Relativistic Mass Variation Research Articles

Filamentation of laser in a magnetized plasma under relativistic and ponderomotive nonlinearities

Filamentation of a circularly polarized short pulse laser propagating along the direction of ambient magnetic field in plasma is studied. The nonlinearity arises through the combined effect of relativistic mass variation and ponderomotive force induced electron cavitation. The growth rate is maximum Γmax for an optimum filament size, qopt−1. Γmax and qopt increases with plasma density and ambient magnetic field.

Parametric excitation of surface plasma waves in an overdense plasma irradiated by an ultrashort laser pulse

A high power laser, obliquely incident on a vacuum-plasma interface, (x=0), resonantly drives plasma oscillations at the second harmonic when 2ω0=ωp, where ωp is the plasma frequency and ω0 is the frequency of the laser. The plasma oscillations parametrically excite a pair of counterpropagating surface plasma waves (ω,kz) and (ω1,k1z) when ω=ω1−2ω0, kz=k1z−2k0z, where k0z is the component of the incident laser wave vector parallel to the interface. The growth rate is maximum for normal incidence of the laser and decreases with the angle of incidence. In a mildly relativistic case, the relativistic mass variation of plasma electrons and collisions detune the second harmonic resonance, lowering the growth rate.

Effect of laser ripple on the beat wave excitation and particle acceleration

Abstract.This paper presents the effect of ripple on the plasma wave excitation process and acceleration of electrons in a laser produced plasma. The plasma wave is generated by the beating of two coaxial lasers of frequencies ω1 and ω2, such that ω1-ω2≅ωp. One of the main laser beams also has intensity spikes. The nonlinearity due to the relativistic mass variation depends not only on the intensity of one laser beam but also on the second laser beam. Therefore the behavior of the first laser beam affects the second laser beam, hence cross-focusing takes place. Owing to the interaction of ripple and the main laser beams, the ripple grows inside the plasma. The behavior of the ripple in the plasma affects the excitation of the electron plasma wave as well as the electron acceleration. The amplitude of the electron plasma wave and the electron energy are calculated, in the presence of ripple.

Filamentation of a relativistic short pulse laser in a plasma

An intense short pulse laser propagating through a plasma undergoes filamentation instability under the combined effects of relativistic mass variation and ponderomotive force-induced electron density depression. These two nonlinearities superimpose each other. In a tenuous plasma, the filament size scales as where ω p is the plasma frequency, a0 is the normalized laser amplitude and γ 0 is the relativistic gamma factor.

Numerical solution of nonlinear wave equations in stratified dispersive media

Nonlinear wave motion in dispersive media is solved numerically. The model applies to laser propagation in a relativistic plasma. The latter causes, besides dispersion, nonlinear effects due to relativistic mass variation in the presence of strong laser pulses. A new variant of the Gautschi-type integrator for reducing the number of time steps is proposed as a fast solver for such nonlinear wave-equations. In order to reduce the number of spatial grid points, a physically motivated quasi-envelope approach (QEA) is introduced. The new method turns out to reduce the computational time significantly compared to the standard leap-frog scheme.

Relativistic self-focusing of a laser beam in an inhomogeneous plasma

This paper presents an analysis of relativistic self-focusing of intense laser radiation in an axially inhomogeneous plasma. The nonlinearity in the dielectric constant arises on account of the relativistic variation of mass for an arbitrary magnitude of intensity. An appropriate expression for the nonlinear dielectric constant has been used in the analysis of laser-beam propagation in the paraxial approximation for a circularly polarized wave. The variations of the beam width parameter with the propagation distance, the self-trapping condition and the critical power have been evaluated. The saturating nature of the nonlinearity yields two values of the critical power for beam self-focusing, . It is seen that the laser beam width tends to attain a constant value depending upon the plasma inhomogenity and the initial laser intensity. Numerical estimates are made for typical values of the laser–plasma interaction applicable for underdense and overdense plasmas. The most important experiments described by this model are related to the fast ignitor concept.

