Nonlinear Ponderomotive Force Research Articles

Second harmonic and ponderomotive forces acting on electrons in an inhomogeneous radio frequency field of an inductive discharge

The nonlinear second harmonic and ponderomotive forces acting on electrons in an inhomogeneous rf field have been derived from the electron equation of motion accounting for the energy dependence of electron–atom collisions. It is shown that in a collisionless plasma (ω≫ν) the second harmonic force F2ω and the ponderomotive Fdc force are similar in magnitude and frequency dependence (ω−2), where ω is the driving frequency and ν is the electron collision frequency. In a collisionally dominated plasma (ω<ν) both forces are diminished and have a different frequency dependence: F2ω∝(ων)−1 and Fdc∝ν−2. Therefore, in a collisional plasma, the second harmonic force is always greater than the ponderomotive force.

2-D numerical simulation of the ambipolar filamentation of turbulent magnetic fields

Magnetic fields play an important role in astrophysics and they often dominate the behavior of magnetized media. We simulate the mechanism (Tagger et al., 1995) by which turbulence in a weakly ionized plasma, as it cascades to the ambipolar scale (where the neutrals are imperfectly coupled to the ions) leads to a filamentation of the magnetic flux tubes: the turbulent velocity of the neutrals is higher in the more ionized regions, because they are better coupled to the ions. This results in a non-linear ponderomotive ( ) force driving them out of the ionized regions, so that the initial ionization inhomogeneities are strongly amplified. This effect causes the ions and magnetic field to condense and separate from the neutrals, resulting in a filamentary structure. We present the first results of a 2-D, 2-fluid (ions and neutrals) simulation, where a magnetized, weakly ionized plasma is submitted to turbulence in the ambipolar frequency range. We discuss the efficiency of this mechanism, the filamentary structure it should produce, and its relevance to the astrophysical context.

Parametric decays of a circularly polarized electromagnetic wave in an electron-positron magnetized plasma

We study the parametric decays of an electromagnetic wave propagating along an external magnetic field in an electron-positron plasma. We include weakly relativistic effects on the particle motions in the wave field and the nonlinear ponderomotive force. We show that there are a number of resonant and nonresonant wave couplings. These include ordinary decay instabilities, in which the pump wave decays into an electroacoustic mode and a sideband wave. There are also nonresonant couplings involving two sideband waves and a nonresonant modulational instability in which the pump wave decays into two sideband modes. Depending on the parameters involved, there is a resonant modulational instability involving a forward-propagating electroacoustic mode and a sideband daughter wave.

The neutrino electron accelerator

It is shown that a wake of electron plasma oscillations can be created by the nonlinear ponderomotive force of an intense neutrino flux. The electrons trapped in the plasma wakefield will be accelerated to high energies. Such processes may be important in supernovas and pulsars.

PARAMETRIC DECAY OF A CIRCULARLY POLARIZED ELECTROMAGNETIC WAVE IN AN ELECTRON-POSITRON MAGNETIZED PLASMA

We study the parametric decays of an electromagnetic wave propagating along an external magnetic field in an electron-positron plasma. We include weakly relativistic effects on the particle motions in the wave field, and the nonlinear ponderomotive force. We find resonant and nonresonant wave couplings. These include, ordinary decay instabilities, in which the pump wave decays into an electro-acoustic mode and a sideband wave. There are also nonresonant couplings involving two sideband waves, and a nonresonant modulational instability in which the pump wave decays into two sideband modes. Depending on the parameters involved, there is a resonant modulational instability involving a forward propagating electro-acoustic mode and a sideband daughter wave.

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.

