Nonlinear properties of two-dimensional wake waves excited by relativistic electron bunches in plasma

The properties of a nonlinear plasma wake wave excited by an axially symmetric relativistic electron bunch are studied. It is shown that the nonlinear dependence of the wake wavelength on the transverse coordinate leads to distortion of the phase front of the wake wave and to steepening and oscillations of the transverse profile of the wakefield. The magnetic field of the wake wave is nonzero and oscillates at a frequency higher than the plasma electron frequency. Because of nonlinearity, the amplitude of the excited wake wave changes with distance from the bunch. The increase in nonlinearity leads to the development of turbulence and chaotization of the wakefield and results in the switching-on of the thermal effects and plasma heating.     

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.     

Nonlinear extraordinary wave in dense plasma

Conditions for the propagation of a slow extraordinary wave in dense magnetized plasma are found. A solution to the set of relativistic hydrodynamic equations and Maxwell’s equations under the plasma resonance conditions, when the phase velocity of the nonlinear wave is equal to the speed of light, is obtained. The deviation of the wave frequency from the resonance frequency is accompanied by nonlinear longitudinal-transverse oscillations. It is shown that, in this case, the solution to the set of self-consistent equations obtained by averaging the initial equations over the period of high-frequency oscillations has the form of an envelope soliton. The possibility of excitation of a nonlinear wave in plasma by an external electromagnetic pulse is confirmed by numerical simulations.     

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.     

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.     

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).     

Oscillatory growth behavior of multistream instabilities

Multistream instabilities in the one-dimensional Vlasov?Poisson system are studied numerically by using plasmas with multi-humped electron distributions. The evolution of the total wave energy of the plasma oscillations excited by (numerical) noise consists of transient, growth, and nonlinear saturation stages. It is found that, in the growth stage, the total wave energy oscillates for odd number of streams, but it does not oscillate for even number of streams. It is also found that different spectral (Fourier) modes can dominate different stages of the “linear” growth and nonlinear saturation stages.     

Nonlinear theory of the collective Cherenkov interaction of a dense relativistic electron beam with a dense plasma in a waveguide

A nonlinear theory of the instability of a straight relativistic dense electron beam in a plasma waveguide is derived for conditions of the stimulated collective Cherenkov effect. A study is made of a waveguide with a dense plasma such that the plasma wave excited by the beam during the instability can be escribed, with a good degree of accuracy, as a potential wave. General relativistic nonlinear equations are btained that describe the temporal dynamics of beam-plasma instabilities with allowance for plasma nonlinearity and the generation of harmonics of the initial perturbation. Under the assumption that the resonant interaction between the beam waves and the plasma waves is weak, the general equations are reduced to relativistic equations with cubic nonlinearities by using the method of expansion in small perturbations of the trajectories and momenta of the beam and plasma electrons. The reduced equations are solved analytically, the time scales on which the instability saturates are determined, and the nonlinear saturation amplitudes are obtained. A comparison between analytical solutions to the reduced equations and numerical solutions to the general nonlinear equations shows them to be in good agreement. Nonlinear processes caused by the relativistic nature of the beam are found to prevent stochastization of the system in the nonlinear stage of the well-developed instability. In contrast, a nonrelativistic electron beam is found to be subject to significant anomalous nonlinear stochastization.     

Ion acoustic cnoidal waves in a dusty plasma with a critical dust density

The propagation of nonlinear periodic ion acoustic waves in a dusty plasma is considered for conditions in which the coefficient in the nonlinear equation that describes the quadratic nonlinearity of the medium is zero. An equation that accounts for the cubic nonlinearity of the system is derived, and its solution is found. The dependence of the phase velocity of a cnoidal wave on its amplitude and modulus is determined. In describing the effect of higher order nonlinearities on the properties of a dust ion acoustic wave, two coupled equations for the first- and second-order potentials are obtained. It is shown that the nonlinear ion flux generated by a cnoidal wave propagating in a medium with a cubic nonlinearity is proportional to the fourth power of the wave amplitude.     

