The effect of friction on nonlinear oscillations of interacting domain walls in an external periodic field

The effect of dissipation on nonlinear oscillations in a system of domain walls experiencing an external harmonic field is studied numerically. The problem is formulated for uniaxial ferromagnet films, with the easy magnetic axis being perpendicular to the surface and with the harmonic field being aligned with the axis. Account is taken of the dynamic redistribution of magnetic poles on the film surface, which enables one to derive, in a natural way, an expression for a restoring force acting on the domain walls. The force is a nonlinear function of domain-wall displacement from the equilibrium position. It is found that the domain walls may execute complicated steady-state quasi-periodic oscillations and long-term chaotic oscillations. Attractors in the phase space of the system are determined.     

Confinement effects in electrical resistivity and spin-valve magnetoresistance in metallic layered structures

Quantum size effects in electronic transport properties of metallic trilayers are analysed theoretically. It is shown that electron confinement leads to oscillations in electrical resistivity with two different periodicities. The short oscillation period is determined by the appropriate Fermi wavelength, whereas the long period depends on the potential step at interfaces. When the outer films in the trilayer are ferromagnetic, then the oscillations in the resistivity give rise to similar oscillations in the spin-valve magnetoresistance.     

Localized plasmons in quantum plasmas

We consider the nonlinear interactions between finite amplitude electron and ion plasma oscillations in a fermionic quantum plasma. Accounting for the quantum statistical electron pressure and the quantum Bohm potential, we derive a set of coupled nonlinear equations that govern the dynamics of modulated electron plasma oscillations (EPOs) in the presence of the nonlinear ion oscillations (NLIOs). We numerically study stationary solutions of our coupled nonlinear equations. We find that the quantum parameter H (equal to the ratio between the plasmonic and electron Fermi energy densities) introduces new features to the electron density and electric potential humps of localized NLIOs in the absence of EPOs. Furthermore, the nonlinear coupling between the EPOs and NLIOs gives rise to a new class of envelope solitons composed of bell shaped electric field envelope of the EPOs, which are trapped in the electron density hole (and an associated negative oscillatory electric potential) that is produced by the ponderomotive force of the EPOs. The knowledge of the localized plasmonic structures is of immense value for interpreting experimental observations in dense quantum plasmas.     

Dynamical electron localization and self-induced transparency in semiconductor superlattices

The mechanisms of the occurrence of self-induced and selective transparencies of semiconductor superlattices in a strong time-dependent electric field are investigated. The association of these mechanisms with Bloch oscillations, dynamical localization, and collapse of electron quasi-energy minibands is analyzed, and a comparison with the properties of Josephson junctions is made. It is shown that the self-induced transparency is due to the fact that the current-contributing component of the electron distribution function is destroyed by collisions at discrete values of the amplitude of the time-harmonic field, while the selective transparency is associated with the nonmonotonic dependence of the spectrum of nonlinear electron oscillations in the electric field on the amplitude of the field. The dynamical localization and collapse of quasi-energy minibands lead to the field energy dissipation and are favorable to destruction of the transparency states of the superlattice.     

Energy levels of oscillations in a nonlinear transmission line filled with saturated ferrite

Stationary solutions in the form of traveling electromagnetic waves in a uniform transmission line filled with saturated ferrite in the absence of damping are studied. Expressions are obtained for the period of nonlinear oscillations as a function of their amplitude. The period of linear oscillations is shown to linearly increase with the current through the line. The group velocity of the stationary wave increases with the oscillation amplitude. A relationship is found between the electromagnetic oscillations and oscillations of the magnetization vector. The oscillations become increasingly anisochronous with increasing the external magnetic field.     

Nonlinear Evolution of Driven Electron Plasma Oscillations in Inhomogeneous Plasmas

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Dephasing by extremely dilute magnetic impurities revealed by Aharonov-Bohm oscillations

We have probed the magnetic field dependence of the electron phase coherence time tau(phi) by measuring the Aharonov-Bohm conductance oscillations of mesoscopic Cu rings. Whereas tau(phi) determined from the low-field magnetoresistance saturates below 1 K, the amplitude of Aharonov-Bohm h/e oscillations increases strongly on a magnetic field scale proportional to the temperature. This provides strong evidence that a likely explanation for the frequently observed saturation of tau(phi) at low temperature in weakly disordered metallic thin films is the presence of extremely dilute magnetic impurities.     

