Nonlinear Cyclotron Resonance Research Articles

Resonant Electron Signatures in the Formation of Chorus Wave Subpackets

AbstractA 2‐D GCPIC simulation in a dipole field system has been conducted to explore the excitation of oblique whistler mode chorus waves driven by energetic electrons with temperature anisotropy. The rising tone chorus waves are initially generated near the magnetic equator, consisting of a series of subpackets, and become oblique during their propagation. It is found that electron holes in the wave phase space, which are formed due to the nonlinear cyclotron resonance, oscillate in size with time during subpacket formation. The associated inhomogeneity factor varies accordingly, giving rise to various frequency chirping in different phases of subpackets. Distinct nongyrotropic electron distributions are detected in both wave gyrophase and stationary gyrophase. Landau resonance is found to coexist with cyclotron resonance. This study provides multidimensional electron distributions involved in subpacket formation, enabling us to comprehensively understand the nonlinear physics in chorus wave evolution.

THE ROLE OF HIGHER MOMENTS ON THE DISTRIBUTION OF PARTICLES IN THE SPACE OF IMPULSES AT CYCLOTRON RESONANCES

The results of the analysis of the dynamics of charged particles under conditions of cyclotron resonances in the field of an intense electromagnetic wave are presented. Particular attention is paid to regimes with dynamic chaos. It is shown that there are two qualitatively different regimes. The appearance of the first one is due to the overlap of nonlinear cyclotron resonances. The second mode is related to intermittency. The moments and spectra of each of these regimes are determined. It is shown that with an increase in the intensity of an external electromagnetic wave, the first regime appears at the beginning and only then the second regime appears. A characteristic feature of the second regime is intermittency. Steps appear on the time dynamics of pulses in the second mode. It is shown that the spectra in the second mode are narrower than in the first mode. A characteristic feature of the second regime (the regime with intermittency) is the fact that the higher moments turn out to be larger than the lower moments. In the first regime, the highest moments decrease rapidly. To find the particle momentum distribution function, the generalized Fokker-Planck equation was used. Solutions of this equation are written out for some important cases.

Scattering of energetic electrons through nonlinear cyclotron resonance with coherent whistler-mode hiss emissions

Recent observations have revealed that plasmaspheric hiss consists of many discrete waves called “hiss elements.” However, the interaction of energetic electrons (10 keV to several MeV) with the plasmaspheric hiss has only been simulated by the quasilinear (QL) diffusion theory, which does not take the fine wave structure into account. The QL theory cannot address nonlinear particle motions determined by the inhomogeneity factor, which influences the scattering of electrons in pitch angle and energy. This study aims to identify differences between the nonlinear wave–particle interaction and QL theory for plasmaspheric hiss emissions. We conduct test particle simulations to demonstrate the nonlinear interactions between hiss waves and electrons. The nonlinear theory is used to model hiss elements consisting of discrete frequencies and continuous phases. Unlike the other theories, the frequency and amplitude variations in time of the hiss packet are taken into account. Frequencies of the packets are determined to satisfy the separability criterion; when the criterion is met, resonance overlapping is absent, and the electrons can generate each wave element independently. The realistic simulation model of hiss waves reproduces the scattering of electrons by both first- and second-order resonances. We also evaluate the efficiency of electron scattering by calculating nonlinear diffusion coefficients. The diffusion coefficient of equatorial pitch angle is of the same order of magnitude as those calculated by the QL diffusion theory, while we find the effective acceleration of resonant electrons by successive nonlinear trapping, which is not evaluated by the QL theory.

Generation of a Periodic Sequence of Ultrashort Electromagnetic Pulses in a Scheme with Two Parallel Radiating and Absorbing Electron Beams

We demonstrate the possibility of generating a periodic sequence of ultrashort electromagnetic microwave pulses in a scheme with two parallel coaxial electron beams formed by a common cathode and transported via common vacuum channel. The external cylindrical tubular beam ensures the amplification of radiation during rectilinear propagation along periodic slow-wave system, while the internal (paraxial) beam accounts for the nonlinear cyclotron-resonance absorption.

Alpha Transmitter Signal Reflection and Triggered Emissions

AbstractRussian Alpha radio navigation system (RSDN‐20) emits F1 = 11.9 kHz signals into the magnetosphere which propagate as whistler mode waves. Observed by waveform continuous burst mode from Electric and Magnetic Field Instrument Suite and Integrated Science (EMFISIS) on Van Allen Probes, a case is presented and featured with ducted propagation, multiple reflections, and triggered emissions. Both risers and fallers appear in the triggered emissions. We use a ray tracing method to demonstrate ducted propagation, which has a similar wave normal angle near 150° as the observation. The arrival time of reflected signals is estimated using propagation analysis and compared with the observed signal arrival time. To test the nonlinear cyclotron resonance theory, the interaction region scale and the order of chirping rate in triggered emission are estimated. The estimated interaction region scale of MLAT = −3° is smaller than the observed MLAT = −6°. The discrepancy may be caused by the parallel propagation assumption and background field model.

