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.     

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.     

Effect of Long-Wavelength Magnetic Field Disturbances on the Generation of Auroral Kilometric Radiation

The effect of long-wavelength magnetic field disturbances typical of the Earth’s auroral region on the generation of auroral kilometric radiation in a narrow three-dimensional plasma cavity in which a weakly relativistic electron flow propagates against the background of cold low-density plasma is analyzed. The dynamics of the propagation and amplification of fluctuation waves with initial group velocities directed toward the higher magnetic field is considered in the geometrical optics approximation. Analysis of wave trajectories shows that the wave amplification coefficients depend on the magnetic field gradient in the reflection region. If the wave reflection point lies in the region where the gradient of the disturbed magnetic field is less than that of the undisturbed dipole field, then the wave amplification coefficients exceed those of waves propagating in the undisturbed field, and vice versa. Thus, the shape of the spectrum of generated waves changes in the presence of long-wavelength disturbances of the dipole magnetic field in such a way that segments with different curvatures can form in the spectrum.     

On the minimal set of plasma parameters to determine the dispersion law of electron whistler waves

The minimal sufficient set of plasma parameters is presented to describe the dispersion properties of electron whistler waves (helicons) in a wide frequency range above the ion cutoff frequency, provided that the wave frequency is significantly lower than the electron plasma frequency. When the gyrofrequency of the lightest ions is much higher than those of heavier ions, it is sufficient to know the relative content of the lightest ions, the highest ion cutoff frequency, the lower hybrid resonance frequency, and the electron gyro- and plasma frequencies. In this case, the frequency of electron whistler waves is determined by the upper root of the biquadratic equation derived, whereas the lower root corresponds to a resonant mode with its refractive index increasing when the frequency tends toward the highest ion gyrofrequency from below. The developed approach is also efficient in plasmas containing a substantial amount of negative ions and/or heavy dust particulates. The accuracy of the approximate solution of the total cold plasma dispersion relation is illustrated graphically.     

Surface waves on the boundary of a conducting medium and their excitation by a relativistic electron beam

Excitation of surface waves by a relativistic electron beam propagating over a conducting cylindrical medium (metal or highly ionized plasma) is investigated theoretically. Dispersion relations describing the linear interaction of surface electromagnetic waves with a monoenergetic electron beam are derived, and the growth rates and spatial amplification factors of excited waves are determined. Condition for the nonlinear trapping of the beam electrons by a surface wave is used to determine the maximum amplitude of the excited wave and the optimal radiator length. The electric field of a surface wave excited by an electron beam is estimated for a particular case.     

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.     

Theory of longitudinal plasma waves with allowance for ion motion

A study is made of the propagation of steady-state large-amplitude longitudinal plasma waves in a cold collisionless plasma with allowance for both electron and ion motion. Conditions for the existence of periodic potential waves are determined. The electric field, potential, frequency, and wavelength are obtained as functions of the wave phase velocity and ion-to-electron mass ratio. Taking into account the ion motion results in the nonmonotonic dependence of the frequency of the waves with the maximum possible amplitudes on the wave phase velocity. Specifically, at low phase velocities, the frequency is equal to the electron plasma frequency for linear waves. As the phase velocity increases, the frequency first decreases insignificantly, reaches its minimum value, and then increases. As the phase velocity increases further, the frequency continues to increase and, at relativistic phase velocities, again becomes equal to the plasma frequency. Finally, as the phase velocity approaches the speed of light, the frequency increases without bound.     

Excitation of RF Oscillations in a Discharge with Negative Differential Conductivity

The excitation of oscillations in a discharge with negative differential conductivity is studied experimentally. The possibility is demonstrated of amplifying oscillations in the cathode dark space at frequencies close to the electron plasma frequency of the positive-column plasma. The phase velocities of waves at these frequencies are determined. When the waves pass from the cathode dark space to the discharge positive column, their phase velocities decrease; the closer the frequency is to the electron plasma frequency, the more pronounced the decrease in the phase velocity. As the intensity of oscillations increases, the discharge becomes non-steady-state. This is confirmed by the time evolution of the current-voltage characteristic. The shape of the current-voltage characteristic, its splitting, and the rate at which it varies depend on the input RF power. The decrease in the cathode dark space indicates that the ionization processes in the discharge are strongly influenced by electron plasma oscillations excited due to the collective interaction of the electron beam formed at the cathode with the discharge plasma. It is these processes that determine the maximum values of both the frequency of the excited oscillations and the power that can be withdrawn from the discharge.     

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.     