Finite-amplitude standing acoustic waves in a cubically nonlinear medium

The acoustic field in a resonator filled with a cubically nonlinear medium is investigated. The field is represented as a linear superposition of two strongly distorted counterpropagating waves. Unlike the case of a quadratically nonlinear medium, the counterpropagating waves in a cubically nonlinear medium are coupled through their mean (over a period) intensities. Free and forced standing waves are considered. Profiles of discontinuous oscillations containing compression and expansion shock fronts are constructed. Resonance curves, which represent the dependences of the mean field intensity on the difference between the boundary oscillation frequency and the frequency of one of the resonator modes, are calculated. The structure of the profiles of strongly distorted “forced” waves is analyzed. It is shown that discontinuities are formed only when the difference between the mean intensity and the detuning takes certain negative values. The discontinuities correspond to the jumps between different solutions to a nonlinear integro-differential equation, which, in the case of small dissipation, degenerates into a third-degree algebraic equation with an undetermined coefficient. The dependence of the intensity of discontinuous standing waves on the frequency of oscillations of the resonator boundary is determined. A nonlinear saturation is revealed: at a very large amplitude of the resonator wall oscillations, the field intensity in the resonator ceases depending on the amplitude and cannot exceed a certain limiting value, which is determined by the nonlinear attenuation at the shock fronts. This intensity maximum is reached when the frequency smoothly increases above the linear resonance. A hysteresis arises, and a bistability takes place, as in the case of a concentrated system at a nonlinear resonance.     

Zener Tunneling between the Landau Levels in a Two-Dimensional Electron System with One-Dimensional Periodic Modulation

Nonlinear magnetotransport in a two-dimensional electron gas in one-dimensional lateral lattices fabricated from a selectively doped GaAs/AlAs heterostructure is investigated. One-dimensional potential modulation is imposed on the two-dimensional electron gas by means of a set of metal strips formed on the planar surface of Hall bars. The dependences of the differential resistance r_xx on the magnetic field B < 0.5 T are studied at a temperature T = 1.6 K in lattices with a period of a ≈ 200nm. It is shown that periodic oscillations in r_xx(1/B) occur in such lattices under the action of a current-induced Hall field due to Zener tunneling between Landau levels. Interference is found between Zener oscillations and commensurability oscillations of r_xx in two-dimensional electron systems with one-dimensional periodic modulation. The experimental results are qualitatively explained by the role of Landau bands in nonlinear transport at large filling factors.     

Synchronization and bifurcations of internal and external degrees of freedom of an atom in a standing light wave

The nonlinear dynamical effects of synchronization and bifurcations of Rabi oscillations and oscillations of the center of mass of an atom moving in the field of a standing light wave are theoretically and numerically examined. After completion of a transient process, synchronized oscillations, stable with respect to small noise, are established both upon ballistic motion of the atom and upon its oscillations in the optical potential well. The bifurcations of limit cycle generation with different periods (tripling of the period is most pronounced) and the passage to a chaotic strange attractor through an intermittency are obtained.     

Nonlinear Plasma Dynanics in the Plasma Wakefield Accelerator

Excitation of nonlinear plasma oscillations by an ultrarelativistic electron beam is considered in this paper. It is shown, by analytical solutions of the fully relativistic nonlinear fluid equations in one dimension, that under certain conditions on the relative densities of the electron beam and the plasma, extremely large longitudinal electric fields can be generated in the wake of the beam. This scheme can be considered as a nonlinear regime of the plasma wakefield accelerator (PWFA), and is seen to have the advantage that the transformer ratio, the ratio of the maximum amplitude of the accelerating field behind the driving beam over the maximum amplitude of the decelerating field inside of the beam, can be made arbitrarily large, dependent only on the length of the driving beam. The effects of beam loading on the efficiency of this scheme are considered, and are shown to be equivalent to those predicted in the linear regime.     

Wire network behavior of superconducting films with lower symmetrical mesoscopic hole arrays

Superconducting films with the same hole density but different geometric symmetry have been designed and fabricated. The R(H) curves show obvious periodic oscillations with several dips at fractional matching fields. It is found that the period of the oscillations in the low field is not necessary equal to that derived from the hole density, but consistent with that from the corresponding wire networks when the large disk-like film regions are regarded as nodes. The experimental results of R(H), T_c(H) and j_c(H) at fractional matching fields within the first oscillation also support the rationality of considering films with large-diametered hole arrays as wire networks. Our results demonstrate that the connectivity of superconducting films with large-diametered hole arrays plays a more important role in the oscillations of R(H) curves.     

THz-field induced nonlinear transport and dc voltage generation in a semiconductor superlattice due to Bloch oscillations

We report on a theoretical analysis of terahertz (THz-) field induced nonlinear dynamics of electrons in a semiconductor superlattice that are capable to perform Bloch oscillations. Our results suggest that for a strong THz-field a dc voltage should be generated. We have analyzed the real-time dynamics using a balance equation approach to describe the electron transport in a superlattice miniband. Taking account of both Bloch oscillations of electrons in a superlattice miniband and dissipation, we studied the influence of a strong THz-field on currently available superlattices at room temperature. We found that a THz-field can lead to a negative conductance resulting in turn in a THz-field induced dc voltage, and that the voltage per superlattice period should show, for varying amplitue of the THz-field, a form of wisted plateaus with the middle points being with high precision equal to the photon energy divided by the electron charge. We show voltage to the finite voltage state, and that in the finite voltage state dynamic localization of the electrons in a miniband occurs.     