Nonlinear Cyclotron Resonance Absorber for a Microwave Subnanosecond Pulse Generator Powered by a Helical-Waveguide Gyrotron Traveling-Wave Tube

A well-known principle for periodical production of high-power ultrashort optical pulses is related to passive mode locking realized when a saturable absorber is incorporated into the laser resonator. A similar effect can be implemented in two-section electronic oscillators comprising an amplifier and a saturable absorber, which should be applicable in the microwave frequency band and suitable for high-power operation. In this paper, we analyze in detail the possibility of realizing a saturable absorber based on cyclotron resonance interaction in the regular waveguide with initially rectilinear electron beam, when saturation is caused by the relativistic dependence of the gyrofrequency on electron energy. Maximum contrast between the absorption of a high-power signal and of a weak signal is achieved in the group synchronism regime when the particle velocity is close to the wave's group velocity. Within the frame of a time-domain self-consistent model, we demonstrate that when such an absorber is installed in the feedback loop of an electron generator powered by existing Ka-band helical-waveguide gyrotron traveling-wave tube, periodical generation of subnanosecond pulses can be provided with peak power up to several hundred kW and sub-GHz repetition frequency. We discuss the influence of deviation from the group synchronism regime on the parameters of generated pulses. Experimental feasibility of the considered scheme is verified based on three-dimensional particle-in-cell simulations.

Comprehensive Observations of Substorm‐Enhanced Plasmaspheric Hiss Generation, Propagation, and Dissipation

AbstractPlasmaspheric hiss is an important whistler‐mode emission shaping the Van Allen radiation belt environment. How the plasmaspheric hiss waves are generated, propagate, and dissipate remains under intense debate. With the five spacecraft of Van Allen Probes, Exploration of energization and Radiation in Geospace (Arase), and Geostationary Operational Environmental Satellites missions at widely spaced locations, we present here the first comprehensive observations of hiss waves growing from the substorm‐injected electron instability, spreading within the plasmasphere, and dissipating over a large spatial scale. During substorms, hot electrons were injected energy‐dispersively into the plasmasphere near the dawnside and, probably through a combination of linear and nonlinear cyclotron resonances, generated whistler‐mode waves with globally drifting frequencies. These waves were able to propagate from the dawnside to the noonside, with the frequency‐drifting feature retained. Approximately 5 hr of magnetic local time away from the source region in the dayside sector, the wave power was dissipated to of its original level.

Features of the dynamics of particles and fields at cyclotron resonances

Some features of the dynamics of particles and fields at cyclotron resonances have been discussed with the focus on chaotic dynamical regimes. It has been shown that the known criterion of the transition of the regular dynamics of particles to chaotic dynamics at cyclotron resonances sometimes describes this transition incorrectly. The reason for such a feature of the criterion has been revealed. The anomalous sensitivity of the dynamics of particles to external fluctuations at autoresonance has been analyzed. A theory of excitation of electromagnetic waves by a beam of phased oscillators under the conditions of isolated nonlinear cyclotron resonance has been developed. It has been shown that the chaotic dynamical regime is due to the periodic change in the structure of the phase portrait of particles in the wave field. It has been shown that higher moments can play a more significant role than lower moments in almost all chaotic dynamical regimes at cyclotron resonances. In this case, the known kinetic diffusion equations should be generalized with the inclusion of these higher moments.

Peculiarities of charged particle dynamics under cyclotron resonance conditions

Peculiarities of the dynamics of charged particles interacting with electromagnetic radiation under nearly autoresonance conditions are analyzed. In particular, analysis of nonlinear cyclotron resonances shows that their widths increase when the autoresonance conditions are approached. In this case, however, the distance between nonlinear resonances increases even faster, due to which nonlinear resonances do not overlap and, accordingly, regimes with dynamic chaos do not occur. According to calculations, the dynamics of charged particles under the autoresonance conditions is very sensitive to fluctuations, the effect of which can be anomalously large and lead to superdiffusion. It is shown that, under the autoresonance conditions, particle dynamics on small time intervals can differ significantly from that on large time intervals. This effect is most pronounced in the presence of fluctuations in the system.

