Electron Oscillation Frequency Research Articles

On-the-Fly AbInitio Semiclassical Evaluation of Electronic Coherences in Polyatomic Molecules Reveals a Simple Mechanism of Decoherence.

Irradiation of a molecular system by an intense laser field can trigger dynamics of both electronic and nuclear subsystems. The lighter electrons usually move on much faster, attosecond timescale but the slow nuclear rearrangement damps ultrafast electronic oscillations, leading to the decoherence of the electronic dynamics within a few femtoseconds. We show that a simple, single-trajectory semiclassical scheme can evaluate the electronic coherence time in polyatomic molecules accurately by demonstrating an excellent agreement with full-dimensional quantum calculations. In contrast to numerical quantum methods, the semiclassical one reveals the physical mechanism of decoherence beyond the general blame on nuclear motion. In the propiolic acid, the rate of decoherence and the large deviation from the static frequency of electronic oscillations are quantitatively described with just two semiclassical parameters-the phase space distance and signed area between the trajectories moving on two electronic surfaces. Because it evaluates the electronic structure on the fly, the semiclassical technique avoids the "curse of dimensionality" and should be useful for preselecting molecules for experimental studies.

Dipole scattering of a short radiation pulse on hydrogen-like atoms

Our theoretical model of forced dipole oscillation demonstrates that when the amplitude of the forcing field is changing fast, the oscillations of the bound electron in the atom or molecule initially proceed at two frequencies: the frequency of the natural electron oscillations and the frequency of the forcing field. Particularly, applied to the science of scattering, this model of transient forced atomic and molecular oscillations suggests that accurate interpretation of the laser scattering experiments using short laser pulses must include both the conventionally known scattering at the laser frequency (Rayleigh) and the predicted by our theoretical spectral emission that corresponds to the natural frequency of the electronic oscillations. This article presents the results of numerical simulations using our model performed for the hydrogen atom. The characteristics of the components of scattered radiation, their polarization, and Doppler thermal broadening are discussed.

Enhancement of laser-driven electron acceleration in an ion channel

A laser beam with duration longer than the period of plasma oscillations propagating through an underdense plasma produces a steady-state positively charged channel in the electron density. We consider a test electron in the two-dimensional plane channel under the combined action of the laser field and the transverse static electric field of the channel. At ultrarelativistic laser wave amplitude (a≫1), the electron is pushed primarily forward. As the electron gradually dephases from the wave, the field it samples and its relativistic γ-factor strongly oscillate. The natural frequency of electron oscillations across the channel (betatron frequency) depends on γ, which couples the betatron oscillations to the longitudinal motion induced by the wave. We show that the modulation of the natural frequency makes the oscillations unstable. The resulting amplification of the oscillations across the channel reduces the axial dephasing between the electron and the wave, leading to a considerable electron energy enhancement well above the ponderomotive energy. We find that there is a well-pronounced laser amplitude threshold a*, above which the enhancement takes place, that scales as a*∝1/n0, where n0 is the ion density. The presented mechanism of energy enhancement is robust with respect to a longitudinal variation of the density, because it relies on a threshold phenomenon rather than on a narrow linear resonance.

Betatron-like resonance in ultra-intense laser mass-limited foil interaction

With the help of three-dimensional particle-in-cell simulations, we study the electron dynamics in radiation pressure acceleration of a mass-limited foil target. When a mass-limited foil is irradiated by a circularly polarized laser pulse, the wing parts of the laser overtake the foil from the foil boundaries. In the laser propagation direction, electrons are significantly accelerated by the laser radiation pressure. In the laser polarization direction, electrons are subjected to a strong radial space-charge force and oscillate in the overtaking laser field. Under their combined actions, electrons execute a betatron-like oscillation and a spatially helix electron bunch is thus formed. A simple analytical model is proposed for interpreting the high electron energies and large oscillating amplitudes. It is shown that, when the electron oscillation frequency coincides with the laser frequency as witnessed by the electron, betatron-like resonance occurs, resulting in hundreds of MeV electron generation.

