Ponderomotive nongradient force acting on a relativistic particle crossing an inhomogeneous electromagnetic wave

The ponderomotive force acting on a relativistic charged particle crossing an inhomogeneous electromagnetic wave is investigated numerically and analytically. The initial velocity of the particle is perpendicular to the electric field vector of the wave and to the direction of its propagation. The wave has zero gradient in the direction of propagation and is inhomogeneous in both transverse directions. It is shown that the ponderomotive force acting on the particle is parallel to the wave vector. The magnitude of the force is determined not only by the extent of wave inhomogeneity in the direction of the translational motion of particle, but also by its inhomogeneity in the transverse direction. It is found that the trajectory of a particle is determined by the action of ponderomotive forces as well as by its drift in a nonuniform field.     

Scattering of relativistic electrons by a focused laser pulse

The problem of the motion of a classical relativistic electron in a focused high-intensity laser pulse is solved. A new three-dimensional model of the electromagnetic field, which is an exact solution of Maxwell’s equations, is proposed to describe a stationary laser beam. An extension of the model is proposed. This extension describes a laser pulse of finite duration and is an approximate solution of Maxwell’s equations. The equations for the average motion of an electron in the field of a laser pulse, described by our model, are derived assuming weak spatial and temporal nonuniformities of the field. It is shown that, to a first approximation in the parameters of the nonuniformities, the average (ponderomotive) force acting on a particle is described by the gradient of the ponderomotive potential, but it loses its potential character even in second order. It is found that the three-dimensional ponderomotive potential is asymmetric. The trajectories of relativistic electrons moving in a laser field are obtained and the cross sections for scattering of electrons by a stationary laser beam are calculated. It is shown that reflection of electrons from the laser pulse and the surfing effect are present in the model studied. It is found that for certain impact parameters of the incident electrons the asymmetic ponderomotive potential can manifest itself effectively as an attractive potential. It is also shown that even in the case of a symmetric potential the scattering cross section contains singularities, known as rainbow scattering. The results are applicable for fields characterized by large (compared to 1) values of the dimensionless parameter η² = e ²〈E ²〉/m ²ω² and arbitrary electron energies.     

Relativistic Derivation of the Ponderomotive Force Produced by Two Intense Laser Fields

The ponderomotive force plays a fundamental role in the absorption of laser light on self-consistent plasma density profiles, in multiple-photon ionization, and in intense field electrodynamics. The relativistic corrections to the ponderomotive force of a transversely polarized electromagnetic wave lead to an approximately 20-percent reduction in the single particle ponderomotive force produced by a 10-?m 1016-W/cm2 laser field. Recent experimental investigations are based on using two intense laser fields to produce desired laser-matter interactions. This paper presents the first derivation of the nonlinear relativistic ponderomotive force produced by two intense laser fields. The results demonstrate that relativistic ponderomotive forces are not additive.     

Ponderomotive transport of a variable-charge granule in a dusty plasma in the field of an intense ion-sound wave

The ponderomotive force acting on a variable-charge granule in a dusty plasma from an intense ion-sound wave is considered. Allowance for oscillations of the granule charge in the field of an ion-sound wave makes it possible to reveal new components of this force that are proportional to the wave vector of the field and the cube of its amplitude. These components do not vanish in the case of a uniform field and also lead to a directed transport of the dust plasma fraction.     

Fully relativistic theory of the ponderomotive force in an ultraintense standing wave

A relativistic field-gradient (ponderomotive) force in a laser standing wave ceases to exist in a familiar form; e.g., the adiabatic Hamiltonian is not separable into kinetic and potential energies for electrons moving in the antinode planes. We show that the force in the direction across the initial motion of an electron reverses its sign and makes the high-field areas attractive for electrons, opposite to a regular ponderomotive force. The reversal occurs at a relativistic-scale incident momentum, and represents the only effect known so far that pins down a distinct borderline between relativistic and nonrelativistic motion.     

Electron acceleration considering pondermotive force effect in a plasma-filled rectangular waveguide by microwave radiation

The electron acceleration inside the plasma-filled rectangular waveguide is numerically investigated for the externally injected single-electron model considering the effects of density modification under a balance between the ponderomotive force and the pressure gradient force. Using Maxwell’s equations, we evaluate the field components of the fundamental mode in the plasma-filled rectangular waveguide, where the obtained equations are solved numerically using the fourth-order Runge–Kutta method for the electric field amplitude of the microwave. Besides, by solving the relativistic momentum and energy equations using the fourth-order Runge–Kutta method, the deflection angle and the total energy of the electron in the waveguide are obtained. Furthermore, it is shown that the electron energy gain can be controlled using superposing microwave fundamental modes. Effects of various parameters on the results are graphically presented.     