Nonlinear phonon-assisted cyclotron resonance via two-photon process in asymmetrical Gaussian potential quantum wells

We theoretically study the combined effect of aluminum concentration and hydrostatic pressure on the nonlinear phonon-assisted cyclotron resonance (PACR) effect in asymmetrical Gaussian potential quantum wells (AGPQWs). The effect of confined and interface phonon modes on PACR is also studied. The analytical expression of the magneto-optical absorption coefficient (MOAC) is obtained by relating it to the transition probability for the absorption of photons. The numerical results are calculated for both bulk GaAs and GaAs/Ga1−xAlxAs materials. The obtained results show that the MOAC decreases in the magnitude and gives a red-shift as both concentration and pressure increase, while the half-width at half-maximum (HWHM) increases with concentration, but decreases with hydrostatic pressure in both one- and two-photon absorption processes. The aluminum concentration and hydrostatic pressure can be used to control the optical properties of the AGPQWs.

Nonlinear phonon-assisted cyclotron resonance via two-photon process in parabolic quantum well

In this work, the combined effect of aluminum concentration, hydrostatic pressure, temperature, and confinement frequency of a parabolic quantum well (PQW) on the phonon-assisted cyclotron resonance (PACR) via two-photon absorption process under applied electric field is investigated theoretically. The analytical expression of the magneto-optical absorption coefficient (MOAC) is obtained by relating it to the transition probability for the absorption of photons. The numerical results are calculated for typical GaAs/GaAlAs quantum well. The obtained results show that the hydrostatic pressure, aluminum concentration, temperature, and confinement frequency have a significant effect on the MOAC as well as on the half-width. Moreover, it has been found that the optical properties of the GaAs/GaAlAs PQW can be modified by changing these parameters. This gives a new capacity for optical device applications.

Linear and nonlinear phonon-assisted cyclotron resonances in parabolic quantum well under the applied electric field

In this work, the linear and nonlinear phonon-assisted cyclotron resonance (PACR) in a parabolic quantum well (PQW) under the applied electric field have been theoretically studied. General analytical expressions for the absorption power are obtained by using the perturbation approach. The effect of the electric field on PACR conditions is also indicated. We investigated numerically the dependence of PACR absorption spectrum as well as PACR-linewidth on the temperature, on the external electric and magnetic fields, and on confinement frequency. The results show that the PACR absorption spectrum is affected by the Landau levels, the electric subband levels and the electric field. Furthermore, external electric field results in increasing the possibility of the electron–phonon scattering, and plays an important role in the blue shift of PACR absorption spectrum.

Nonlinear cyclotron resonance of a massless quasiparticle in graphene

We consider the classical motion of a massless quasiparticle in a magnetic field and under a weak electromagnetic radiation with the frequency $\ensuremath{\omega}$. Due to the nonparabolic linear energy dispersion, the particle responds not only at the frequency $\ensuremath{\omega}$ but generates a broad frequency spectrum around it. The linewidth of the cyclotron resonance turns out to be very broad even in a perfectly pure material which allows one to explain recent experimental data in graphene.

On the numerical modelling of VLF chorus dynamical spectra

Abstract. This paper presents a study of the use of a one-dimensional Vlasov Hybrid Simulation (VHS) computer code to simulate the dynamical spectra (i.e. frequency versus time spectrograms) of ELF/VLF chorus signals (from ~a fraction to ~10 kHz). Recently excellent measurements of chorus have been made in the source region close to the geomagnetic equator aboard the four spacecraft Cluster mission. Using Cluster data for wave amplitude, which is up to 300 pT, local gyrofrequency, cold plasma density, and L-shell, observed chorus signals are reproduced with remarkable fidelity and, in particular, sweep rates in the range 1–10 kHz result as observed. Further, we find that the sweep rate is a falling function of increasing cold plasma density, again in accord with observations. Finally, we have satisfactorily simulated the rather rare falling frequency elements of chorus which are sometimes observed aboard Cluster in the generation region. For both rising and falling chorus we have presented detailed structural analyses of the generation regions. The main contributor to the frequency sweep rate is primarily the establishment of wave number/frequency gradients across the generation region by the out of phase component of the resonant particle current. The secondary contributor is the shortening of the wavelength of resonant particle current relative to that of the wave field. In view of the close agreement between observation and simulation, we conclude that nonlinear electron cyclotron resonance is indeed the mechanism underlying the generation of chorus signals just outside the plasmasphere.

Nonlinear cyclotron harmonic absorption

Nonlinear oscillations of particle’s energy occur when a particle stays in a resonance zone. In this work, we found that collisionless heating of particles occurs when they pass the microwave beam at first, second, and third harmonic resonances. It is found that the net energy gain of particles from the microwaves is inversely proportional to the wave frequency. It is also found that the net energy gain is dependent on the microwave beam width. The energy gain of particles from a single pass through a resonance zone has been formulated analytically. A numerical calculation has been performed and the results are in good agreement with the analytic calculation. Both analytic and numerical calculations show a strong frequency dependence and a beam width dependence of nonlinear cyclotron resonance heating.

