Stochastic Electron Motion Research Articles

Stochastic electron motion in colliding plane waves.

The stochastic dynamics of an electron in counterpropagating linearly polarized laser beams is analyzed using a recently developed 3/2-dimensional Hamiltonian approach. It is shown that perpendicular canonical momenta suppress stochasticity, helping to explain the results from recently reported numerical studies of stochastic dynamics in a similar setting. The stochasticity in a perpendicular polarization setup is demonstrated. Lastly, the impact of radiation friction effects is considered, and shown to be negligible in the classical radiation reaction limit.

Laser-driven electron acceleration in nanoplate array targets.

This paper proposes a model of the laser-driven electron acceleration that occurs when a high-intensity laser interacts with a nanoplate target. It shows that quasistatic electric E_{qs} and magnetic B_{qs} fields can be formed when the laser, polarized normal to the nanoplates, extracts electrons from the nanoplates. Considering the physical natures of E_{qs} and B_{qs}, the amplitude of E_{qs} is relatively larger than B_{qs}. Such a residual between static electric and magnetic field is shown to be crucial for the electron acceleration beyond the ponderomotive scaling, as it can cause onset of stochastic electron motion. The analysis demonstrates that the maximum electron energy in units of ponderomotive scaling depends on a single universal parameter, which is composed of laser amplitude, spacing between nanoplates, and electron initial conditions. The analytical results are confirmed by a series of two-dimensional particle-in-cell simulations using epoch code.

Study on electron stochastic motions in the magnetosonic wave field: Test particle simulations

Using the test particle simulation method, we investigate the stochastic motion of electrons with energy of 300 keV in a monochromatic magnetosonic (MS) wave field. This study is motivated by the violation of the quasi-linear theory assumption, when strong MS waves (amplitude up to ~1 nT) are present in the Earth’s magnetosphere. First, electron motion can become stochastic when the wave amplitude exceeds a certain threshold. If an electron initially resonates with the MS wave via bounce resonance, as the bounce resonance order increases, the amplitude threshold of electron stochastic motion increases until it reaches the peak at about the 11th order in our study, then the amplitude threshold slowly declines. Further, we find that the coexistence of bounce and Landau resonances between electrons and MS waves will significantly reduce the amplitude threshold. In some cases, the electron motion can become stochastic in the field of an MS wave with amplitudes below 1 nT. Regardless, if neither the bounce nor Landau resonance condition is satisfied initially, then the amplitude threshold of stochastic motion shows an increasing trend for lower frequencies and a decreasing trend for higher frequencies, even though the amplitude threshold is always very large (> 5 nT). Our study suggests that electron stochastic motion should also be considered when modeling electron dynamics regulated by intense MS waves in the Earth’s magnetosphere.

Stochastic electron acceleration in relativistic laser pulse and stationary periodic electric and magnetic fields

The mechanisms of stochastic electron acceleration in relativistic laser pulses and stationary periodic electric and magnetic fields are investigated by employing a new Hamiltonian approach. The new Hamiltonian is the dephasing rate between the electron and laser pulse such that it is time independent when the stationary fields are absent. The physics underlying stochastic electron motion is clearly revealed, and the conditions for triggering stochastic instability are obtained by finding the Chirikov-like mapping. It demonstrates that if the amplitudes of the stationary fields exceed some threshold values, the Hamiltonian can be randomly changed, and thus, net energy transfer between electrons and the laser radiation are possible. The maximum electron energy gained from the stochastic motion has a weak dependence on the amplitude of stationary fields and can significantly exceed the vacuum ponderomotive energy. All these analytical results have been confirmed by the numerical simulations.

Stochastic electron heating in the laser and quasi-static electric and magnetic fields

The dynamics of relativistic electrons in the intense laser radiation and quasi-static electromagnetic fields both along and across the laser propagating direction are studied in the 3/2 dimensional (3/2D) Hamiltonian framework. It is shown that the unperturbed oscillations of the relativistic electron in these electric fields could exhibit a long tail of the amplitude of harmonics which makes an onset of stochastic electron motion be a primary candidate for electron heating. Chirikov-like mappings which describe the recurrence relations of electron energy and time passing through zero canonical momentum plane are derived, and then, the criteria for instability are obtained. It follows that for both transverse and longitudinal electric fields, there exist upper limits of the stochastic electron energy depending on the laser intensity and electric field strength. These maximum energies could be increased by a weak electric field. However, the maximum energy is reduced for the superluminal phase velocity in both cases. The impacts of the magnetic fields on the electron dynamics are different for these two cases and discussed qualitatively. These analytic results are confirmed by the numerical simulations of solving the 3/2D Hamiltonian equations directly.