Generation of strong magnetic fields by counterpropagating moderate-intensity laser pulses in a low-density plasma

A study is made of the generation of strong quasistatic magnetic fields by counterpropagating moderate-intensity laser pulses of different frequencies in a low-density plasma. Strong magnetic fields are generated by small-scale large-amplitude plasma waves excited at different frequencies by ponderomotive forces in the interaction region of laser pulses. It is shown that magnetic fields are generated most efficiently under resonance conditions such that the frequency difference between laser pulses coincides with the plasma frequency. The spatial distribution of quasistatic magnetic fields is investigated, and the pattern of the contour lines of the electric current is calculated.     

Emission of low-frequency electromagnetic waves by a short laser pulse propagating in a plasma with density fluctuations

It is shown that a short laser pulse propagating in a plasma with electron density fluctuations can emit electromagnetic waves with frequencies much lower than the laser carrier frequency. Emissions with frequencies close to the plasma frequency and the doubled plasma frequency in a nonisothermal plasma, as well as emission generated in a turbulent plasma, are examined. The effects in question are related to the transformation of the laser pulse wakefield into electromagnetic radiation by electron density fluctuations. The phenomenon under study opens new possibilities for diagnostics of both plasma fields excited by laser pulses and electron density fluctuations in a plasma.     

Effect of a strong monochromatic electromagnetic wave with circular polarization on one-dimensional wake waves in plasma

A study is made of the excitation of wake waves by a one-dimensional bunch of charged particles in an electron plasma in the presence of an intense monochromatic pump wave with circular polarization. In the main state (in the absence of a bunch), the interaction between a pump wave and a plasma is described by the Maxwell equations and the nonlinear relativistic hydrodynamic equations for a cold plasma. The excitation of linear waves by a one-dimensional bunch is investigated against a cold plasma background. It is shown that, in a certain range of the parameter values of the bunch, pump wave, and plasma, the amplitude of the excited transverse waves grows as the energy of the bunch particles increases until the relativistic factor of the bunch reaches a certain threshold value above which the transverse wave amplitude becomes essentially independent of the bunch particle energy and grows as the intensity and frequency of the pump wave increase. The amplitude and wavelength of the longitudinal field, which is shown to depend weakly on the energy of the bunch particles, grows with increasing the pump wave intensity.     

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.     

Excitation of growing wake waves by an electron bunch in a plasma in an intense pump wave

A study is made of the excitation of wake waves by a one-dimensional electron bunch in an electron plasma in the presence of an intense monochromatic pump wave with circular polarization. In the main state (in the absence of a bunch), the interaction between a pump wave and a plasma is described by Maxwell's equations and the nonlinear relativistic hydrodynamic equations for a cold plasma. The excitation of linear waves by a one-dimensional bunch is investigated against a cold plasma background. It is shown that, in a certain range of parameter values of the bunch, pump wave, and plasma, the excitation is resonant in character and the amplitude of the excited wake waves increases with distance from the bunch.     

Generation of ion-acoustic and magnetoacoustic waves in an RF helicon discharge

A study is made of the generation of ion-acoustic and magnetoacoustic waves in a discharge excited in an external magnetic field by an electromagnetic wave in the whistler frequency range (ω_LH ? ω ? ω_He, where ω_LH = $\sqrt {\omega _{He} \omega _{Hi} } $ and ω_He and ω_Hi are the electron and ion gyrofrequencies, respectively). The excitation of acoustic waves is attributed to the decay of a high-frequency hybrid mode forming a plasma waveguide into low-frequency acoustic waves and new high-frequency waves that satisfy both the decay conditions and the waveguide dispersion relations. The excitation of acoustic waves is resonant in character because the conditions for the generation of waveguide modes and for the occurrence of the corresponding nonlinear wave processes should be satisfied simultaneously. An unexpected effect is the generation of magnetoacoustic waves by whistlers. A diagnostic technique is proposed that allows one to determine the thermal electron velocity by analyzing decay conditions and dispersion relations for waves in the discharge channel.     

Spectral Properties of Plasma Waves in Periodic Plasma-Filled Structures

The dispersion properties and field distribution of plasma waves in a periodic plasma-filled waveguide are correctly analyzed for the first time with allowance for all spatial harmonics. It is shown that the plasma wave spectrum has a zonal structure and a lower cutoff frequency. The widths of the forbidden bands and the lower cutoff frequency are determined by the waveguide corrugation depth. For a planar periodic plasma-filled waveguide, the allowed and forbidden frequency bands are evaluated analytically. The waveguide periodicity substantially influences the field of the plasma waves at frequencies close to the forbidden bands. This leads to the formation of regions in which the energy density of plasma waves exceeds the average level by more than one order of magnitude. This effect is related to the contribution from the higher spatial harmonics.     