Theory of charged particle heating by low-frequency Alfvén waves

The heating of charged particles by a linearly polarized and obliquely propagating shear Alfvén wave (SAW) at frequencies a fraction of the charged particle cyclotron frequency is demonstrated both analytically and numerically. Applying Lie perturbation theory, with the wave amplitude as the perturbation parameter, the resonance conditions in the laboratory frame are systematically derived. At the lowest order, one recovers the well-known linear cyclotron resonance condition k∥v∥−ω−nΩ=0, where v∥ is the particle velocity parallel to the background magnetic field, k∥ is the parallel wave number, ω is the wave frequency, Ω is the gyrofrequency, and n is any integer. At higher orders, however, one discovers a novel nonlinear cyclotron resonance condition given by k∥v∥−ω−nΩ∕2=0. Analytical predictions on the locations of fixed points, widths of resonances, and resonance overlapping criteria for global stochasticity are also found to agree with those given by computed Poincaré surfaces of section.

Modeling of nonlinear electron cyclotron resonance heating and current drive in a tokamak

Electron cyclotron resonance heating and current drive are modeled in tokamak geometry taking into account nonlinear wave-particle interaction and the inhomogeneity of the distribution function on magnetic surfaces. The model includes self-consistently coupled beam tracing and Monte Carlo computations of the electron distribution function. The method of Green’s function for the computation of the generated current is described. For the Axisymmetric Divertor Experiment Upgrade [Leuterer et al., Fusion Eng. Des. 53, 485 (2001)] parameters and high beam focusing, nonlinear wave-particle interaction effects appear to be important for perpendicular launch of the microwave beam and not important for oblique launches where they stay below the “threshold.” With defocusing the beam two to three times along the direction of the magnetic field nonlinear effects of wave-particle interaction start to be important also for oblique launches. The effect of decreased current in case of increasing the microwave beamwidth is demonstrated. The decrease of both power absorption and generated current around low-order rational magnetic surfaces is found. Its possible effect on the tearing mode stability index is discussed.

Theory of nonlinear cyclotron resonance in quasi-two-dimensional electronsystems

Momentum-and energy-balance equations are developed for steady-stateelectron transport and optical absorption under the influence of a dc electricfield and an intense ac electric field of terahertz (THz) frequency in atwo-dimensional (2D) semiconductor in the presence of a strong magnetic fieldperpendicular to the 2D plane. These equations are applied to study theintensity-dependent cyclotron resonance (CR) in far-infrared transmission andTHz-radiation-induced photoconductivity of GaAs heterostructures in theFaraday geometry. We find that the CR peaks and line shapes of thetransmittance exhibit different intensity dependences when the intensity ofthe THz field increases in the ranges above or below a certain criticalvalue. The CR in the photoresistivity, however, is always enhanced onincreasing the intensity of the THz field. These results agree qualitativelywith the experimental observations. We have clarified that the CR in thephotoconductivity is not only a result of the electron heating, but alsoarises from photon-assisted scattering enhancement, especially at hightemperatures. The effects of an intense THz field on the Faraday angleand ellipticity of magnetically biased 2D semiconductors have also beendemonstrated.

Kinetic modeling of nonlinear electron cyclotron resonance heating

A numerical method is proposed for modeling electron cyclotron resonance heating (ECRH) and current drive in fusion devices with, generally speaking, nonlinear wave–particle interaction. Considered is the case of second harmonic extraordinary wave resonance. The method is applied to model the electron distribution function in a simplified magnetic field geometry. Various combined effects of wave–particle interaction and Coulomb collisions are demonstrated. The model is compared to the bounce-averaged quasilinear Fokker–Planck equation for the case of perpendicular propagation of the wave beam with respect to the magnetic field. In addition, the absorption coefficients computed from these two models are compared to the results of both the linear and the adiabatic model. Significant differences between results are found for present-day ECRH power levels and fusion device parameters.

Nonlinear doppler-shifted cyclotron resonance in aluminum

The Doppler-shifted cyclotron resonance in an aluminum plate in the geometry when constant magnetic field H is directed along the [100] crystallographic axis oriented normally to the surface of the plate is studied theoretically. The analysis is performed for a simple model Fermi surface possessing fourth-order symmetry. Capture of holes by the magnetic field of a radio-frequency wave is shown to considerably decrease the effectiveness of cyclotron absorption at large exciting field amplitudes. This suppresses the collisionless damping of dopplerons (propagating modes related to odd cyclotron resonance harmonics). As a result, the sample becomes more transparent to radio-frequency radiation.