collisions. By using the Vlasov and Poisson equations for the electric and magnetic fields of arbitrary strengths and by expanding the radial eigenfunctions in Bessel functions, a dispersion relation is obtained for the modified ion cyclotron frequencies. The dispersion relation obtained is solved for the case of hot plasma electrons. At low ion densities, the oscillation spectra are stable and are described by the families of dispersion curves lying closely around the harmonics of the modified cyclotron frequency (including the zeroth harmonic). At higher ion densities, the dispersion curves for the frequencies of the lowest radial oscillation modes in neighboring families can intersect, leading to instability. The maximum instability growth rate can be several tenths of the modified ion cyclotron frequency.