High-frequency surface waves at a plasma-metal interface: II. Dispersion of a nonlinear wave

A study is made of the dispersion properties of nonlinear surface waves propagating along a plasma-metal interface under conditions corresponding to the formation of a space charge sheath that equalizes the electron and ion fluxes to the wall. Oscillations of the plasma boundary under the action of the surface wave field are taken into account. It is shown that these oscillations are the main nonlinear mechanism for generating wave field harmonics and are analogous to the nonlinearity in the current-voltage characteristic of the space charge sheath. The effect of the nonlinearity on the dispersion properties of surface waves due to the relationship between the sheath thickness and wave amplitude is calculated with allowance for harmonic generation. The energy transported by surface waves under conditions typical of RF and microwave discharges is calculated.     

Self-Excitation of Low-Frequency Oscillations in the Plasma Ring Formed by an ECR Discharge in a Narrow Coaxial Cavity

The conditions for the excitation of low-frequency oscillations in a plasma ring formed by an ECR discharge in a narrow coaxial cavity filled with argon were studied experimentally. The domain of the discharge parameters where these oscillations are stable is determined. It is supposed that the oscillations recorded are excited due to the appearance of an electrostatic wave propagating in the azimuthal direction.     

Breaking of a wake wave excited by a narrow laser pulse in a low-density plasma

The spatial structure of a wake wave excited in a low-density plasma by a laser pulse with a small focal spot radius is studied both analytically and numerically. Numerical study shows that, in a small-amplitude laser field, a wake wave breaks after the formation of an off-axis density maximum, which grows in height away from the pulse to become infinitely high after several periods. Analytical and numerical calculations show that the singularity in the density arises from the intersection of the trajectories of neighboring particles. Numerical simulations demonstrate that, as the laser field amplitude increases, the breaking point of the wake wave rapidly approaches the pulse trailing edge. For weakly nonlinear conditions, an analytic dependence of the coordinate of the breaking point on the amplitude and transverse size of the laser pulse is obtained.     

Breaking of nonlinear cylindrical plasma oscillations

Nonlinear axisymmetric cylindrical plasma oscillations are investigated analytically and numerically. It is shown that the breaking of strongly nonlinear oscillations is attributed to a singularity in the electron density and occurs several periods after the onset of an off-axis density maximum. For weakly nonlinear conditions, an analytic dependence of the breaking time of the oscillations on their amplitude is obtained based on the effect of intersection of electron trajectories and is shown to agree with numerical results.     

Nonlinear theory of coupled waves exemplified by beam-plasma instability

The nonlinear stage of instability of an annular electron beam spatially separated from an annular plasma is investigated. The equations describing coupled waves for an arbitrary ratio between the beam and plasma densities are derived. It is shown that instability saturates at distances on the order of several inverse spatial growth rates. The saturation is caused by relativistic nonlinearity, generation of the second harmonic, and low-frequency modulation of the electromagnetic field. At larger distances, resonant generation of low-frequency beam oscillations becomes a dominant factor. In the case of a low-density beam, an expression for the maximum power of the generated plasma wave is obtained in an explicit form.     

Nonlinear theory of the excitation of azimuthal surface waves during dissipative instability

A theoretical study is made of the surface electromagnetic eigenmodes that are excited by an annular charged-particle beam due to dissipative instability and propagate across the external axial magnetic field in a cylindrical metal waveguide partially filled with plasma. A self-consistent set of differential equations for a cold low-density charged-particle beam moving above the plasma surface is constructed in the single-mode approximation and is solved numerically. It is shown that the larger the dissipation, the slower the instability growth rate and the larger the wave amplitude in the saturation stage of the instability. An increase in the transverse dimensions of a charged-particle beam results in a slower growth of the dissipative instability, in which case, however, the beam transfers a larger fraction of its kinetic energy to the wave.     

