Trapping of electrons and acceleration of the electron bunch in a wake wave

The process of electron trapping by a wake wave excited by a laser pulse in a plasma channel in the case where the electron bunches are injected into the vicinity of the maximum of the wakefield potential at a velocity lower than the wave phase velocity is considered. The mechanism for the formation of a compact electron bunch in the trapping region when only the electrons of the injected bunch that are trapped in the focusing phase mainly undergo the subsequent acceleration in the wakefield is analyzed. The influence of the spatial dimensions of the injected bunch and its energy spread on the length of the trapped electron bunch and the fraction of trapped electrons is studied analytically and numerically. For electron bunches with different ratios of their spatial dimensions to the characteristic dimensions of the wake wave, the influence of the injection energy on the parameters of the high-energy electron bunch trapped and accelerated in the wake-field is studied.     

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.     

Acceleration of electron bunches injected into a wake wave

The process of trapping and acceleration of nonmonoenergetic electron bunches by a wake wave excited by a laser pulse in a plasma channel is investigated. The electrons are injected into the vicinity of the maximum of the wakefield potential with a velocity lower than the wave phase velocity. The study is aimed at utilizing specific features of a wakefield with substantially overlapped focusing and accelerating phases for achieving monoenergetic electron acceleration. Conditions are found under which electrons in a finite-length nonmonoenergetic bunch are accelerated to high energies, while the energy spread between them is minimal. The effect of energy grouping of electrons makes it possible to obtain compact high-energy electron bunches with a small energy spread during laser plasma acceleration.     

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.     

Radial structure of the wakefield excited during the self-modulation of a laser pulse in a plasma

A study is made of the structure of the wakefield excited in the linear stage of the self-modulation of a high-power laser pulse in a homogeneous underdense plasma. It is shown that the fronts of the wake wave are curved and the profile of the wakefield amplitude differs strongly from the intensity profile of the laser pulse. The diffraction effects are found to play a key role in the formation of the transverse profile of the wakefield.     

Wakefield excitation by a relativistic electron bunch in a magnetized plasma

The excitation of a wake wave by a relativistic electron beam in an unbounded magnetized plasma and a plasma waveguide is studied theoretically. It is shown that, in a waveguide partially filled with a plasma, the energy that the electrons of the accelerated beam can gain is 37 times higher than the energy of the electrons of the beam generating wakefield.     

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.     

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.     

Dynamics of an Electron Bunch Accelerated by a Wakefield

The energy characteristics of an electron bunch accelerated by a wakefield are largely determined by the initial bunch dimensions. Present-day injectors are still incapable of ensuring the initial spatial parameters of the bunches required for their acceleration without increasing the energy spread of the bunch electrons. In connection with this, the possibility is studied of improving the energy characteristics of an accelerated bunch by precompressing it in the longitudinal direction in the stage of trapping by a wakefield. Analytic formulas are derived that describe the one-dimensional dynamics of the spatial and energy characteristics of a short (much shorter than the wakefield wavelength) electron bunch in both the trapping and acceleration stages. The analytical results obtained are shown to agree fairly well with the results from one-dimensional and three-dimensional simulations, provided that the electrons are injected into the region that is optimum for acceleration. The possibility is discussed of forming compressed bunches so as to ensure the high quality of the bunch in the course of its acceleration to high energies.     

Acceleration of an electron bunch injected in front of a laser pulse generating an accelerating wake wave

A study is made of a promising method for injecting an electron bunch into an accelerating laser-plasma system. A bunch is injected ahead of the front of a laser pulse generating a wake wave that propagates in a direction collinear with the pulse and has a velocity lower than the pulse group velocity. The influence of the initial nonmonoenergetic character of the bunch on its trapping and acceleration is investigated. By appropriately choosing the laser pulse parameters and the bunch injection energy, it is possible to create such conditions for the trapping of an initially nonmonoenergetic bunch by the wake wave that, over a certain acceleration distance, there will be no energy spread of the bunch due to its initial nonmonoenergetic character, a circumstance that allows compact electron bunches to be accelerated to high energies, with a minimum energy spread.     

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.     