Bright Betatronlike X Rays from Radiation Pressure Acceleration of a Mass-Limited Foil Target

By using multidimensional particle-in-cell simulations, we study the electromagnetic emission from radiation pressure acceleration of ultrathin mass-limited foils. When a circularly polarized laser pulse irradiates the foil, the laser radiation pressure pushes the foil forward as a whole. The outer wings of the pulse continue to propagate and act as a natural undulator. Electrons move together with ions longitudinally but oscillate around the latter transversely, forming a self-organized helical electron bunch. When the electron oscillation frequency coincides with the laser frequency as witnessed by the electron, betatronlike resonance occurs. The emitted x rays by the resonant electrons have high brightness, short durations, and broad band ranges which may have diverse applications.

Parametric Amplification of Laser-Driven Electron Acceleration in Underdense Plasma

A new mechanism is reported that increases electron energy gain from a laser beam of ultrarelativistic intensity in underdense plasma. The increase occurs when the laser produces an ion channel that confines accelerated electrons. The frequency of electron oscillations across the channel is strongly modulated by the laser beam, which causes parametric amplification of the oscillations and enhances the electron energy gain. This mechanism has a threshold determined by a product of beam intensity and ion density.

Plasma wave propagation with a plasma density gradient

Plasma waves with the plasma diffusion velocity un due to a plasma density gradient are described in a positive column plasma. The ion wave is generated by the perturbation of the operating frequency 106 s−1 and it propagates with the group velocity ug∼cs2/un∼(105–106) m/s, where cs is the acoustic velocity in a fine tube fluorescent lamp, while the electron wave cannot be generated with a turbulence of low frequency less than the electron oscillation frequency ωpe. The propagation of the lighting signal observed in long tube fluorescent lamps is well understood with the propagation of ion waves occurring along the plasma density gradient.

Surface plasmon resonance in nanostructured metal films under the Kretschmann configuration

We systematically investigated the surface plasmon resonance in one-dimensional (1D) subwavelength nanostructured metal films under the Kretschmann configuration. We calculated the reflectance, transmittance, and absorption for varying the dielectric fill factor, the period of the 1D nanostructure, and the metal film thickness. We have found that the small dielectric slits in the metal films reduce the surface plasmon resonance angle and move it toward the critical angle for total internal reflection. The reduction in surface plasmon resonance angle in nanostructured metal films is due to the increased intrinsic free electron oscillation frequency in metal nanostructures. Also we have found that the increasing the spatial frequency of the 1D nanograting reduces the surface plasmon resonance angle, which indicates that less momentum is needed to match the momentum of the surface plasmon-polariton. The variation in the nanostructured metal film thickness changes the resonance angle slightly, but mainly remains as a mean to adjust the coupling between the incident optical wave and the surface plasmon-polariton wave.

Ultrafast Electron Relaxation Dynamics in Coupled Metal Nanoparticles in Aggregates

We report the effect of aggregation in gold nanoparticles on their ultrafast electron-phonon relaxation dynamics measured by femtosecond transient absorption pump-probe spectroscopy. UV-visible extinction and transient absorption of the solution-stable aggregates of gold nanoparticles show a broad absorption in the 550-700-nm region in addition to the isolated gold nanoparticle plasmon resonance. This broad red-shifted absorption can be attributed to contributions from gold nanoparticle aggregates with different sizes and/or different fractal structures. The electron-phonon relaxation, reflected as a fast decay component of the transient bleach, is found to depend on the probe wavelength, suggesting that each wavelength interrogates one particular subset of the aggregates. As the probe wavelength is changed from 520 to 635 nm across the broad aggregate absorption, the rate of electron-phonon relaxation increases. The observed trend in the hot electron lifetimes can be explained on the basis of an increased overlap of the electron oscillation frequency with the phonon spectrum and enhanced interfacial electron scattering, with increasing extent of aggregation. The experimental results strongly suggest the presence of intercolloid electronic coupling within the nanoparticle aggregates, besides the well-known dipolar plasmon coupling.

Confinement-Enhanced Electron Transport across a Metal-Semiconductor Interface

We present a combined scanning tunneling microscopy and ballistic electron emission microscopy study of electron transport across an epitaxial Pb/Si(111) interface. Experiments with a self-assembled Pb nanoscale wedge reveal the phenomenon of confinement-enhanced interfacial transport: a proportional increase of the electron injection rate into the semiconductor with the frequency of electron oscillations in the Pb quantum well.