Electron dynamics in the laser and quasi-static electric and magnetic fields

3/2 dimensional Hamiltonian equations, accounting for arbitrary polarized plane wave laser radiation and arbitrary electric and magnetic fields in the directions both along and across to the direction of the laser beam propagation, are derived for superluminal phase velocity of the laser radiation. An impact of superluminal laser radiation phase velocity on the transition to stochastic electron motion is studied.

Electron heating in the laser and static electric and magnetic fields

A 2D slab approximation of the interactions of electrons with intense linearly polarized laser radiation and static electric and magnetic fields is widely used for both numerical simulations and simplified semi-analytical models. It is shown that in this case, electron dynamics can be conveniently described in the framework of the 3/2 dimensional Hamiltonian approach. The electron acceleration beyond a standard ponderomotive scaling, caused by the synergistic effects of the laser and static electro-magnetic fields, is due to an onset of stochastic electron motion.

Electron residual energy due to stochastic heating in field-ionized plasma

The electron residual energy originated from the stochastic heating in under-dense field-ionized plasma is investigated here. Initially, the optical response of plasma is modeled by using two counter-propagating electromagnetic waves. In this case, the solution of motion equation of a single electron indicates that by including the ionization, the electron with higher residual energy compared with that without ionization could be obtained. In agreement with chaotic nature of the motion, it is found that the electron residual energy will be significantly changed by applying a minor change in the initial conditions. Extensive kinetic 1D-3V particle-in-cell simulations have been performed in order to resolve full plasma reactions. In this way, two different regimes of plasma behavior are observed by varying the pulse length. The results indicate that the amplitude of scattered fields in a proper long pulse length is high enough to act as a second counter-propagating wave and trigger the stochastic electron motion. On the contrary, the analyses of intensity spectrum reveal the fact that the dominant scattering mechanism tends to Thomson rather than Raman scattering by increasing the pulse length. A covariant formalism is used to describe the plasma heating so that it enables us to measure electron temperature inside and outside of the pulse region.

General electronegativity profile of a hydrogen molecule

The general method for studying the equilibrium state of a system through finding the extremum of the appropriate characteristic function can be applied to an isolated molecule, since its state is determined by averaging the stochastic electron motion in the nuclear electric field. Selection of electron energy as the function of state of a hydrogen molecule H2 depending on interatomic distance R(H-H) yields the classical attraction-type potential curve. The use of electronic chemical potential of a hydrogen molecule (μ(H2)) probably also enables one to determine the equilibrium state as there is an advantage in this case that the electronic chemical potential value μ not only can be calculated but also can be experimentally assessed. It was demonstrated that the numerically determined μ(H2) versus interatomic distance dependence is also of the attraction type and has an extremum at the equilibrium R(H-H) value of ∼ 0.74–0.75 A for a certain calculation procedure. This dependence for hydrogen anion H 2 − does not have a well-defined extremum, while the potential energy curve for hydrogen anion H 2 − is of the repulsion type.

Enhanced relativistic laser–plasma coupling utilizing laser-induced micromodified target

The interaction of slighly relativistic femtosecond laser radiation with microstructured Si targets was studied. The microstructuring was performed by nanosecond pulse laser ablation with additional chemical etching of the target material. An analysis was made of the optical damage under the action of femtosecond radiation near the ablation threshold. It was experimentally demonstrated that the hot electron temperature increases appreciably in the laser-driven plasma (from ~370 to almost 500 keV) as well as radiation yield in the MeV range at the interaction of a high power femtosecond laser pulse with a microstructured surface in comparison with a flat surface. Numerical simulations using 3D3V PIC code Mandor revealed that the charged particle energy growth is caused by the stochastic motion of electrons in the complex field formed by the laser field and the quasistatic field at the sharp tips of micromodifications.