Physical mechanisms leading to high currents of highly charged ions in laser-driven ion sources

Heavy ion sources for the big accelerators, for example, the LHC, require considerably more ions per pulse during a short time than the best developed classical ion source, the electron cyclotron resonance (ECR) provides; thus an alternative ion source is needed. This can be expected from laser-produced plasmas, where dramatically new types of ion generation have been observed. Experiments with rather modest lasers have confirmed operation with one million pulses of 1 Hz, and 1011C4+ions per pulse reached 2 GeV/u in the Dubna synchrotron. We review here the complexities of laser-plasma interactions to underline the unique and extraordinary possibilities that the laser ion source offers. The complexities are elaborated with respect to keV and MeV ion generation, nonlinear (ponderomotive) forces, self-focusing, resonances and “hot” electrons, parametric instabilities, double-layer effects, and the few ps stochastic pulsation (stuttering). Recent experiments with the laser ion source have been analyzed to distinguish between the ps and ns interaction, and it was discovered that one mechanism of highly charged ion generation is the electron impact ionization (EII) mechanism, similar to the ECR, but with so much higher plasma densities that the required very large number of ions per pulse are produced.

Ponderomotive acceleration in the auroral region: A kinetic simulation

Alfvén waves with frequencies of the order of several Hertz have been observed in the auroral region. These waves are thought to be responsible for the acceleration of ionospheric particles out of the ionosphere and into the magnetosphere. As an Alfvén wave propagates into an inhomogeneous ionosphere, the amplitude of the wave decreases resulting in a gradient in the electric field and a ponderomotive force. The nature of the ponderomotive force is to accelerate ions out of the ionosphere, while accelerating electrons into the ionosphere decreasing the ambipolar electric field. Ponderomotive acceleration of ions can penetrate to low enough altitudes affecting the production regions for O+ and H+ ions. To understand the influences of ponderomotive acceleration on the lower ionosphere, a one‐dimensional hybrid particle code is used. The simulation model allows for multiple species, atmospheric chemistry and photoionization, tilted dipolar coordinate system, corotation, and convection. The electrons are treated as a charge neutralizing fluid where the parallel and perpendicular temperatures and heat flows are given by the 16‐moment transport equations. Coulomb, ion‐neutral, and electron‐neutral collisions are included in the hybrid simulation using newly developed collision techniques applicable to kinetic simulations. The altitude dependence of an Alfvén wave propagating from 6000 to 200 km in an inhomogeneous ionosphere is determined by solving Maxwell's equations. The parallel and perpendicular envelopes are determined and the resulting nonlinear, non‐resonant ponderomotive acceleration of ionospheric ions is calculated. The ponderomotive force is included in the kinetic simulation in the same fashion as gravity or the self‐consistent electric field. The acceleration event lasts for 10 min, by which time the density and flow speed profiles have reached equilibrium. The density and flow speed at 2500 km after 10 min of acceleration increase from 4.3 cm−3 and 1.6 km/s to 34 cm−3 and 6.0 km/s for H+, while the same quantities for O+ increase from 1670 cm−3 and −0.0009 km/s to 4795 cm−3 and 7.0 km/s. Collisional coupling between the H+ and O+ contributes to enhancing the outflow of H+. The net response of the ionosphere to the nonlinear ponderomotive force is an enhancement in ionospheric outflow of ions into the magnetosphere.

Laser acceleration of electrons in vacuum.

Several features of vacuum laser acceleration are reviewed, analyzed, and discussed, including electron acceleration by two crossed laser beams and acceleration by a higher-order Gaussian beam. In addition, the vacuum beat wave accelerator (VBWA) concept is proposed and analyzed. It is shown that acceleration by two crossed beams is correctly described by the Lawson-Woodward (LW) theorem, i.e., no net energy gain results for a relativistic electron interacting with the laser fields over an infinite interaction distance. Finite net energy gains can be obtained by placing optical components near the laser focus to limit the interaction region. The specific case of a higher-order Gaussian beam reflected by a mirror placed near focus is analyzed in detail. It is shown that the damage threshold of the mirror is severely limiting, i.e., substantial energy gains require very high electron injection energies. The VBWA, which uses two copropagating laser beams of different frequencies, relies on nonlinear ponderomotive forces, thus violating the assumptions of the LW theorem. Single-particle simulations confirm that substantial energy gains are possible and that optical components are not needed near the focal region.