Plasma resonance in granular gallium films deposited on rough NACl and KCl single-crystal surfaces

Granular gallium films deposited in high vacuum on the rough surfaces of NaCl and KCl single crystals maintained at 400°C consist of two layers, in which two resonance bands are excited simultaneously. In isolated grains of the upper layer, a band at the normal electron oscillation frequency ω0 is excited. As a result of supercooling, the grains are in the liquid state. The gallium plasma frequency calculated from the measured ω0 and dielectric constants of NaCl and KCl coincides with that obtained by other authors by metallooptic methods. In gallium deposited on room-temperature substrates, only one resonance band is excited, with the interband absorption band superposed on its low-frequency edge.

Heterostructure as a nonlinear crystal

The motion of an electron in the potential well of a heterostructure is considered. The cubic susceptibility of electrons in such a system in the presence of an electromagnetic field is calculated. The nonlinearity of the electron motion in the electromagnetic field is explained by the nonparabolic dependence of the energy on the quasi-momentum. However, the cubic susceptibility grows drastically in the case of resonance when the effective electron oscillation frequency, ω 0, in the potential well is close to the electromagnetic field frequency, ω.

Electrostatic wave noise in the neutral sheet in the earth's geomagnetic tail

Numerical solutions are obtained from analytic dispersion relations for electrostatic waves in a self-consistent, one-dimensional magnetic neutral sheet. The dispersion relations are solved in the real wave number and complex frequency domain. The properties of wave modes will be described, with special emphasis on instability. Several regimes of instability are identified which may generally be divided into two classes. Wave growth is associated firstly with counterstreaming between ions and electrons, giving rise to low frequency waves similar to the usual electrostatic two-stream mode. In addition, high frequency growing waves occur, associated with harmonics of the electron oscillation frequency across the neutral plane.

Common properties of free electron lasers

A general theory of microwave devices (in particular, ubitron, gyrotron) based on the ultrarelativistic Doppler up-conversion of electron oscillation frequency is developed. The wave growth rate for the amplifier and the start current for the generator are obtained. A universal relation between the frequency conversion factor and the efficiency of the laser is derived.

High-Power Microwaves from a Nonisochronic Reflecting Electron System

High-power microwave radiation is observed when a positive pulse is applied to an anode of a reflex triode. The frequency of radiation varies as $f\ensuremath{\sim}\frac{{V}^{\frac{1}{2}}}{{D}^{n}}$, where $V$ is the anode voltage, $D$ is the cathode-virtual-cathode spacing, and $0<n<~1$. The basic features of the radiation are explained by a theoretical model which predicts particle bunching as a result of the energy dependence of the electron oscillation frequency.

Nonlinear behaviour of a finite amplitude electron plasma wave I. Electron trapping effects

Nonlinear effects in the propagation of longitudinal plasma waves due to trapped electrons are considered. The spatial evolution of a stable, finite amplitude wave is compared with theory and shown to be characterized by the ratio of the trapped electron oscillation frequency to the linear Landau damping rate. The ‘sideband’ instability which develops at larger amplitudes is examined in considerable detail experimentally, and comparison with theory enables the conclusion to be reached that trapped particles are essential to the mechanism of the instability. Regimes are defined in which these types of nonlinear behaviour occur, and the importance of the instability in the development of strong turbulence is discussed.

Crossing of an incoherent integral resonance in the electron ring accelerator

In one mode of operation of an electron ring accelerator (ERA), at the end of compression rings are slowly moved through the radial integral betatron resonance Q r = 1. Although the coherent radial oscillation frequency of the ring as a whole remains below unity, the oscillation frequencies of individual electron are (incoherently) caused to pass through the resonance because of the additional focusing from ions trapped in the ring. In this paper the effect of field errors on ring major and minor radii is evaluated-theoretically-for the cases in which the spread in the square of the electron oscillation frequency ( Δ 2) is (a) much smaller and (b) much larger than the contribution to the square of the oscillation frequency from the ions ( Δ 2). It is shown that for the ERA, where case (a) applies, the increase in ring minor dimensions, for given field errors and rate of resonance crossing, is less than in case (b) by a factor of ( Δ Λ ) 2 . Numerical examples show that the degradation of ring quality in case (b) should, with suitable attention to the design and construction of the ERA apparatus, be acceptably small.