Effect of relativistic mutual interaction of two laser beams on the growth of laser ripple in plasma

This paper presents an effect of relativistic mutual interaction of two laser beams of different frequencies on the growth of a laser ripple in laser produced plasmas. The nonlinearity due to relativistic mass variation depends not only on the intensity of one laser but also on the second laser. Therefore, one laser beam affects the dynamics of the second beam and hence a mutual nonlinear interaction (cross-focusing) takes place. The dynamical equations governing the laser intensity of two laser beams and the perturbation present on one laser beam (ripple) have been set up and a numerical solution has been presented for typical laser plasma parameters. It is found that a change in the intensity of the second laser beam can affect the growth of the laser ripple significantly. This study is important in plasma beat wave excitation and collective laser particle accelerators.

Envelope solitons associated with electromagnetic waves in a magnetized pair plasma

The amplitude modulation of magnetic field-aligned circularly polarized electromagnetic (CPEM) waves in a magnetized pair plasma is reexamined. The nonlinear frequency shifts include the effects of the radiation pressure driven density and compressional magnetic field perturbations as well as relativistic particle mass variations. The dynamics of the modulated CPEM wave packets is governed by a nonlinear Schrödinger equation, which has attractive and repulsive interaction potentials for fast and slow CPEM waves. The modulational stability of a constant amplitude CPEM wave is studied by deriving a nonlinear dispersion from the cubic Schrödinger equation. The fast (slow) CPEM mode is modulationally unstable (stable). Possible stationary amplitude solutions of the modulated fast (slow) CPEM mode can be represented in the form of bright and dark/gray envelope electromagnetic soliton structures. Localized envelope excitations can be associated with the microstructures in pulsar magnetospheres and in laboratory pair magnetoplasmas.

Beat-wave excitation of electron plasma wave by cross-focusing of two intense laser beams

This paper presents the cross-focusing of two intense laser beams in a collisionless plasma, taking into account the relativistic non-linearity. The non-linearity is not bound to large irradiances and this non-linearity is only a perturbation. It should be noted here that while considering the self-focusing due to relativistic electron mass variation, the electron ponderomotive density depression in the channel may also be important. Therefore, these two non-linearities may simultaneously affect the self-focusing process. In the present paper we have considered the situation when only relativistic non-linearity is important. The non-linearity due to relativistic mass variation depends not only on the intensity of one laser but also on the second laser. Therefore, one laser beam affects the dynamics of the second beam and hence a cross-focusing process takes place. The electric field amplitude of the excited electron plasma wave (EPW) has been calculated and its effect on the cross-focusing process has also been discussed. It is observed that the inclusion of a resonantly excited EPW on cross-focusing is significant and the accelerating electric field of the generated EPW becomes affected. A comparison of the theory with the recent experimental observations has also been presented.

Asymmetric self-focusing of a laser pulse in plasma

An intense short-pulse laser propagating through a plasma undergoes self-pulse distortion due to the combined effects of nonlinearity-induced self-focusing and dispersion. The nonlinearity arises as a result of relativistic mass variation. The low-intensity front of the pulse converges mildly, while the high-intensity later portions self-focus strongly. However, at the intensity maxima, the self-focusing effect is masked by the saturation effect of the nonlinear refractive index. The group velocity is also a function of intensity; as a result, the front of the pulse becomes sharpened, while the tail tends to be broadened.

