Nonlinear Electron Plasma Waves Research Articles

Multiphase nonlinear electron plasma waves.

We present a method for constructing multiphase excitations in the generally nonintegrable system of warm fluid equationsdescribing plasma oscillations. It is based on autoresonant excitation of nonlinear electron plasma waves by phase locking with small amplitude chirped-frequency ponderomotive drives. We demonstrate the excitation of these multiphase waves by performing fully nonlinear numerical simulations of the fluid equations. We develop a simplified model based on a weakly nonlinear analytical theory by applying Whitham's averaged Lagrangian procedure. The simplified model predictions are in good agreement with the results from the warm fluid simulations. Such autoresonantly excited multiphase waves form coherent quasicrystalline structures, which can potentially be used as plasma photonic or accelerating devices. Finally, we discuss the laser parameters required for the autoresonant excitation of nonlinear waves in a plasma.

Nonlinear adiabatic electron plasma waves. II. Applications

In this article, we use the general theory derived in Paper I [M. Tacu and D. Bénisti, Phys. Plasmas 29, 052108 (2022)] in order to address several long-standing issues regarding nonlinear electron plasma waves (EPWs). First, we discuss the relevance and practical usefulness of stationary solutions to the Vlasov–Poisson system, the so-called Bernstein–Greene–Kruskal modes, to model slowly varying waves. Second, we derive an upper bound for the wave breaking limit of an EPW growing in an initially Maxwellian plasma. Moreover, we show a simple dependence of this limit as a function of kλD, with k being the wavenumber and λD the Debye length. Third, we explicitly derive the envelope equation ruling the evolution of a slowly growing plasma wave, up to an amplitude close to the wave breaking limit. Fourth, we estimate the growth of the transverse wavenumbers resulting from wavefront bowing by solving the nonlinear, nonstationary, ray tracing equations for the EPW, together with a simple model for stimulated Raman scattering.

Electrostatic electron plasma wave envelope with nonlinear Landau damping in nonthermal plasmas

The characteristics of nonlinear electrostatic electron plasma wave modulation are investigated in collisionless plasmas in the context of the Cairns and Kappa (generalized Lorentzian distribution with spectral index κ) nonthermal electron distribution, with particular attention to the nonlinear Landau damping process with resonance effect at the group velocity of the modulated wave. A modified nonlinear Schrödinger equation (mNLSE) with a nonlocal nonlinear Landau damping term governs the dynamics of the wave modulations. The results predict a far equilibrium region () where the Kappa distributed electrons lead to new dispersive corrections, an overall reduction of the carrier wave frequency () and the phase velocity and the existence of parameter regions where . On the contrary, the results in the near equilibrium region () are qualitatively similar to that of Cairns distributed electrons. The carrier waves always become damped by transferring energy to the side band waves due to nonlinear Landau damping and nonthermal particles enhance the energy transfer rate. The mNLSE is simulated extensively by a 2nd order split-step Fourier method with various initial pulses in different parameter regions.

Nonlinear electron plasma waves in fully relativistic plasmas

Propagation of nonlinear electron plasma waves is investigated in a fully relativistic election-ion plasma using two-fluid hydrodynamic model. The relationship between pressure and density is assumed to be of polytropic form for relativistic electrons. The conditions for the validity of adiabatic equation of state for electron fluid is also discussed. The well-known pseudopotential approach is employed for arbitrary amplitude wave analysis and superluminous and subluminous wave phase speed cases are discussed in two special frames of references transformed under Lorentz-transformation. The set of model equations is solved analytically as well as numerically to obtain nonlinear periodic wave structures of electron plasma waves in a fully relativistic plasmas. A special case of solitary wave structure formed in subluminous phase speed case is also discussed in detail, which has not been done in the previous published literature. The effects of electron temperature and phase speed of the plasma wave (i.e., for subluminous and superluminous wave phase speed cases) on the amplitude of nonlinear periodic wave and solitary wave structures are also presented with its possible applications to the astorphysical environment.