Variable density formation by intense microwave beams near the critical density

Modification of electron density of an inhomogeneous, unmagnetized plasma by the relativistic ponderomotive force of intense microwave beams near the critical density is studied. Using the Maxwell and fluid equations and taking into account the relativistic mass, relativistic ponderomotive force, linear inhomogeneity for electron temperature, and tangential inhomogeneity for electron density, the non‐linear electron density, non‐linear dielectric permittivity, and non‐linear wave equations are derived. Results show that positive and negative values of σ₁ and σ₂ (degree of inhomogeneity of the background electron density and electron temperature, respectively) parameters can affect the electric and magnetic field profiles. In addition, profiles of the non‐linear electron density indicate that by decreasing the σ₁ parameter, the amplitude of the peaks increases near the critical density. For positive values of the σ₂ parameter, by increasing this parameter the amplitude of the peaks increases, while for negative values of the σ₂ parameter, by decreasing this parameter the amplitude of the peaks increases.     

Self-focusing in a plasma due to ponderomotive forces and relativistic effects

The propagation of intense laser pulses in a plasma is discussed in terms of a constant shape, paraxial ray approximation. Self-focusing due to ponderomotive forces and relativistic effects is investigated. It is found that the stationary self-focusing behaviour of each mechanism treated separately is similar, with several orders of magnitude difference in critical power. In stationary self-focusing due to the combined mechanisms, complete saturation of ponderomotive self-focusing prevents the occurrence of relativistic effects. Self-focusing lengths and minimum radii are given for a large range of beam powers. A characteristic focal spot radius is found which depends only on the plasma density.     

Equilibrium profiles for RF-plasma sources with ponderomotiveforces

An analysis is given of the influence of the electron ponderomotive force on the equilibrium plasma profiles of partially ionized, radio frequency discharge sources, The ponderomotive force can be written as a gradient of a potential varying with the square of the RF field in the plasma and is largest for electrons, The impact of this electron ponderomotive force on density and electrostatic potential profiles is demonstrated using a one-dimensional analytic model with supporting numerical solutions and a two dimensional fluid simulation. For nearly collisionless plasmas the ponderomotive force is valid when ω_ce^h/ω<1 where ω_ce ^h is the electron cyclotron frequency due to the RF magnetic field and ω is the RF driving frequency, In processing plasmas with parameters that satisfy this validity criteria, the equilibrium density profiles are weakly modified, For nearly collisionless processing plasmas with parameters such that ω_ce^h /ω>1, the ponderomotive force, is modified by other nonlinear force terms that need to be evaluated     

Particle Simulation of Relativistic Laser Pulse Density Channeling

1IntroducionThereiScurrentlymuhinterestintheinteractionofhighintensityultrashortlaserpulseswhhplasIna.ThisispartiyduetoaVallabilityoflaserscaPableofdeliveriflgintensihesaboVe1o"WcmzandtheadvntofthefastightorconePtinthecontextofinertialcoofnementfuAn.ThkeyconceptofthefastwttionistoheatthecomressedcorebythesuPrathermalelectronsandtheenergeticbogeneratedbyaveryintensepulse,afterthemainlaserpulsehascomPletedtheimPIosdri.Toachievethis,itisneededthatachannelingintenselaserpulsepenetratesasclose…     

Evolution of the polarization of electromagnetic waves in weakly anisotropic inhomogeneous media — a comparison of quasi-isotropic approximations of the geometrical optics method and the Stokes vector formalism

The main methods describing polarization of electromagnetic waves in weakly anisotropic inhomogeneous media are reviewed: the quasi-isotropic approximation (QIA) of geometrical optics method that deals with coupled equations for electromagnetic field components, and the Stokes vector formalism (SVF), dealing with Stokes vector components, which are quadratic in electromagnetic field intensity. The equation for the Stokes vector evolution is shown to be derived directly from QIA, whereas the inverse cannot be true. Derivation of SVF from QIA establishes a deep unity of these two approaches, which happen to be equivalent up to total phase. It is pointed out that in contrast to QIA, the Stokes vector cannot be applied for a polarization analysis of the superposition of coherent electromagnetic beams. Additionally, the ability of QIA to describe a normal modes conversion in inhomogeneous media is emphasized. Presented at 9-th International Workshop on Nonlinear Optics Applications, NOA 2007, May 17–20, 2007, Świnoujście, Poland     

Particle Simulation of Relativistic Laser Pulse Density Channeling

Two-dimensional particle simulation is carried out to study the interaction between a high-intensity finite-size spot laser beam and a plasma with linear density profile. The laser is allowed to propagate in underdense corona until it is cut off near the critical surface. The intense laser can drive various instabilities through particle collective motion and result in electron heating,while relativistic effect and ponderomotive force can bring strong energy absorption and electron heating in the overdense region. As the laser beam is nonuniform in the transverse direction,a density channel forms and hole boring effect occurs as a result of strong ponderomotive force pushing particle outwards. These processes can be investigated well by particle simulation.     

Current elements in relativistic field theory

Many previously reported experiments involving electrical circuits have demonstrated effects thought to be beyond the scope of modern relativistic field theory. The troubling effects include unexpected external electromotive forces and internal ponderomotive forces. The existence of such forces challenges long-cherished beliefs in relativistic field theory. The present note proposes a possible resolution for this situation.     