Ion Oscillations in a Plasma

ABS>The oscillation intensity in a hog-cathode mercury vapor plasma was observed as a function of discharge current. The frequency of the strongest oscillation noted increased with the discharge current and was observed simultaneously with the electron oscillation frequency. This main oscillation was identified as the ion oscillation, which proved to be unaffected by a weak magnetic field. It was also coexistent with the other large fluctuation. (D.C.W.)

The Excitation of Plasma Oscillations

A beam of high-energy electrons, injected into the plasma of a dc discharge from an auxiliary electron gun, excited oscillations in the plasma at the plasma electron oscillation frequency given by the Tonks-Langmuir equation. A movable probe showed the existence of standing-wave patterns of the oscillatory energy in the region of the plasma in and around the electron beam. Nodes of the patterns coincided with the electrodes which limited the region of the plasma traversed by the beam. The standing-wave patterns were independent of the frequency of the oscillation. At any particular frequency, the standing wave was determined by the thickness of the ion sheaths on the bounding electrodes. The mechanism of the energy transfer from the electron beam to the oscillation of the plasma electrons was established as a velocity-modulation process by the detailed behavior of the frequency of oscillation and the transitions in the standing-wave patterns as the sheath thickness was varied. Experimental attempts to produce plasma oscillations as predicted by Bohm and Gross proved to be fruitless.

Investigations in the Field of the Ultra-short Electromagnetic Waves. IV. On the Dependence of the Ultra-short Electromagnetic Waves upon the Heating Current and upon the Amplitude of the Oscillations

An investigation has been made of the dependence of the length of the ultrashort electromagnetic waves generated by vacuum tubes on the magnitude of the heating current. It is shown that the normal waves (i.e., waves the frequency of which corresponds to the frequency of the oscillations of the electrons about the grid of the tube) differ from the dwarf waves (i.e., waves with frequency ceeding several times the frequency of electronic oscillations) in their dependence on the heating current. The length of the normal waves increases, while the length of the dwarf waves of all orders decreases as the heating current is decreased. Therefore, as the heating current is decreased, there is a better agreement between the observed and computed values of wave-lengths of the normal and of the dwarf waves. At low heating currents the product ${\ensuremath{\lambda}}^{2}{E}_{g}$ for dwarf waves of different orders is very close to the theoretical values ${\ensuremath{\lambda}}^{2}{E}_{g}=\frac{{\mathrm{const}.}_{0}}{{n}^{2}} n=2, 3, 4, \ensuremath{\cdots}$ where ${\mathrm{const}.}_{\mathrm{o}}$ corresponds to the value of the product ${\ensuremath{\lambda}}^{2}{E}_{g}$ for normal waves. The results of the experiments are in agreement with the theory of P. S. Epstein, which explains the discrepancy between the calculated and the observed length of the normal and the dwarf waves being due to the influence of the alternating potentials appearing on the electrodes of the tube during oscillations. In the limit, at infinitely low amplitudes of these potentials, the ratio of the values of the products ${\ensuremath{\lambda}}^{2}{E}_{g}$ for normal and for dwarf waves approaches the theoretical value within the limits of the experimental error. Neglecting these alternating potentials introduces the largest error in the results of the existing theories of the generation of ultra-short waves. At sufficiently intensive oscillations, this error exceeds all the others taken together, including the error introduced through the simplifying assumption of plane electrodes. The limiting value of ${\mathrm{const}.}_{0}$ corresponding to infinitely low amplitudes of the alternating potentials, approaches very closely the value of the product ${\ensuremath{\lambda}}^{2}{E}_{g}$ calculated from the formulas of H. Barkhausen and A. Scheibe. This shows that normal waves really do correspond to a complete period of oscillations of the electrons about the grid, i.e., to the time the electrons take to pass from the filament to the grid and back to the filament.