Drift Resonance Research Articles

Sources, Sinks, and Transport of Energetic Electrons Near Saturn's Main Rings

AbstractThe inner boundary of Saturn's electron radiation belts, near the planet's A ring (∼2.27 Rs), is studied using Cassini's proximal orbit measurements. We find that variable convective flows transport energetic electrons to the A ring, which absorbs them instantaneously, forming the inner belt boundary. These flows are also responsible for a variable and longitudinally asymmetric boundary configuration. Prenoon, the boundary oscillates toward and away from the A ring with a 2‐week period. Postnoon, it maps persistently near the F ring (∼2.32 Rs) and coexists with localized MeV electron intensity enhancements (microbelts). We propose that the microbelts contain electrons in drift resonance with corotation, trapped in local time‐confined trajectories, which result from the aforementioned convective flows. The microbelts' collocation with the F ring implies either a local, secondary electron production due to galactic cosmic ray collisions with F ring dust or an enhanced resonant electron trapping due to an electrodynamic interaction between the F ring and Saturn's magnetosphere.

Global‐Scale ULF Waves Associated With SSC Accelerate Magnetospheric Ultrarelativistic Electrons

AbstractWe study electron behavior in the outer radiation belts during the 16 July 2017 storm sudden commencement (SSC), in which prompt intensification of ultrarelativistic electron fluxes was observed at around L = 4.8 by Van Allen Probe B immediately after an interplanetary shock. The electron fluxes in multiple energy channels show clear oscillations in the Pc5 frequency range, although the oscillation characteristics are quite different in different energy channels. At energies above ∼1 MeV, the oscillation periods were very close to the electron drift period, which resembles an energy spectrogram evolution expected for an energetic particle injection event and its drift echoes. At lower energies, however, the oscillation periods hardly depended on the energy: They were very close to the ultralow frequency (ULF) wave period derived from electric field measurements (about 250 s according to wavelet analysis). These complex signatures are consistent with the picture of drift resonance between electrons and short‐lived ULF waves with low azimuthal wave numbers. Good agreement between the observations and numerical simulations confirms that shock‐induced global‐scale ULF waves can efficiently accelerate outer belt ultrarelativistic electrons up to 3.4 MeV over a time scale shorter than 1 hr.

Excitation of Storm Time Pc5 ULF Waves by Ring Current Ions Based on the Drift‐Kinetic Simulation

AbstractStorm time Pc5 waves are considered to be excited through the drift‐bounce resonance by ring current ions associated with the injection from the magnetotail. Using the Geospace Environment Modeling System for Integrated Studies–Ring Current simulation, a drift‐kinetic and self‐consistent model for ring current particles, we investigate the excitation mechanism of these waves in the inner magnetosphere. The power spectra of electromagnetic field fluctuations show the excitation of both poloidal and toroidal mode waves in Pc5 frequency range. It is found that these waves are fundamental mode waves with the azimuthal wave number m~ − 20 and excited through the drift resonance with the drifting ions with energies of 80–120 keV. The simulation indicates that global distribution of wave power coincides with the positive local growth rate mainly contributed by the positive phase space density gradient in energy.

Electron Orbital Motion and the Threshold Voltage for Spatial-Harmonic Magnetrons

The Buneman-Hartree relation is a condition that determines the excitation of oscillations in magnetrons. However, experiments of different years indicate that for a whole class of similar generators, it is not accurate enough. In particular, this is observed for the so-called spatial-harmonic magnetrons, which have significant advantages over conventional ones in millimeter and subterahertz ranges. The operating parameters of these generators are close to the Hull cutoff parabola, i.e., they have substantially larger transverse dimensions of the interaction space for the same values of the operating voltage and magnetic field, and accordingly, a larger-sized slow-wave system is possible. The results obtained in the development of spatial-harmonic magnetrons for radars can serve to estimate the limits of applicability of the Buneman-Hartree condition. Experiments show that the initial voltage at which generation occurs is significantly higher than the value calculated from the conventional formula. Probable causes are a change in the pattern of motion of an electron near the Hull cutoff parabola and the possibility of exciting gyroresonances. The analysis of the experiments fully confirms that even for millimeter-band magnetrons operating under purely drift (conventional) resonance, an analytical model that takes into account the orbital motion of electrons more accurately describes the physical processes near the cutoff parabola and significantly improves the accuracy of the choice of generator parameters and operating modes.

