Nonlinear interactions between electromagnetic waves and electron plasma oscillations in quantum plasmas

We consider nonlinear interactions between intense circularly polarized electromagnetic (CPEM) waves and electron plasma oscillations (EPOs) in a dense quantum plasma, taking into account the electron density response in the presence of the relativistic ponderomotive force and mass increase in the CPEM wave fields. The dynamics of the CPEM waves and EPOs is governed by the two coupled nonlinear Schr?dinger equations and Poisson's equation. The nonlinear equations admit the modulational instability of an intense CPEM pump wave against EPOs, leading to the formation and trapping of localized CPEM wave pipes in the electron density hole that is associated with a positive potential distribution in our dense plasma. The relevance of our investigation to the next generation intense laser-solid density plasma interaction experiments is discussed.     

Formation and dynamics of relativistic electromagnetic solitons in plasmas containing high-and low-energy electron components

We present theoretical and numerical studies of the nonlinear interactions between intense electromagnetic waves in plasmas containing high-and low-energy electron components. Such plasmas are frequently observed in laser-plasma experiments, where the hot electron component is created by the acceleration of electrons by strong electrostatic waves that are created by the laser-induced Raman forward and backward instabilities. The two-component electron plasma is described by the Vlasov equation for the hot electrons and the hydrodynamic equations for the cold electrons, which are coupled nonlinearly to the electromagnetic wave equation and the Poisson equation for the potential. The present nonlinear system is shown to admit electromagnetic solitary waves correlated with a positive potential and trapped electron islands from the hot electron population. The text was submitted by the authors in English.     

Phase-space moment-equation model of highly relativistic electron-beams in plasma-wakefield accelerators

We formulate a new procedure for modelling the transverse dynamics of relativistic electron beams with significant energy spread when injected into plasma-based accelerators operated in the blow-out regime. Quantities of physical interest, such as the emittance, are furnished directly from solution of phase space moment equations formed from the relativistic Vlasov equation. The moment equations are closed by an Ansatz, and solved analytically for prescribed wakefields. The accuracy of the analytic formulas is established by benchmarking against the results of a semi-analytic/numerical procedure which is described within the scope of this work, and results from a simulation with the 3D quasi-static PIC code HiPACE.     

A Hilbert-Vlasov code for the study of high-frequency plasmabeatwave accelerator

High-frequency beatwave simulations relevant to the University of California at Los Angeles (UCLA) experiment with relativistic eulerian hybrid Vlasov code are presented. These Hilbert-Masov simulations revealed a rich variety of phenomena associated with the fast particle dynamics induced by beatwave experiment for a high ratio of driver frequency to plasma frequency ω_pump/ω_plasma ≈33. The present model allows us to extend detailed modeling to frequency ratios greater than the current practical maximum of 10 or so, for Vlasov or particle-in-cell (PIC) codes, by replacing the Maxwell equations by mode equations for the electromagnetic Vlasov code. Numerical results, including beat frequency chirping (i.e., pump frequency linearly decreasing with time), show that the amplitude limit due to relativistic detuning can be enhanced with accelerated particles up to the ultrarelativistic energies with a high-acceleration gradient of more than 25 GeV/m     

Relativistic generalization of quasi-Chaplygin equations

A relativistic generalization of quasi-Chaplygin (quasi-gas) equations describing the evolution of unstable media with negative compressibility is proposed. Examples of the media whose dynamics can be described by the proposed equations are considered. An analytic solution to these nonlinear equations is obtained for the 1D case.     

Nonlinear Behavior of Electromagnetic Waves in Ultra‐Relativistic Electron‐Positron Plasmas

A set of nonlinear equations which can self‐consistently describe the behavior of high frequency Electromagnetic (EM) waves in un‐magnetized, ultra‐relativistic electron‐positron (e‐p) plasmas is obtained on the basis of Vlasov‐Maxwell equations. Nonlinear wave‐wave, wave‐particle interactions lead to the coupling of high frequency EM waves with low frequency density perturbations which result from EM waves radiation pressure. The same as that in conventional electron‐ion (e‐i) plasmas, strong EM waves in e‐p plasmas will give rise to density depletion in which itself are trapped. But on the contrary to that in e‐i plasmas, there no longer exists electrostatic acoustic–like wave in e‐p plasmas due to the absence of mass difference. For linear polarized EM waves, a stationary EM soliton with a spiky structure will be formed. The possible relation of the localized field to pulsar radio pulse is discussed (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Neutrino beam plasma instability

We derive relativistic fluid set of equations for neutrinos and electrons from relativistic Vlasov equations with Fermi weak interaction force. Using these fluid equations, we obtain a dispersion relation describing neutrino beam plasma instability, which is little different from normal dispersion relation of streaming instability. It contains new, nonelectromagnetic, neutrino-plasma (or electroweak) stable and unstable modes also. The growth of the instability is weak for the highly relativistic neutrino flux, but becomes stronger for weakly relativistic neutrino flux in the case of parameters appropriate to the early universe and supernova explosions. However, this mode is dominant only for the beam velocity greater than 0.25c and in the other limit electroweak unstable mode takes over.     