The kinetic theory of the nonlinear low-frequency response of a collisionless plasma to high-frequency electromagnetic radiation

A kinetic theory of nonlinear currents, quasi-stationary electric and magnetic fields and the ponderomotive effect of high-frequency electromagnetic radiation on a collisionless plasma is developed. General expressions for nonlinear current densities, fields and ponderomotive forces that are applicable in a broad range of space-time scales, characteristie of low-frequency motion in plasma, are obtained. These expressions are compared with the results of previous papers.

Ponderomotive mass transport in the magnetosphere

It has recently been suggested that the nonlinear ponderomotive force of hydromagnetic waves in the magnetosphere may cause significant mass transport along the ambient magnetic field. To investigate this further, a two‐dimensional nonlinear hydromagnetic computer code is applied to box magnetospheres with two different radial variations of β, the ratio of plasma pressure to magnetic pressure. It is found that the rate at which density structure develops is dependent on the local sound speed. For fundamental standing waveforms along the magnetic field both the size of maximum equatorial density enhancements and the time for enhancements to develop decrease with increasing sound speed. Density enhancements are limited at each radial position by the propagation of density fronts from the equator toward the ionospheres. The propagation is confined to a given field line, supporting the idea that the fronts propagate in the slow magnetosonic mode. Simple predictors Dsm (for the maximum relative density change) and tsm (for the time to reach maximum density) derived from second‐order theory are tested against the numerical simulations and are found to give quite good results. A dipolelike magnetosphere model is then set up with plausible plasma and magnetic field parameters. Radial variations of Dsm and tsm are obtained for observationally reasonable models of cavity modes and Alfvén resonances. It is found that maximum density enhancements in the inner plasmasphere and in the plasma sheet are relatively small. However, large density enhancements are obtained in the outer plasmasphere and plasma trough. The size of these enhancements depends on the mean ion temperature and the effective ion mass in that region and is also likely to depend on how strongly slow magnetosonic waves are Landau damped.

The Gauge and Lorentz invariance of the non-linear ponderomotive 4-force

The non-linear ponderomotive force of laser-plasma interactions given by HORA (1985, Physics Fluids 28, 3706) is used as a basis for deriving the Lorentz and Gauge invariant expression. Hora's expression is reformulated as a 4-force in Minkowski space-time. The stress-energy tensor of this system is also derived. The Gauge invariance and Lorentz invariance are a direct result of the reformulation.

Increased gain of the lateral-injection free-electron laser and the use of clusters for amplication in the X-ray range

Using radial plasma acceleration in a laser beam, an alternative type of free electron laser has been developed by radial injection of electrons. Its properties have been elaborated for a laser amplifier of 400 μtm wavelength. To overcome the difficulties of this FEL, a basically new laser amplifier concept has been developed where a laser pulse is amplified by nearly lateral injection of solid particles (clusters, pellets etc.) whose kinetic energy (at appropriate adjustment and synchronisation) is converted into 80% optical energy of the laser pulse. The mechanism of energy transfer is the radial slowing down by nonlinear ponderomotive forces of the plasma made from the cluster reaching the beam axis, and the switching-off process of the beam with regard to the transient nonlinear force processes. It is an inversion of the plasma ejection with ponderomotive self-focussing. Apart from the unusually high efficiency, a relatively high gain is expected even for such small laser wavelengths as 10 nm. Furthermore, the difficult problem of modification of phase fronts and convergence (focussing, directing of X-ray beams) should be solved by the optical plasma properties at injection.

Resonant excitation of helicon waves by two microwave beams in a solid state plasma

AbstractAn investigation is made of resonant excitation of helicon waves at the difference frequency of two microwave beams propagating in a magneto‐active solid state plasma viz. n‐InSb. The two beams propagating obliquely with the magnetostatic field interact in the semiconductor to give rise to a nonlinear ponderomotive force at the difference frequency which resonantly excites helicon waves if the dispersion relation corresponding to helicon waves is satisfied. The results show that microwave beams of power densities 1 MW cm−2 can excite helicon waves of power density 0.98 kW cm−2 when ωc/ω = 25. The power carried by helicon waves depends on the direction of propagation of the pumps relative to magnetostatic field. For the parameters under consideration the power gets optimised at an angle θ = 63.4°. Helicon waves are not excited if the pumps propagate parallel or perpendicular to the magnetic field. The increase in magnetic field increases the power density of the excited helicon wave.