Plasma Waves and Particles during Multi-dip Storms Invoked by Turbulent Solar Wind

Abstract The temporal variations of the disturbance storm time index show the occurrence of multi-dip storms during 2015 April. Specifically, a double-dip storm was observed during April 9–12 and a six-dip storm occurred during April 13–21. This work analyzes the data from the electric field and wave (EFW) instrument, relativistic electron proton telescope (REPT), and electric and magnetic field instrument suite (EMFISIS) on board radiation belt storm probe A (RBSP-A) during the selected multi-dip storms. The ultra low-frequency (ULF) as well as very low-frequency (VLF) electromagnetic oscillations were observed by EFW and EMFISIS simultaneously with the REPT observed fluctuating fluxes of relativistic electrons in the slot and outer Van Allen belt. The timescales, for relativistic electrons flux increase in slot and depletion, refilling of the outer Van Allen belt, were much faster than the temporal variations expected from the radial diffusion driven by drift resonance between ULF waves and relativistic electrons. Therefore, the contribution of VLF interaction with the relativistic electrons is important for understanding rapid flux variations on times of few hours during the considered multi-dip geomagnetic storms. The findings of this study may be helpful for understanding the relativistic electrons dynamics and transport in the Earth’s magnetosphere during multi-dip geomagnetic storms.

Toroidal modeling of resistive wall mode stability and control in HL-2M tokamak

Effects of toroidal plasma flow, magnetic drift kinetic damping as well as feedback control, on the resistive wall mode instability in HL-2M tokamak are numerically investigated, using the linear stability codes MARS-F/K (Liu et al 2000 Phys. Plasmas 7 3681, Liu et al 2008 Phys. Plasmas 15 112503). It is found that the precession drift resonance damping due to trapped thermal particles ensures a robust passive stabilization of the n = 1 (n is the toroidal mode number) RWM in the 2 MA double-null advanced plasma scenario designed for HL-2M, provided that the toroidal flow speed is not too fast: . With two rows of magnetic control coils designed for HL-2M, the optimal poloidal location for the RWM stabilization is found to be . Toroidal modeling also shows that the plasma flow damping, drift kinetic damping and magnetic feedback can be arranged to synergistically stabilize the RWM in HL-2M, by tuning the feedback gain phase and/or including derivative actions in the control loop. The numerical results obtained by MARS-F/K are qualitatively well re-produced by an analytic single-pole model.

Dynamics of Spiral Waves Induced by Periodic Mechanical Deformation with Phase Difference**Supported by the Natural Science Foundation of Zhejiang Province under Grant Nos. LQ14A050003 and LR17A050001; and the National Natural Science Foundation of China under Grant Nos. 11674080 and 11674379

The dynamics of spiral waves under the influences of periodic mechanical deformation are studied. Here, the mechanical deformation propagating along the medium with phase differences are considered. It is found that weak mechanical deformation may lead to resonant drift of spiral waves. The drift direction and velocity can be changed by the wave length of the deformation. Strong mechanical deformation may result in breakup of spiral waves. The characteristics of breakup are discussed. The critical amplitudes are determined by two factors, i.e. the wave length and frequency of the periodic mechanical deformation. When the wave length of mechanical deformation is comparable to the spiral wave, simulation shows that the critical amplitude is substantially increased. As the frequency of the mechanical deformation is around 1.5 times of the spiral wave, the critical amplitudes are minimal.

Drift Resonance of Compressional ULF Waves and Substorm‐Injected Protons From Multipoint THEMIS Measurements

AbstractA compressional Pc5 wave associated with localized hot proton injection was observed by the five THEMIS (Time History of Events and Macroscale Interactions during Substorms) spacecraft in the dusk sector of the Earth's magnetosphere at L ∼ 10RE on 21 May 2007. The wave magnetic field perturbation transverse to the background magnetic field was primarily poloidal, in agreement with the predominately azimuthal wave vector direction (with westward phase velocity). The observation followed two consecutive substorms, when the cloud of energetic particles comprised of the lower‐energy protons from the earlier substorm was mixed with higher‐energy protons from the subsequent one. The clear signatures of the wave‐particle drift resonance of protons modulated by the wave were observed. The wave period was found to be about 2 times longer than the corresponding Alfvén wave eigenmode period on the same L‐shells calculated with the THEMIS data. The increase of the particle energy with the distance from the Earth and the observed strong dependence of the wave frequency on the azimuthal wave number constitutes conditions for the gradient instability of the drift compressional mode (for the Alfvén mode one supposes the particle energy decrease with radial distance). Based on these results, we conclude that the observed wave was the drift compressional mode generated by the gradient instability.

