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.     

Electron acceleration by net inverse bremsstrahlung of a laser wave in a uniform magnetic field and longitudinal electric waves

The nonzero net dc (ponderomotive force) acting on high-energy beam electrons due to net inverse bremsstrahlung (the absorption by inverse bremsstrahlung minus the emission by stimulated bremsstrahlung) of the electromagnetic wave in a uniform magnetic field and longitudinal electric waves is calculated by using quantum kinetics in accordance with the correspondence principle. It is found that the ponderomotive force can be far stronger than the Lorentz force of the laser wave for an electron-energy range far beyond the free electron lasing regime.     

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.     

Crack extension force and rate of mechanical work of fracture in linear dielectrics and piezoelectrics

The physical significance of the crack extension force produced by mechanical loads and electric fields in linear dielectric and piezoelectric materials is examined using simple thermodynamic arguments. General expressions are derived for the crack extension force in dielectrics and piezoelectrics, under mechanical and electrical loads, in terms of the measurable parameters elastic compliance and electric capacitance . It is shown that the crack extension force produced by an electric field on an impermeable crack is always negative and it is argued that under combined electromechanical loads the total crack extension force in a piezoelectric cannot be separated into a mechanical component and an electrical component. Expressions for the crack extension force in terms of mechanical and electrical intensity factors are also given. Their derivation from available solutions for the electromechanical field at the crack tip (in a transversely isotropic material of crystal class 6 mm) is presented in detail to emphasize the physical significance of the coefficients that appear in the final expressions. In the light of these results, existing experimental observations that appear to be inconsistent with theoretical expectations are re-examined. The suggestion that the crack extension force is not a valid parameter to characterize the fracture behaviour of ferroelectrics is justified on physical grounds. Its importance is discussed and the rate of mechanical work of fracture is proposed as a more suitable parameter for those cases where the electric field does not produce dielectric rupture, nor degradation of the material at the crack tip.     

Relativistic ponderomotive forces

The interaction of a relativistic classical electron with an inhomogeneous electromagnetic field is investigated. In second-order perturbation theory the motion is separated into fast and slow motions, and the relativistic Newtonian equation is averaged over the fast oscillations. The rate of change obtained for the slow component of the electron momentum is interpreted as a relativistic ponderomotive force. The result is generalized to the relativistic case of the wellknown expression for the Gaponov-Miller force acting on an electron at rest. The expressions obtained for the relativistic ponderomotive forces are very complicated in the general case. They simplify in the limit of a stationary field (pulses of long duration) and a small gradient. The most typical and simplest special case of an inhomogeneous field—a stationary plane-focused beam—is investigated. The main difference between relativistic ponderomotive forces and their nonrelativistic limit is they have multiple components. In addition to the usual force directed along the gradient of the field, the relativistic case is also characterized by force components that do not have the form of the gradient of a potential and are parallel to the wave vector and the direction of the field polarization. It is shown that when a relativistic electron travels in a direction close to the direction of the wave vector of a focused laser beam, these components can greatly exceed the gradient force. A force directed along the field polarization vector arises even when the gradient of the field in this direction is zero. Zh. éksp. Teor. Fiz. 116, 1198–1209 (October 1999)     

双频激光辐照的等离子体中的稳态电场结构和密度分布

本文导出了法向入射时,双频激光辐照的等离子体中的稳态电场强度和局域标度长度的解析表达式。结果表明,双频辐照的有质动力可以导致临界面附近出现密度凹坑和临界密度处的局域标度长度在某个强度范围内的反常增加和起伏。 关键词：     

The Ponderomotive Force on a Charge q,Moving in an Electromagnetic Field

Equations of motion of a single charged particle are derived to second order in E where E is an electromagnetic field. By averaging over the wave-period we find the ponderomotive force on the particle. This force may lead to a transport of matter as is also the case in ordinary hydrodynamics. There the effect is called acoustic streaming. We also suggest that the well-known Landau damping may be considered as beeing due to a ponderomotive force.     

Generation of collimated beams of relativistic ions in laser-plasma interactions

A method is proposed for generating collimated beams of fast ions in laser-plasma interactions. Two-dimensional and three-dimensional particle-in-cell simulations show that the ponderomotive force expels electrons from the plasma region irradiated by a laser pulse. The ions with unneutralized electric charge that remain in this region are accelerated by Coulomb repulsive forces. The ions are focused by tailoring the target and also as a result of pinching in the magnetic field produced by the electric current of fast ions.     

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     

Theoretical estimates of radial electric fields and plasma rotation induced in H-1NF by RF waves

The purpose of this study is to estimate, for planned experiments at the H-1NF heliac, nonlinear variations of the stationary radial electric field, and poloidal and toroidal plasma rotation, that result from ponderomotive forces exerted by large amplitude RF waves in the H-1NF. Similarly as in the previous studies of nonlinear transport effects induced by RF waves, the nonlinear ponderomotive force effects on the radial electric field, toroidal and poloidal plasma rotation become important for dissipated powers of the order of 1 MWm^–3 for RF waves with frequency of about 10 MHz. At these high RF powers, the nonlinear ponderomotive force effects might therefore result in important changes in plasma confinement and RF wave coupling in H-1NF.This work has been partially supported by the Australian National University, by the DIST Department of the Australian Government, by the Czech Grant Agency grants No. 202/96/1355 and 1350, and by the Queen Elisabeth II grant administered by G.G. Borg. The author is grateful to G.G. Borg and R.L. Dewar for many stimulating discussions.     