Interaction of the variable-coefficient long-wave–short-wave resonance interaction equations

Long-wave–short-wave resonance interaction (LSRI) equations have been studied in the plasmas, gravity waves, nonlinear electron-plasma and ion-acoustic waves. By virtue of the bilinear method, two soliton solutions of the variable-coefficient LSRI equations are attained. Interaction of the solitons are studied when the coefficients are taken as the generalized Gauss functions. New types of the soliton interaction are exhibited. Position and width of the disturbances can be controlled.

Stability of electron wave spectra in weakly magnetized plasmas

Analytical models for nonlinear electron plasma waves in weakly magnetized plasmas are developed for single as well as multi-mode conditions, with continuous wave spectra being a limiting case. The conditions for wave decay as well as modulational instabilities are analysed. Our results demonstrate that slow or nearly stationary plasma density variations can be found for weakly magnetized plasmas even for weakly nonlinear electron plasma waves without involving cavitation of large amplitude plasma waves. A reduction of the growth rates for decay as well as modulational instabilities are found when the spectral width of the wave spectrum is increased. Some of our results are relevant for the interpretation of the nonlinearly enhanced ion acoustic lines often observed in non-equilibrium ionospheres.

Langmuir wave filamentation in the kinetic regime. II. Weak and strong pumping of nonlinear electron plasma waves as the route to filamentation

We consider two kinds of pumped Langmuir waves (LWs) in the kinetic regime, kλD≳0.2, where k is the LW wavenumber and λD is the Debye length, driven to finite amplitude by a coherent external potential whose amplitude is either weak or strong. These dynamically prepared nonlinear LWs develop a transverse (filamentation) instability whose nonlinear evolution destroys the LW's transverse coherence. Instability growth rates in the weakly pumped regime are the same as those of Bernstein-Greene-Kruskal modes considered in Part I (D. A. Silantyev et al., Phys. Plasmas 24, 042104 (2017)), while strongly pumped LWs have higher filamentation grow rates.

Collapse of nonlinear electron plasma waves in a plasma layer

The excitation of nonlinear electron plasma waves in the plasma layer is investigated theoretically. This excitation is realized by means of initial oscillatory perturbations of the volume electron concentration or by initial oscillatory distributions of the longitudinal electron velocity. The amplitudes of the initial perturbations are small and the manifestation of the volume nonlinearity is absent. When the amplitudes of the initial perturbations exceed some thresholds, the values of the electron concentration near the plasma boundary increase catastrophically. The maxima of the electron concentration reach extremely high magnitudes, and sharp peaks in the electron concentration occur, which are localized both in the longitudinal and transverse directions. This effect is interpreted as wave collapse near the plasma boundary.

Kinetic simulations and reduced modeling of longitudinal sideband instabilities in non-linear electron plasma waves

Kinetic Vlasov simulations of one-dimensional finite amplitude Electron Plasma Waves are performed in a multi-wavelength long system. A systematic study of the most unstable linear sideband mode, in particular its growth rate γ and quasi- wavenumber δk, is carried out by scanning the amplitude and wavenumber of the initial wave. Simulation results are successfully compared against numerical and analytical solutions to the reduced model by Kruer et al. [Phys. Rev. Lett. 23, 838 (1969)] for the Trapped Particle Instability (TPI). A model recently suggested by Dodin et al. [Phys. Rev. Lett. 110, 215006 (2013)], which in addition to the TPI accounts for the so-called Negative Mass Instability because of a more detailed representation of the trapped particle dynamics, is also studied and compared with simulations.