Study of propagation of ultraintense electromagnetic wave throughplasma using semi-Lagrangian Vlasov codes

Interaction of relativistically strong laser pulses with underdense and overdense plasmas is investigated by a semi-Lagrangian Vlasov code. These Vlasov simulations revealed a rich variety of phenomena associated with the fast particle dynamics induced by the electromagnetic wave as electron trapping, particle acceleration, and electron plasma wavebreaking. To describe the distribution of accelerated particle momenta and energy will require a very detailed analysis of the kinetic and time history of the plasma wave evolution. The semi-Lagrangian Vlasov code allows us to handle the interaction of ultrashort electromagnetic pulse with plasma at strongly relativistic intensities with a great deal of resolution in phase space     

A discontinuous Galerkin method for the Vlasov–Poisson system

A discontinuous Galerkin method for approximating the Vlasov–Poisson system of equations describing the time evolution of a collisionless plasma is proposed. The method is mass conservative and, in the case that piecewise constant functions are used as a basis, the method preserves the positivity of the electron distribution function and weakly enforces continuity of the electric field through mesh interfaces and boundary conditions. The performance of the method is investigated by computing several examples and error estimates of the approximation are stated. In particular, computed results are benchmarked against established theoretical results for linear advection and the phenomenon of linear Landau damping for both the Maxwell and Lorentz distributions. Moreover, two nonlinear problems are considered: nonlinear Landau damping and a version of the two-stream instability are computed. For the latter, fine scale details of the resulting long-time BGK-like state are presented. Conservation laws are examined and various comparisons to theory are made. The results obtained demonstrate that the discontinuous Galerkin method is a viable option for integrating the Vlasov–Poisson system.     

The dynamical equation of the spinning electron

We obtain the relativistic and non-relativistic invariant dynamical equations of the spinning electron by means of invariance arguments. The dynamics expresses the evolution of the point charge which satisfies a fourthorder differential equation or, alternatively, by describing the evolution of both the center of mass and center of charge of the particle. These equations and the interaction between two electrons will be analyzed.     

Ultrarelativistic excitation of beat waves in a hot magnetized plasma

Summary A theoretical investigation is made on the nonlinear relativistic excitation of an electrostatic electron plasma wave at the beat frequency of two high-power colinear laser beams in a hot, homogeneous and magnetized plasma. The relativistic Vlasov equation expressed in gyrokinetic variables has been employed to find the nonlinear response of the magnetized plasma electrons. It is noted that the power density associated with the excited beat wave is much higher for the relativistic consideration than that for the nonrelativistic consideration. The authors of this paper have agreed to not receive the proofs for correction.     

Short-time correlations of many-body systems described by nonlinear Fokker–Planck equations and Vlasov–Fokker–Planck equations

Analytical expressions for short-time correlation functions, diffusion coefficients, mean square displacement, and second order statistics of many-body systems are derived using a mean field approach in terms of nonlinear Fokker–Planck equations and Vlasov–Fokker–Planck equations. The results are illustrated for the Desai–Zwanzig model, the nonlinear diffusion equation related to the Tsallis statistics, and a Vlasov–Fokker–Planck equation describing bunch particles in particle accelerator storage rings.     

Nonlinear Waves in Carbon Nanotubes under Conditions of Electron-Phonon Bonding

Relative simplicity of the atomic structure of carbon nanotubes being hollow cylinders with walls formed by rings of six carbon atoms (generally, the walls can be multilayered) enables the researchers to use this class of substances as model one to reveal the basic mechanisms of the dynamics of quasi-one—dimensional systems. The present work studies the nonlinear properties of carbon nanotubes with strong electron interactions described by the Hubbard Hamiltonian. A microscopic Hamiltonian describing electrons in carbon nanotubes with allowance for the electron mobility, Coulomb repulsion of electrons in one site of carbon nanotubes, and changes in spacing of the neighboring sites caused by acoustic oscillations is suggested. An effective nonlinear system of equations describing the dynamics of electron wave functions within the framework of the suggested Hamiltonian is derived. The existence of nonlinear stable periodic oscillations of electron wave functions in the examined model, in particular, corresponding to acoustic oscillations with different polarization states is established. The influence of the problem parameters on the character of nonlinear wave stability is revealed. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 76–81, June, 2005.     

A Numerical Investigation of the Pinning Phenomenon in Quasi-Periodic Frenkel Kontrova Model Under an External Force

We derive the relativistic Vlasov equation from quantum Hartree dynamics for fermions with relativistic dispersion in the mean-field scaling, which is naturally linked with an effective semiclassic limit. Similar results in the non-relativistic setting have been recently obtained in Benedikter et al. (Arch Rat Mech Anal 221(1): 273–334, 2016). The new challenge that we have to face here, in the relativistic setting, consists in controlling the difference between the quantum kinetic energy and the relativistic transport term appearing in the Vlasov equation.     

Fast formation of magnetic islands in a plasma in the presence of counterstreaming electrons

With the help of 2D-3V (two dimensional in space and three dimensional in velocity) Vlasov simulations we show that the magnetic field generated by the electromagnetic current filamentation instability develops magnetic islands due to the onset of a fast reconnection process that occurs on the electron dynamical time scale. This process is relevant to magnetic channel coalescence in relativistic laser plasma interactions.     

Nonlinear plasma resonance in inhomogeneous relativistic plasma

We present a theoretical study of relativistic electron plasma oscillations in the plasma resonance region based on the renormalization group symmetry method. A steady-state solution to equations describing the electron dynamics in the vicinity of the plasma resonance is found and spatial-temporal and spectral characteristics of the potential electric field are discussed.     

Normal modes of a relativistic quantum plasma; The one-component plasma

The normal modes of a relativistic electron gas are studied on the basis of the Boltzmann-Vlasov kinetic equation via a projection operator formalism. A general framework is constructed in which the fully relativistic Vlasov self-consistent force term appears as a symmetric operator acting in the Hilbert space of one-particle states. The plasma-dynamical equations are obtained by projecting onto the subspace consisting of the charge, energy and momentum densities, plus the nonconserved current density. The eigenmodes of these equations include two transverse and two longitudinal plasma modes, and one damped heat mode. They are explicitly calculated up to second order in the wave vector and to first order in the collision frequency.