Nonlinear dynamical modelling of chaotic electrostatic ion cyclotron oscillations by jerk equations

Plasma being a nonlinear and complex system, is capable of sustaining a wide spectrum of waves, oscillations and instabilities. These fluctuations interact nonlinearly amongst themselves and also with particles: electrons/ions and thus lead to nonlinear wave-wave or wave-particle interaction. In the presence of coherent waves the particles are accelerated whereas irregular oscillations can give rise to particle heating which is also called stochastic heating. Particle orbits are known to be randomized by the wave fields such that their motion can also become stochastic. For fusion to be sustained one needs a very high temperature plasma for an extended duration. It quite common to deploy external waves like electron cyclotron waves or ion cyclotron waves for plasma heating and current drive. These external waves also work only in certain regimes. Conventional plasma techniques have been able to answer several of the observations of the above processes related to heating transport etc, but nonlinear dynamics as a tool has helped in comprehending the plasma oscillations better. We have for the first time obtained a Third Order nonlinear ordinary differential equation (TONLODE) also known as jerk equation to describe the electrostatic ion cyclotron plasma oscillations in a magnetic field. The interesting feature of this equation is that it does not require an external forcing term to obtain chaotic behaviour.     

Self-oscillations in semiconductor superlattices

An investigation is made of nonlinear oscillations of the field and current in semiconductor superlattices driven by strong terahertz radiation. Regimes of periodic, quasi-periodic, and stochastic self-oscillations are determined and mechanisms for their formation are discussed. It is shown that the self-oscillation spectra are many-valued functions of the external field amplitude and the static field in them is either absent, weak, or fractionally quantized. Previously predicted states of self-induced superlattice transparency and dynamic electron localization are destroyed as a result of the evolution of dissipative and parametric instabilities and can only be observed in transient processes whose duration decreases with increasing electron concentration.     

Nonlinear structure of Gaussian laser beam in an axial non-uniform collisional plasma

Nonlinear structure of Gaussian laser beam in axial non-uniform underdense collisional plasma is investigated. Due to the combination effect of nonlinear ohmic heating and non-uniform of plasma, and which it modifies electrons temperature and density distribution. On the one hand, due to the effect of the nonlinear ohmic heating, electron temperature and electron density oscillations become highly peaked. On the other hand, due to add the influence of non-uniform of plasma, lead to the departure from sinusoidal shape of electrons temperature, electron density and electromagnetic fields distributions. With the increase of laser intensity, these nonlinear variations become more and more obvious, and their oscillations wavelength decrease.     

On nonlinear oscillations in an inhomogeneous electron flux

This work considers nonlinear oscillations in an inhomogeneous electron flux moving in a high-frequency field between two parallel planes placed perpendicular to the beam motion. It is shown with the help of the Hamiltonian formalism in the threewave approximation that under specific conditions there occurs a periodic exchange of energy between the high-frequency field and the electron flux and also between the long-wave and short-wave harmonics of the flux.The authors express thanks to N. M. Filipenko who participated in the discussion of the obtained results.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 88–93, June, 1981.     

Natural electron oscillations in granular indium films deposited on rough surfaces of NaCl and KCl single crystals

Two plasma resonance bands were simultaneously observed in granular indium films deposited on rough surfaces of NaCl and KCl single crystals; one of them is caused by a combined action of the light-wave field and of the field created by the dipole grains, and the other, by the light-wave field alone with the frequency of natural electron oscillations ω₀ in the grains. The indium plasma frequency, calculated from the measured frequencies ω₀ and known dielectric constants of NaCl and KCl, agrees well with the known plasma frequency of bulk indium. An anisotropy in the plasma resonance band of granular indium films deposited on a rough NaCl surface was found and interpreted.     

Analysis of 90° pulsed magnetization signals of ferrite-garnet films with easy plane-type anisotropy

The results from a numerical analysis of 90° pulsed magnetization signals of ferrite-garnet films with easy plane-type anisotropy are discussed. The possibility of nonlinear magnetization oscillations occurring at a magnetizing pulse front several times greater than the oscillation period is shown. The results from the calculations describe the actual shape of the longitudinal and transverse signals quite well. The calculated values of the oscillation frequency (∼500 MHz) are also in good agreement with the experimental data.     

Fermi energy and electron thermopower in quantum films of an asymmetric profile

The behavior of the Fermi energy and the electron thermoelectric power in an asymmetric quantum well of the Morse potential type as a function of electron concentration are studied. It is shown that the Fermi energy is a piecewise-linear function, and the electron thermoelectric power is an oscillating function. The analysis shows that the nature of these oscillations differs significantly from that in films of a parabolic and rectangular profile, namely, the oscillation period is a nonmonotonic function and reaches a maximum at some value of the electron concentration. The possibility of estimating the parameters of the film profile (quantum well) is proposed. A comparison with the experiment shows a qualitative agreement.