Modulational stability of electron plasma wave spectra

Analytical models for weakly nonlinear electron plasma waves are considered in order to obtain dynamic equations for the space-time evolution of their local power spectra. The model contains the wave kinetic equation as a limiting case for slow, long wavelength modulations. It is demonstrated that a finite spectral width in wavenumbers has a stabilizing effect on the modulational instability. The results invite a simple heuristic relation between the spectral width and the root-mean-square amplitude of stable stationary turbulent Langmuir wave spectra. A non-local average dispersion relation is derived as a limiting form by using the formalism developed for the spectral dynamics.

Kinetic simulations of the self-focusing and dissipation of finite-width electron plasma waves.

Two-dimensional simulations, both Vlasov and particle-in-cell, are presented that show the evolution of the field and electron distribution of finite-width, nonlinear electron plasma waves. The intrinsically intertwined effects of self-focusing and dissipation of field energy caused by electron trapping are studied in simulated systems that are hundreds of wavelengths long in the transverse direction but only one wavelength long and periodic in the propagation direction. From various initial wave states, both the width at focus Δm relative to the initial width Δ0 and the maximum field amplitude at focus are shown to be a function of the growth rate of the transverse modulational instability γTPMI divided by the loss rate of field energy νE to electrons escaping the trapping region. With dissipation included, an amplitude threshold for self-focusing γTPMI/νE∼1 is found that supports the analysis of Rose [Phys. Plasmas 12, 012318 (2005)].

Coherent relativistic wake wave of a charged object moving steadily in a plasma

Nonlinear electron plasma waves driven by a finite-charged particle pulse or rigid object moving at relativistic speeds are investigated. Quasi-stationary smooth and spiky wake waves comoving with the object are found. Localized soliton-like solutions are also shown to exist. Relativistic effects tend to prevent their formation because of the electron mass increase. The application of the very-large-amplitude wake density waves as a source of ultrahigh-energy cosmic-ray events is discussed.

Two-dimensional Vlasov simulation of electron plasma wave trapping, wavefront bowing, self-focusing, and sideloss

Two-dimensional Vlasov simulations of nonlinear electron plasma waves are presented, in which the interplay of linear and nonlinear kinetic effects is evident. The plasma wave is created with an external traveling wave potential with a transverse envelope of width Δy such that thermal electrons transit the wave in a “sideloss” time, tsl~Δy/ve. Here, ve is the electron thermal velocity. The quasisteady distribution of trapped electrons and its self-consistent plasma wave are studied after the external field is turned off. In cases of particular interest, the bounce frequency, ωbe=keϕ/me, satisfies the trapping condition ωbetsl>2π such that the wave frequency is nonlinearly downshifted by an amount proportional to the number of trapped electrons. Here, k is the wavenumber of the plasma wave and ϕ is its electric potential. For sufficiently short times, the magnitude of the negative frequency shift is a local function of ϕ. Because the trapping frequency shift is negative, the phase of the wave on axis lags the off-axis phase if the trapping nonlinearity dominates linear wave diffraction. In this case, the phasefronts are curved in a focusing sense. In the opposite limit, the phasefronts are curved in a defocusing sense. Analysis and simulations in which the wave amplitude and transverse width are varied establish criteria for the development of each type of wavefront. The damping and trapped-electron-induced focusing of the finite-amplitude electron plasma wave are also simulated. The damping rate of the field energy of the wave is found to be about the sideloss rate, νe~tsl-1. For large wave amplitudes or widths Δy, a trapping-induced self-focusing of the wave is demonstrated.

Relativistic warm plasma theory of nonlinear laser-driven electron plasma waves

A relativistic, warm fluid model of a nonequilibrium, collisionless plasma is developed and applied to examine nonlinear Langmuir waves excited by relativistically intense, short-pulse lasers. Closure of the covariant fluid theory is obtained via an asymptotic expansion assuming a nonrelativistic plasma temperature. The momentum spread is calculated in the presence of an intense laser field and shown to be intrinsically anisotropic. Coupling between the transverse and longitudinal momentum variances is enabled by the laser field. A generalized dispersion relation is derived for Langmuir waves in a thermal plasma in the presence of an intense laser field. Including thermal fluctuations in three-velocity-space dimensions, the properties of the nonlinear electron plasma wave, such as the plasma temperature evolution and nonlinear wavelength, are examined and the maximum amplitude of the nonlinear oscillation is derived. The presence of a relativistically intense laser pulse is shown to strongly influence the maximum plasma wave amplitude for nonrelativistic phase velocities owing to the coupling between the longitudinal and transverse momentum variances.