Eigenmodes of the Transverse Alfvénic Resonator at the Plasmapause: A Van Allen Probes Case Study

AbstractA Pc4 ultralow frequency wave was detected at spacecraft B of the Van Allen Probes at the plasmapause. A distinctive feature of this wave is the strong periodical modulation of the wave. It is assumed that this modulation is a beating of oscillations close in frequency: at least two harmonics with frequencies of 15.3 and 13.6 MHz are found. It is shown that these harmonics can be the eigenmodes of the transverse resonator at the local maximum of the Alfvén velocity. In addition, the observed wave was in a drift resonance with energetic 80‐keV protons and could be generated by an unstable bump on tail distribution of protons simultaneously observed with the wave. The estimate of the azimuthal wave number m made from the drift resonance condition gives a value of about −100, that is, it is a westward propagating azimuthally small‐scale wave.

Nonlinear Drift Resonance Between Charged Particles and Ultralow Frequency Waves: Theory and Observations

AbstractIn Earth's inner magnetosphere, electromagnetic waves in the ultralow frequency (ULF) range play an important role in accelerating and diffusing charged particles via drift resonance. In conventional drift resonance theory, linearization is applied under the assumption of weak wave‐particle energy exchange so particle trajectories are unperturbed. For ULF waves with larger amplitudes and/or durations, however, the conventional theory becomes inaccurate since particle trajectories are strongly perturbed. Here we extend the drift resonance theory into a nonlinear regime, to formulate nonlinear trapping of particles in a wave‐carried potential well, and predict the corresponding observable signatures such as rolled‐up structures in particle energy spectrum. After considering how this manifests in particle data with finite energy resolution, we compare the predicted signatures with Van Allen Probes observations. Their good agreement provides the first observational evidence for the occurrence of nonlinear drift resonance, highlighting the importance of nonlinear effects in magnetospheric particle dynamics under ULF waves.

Toroidal drift modes driven by the magnetic drift resonances

Here, we find that the kinetic and fluid linear drift resonances have several similarities. The reason for our interest in this is that our fluid model has recently been shown to be exact for drift waves and other modes in that frequency range. Thus, transport is driven by the fluid linear growth rate and our drift wave system behaves like a cold beam-plasma system although it has a finite temperature. A main similarity is that neither fluid nor kinetic responses should be expanded in the curvature in the bulk interior of tokamaks. That we can use the fluid response close to the magnetic drift resonance is a consequence of the fact that the closure is exact. A systematic orbit integration technique is introduced for deriving the fluid model and evaluating the effects of nonlinearities.

Drift‐Bounce Resonance Between Pc5 Pulsations and Ions at Multiple Energies in the Nightside Magnetosphere: Arase and MMS Observations

AbstractA Pc5 wave is observed by the Exploration of energization and Radiation in Geospace Arase satellite in the inner magnetosphere (L ~5.4–6.1) near postmidnight (L‐magnetic local time ~1.8–2.5 hr) during the storm recovery phase on 27 March 2017. Its azimuthal wave number (m‐number) is estimated using two independent methods with satellites and ground observations to be −8 to −15. The direct measurement of the m‐number enables us to calculate the resonance energy. The flux oscillations of H+ and O+ ions at ≥ 56.3 keV are caused by drift resonance and those of O+ ions at ≤ 18.6 keV by bounce resonance. Resonances of O+ ions at multiple energies are simultaneously observed for the first time. The enhancement of the O+/H+ flux ratio at ≤ 18.6 keV indicates selective acceleration of O+ ions through bounce resonance.

Determining the Mode, Frequency, and Azimuthal Wave Number of ULF Waves During a HSS and Moderate Geomagnetic Storm.