Interaction of a high-current electron beam with hybrid waveguide and plasma modes in a dielectric Cherenkov maser with a plasma layer

The characteristics of a high-current electron beam-driven microwave amplifier—a dielectric Cherenkov maser—are investigated in the framework of linear theory for the case of a plasma layer present at the surface of the maser slow-wave structure. The dispersion relation for axisymmetric perturbations is obtained for the conventional configuration (a circular dielectric-lined waveguide and a thin annular beam propagating within the vacuum region inside the annular plasma) in the model of a fully magnetized plasma and beam. The results of numerically solving the dispersion relation for different beam and plasma parameters are presented, and an analysis based on these results is given with regard to the features of the beam interaction with the hybrid waves of the system (both hybrid waveguide and hybrid plasma modes). For the hybrid waveguide mode, the dependences of the spatial growth rate on the frequency demonstrate an improvement in the gain at moderate plasma densities, along with narrowing the amplification band and shifting it toward higher frequencies. For the hybrid plasma mode, the interaction with a mildly relativistic (200–250 keV) beam, when the wave phase velocity is close to the speed of light in the dielectric medium, is most interesting and, therefore, has been studied in detail. It is shown that, depending on the beam and plasma parameters, different regimes of the hybrid plasma mode coupling to the hybrid waveguide mode or a usual, higher order plasma mode take place; in particular, a flat gain vs. frequency dependence is possible over a very broad band. The parameters at which the ?3-dB bandwidth calculated for the 30-dB peak gain exceeds an octave are found.     

Magnetosonic oscillations of thin plasma columns

Oscillations of a plasma column in a longitudinal magnetic field are considered. It is found that eigenmodes with frequencies close to the ion cyclotron frequency can be excited in columns the radii of which are smaller than the characteristic wavelength of magnetosonic oscillations predicted by the theory of homogeneous plasma. The eigenmodes have the form of waves running around the column axis in the direction of electron gyration in the magnetic field. Magnetosonic oscillations can be excited as a side effect when using helical antennas for ion cyclotron resonance heating of plasma. These oscillations should enhance electron heating in the plasma core, as well as both electron and ion heating at the periphery of the plasma column. The spectrum of eigenmodes of inhomogeneous plasma columns includes oscillations of different nature. Comparative analysis of their properties performed in the present paper is useful for understanding the full picture of the physical processes occurring during ion cyclotron resonance heating and clarifying the characteristic features of the magnetosonic oscillations under study.     

Possible mechanism for radial ion acceleration in a beam-plasma discharge

A mechanism is proposed that can lead to radial ion acceleration in a plasma discharge excited by an electron beam in a relatively weak longitudinal magnetic field. The mechanism operates as follows. The beam generates an azimuthally asymmetric slow potential wave, which traps electrons. Trapped magnetized electrons drift radially with a fairly high velocity under the combined action of the azimuthal wave field (which is constant for them) and a relatively weak external longitudinal magnetic field. The radial electron flux generates a radial charge-separation electric field, which accelerates unmagnetized plasma ions in the radial direction. The ion flux densities and energies achievable in experiments with kiloelectronvolt electron beams in magnetic fields of up to 100 G are estimated.     

Theory of the acoustic instability and behavior of the phase velocity of acoustic waves in a weakly ionized plasma

The amplification of acoustic waves due to the transfer of thermal energy from electrons to the neutral component of a glow discharge plasma is studied theoretically. It is shown that, in order for acoustic instability (sound amplification) to occur, the amount of energy transferred should exceed the threshold energy, which depends on the plasma parameters and the acoustic wave frequency. The energy balance equation for an electron gas in the positive column of a glow discharge is analyzed for conditions typical of experiments in which acoustic wave amplification has been observed. Based on this analysis, one can affirm that, first, the energy transferred to neutral gas in elastic electron-atom collisions is substantially lower than the threshold energy for acoustic wave amplification and, second, that the energy transferred from electrons to neutral gas in inelastic collisions is much higher than that transferred in elastic collisions and thus may exceed the threshold energy. It is also shown that, for amplification to occur, there should exist some heat dissipation mechanism more efficient than gas heat conduction. It is suggested that this may be convective radial mixing within a positive column due to acoustic streaming in the field of an acoustic wave. The features of the phase velocity of sound waves in the presence of acoustic instability are investigated.