Propagation and Damping of Nonlinear Plasma Wave Packets

Nonlinear electron plasma wave packets are shown to locally damp at the rear of the packet. Resonant particles enter the back of the packet and linearly damp the first few wavelengths, thereby carrying energy away from the back edge and eventually eroding the packet. This process could significantly affect the recurrence and long-time behavior of stimulated Raman scattering because it is predicted that a nonlinear packet will erode away before it travels a speckle length. The effects of a density gradient on the packet's propagation are also discussed.

Trapping, dark current, and wave breaking in nonlinear plasma waves

The trapping of thermal electrons in a nonlinear electron plasma wave of arbitrary phase velocity is investigated. Using a model based on single-particle dynamics, various thermal effects are calculated, such as the evolution of the plasma temperature. Assuming a broad (one-dimensional) plasma wave driver, the threshold plasma wave amplitude for electron trapping is calculated, thereby determining the fraction of trapped plasma electrons and the expected dark current in a plasma-based accelerator. It is shown that the trapping threshold is increased within the region of the laser pulse. The laser intensity required to excite plasma waves of sufficient amplitude to trap background electrons is determined. The hydrodynamic wave breaking field amplitude is recovered from particle trapping considerations. Implications for experimental and numerical studies of plasma accelerators are discussed.

Nonlinear effects at the boundary of an electron plasma

Two solutions for nonlinear electron plasma waves propagating along a cold plasma boundary are reported. Thus, the nonlinear frequency shift caused by the harmonic generation as well as new localized nonlinear perturbations are found.

Electron Acceleration by Nonlinear High Frequency Waves inWeakly Magnetized Plasmas

The evolution of nonlinear electron plasma waves in weaklymagnetized plasmas is studied numerically. The analysis is based on anelectrostatic fluid model where the principal waves are assumed topropagate along the magnetic field lines. Numerical results using aspectral method with periodic boundary conditions demonstrate“quasi-collapsing” solutions for localizedinitial conditions with sufficiently high amplitude. For smallerinitial amplitudes quasi-recurrent variations are found, which havenot been treated previously. The emphasis of the study is placed on aninvestigation of the acceleration of electrons by the high-frequencywaves. This problem is analyzed using the numerically obtainedwave-field as an input for a code where particles are traced in spaceand time. It is found that electrons can gain significant energy inone part of the wave-packet and loose this energy again in anotherpart, without the net particle acceleration necessarily beingsignificant.

Application of a general formalism to nonlinear wave phenomena in unbounded and bounded plasmas

A general symbolic formalism for economically handling quadratically nonlinear systems is demonstrated by way of application to weakly nonlinear electron plasma waves in the 3-harmonic approximation. For the first time, it is shown that the nonlinear corrections depend on a certain additional assumption (constant velocity or constant current), and a symbolic formulation of boundary conditions is proposed. Further applications, such as to fusion plasmas, are envisaged.

Weakly nonlinear high frequency waves in magnetized plasmas

The evolution of nonlinear electron plasma waves in weakly magnetized plasmas is studied for conditions where the principal waves propagate along the magnetic field lines. The analysis is based on an electrostatic fluid model for the waves. Numerical results using a spectral method with periodic boundary conditions demonstrate “quasi-collapsing” solutions for localized initial conditions with sufficiently high amplitude. The possibility of acceleration of electrons by the high-frequency waves is discussed. It is demonstrated that electrons are likely to gain energy in parts of the nonlinear wavepacket and to loose all, or most of, this energy again in other parts.