Stimulated ionization scattering of a wave beam forming a discharge channel in a magnetic mirror trap

The stimulated scattering of a whistler wave beam forming an extended discharge channel in a magnetic mirror trap is discovered and investigated experimentally. It is shown that the beam is scattered by relaxaction oscillations of the lattice of plasma inhomogeneities excited by the beam field. The spectrum of the pump field in the RF discharge plasma is found to broaden considerably and to contain individual modulation peaks corresponding to lattice oscillations. The peaks are observed at working gas pressures at which the electron mean free path is close to the wavelength of the standing wave forming the discharge channel. A physical model describing the phenomena observed is developed.     

Diagnostics of plasma oscillations by the field of surface waves guided by a dielectric waveguide

The potentialities of the diagnostic method for determining the plasma parameters by recording the surface waves guided by a dielectric waveguide and scattered by plasma oscillations are discussed. The use of surface (slowed) waves makes it possible to improve both the sensitivity and spatial resolution of measurements. The scattering is the most intense near the waveguide cutoff, at which the dependence of the wave propagation constant on the plasma density is the steepest. It is shown experimentally that the method proposed makes it possible to determine the discharge plasma density and electron energy and to estimate the amplitude of the RF field of the plasma waves forming the discharge and the amplitude of plasma density oscillations in these waves. The data obtained from the measurements of the amplitudes of both high-and low-frequency plasma density oscillations by the proposed method agree satisfactorily with theoretical predictions. The experimental data on the plasma density are confirmed by other diagnostic measurements. The ways of reducing measurement errors are proposed.     

Nonlinear ion flux caused by a periodic ion-acoustic wave in plasma with two-temperature electrons

The propagation of periodic ion-acoustic waves in plasma with two-temperature electrons and cold ions is analyzed. The equations for the wave potential are derived in the first- and second-orders of the perturbation theory, and their nonsecular periodic solutions are obtained. The average nonlinear ion flux is determined, and its properties are studied as functions of the ratios between the densities and temperatures of the cold and hot electron components. The conditions are analyzed under which the ion flux is co- or counter-directed to the wave propagation direction. For the case in which, depending on the plasma parameters, the ion flux at a given wave amplitude can be either positive or negative, the domains of existence of positive and negative ion fluxes in the “temperature ratio-density ratio” plane are determined.     

Nonlinear relativistic plasma resonance: Renormalization group approach

An analytical solution to the nonlinear set of equations describing the electron dynamics and electric field structure in the vicinity of the critical density in a nonuniform plasma is constructed using the renormalization group approach with allowance for relativistic effects of electron motion. It is demonstrated that the obtained solution describes two regimes of plasma oscillations in the vicinity of the plasma resonance— stationary and nonstationary. For the stationary regime, the spatiotemporal and spectral characteristics of the resonantly enhanced electric field are investigated in detail and the effect of the relativistic nonlinearity on the spatial localization of the energy of the plasma relativistic field is considered. The applicability limits of the obtained solution, which are determined by the conditions of plasma wave breaking in the vicinity of the resonance, are established and analyzed in detail for typical laser and plasma parameters. The applicability limits of the earlier developed nonrelativistic theories are refined.     

Nonlinear oscillations of a semiconductor plasma with a nonrelativistic electron beam

Nonlinear oscillations of a semiconductor plasma with a low-density electron beam in the absence of an external magnetic field are studied in the hydrodynamic approximation. The beam is assumed to be nonrelativistic and monoenergetic. Cases are studied in which the Langmuir frequency of the electron oscillations in a semiconductor is much higher or much lower than the electron momentum relaxation rate. The self-similar solution obtained for the first case describes the damping of the nonlinear oscillations of the wave potential. Numerical analysis of the second case shows that the electric field distribution in the beam may correspond to that in a shock wave.