Ion-acoustic “Houston's horse” effect

The structure of an ion-acoustic forerunner excited by a shock wave in a weakly ionized plasma is studied. It is shown that, when the shock velocity exceeds the ion-acoustic speed, a soliton bunch is produced at the perturbation front. The increase in the shock velocity to a certain critical value is accompanied by an increase in the soliton amplitude. A further increase in velocity leads to an explosive-like collapse of the bunch, which results in a decrease in the medium resistance. This phenomenon is analogous to the “Houston's horse” effect in narrow-channel hydrodynamics.     

Effect of plasma nonlinearity on the beam-plasma interaction in a hybrid plasma waveguide

A study is made of the characteristic features of the effect of plasma nonlinearity in a slow-wave structure on microwave generation by an electron beam and on electron beam energy losses. Theoretical results on the plasma density variation, the amplitude of the excited microwaves, and the velocity distribution function of the beam electrons are compared with the experimental data. It is shown that the self-consistency between the decreasing plasma density gradient and the spatial variation of the amplitude of an amplified wave in a slowwave structure leads to a significant (severalfold) increase in the efficiency with which the electron beam energy is converted into microwave energy in short pulses. The predictions of the theoretical model developed to describe the non-steady-state beam-plasma interaction agree well with the experimental data.     

Electron bunch acceleration in the wake wave breaking regime

Results are presented from theoretical analysis and 2D PIC simulations of electron acceleration in a breaking wake plasma wave generated by a short intense laser pulse during its interaction with a finite-length underdense plasma layer. The high energy electron energy spectrum and transverse emittance are obtained. It is shown that, for laser pulse lengths above the plasma wake wavelength, the wakefield-accelerated electrons are further accelerated by the electromagnetic wave. Published in Russian in Fizika Plazmy, 2006, Vol. 32, No. 4, pp. 291–310. The text was submitted by the authors in English.     

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.     

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.     

Wakefield acceleration of nonmonoenergetic electron bunches

The process of trapping and acceleration of a nonmonoenergetic electron bunch of finite length is investigated analytically in terms of a one-dimensional model, and relevant three-dimensional simulations are performed. The bunch is assumed to be injected into the region of maximum wake wave potential, the injection energy being such that the electron velocities are lower than the wave phase velocity. The study is aimed at clarifying how the spatial and energy parameters of the injected bunch in the trapping and acceleration stages depend on its initial energy spread. Formulas are obtained that describe the change in the bunch length and its energy spread in the course of acceleration. In some important limiting cases, the formulas are simple enough for them to be conveniently used for practical estimates. The injection conditions are discussed under which the electrons of a nonmonoenergetic bunch can be accelerated to high energies and the energy spread of the bunch electrons after acceleration is weakly sensitive to their initial energy spread. The analytical results agree well with the results of numerical simulations.     

Spectra from stimulated Raman scattering of short relativistically strong laser pulses in an underdense plasma

A set of equations describing large-angle stimulated Raman scattering (SRS) of a short, relativistically strong laser pulse propagating in an underdense plasma is derived and investigated numerically. It is shown that the SRS spectrum depends strongly on the pulse shape. If a pulse with a sharp leading edge excites a strongly nonlinear wake wave, the scattering occurs in relativistic electron flows and is accompanied by the Doppler frequency shift. When the electron flow is directed oppositely to the pulse propagation direction, the frequency upshift is maximum for the direct-backward SRS and decreases with decreasing scattering angle.     

Generation of a wakefield during gas ionization

One-dimensional equations are derived that describe the hydrodynamic and electrodynamic properties of a plasma created through gas ionization by a short intense laser pulse. Different approaches (in particular, the particle-in-cell method) are used to show that, with ionization processes included, the excitation of a wakefield by an intense laser pulse can be described by the method of slowly varying amplitudes. It is shown that ionization processes enhance the wakefield excited by a moderate-intensity laser by about 10% in the case of a linearly polarized laser and by about 50% in the case of a circularly polarized laser. Ionization processes in light gases irradiated with high-intensity laser pulses have essentially no effect on the wakefield during the resonant excitation of a plasma wave by the ponderomotive force and play a governing role far from the resonance.     

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.