Relativistic electron precipitation events driven by electromagnetic ion-cyclotron waves

We adopt a canonical approach to describe the stochastic motion of relativistic belt electrons and their scattering into the loss cone by nonlinear EMIC waves. The estimated rate of scattering is sufficient to account for the rate and intensity of bursty electron precipitation. This interaction is shown to result in particle scattering into the loss cone, forming ∼10 s microbursts of precipitating electrons. These dynamics can account for the statistical correlations between processes of energization, pitch angle scattering, and relativistic electron precipitation events, that are manifested on large temporal scales of the order of the diffusion time ∼tens of minutes.

Stochastic electron motion driven by space plasma waves

Abstract. Stochastic motion of relativistic electrons under conditions of the nonlinear resonance interaction of particles with space plasma waves is studied. Particular attention is given to the problem of the stability and variability of the Earth's radiation belts. It is found that the interaction between whistler-mode waves and radiation-belt electrons is likely to involve the same mechanism that is responsible for the dynamical balance between the accelerating process and relativistic electron precipitation events. We have also considered the efficiency of the mechanism of stochastic surfing acceleration of cosmic electrons at the supernova remnant shock front, and the accelerating process driven by a Langmuir wave packet in producing cosmic ray electrons. The dynamics of cosmic electrons is formulated in terms of a dissipative map involving the effect of synchrotron emission. We present analytical and numerical methods for studying Hamiltonian chaos and dissipative strange attractors, and for determining the heating extent and energy spectra.

Quantum behavior derived as an essentially stochastic phenomenon

We study the behavior of the atomic matter immersed in a zero-point radiation field, which is taken as the source of the endless stochastic motion of electrons. The starting point is a statistical phase-space equation for a particle in interaction with the field. Under certain natural approximations, the system reaches a stationary condition; the corresponding reduced description obtained in configuration space is just the Schrödinger quantum mechanics. Quantum nonlocality is revisited from this point of view and is shown to appear as an artifact of the reduced description. The theory presented also serves to explain why usual quantum mechanics is not amenable to a phase-space formulation.

Efficient acceleration of electrons with counterpropagating intense laser pulses in vacuum and underdense plasma.

We propose that efficient acceleration of electrons in vacuum and underdense plasmas by an intense laser pulse can be triggered in the presence of another counterpropagating or intersecting laser pulse. This mechanism works when the laser fields exceed some threshold amplitudes for stochastic motion of electrons, as found in single-electron dynamics. Particle-in-cell simulations confirm that electron heating and acceleration in the case with two counterpropagating laser pulses can be much more efficient than with one laser pulse only. Two different diagnoses show that the increased heating and acceleration are caused mainly by direct laser acceleration rather than by plasma waves. In plasma at moderate densities such as a few percent of the critical density and when the underdense plasma region is large enough, the Raman backscattered and side-scattered waves can grow to a sufficiently high level to serve as the second counterpropagating or intersecting pulse and trigger the electron stochastic motion. As a result, even with a single intense laser pulse only in plasma, electrons can be accelerated to an energy level much higher than the corresponding laser ponderomotive potential.

Stochastic heating and acceleration of electrons in colliding laser fields in plasma.

We propose a mechanism that leads to efficient acceleration of electrons in plasma by two counterpropagating laser pulses. It is triggered by stochastic motion of electrons when the laser fields exceed some threshold amplitudes, as found in single-electron dynamics. It is further confirmed in particle-in-cell simulations. In vacuum or tenuous plasma, electron acceleration in the case with two colliding laser pulses can be much more efficient than with one laser pulse only. In plasma at moderate densities, such as a few percent of the critical density, the amplitude of the Raman-backscattered wave is high enough to serve as the second counterpropagating pulse to trigger the electron stochastic motion. As a result, even with one intense laser pulse only, electrons can be heated up to a temperature much higher than the corresponding laser ponderomotive potential.

Generation of unmagnetized motion of plasma sheet electrons and its possible causes

Results of experimental and theoretical studies of unmagnetized stochastic motion of the plasma sheet electrons and the mixing of plasma in the plasma sheet are presented. Analysis of the electron temperature distributions within the plasma sheet is undertaken using the data from Intercosmos‐Bulgaria‐1300 polar orbiting satellite. The electron temperature is obtained with consideration of acceleration of precipitating electrons by the field‐aligned potential drop; this temperature is nearly constant in the meridional direction and has no longitudinal dependence during quiet geomagnetic conditions. Analysis of spacial fluctuations of precipitating electron fluxes for a fixed electron energy shows that fluctuation spectra of primary electrons have a power dependence and resemble the spectra of electric field fluctuations observed within the plasma sheet. The satellite observations are interpreted in terms of stochastic motion of the plasma sheet electrons and intensive mixing of plasma in the sheet. It is suggested that the electron motion in the electric field with a characteristic scale comparable with the electron Larmor radius is a source of stochastization; chaotization of the particle trajectories could be a part of stochastization process. The particle motion in a homogeneous magnetic field and in a regular inhomogeneous electric field with a sinusoidal distribution in one direction and a homogeneous distribution in the perpendicular direction is analyzed as an example of the chaotic motion.