Kinetics of a phase transition into an inhomogeneous state in a ferroelectric plate

The kinetics of the emergence of a polarization vector field after a ferroelectric sample is rapidly cooled is investigated in two cases, in which the rate of growth of the polarization vector is determined by viscous forces of phonon origin or by the diffusion of charged particles. Analytic expressions are obtained for the rate of growth of the polarization vector and the period of the inhomogeneous phase as a function of the degree of supercooling of the sample. The existence of a slow relaxation process in the domain structure is established and the time dependence of this process is found. Zh. éksp. Teor. Fiz. 114, 2238–2245 (December 1998)     

Non-paraxial theory of self-defocusing/focusing of a laser pulse in a multiple-ionizing gas

The self-focusing of a laser pulse through a tunnel ionizing gas (helium) has been studied in both non-relativistic and relativistic regimes, relaxing the near-axis approximation. In the non-relativistic regime, the laser pulse produces multiple ionization of the gas and faces strong defocusing due to the steep radial density gradient caused by the same. The uneven defocusing of paraxial and marginal rays leads to a beam acquiring a ring shaped intensity distribution. In the relativistic regime, the laser pulse produces fully ionized plasma within a few wave periods, subsequently the relativistic mass effect and the ponderomotive force induced electron cavitation cause periodic self-focusing. PACS 52.38.Hb; 42.65.Jx     

Effects of relativistic and ponderomotive nonlinearities on the interaction of high-power laser beam with an inhomogeneous warm plasma

The influence of relativistic-ponderomotive nonlinearities and the plasma inhomogeneity on the nonlinear interaction between a high-power laser beam and a warm underdense plasma are studied. It is clear that the relativistic ponderomotive force and the electron temperature modify the electron density distribution and consequently change the dielectric permittivity of the plasma. Therefore, by presenting the modified electron density and the nonlinear dielectric permittivity of the warm plasma, the electromagnetic wave equation for the propagation of intense laser beam through the plasma is derived. This nonlinear equation is numerically solved and the distributions of electromagnetic fields in the plasma, the variations of electron density, and plasma refractive index are investigated for two different background electron density profiles. The results show that the amplitude of the electric field and electron density oscillations gradually increase and decrease, during propagation in the inhomogeneous warm plasma with linear and exponential density profiles, respectively, and the distribution of electron density becomes extremely sharp in the presence of intense laser beam. It is also indicated that the electron temperature and initial electron density have an impact on the propagation of the laser beam in the plasma and change the plasma refractive index and the oscillations' amplitude and frequency. The obtained results indicate the importance of a proper choice of laser and plasma parameters on the electromagnetic field distributions, density steepening, and plasma refractive index variations in the interaction of an intense laser beam with an inhomogeneous warm plasma.     

Relativistic ponderomotive forces in the field of intense laser radiation

The motion of a relativistic charged particle in the presence of the field of high-power laser radiation represented in the form of a Gaussian beam of arbitrary mode is analyzed. The vector potential of the radiation field is expanded in terms of a small parameter (the ratio of the wavelength to the Gaussian beam waist). A specific feature of averaging with respect to the phases of the high-mode Gaussian beams is demonstrated. The averaged equations for the motion of particle and a general expression for the ponderomotive relativistic force for the circularly polarized radiation are derived. It is demonstrated that relativistic effects suppress the averaged action of high-power laser radiation on the particle.     

在弱相对论条件下哨声波的调制不稳定性

本文在研究哨声波调制不稳定性时,除考虑由有质动力引起的密度变化和流速改变两个非线性效应外,还计及由弱相对论效应引起电子质量变化的非线性效应,得到了在形成孤子的条件、产生不稳定性的条件、和不稳定性增长率等方面与非相对论情况不同的结果。     

Microwave ponderomotive action on the inhomogeneous collisionless and collisional plasmas

The nonlinear interaction of a high-power microwave (MW) with an unmagnetized inhomogeneous plasma is investigated in collisionless and collisional regimes. The electron density distribution and the nonlinear wave equation in an inhomogeneous plasma are obtained by taking into account the ponderomotive force due to the high-power MW. It is shown that the electron density distribution becomes very steepened in the presence of the ponderomotive force. In the collisional regime, the expression for electron temperature is also found by considering ohmic heating. It is indicated that the amplitude of oscillations of the electron temperature and dielectric permittivity increases and the wavelength of these oscillations decreases with increasing energy flux, hence modulation occurs.     

Electron spin polarization in field emission: Calculation of the effects due to external fields

In field emission experiments with spin polarized electrons a magnetic field is superposed on the electric emission field to define the preferred spin direction. The motion of the polarization vector in these fields was calculated for rays emanating from individual points of the emitter by integrating the equation of motion and taking into account relativistic terms. There is a slight shift of the polarization vector from its initial direction. If the initial polarization is aligned with the magnetic field and the emission tip is sufficiently well centred in the magnetic field, the tilting of the polarization vector for a beam of electrons starting not too far from the tip apex is less than 10°.