The transient electrodynamic forces at laser–plasma interaction

In the discussion of the concerning of the transient terms of the nonlinear (ponderomotive) forces of laser–plasma interaction, the recent result by Zeidler et al. [Phys. Fluids 28, 372 (1985)] can be used to confirm the strength of Schlüter’s term and to provide an analogy to conclude a more general transient term.

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-μm 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.

Nonlinear propagation and ponderomotive force of electromagnetic plane waves of arbitrary polarisation in a magnetoplasma

Ponderomotive self-effects of plane uniform electromagnetic modes of a magnetoplasma introduce stop- and pass-band structures in the dispersion characteristics of the waves resulting in Bragg reflection, etc.

Analysis of the Inverted Double Layers Produced by Nonlinear Forces in a Laser-Produced Plasma

By use of a hydrocode it is shown that the interaction of high-intensity light with an expanding plasma surface produces a positive plasma cloud followed by a negative plasma cloud. This result, which is opposite to that without the laser light, is the result of the non-linear (ponderomotive) force.

High electrostatic fields at ponderomotive laser driving of plasmas by nonlinear forces

The very short time step numerical two-fluid computation of laser-plasma interaction including complete nonlinear optical constants and the nonlinear (ponderomotive) force results in detailed information on plasma oscillations and damping and in the generation of electrostatic fields of 10 8 V/cm for neodymium glass laser pulses of 10 16 W/cm 2 intensity. The decoupling of interaction after caviton generation occurs as in preceding one-fluid calculations, after having permitted sufficient nonlinear force pushing of shells for fusion.

Laser light backscattering off an electron beam-plasma system

The case of stimulated backscattering Raman instability that is combined with a two-stream Buneman instability has been analyzed. This problem bears on fabricating a rapidly tunable free electron laser (FEL) for IR countermeasures in the 8-10 \mu m wavelength range. The analysis is based on a weakly nonlinear theory and assumed a cold nonrelativistic electron beam and an equilibrium plasma to be described with a two-fluid model. The physical mechanism is based on the coherent bunching of the beam-plasma system due to the nonlinear ponderomotive force and the slow beam wave having negative energy. This paper analyzes a novel scattering configuration in which the IR (CO 2 ) laser at 10.6 μm collides head-on against a nonrelativistic e -beam firing through a puff of laser produced plasma of n_{p} \lsim 10^{16} cm-3, which has been previously produced by the CO 2 laser itself (e.g., producing the critical density 1019cm-3and the reduced quiver velocity \upsilon_{0s}/c = 0.1-0.01 at pulsed 1014-1012W/cm2) and becomes underdense subsequently. The upshifted radiation is tunable at an aribtrary Ω 1 determined by the Doppler frequency relationship \Omega_{1} = \Omega_{0}(1 + \beta_{0})/ (1 - \beta_{0}) , where Ω 0 is the IR pump frequency and \beta_{0} = V_{0}/c (≈0.14 for the 8 μm wavelength) is the e -beam parameter of 5.11 keV and A/cm2such that n_{b}/n_{p} \approx 10^{-6} . The synergic backscattering growth rate is the sum of both instabilities, e.g., [(\sqrt{3}/2) (n_{b}/2n_{p})^{1/3} + (\upsilon_{0s}/ 4c) (\Omega_{0}/\omega_{0p})^{1/2}] \omega_{0p} , and may be referred to as the plasmon avalanche instability. Assuming the wide-interval-pulsed (WIP) e -beam can be piecewisely flushed outside the interaction chamber after streaming through a laser produced plasma on each pass, then a useful free electron laser operation will result. Such a device is appropriately called the quasi-free electron laser (QFEL). The effect of axial magnetic field within the interaction chamber has also been included in the analysis. The advantages of QFEL result from 1) efficient use of the nonrelativistic e -beam generation and two-stream bunching, 2) use of proven CO2 laser technology, and 3) its rapid tunability.