Motion and acceleration of electrons in high-intensity laser standing waves

The motion and the energy of electrons driven by the ponderomotive force in linearly polarized high-intensity laser standing wave fields are considered. The results show that there exists a threshold laser intensity, above which the motion of electrons incident parallel to the electric field of the laser standing waves undergoes a transition from regulation to chaos. We propose that the huge energy exchange between the electrons and the strong laser standing waves is triggered by inelastic scattering, which is related to the chaos patterns. It is shown that an electron's energy gain of tens of MeV can be realized for a laser intensity of 10²⁰ W/cm².     

On the motion of charged particles in an alternating nonuniform electric field

The equations of motion for a charged particle in an electric field featuring a stationary and an oscillating component are considered for the case where the force of friction is linear in the particle velocity. The averaging of these equations over the period of field oscillations is legitimate under some specific conditions. The most general expression for an additional stationary force acting on the particle under these conditions is derived, and the limiting values of this force are found. Applications of the results obtained in the present study are considered. Such applications include the use of pulsed currents in the electrochemical dimensional treatment of materials.     

Quantum effects on magnetization due to ponderomotive force in cold quantum plasmas

The quantum effects on the magnetization due to the ponderomotive force are investigated in cold quantum plasmas. It is shown that the ponderomotive force of the electromagnetic wave induces the magnetization and cyclotron motion in quantum plasmas. We also show that the magnetic field would not be induced without the quantum effects in plasmas. It is also found that the quantum effect enhances the cyclotron frequency due to the ponderomotive force related to the time variation of the field intensity. In addition, it is shown that the magnetization diminishes with an increase of the frequency of the electromagnetic field.     

Quasistationary magnetic field generated in a plasma by a whistler-mode radio pulse

It has been shown experimentally that a quasistationary magnetic field is generated in a weakly collisional magnetized plasma by a spatially nonuniform high-frequency whistler-mode field. The sources of the quasistationary magnetic field are nonlinear currents generated due to the longitudinal and transverse components of the ponderomotive force, acting on charged particles in the spatially localized high-frequency pump field. The dynamics of the excited magnetic fields has been analyzed. It was found that the settling time of the quasistationary magnetic field is determined by the switching-on time of the high-frequency field and the propagation of pulsed current and magnetic fields from the region of their generation occurs with the velocity of low-frequency whistler waves.     

Rheology of polymer suspensions: I. Local flow effects

A systematic study is made of the average local velocity field acting at a selected particle in a fluid suspension. The flow disturbance due to a single particle is analyzed in terms of force multipoles. The theory is developed in close analogy to that for the corresponding problem of the local electric field at a molecule in a polarizable medium. Closed expressions are derived in continuum approximation for the average local velocity, vorticity and strain in terms of the macroscopic average velocity field and force multipole densities. The effect of correlations is discussed briefly.     

On the ponderomotive force and the effect of loss reaction on parametric instability

In this paper, the growth rate, ponderomotive force and the exciting condition for parametric instability are derived by considering the loss reaction using a new method. On the basis of the hydrodynamic equations, we take the production and loss reactions in plasma into account to derive the coupling equations for the electron plasma oscillation and ion acoustic oscillation, and obtain the growth rate for the parametric instability, the ponderomotive force and the exciting condition. The result shows that (a) the production reaction has no effect on the parametric instability, and the effect of loss reaction on the parametric instability is a damping one, (b) the more intensive the external field or pump is, the larger the growth rate is, (c) there exist two modes of the ponderomotive force, i.e.\ the high frequency mode and the low frequency mode, and (d) when ponderomotive force counteracts the damping force, the oscillations become non-damping and non-driving. The ratio of the electron plasma oscillation to ion acoustic oscillation is independent of the loss reaction and the external field.     

Nonlinear propagation of neutrinos in a strongly magnetized medium

The nonlinear propagation of an intense neutrino flux in an electron-positron plasma with equilibrium density and magnetic field inhomogeneities is considered. It is found that the neutrinos are nonlinearly coupled with electrostatic and electromagnetic disturbances due to weak Fermi interaction and ponderomotive forces. The process is governed by a Klein-Gordon equation for the neutrino flux and a wave equation for the plasma oscillations in the presence of the ponderomotive force of the neutrinos. This pair of equations is then used to derive a nonlinear dispersion relation which exhibits that nonthermal electrostatic and electromagnetic fluctuations are created on account of the energy density of the neutrinos. The relevance of our investigation to the anomalous absorption of neutrinos in a nonuniform magnetized medium is pointed out.     

Local effect of electric and magnetic fields on the position of an attached shock in a supersonic diffuser

Effective ways for controlling shock wave configurations by means of external actions are sought. One such way is a local effect of electric and magnetic fields. In this paper, the local effect of external fields is implemented by current localization in a limited region of a diffuser. The experiment is carried out in a diffuser providing the complete internal compression of the gas with a Mach number at the inlet M=4.3. As a working medium, a xenon plasma is used. The plasma flow is formed in a shock tube equipped with an accelerating nozzle. Two ways of current localization are tested. In the first one, the diffuser inlet is a short channel of Faraday generator type. In this case, the ponderomotive force basically decelerates or accelerates the flow depending on the direction of the electric field. In the second way, the current flows through a narrow near-wall region between adjacent electrodes. In this case, the ponderomotive force compresses or expands the gas. In both cases, it is shown that the angle of an attached shock due to MHD interaction can be both decreased and increased. The central problem with the MHD control of shock waves is near-electrode and near-wall phenomena.     

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.