Theories of relativistic ion cyclotron instabilities

A perturbation theory and a kinetic theory are developed to investigate the novel physics of relativistic ion cyclotron instabilities. The existence of the instabilities is determined by the normalized mass deficits per nucleon of fast and slow ions (δmf and δms, respectively), and by their Lorentz factors (γf and γs, respectively); while the ion bunching is caused by the relativistic variation of ion mass. If δmf−δms−γf+γs>0, only a quadratic instability can occur at high cyclotron harmonics of the fast ion in the lower-hybrid frequency regime and above; the threshold on the harmonic number is determined by the dielectric constant of the slow ion. The peak growth rate is higher at the harmonics just above the threshold. If it is negative, both a cubic instability (or instead a coupled quadratic instability if the resonant slow ion cyclotron harmonic is the first harmonic) and the high harmonic quadratic instability can be driven. The cubic instability is due to the harmonic interaction of fast and slow ion cyclotron motions with the wave frequency in between. This introduces a novel instability concept, namely, a two-streaming process in gyrospace. Thus, the cubic instability is also called a two-gyro-stream instability even without beams in real space in contrast to conventional two-stream instability. Both theories show that, as compared to the conventional axial phase bunching mechanism, the importance of the inclusion of the relativistic mass variation effect (and the gyro-bunching mechanism) depends on the phase velocity of the wave along the external magnetic field, and is not related to the Lorentz factors (or kinetic energies); that is, if ω/kz>c (e.g., kz=0), the relativistic gyro-bunching mechanism always dominates. While the importance of this study in fundamental plasma physics is emphasized here, some issues (e.g., nonlinear saturation, wave polarization, and nonuniform magnetic field) related to its application are also discussed.

Relativistic self-focusing of a rippled laser beam in a plasma

This paper presents an analysis of the relativistic self-focusing of a rippled Gaussian laser beam in a plasma. Considering the nonlinearity as arising owing to relativistic variation of mass, and following the WKB and paraxial-ray approximations, the phenomenon of self-focusing of rippled laser beams is studied for arbitrary magnitude of nonlinearity. Pandey et al. [Phys. Fluids82, 1221 (1990)] have shown that a small ripple on the axis of the main beam grows very rapidly with distance of propagation as compared with the self-focusing of the main beam. Based on this analogy, we have analysed relativistic self-focusing of rippled beams in plasmas. The relativistic intensities with saturation effects of nonlinearity allow the nonlinear refractive index in the paraxial regime to have a slower radial dependence, and thus the ripple extracts relatively less energy from its neighbourhood.

Selective gyrobroadening of alpha particle energy spectrum

Lower-hybrid alpha cyclotron waves driven by energetic alphas due to relativistic mass variation and their interaction are studied with particle-in-cell simulations. In contrast to the anomalous thermalization of protons (whose driven instability is stable for the alphas), the interaction due to a different instability is selective (i.e., only alphas with perpendicular momentum above threshold are gyrobroadened) and it stops when they are slowed down to the threshold. An explanation is given. The interaction persists in the case of a magnetic field with a sinusoidal non-uniformity.

Relativistic simple waves in radiation magnetohydrodynamics

A description of nonstationary simple waves and Riemann invariants in a relativistically hot electron-positron magnetoplasma is presented. It is noted that at relativistic temperatures the photon energy far exceeds the internal kinetic energy and that the particle effective mass depends strongly on the temperature. Starting from a set of relativistic radiation magnetohydrodynamic equations, the nonlinear characteristics and velocities of simple waves are obtained. The equations are further employed to examine the Riemann invariants in the presence of isentropic flow. It is found that at ultra-relativistic temperatures the photon pressure and the relativistic mass variation play a very important role.

Nonlinear coupling of a superluminal electromagnetic wave to a relativistic electron beam

The nonlinear propagation of a superluminal, linearly polarized electromagnetic wave in the presence of a relativistic cold electron beam is investigated. At large amplitudes the wave couples to the electron-beam plasma mode owing to two important nonlinear effects, namely the relativistic variation of the electron mass and the excitation of longitudinal space charge fields by strong v × B forces. The nonlinear propagation equations for the coupled electromagnetic and longitudinal waves are derived within the context of a relativistic cold-fluid model. Nonlinear travelling-wave solutions are sought to describe the saturated state of the coupled system. Using Hamiltonian techniques, a wide variety of solutions are obtained and their characteristics discussed.