Theory of magnetic-breakdown oscillations of the galvanomagnetic properties of aluminum taking account of the spin of the conduction electrons

The theory of magnetic breakdown, taking account of the spin of the conduction electrons, is used to calculate the galvanomagnetic properties of aluminum, where the system of electron trajectories in a magnetic field contains small β orbits. Expressions are obtained for the magnetoresistance and Hall resistance in the case of a two-dimensional magnetic-breakdown network of trajectories on the basis of stochastic electron motion on large orbits and coherent electron motion on the β orbits. Qualitative agreement is obtained with the existing experimental data.

Transition to stochasticity in the relativistic and the nonrelativistic versions of a dynamical system

Issues related to the transition to stochastic relativistic and nonrelativistic motion of electrons in an electromagnetic wave propagating obliquely to a uniform magnetic field, such as stability, structure of the diagrams of characteristics, and the morphology of the bifurcation sequence in the latter, are thoroughly investigated. The spatiotemporal distributions of the electron energies, relativistically and nonrelativistically, are also examined. Major, qualitative, as well as quantitative differences in all aspects related to the transition to stochasticity and energy distribution are found. These dramatic differences lead to the conclusion that, at least as far as stochasticity is concerned, the nonrelativistic approximation is invalid even in the weakest possible relativistic case

Chaotic electron motion caused by sidebands in free electron lasers

The electron dynamics in a free electron laser (FEL) is studied in the case when the radiation field contains many modes. This situation arises when unstable modes (sidebands) are excited during operation. It is observed that when the strength of these sidebands exceeds certain levels the electron motion becomes chaotic. This may lead to extensive particle detrapping and loss of amplification for the FEL signal. The threshold for the onset of stochastic electron motion is computed. The evolution of the trapped electron distribution exhibits a diffusive behavior. The rate of particle detrapping is parametrized by the diffusion coefficient 𝔇 in action space. The e-folding length for the number of trapped electrons is parametrized by J2s/𝔇, where Js is the action at the separatrix. It is found that the diffusion rates are related to the type of the sideband spectrum. The diffusion coefficient is always proportional to the ratio of the sideband power in all frequencies to the power of the carrier signal. The coefficient of the proportionality, however, scales differently on the FEL parameters for each of the three spectral categories: a narrow, a broad discrete, and a broad continuous spectrum. The diffusion coefficient is computed analytically for the last two cases and is in good agreement with numerical results. The narrow spectrum yields the highest and the broad continuous the lowest diffusion rates under constant sideband power. It is also found that, in all cases, the diffusion length, measured in wiggler periods, is independent of the electron energy γ.

Stochastic electron detrapping in FELs caused by sidebands

The growth of sidebands in an FEL above a certain threshold will result in stochastic electron motion. This may lead to significant electron detrapping and loss of amplification for the radiation field. The threshold in the sideband amplitude for the stochastic transition is computed. The rate trapped electrons leak outside the separatrix is measured by the diffusion coefficient in action space. This approach is general and covers both tapered and untapered wigglers. Three general types of spectra are examined: a narrow, a broad discrete and a broad continuous. Each type is associated with a particular scaling of the diffusion coefficient on the FEL parameters. Numerical results, obtained for constant radiation amplitudes, show good agreement with the theoretical predictions. The diffusion rate is always proportional to the total sideband-to-carrier power ratio, with different coefficients of proportionality for each spectral type. The narrow type of spectrum causes the highest diffusion rates and the broad continuous spectrum causes the lowest diffusion rates under constant total sideband power. The diffusion length, measured in wiggler periods, is independent of the beam energy γ. Serious deterioration in the FEL efficiency will result when the diffusion length becomes shorter than the wiggler length.