Relativistic transverse modulational instability of two electron cyclotron waves

The transverse modulational instabilities of two finite-amplitude electron-cyclotron waves due to the ponderomotive force and relativistic mass variation of electrons are considered using the coupled nonlinear Schrödinger equation model. The waves are modulationally unstable, with maximum growth rate larger than that of a single wave. The stable waves can be unstable by the effect of coupling. The instability is caused only by the mass variation of electrons, and the contribution of the ponderomotive force is negligibly small. The instability of copropagating waves has a convective nature and that due to the counterpropagating waves has an absolute nature, no matter how large the pump intensities are. The threshold of modulational instability is also considered for finite-length plasmas.

Nonlinear Propagation of Pulsar Radiation

AbstractThe nonlinear propagation of pulsar radiation in an electronpositron plasma is considered. Accounting for the pulsar radiation ponderomotive force, the relativistic mass variation, and the plasma magnetization, we obtain a pair of nonlinear equations which exhibit coupling of pulsar radiation with the background plasma slow motions in magnetized plasmas. The modulational/filamentation instability as well as the localization of pulsar radiation are investigated. We conclude that our investigation is relevant to the microstructures in the pulsar magnetosphere.

Gyrobroadening of fast ion energy spectrum due to relativistic mass variation

A gyrobroadening process causing the perpendicular energy of fast ions to be broadened by cyclotron instabilities due to the relativistic mass variation of the fast ions in a magnetized plasma is reported. At low cyclotron harmonics, a two-gyro-stream instability can be excited with the involvement of thermal ions if the condition lfwcf < w < lswcs is satisfied. The fast ions can be anomalously thermalized. Their lost energy goes to bulk ion heating. While the fusion produced protons can satisfy the condition, the alphas cannot. The low harmonics are linearly stable for the alphas. Therefore, for low harmonics one has to inject waves to affect the alpha dynamics. However, the alphas can excite high harmonic cyclotron waves in the lower hybrid regime, in which thermal ions respond as cold plasma. The interaction becomes selective. Only alphas with high pitch angle are involved. The implications of this process for fusion ignition and fast ion confinement are assessed

Relativistic and ponderomotive self-focusing of a laser beam in a radially inhomogeneous plasma. I. Paraxial approximation

The propagation of a high-irradiance laser beam in a plasma whose optical index depends nonlinearly on the light intensity is investigated through both theoretical and numerical analyses. The nonlinear effects examined herein are the relativistic decrease of the plasma frequency and the ponderomotive expelling of the electrons. This paper is devoted to focusing and defocusing effects of a beam assumed to remain cylindrical and for a plasma supposed homogeneous along the propagation direction but radially inhomogeneous with a parabolic density profile. A two-parameter perturbation expansion is used; these two parameters, assumed small with respect to unity, are the ratio of the laser wavelength to the radial electric-field gradient length and the ratio of the plasma frequency to the laser frequency. The laser field is described in the context of a time envelope and spatial paraxial approximations. An analytical expression is provided for the critical beam power beyond which self-focusing appears; it depends strongly on the plasma inhomogeneity and suggests the plasma density tailoring in order to lower this critical power. The beam energy radius evolution is obtained as a function of the propagation distance by numerically solving the paraxial equation given by the two-parameter expansion. The relativistic mass variation is shown to dominate the ponderomotive effect. For strong laser fields, self-focusing saturates due to corrections of fourth order in the electric field involved by both contributions.

The modulation of radiation in an electron–positron plasma

The modulational instability of a large-amplitude, linearly polarized electromagnetic wave propagating in an electron-positron plasma is considered, including the combined effect of relativistic mass variation of the plasma particles, harmonic generation, and the non-resonant, finite-frequency electrostatic density perturbations, all caused by the large-amplitude radiation field. The radiation from many strong sources, such as AGN and pulsars, has been observed to vary over a host of time-scales. It is possible that the extremely rapid variations in the non-thermal continuum of AGN, as well as in the non-thermal radio radiation from pulsars, can be accounted for by the modulational instabilities to which radiation may be subjected during its propagation out of the emission region.