Ultralow frequency (ULF) waves play a fundamental role in the dynamics of the inner magnetosphere and outer radiation belt during geomagnetic storms. Broadband ULF wave power can transport energetic electrons via radial diffusion, and discrete ULF wave power can energize electrons through a resonant interaction. Using observations from the Magnetospheric Multiscale mission, we characterize the evolution of ULF waves during a high‐speed solar wind stream (HSS) and moderate geomagnetic storm while there is an enhancement of the outer radiation belt. The Automated Flare Inference of Oscillations code is used to distinguish discrete ULF wave power from broadband wave power during the HSS. During periods of discrete wave power and utilizing the close separation of the Magnetospheric Multiscale spacecraft, we estimate the toroidal mode ULF azimuthal wave number throughout the geomagnetic storm. We concentrate on the toroidal mode as the HSS compresses the dayside magnetosphere resulting in an asymmetric magnetic field topology where toroidal mode waves can interact with energetic electrons. Analysis of the mode structure and wave numbers demonstrates that the generation of the observed ULF waves is a combination of externally driven waves, via the Kelvin‐Helmholtz instability, and internally driven waves, via unstable ion distributions. Further analysis of the periods and toroidal azimuthal wave numbers suggests that these waves can couple with the core electron radiation belt population via the drift resonance during the storm. The azimuthal wave number and structure of ULF wave power (broadband or discrete) have important implications for the inner magnetospheric and radiation belt dynamics.

Giant Pulsations Excited by a Steep Earthward Gradient of Proton Phase Space Density: Arase Observation

AbstractWe present observational evidence of drift resonance between westward propagating odd mode standing ultralow frequency waves and energetic protons. Compressional ∼13 mHz (Pc4 band) waves and proton flux oscillations at >50 keV were detected at ∼03 hr magnetic local time by the Arase satellite on 15 April 2017. The azimuthal wave number (m number) is estimated to be ∼−50 from ground observations, while the theory of drift resonance gives m ∼− 49 for odd mode waves and ∼110‐keV protons, providing evidence that the drift resonance indeed took place in this event. We also found a steep earthward gradient of proton phase space density, which can quantitatively explain the wave excitation. The observed waves show typical features of giant pulsations (Pgs), regarding local time, m number, and flux oscillations. This study, therefore, has great implications to the field line mode structure and excitation mechanism of Pgs.

Formation of Butterfly Pitch Angle Distributions of Relativistic Electrons in the Outer Radiation Belt With a Monochromatic Pc5 Wave

AbstractRadial transport of relativistic electrons in the inner magnetosphere has been considered one of the acceleration mechanisms of the outer radiation belt electrons and can be driven by the drift resonance with Pc5 ultralow‐frequency waves. In this study, we focus on the pitch angle dependences of the radial transport and investigate the pitch angle distributions (PADs) of the relativistic electrons after interaction with a monochromatic Pc5 wave, using two simulation models of the inner magnetosphere: Geomagnetic Environment Modeling System for Integrated Studies (GEMSIS)‐Ring Current and GEMSIS‐Radiation Belt models. The results show that butterfly‐like PADs (two peaks in small pitch angles) are produced at a fixed radial distance (L‐shell) and energy, where the electrons with small pitch angles satisfy the resonance condition. The radial range and timescale of the butterfly PAD appearance correspond to the maximum radial transport of the electron (i.e., resonant width) and its oscillation period in the radial direction, respectively. We analytically derive the resonant width and oscillation period of relativistic electrons interacting with a monochromatic Pc5 wave, assuming conservation of first and second adiabatic invariants, and compare them with the simulation result. The results show that electrons with small equatorial pitch angles at a fixed magnetic moment can interact with a monochromatic Pc5 wave in a wider L‐shell range than perpendicular electrons due to the pitch angle changes, in the course of the radial transport.

Poloidal Mode Wave‐Particle Interactions Inferred From Van Allen Probes and CARISMA Ground‐Based Observations

AbstractUltralow‐frequency wave and test particle models are used to investigate the pitch angle and energy dependence of ion differential fluxes measured by the Van Allen Probes spacecraft on 6 October 2012. Analysis of the satellite data reveals modulations in differential flux resulting from drift resonance between H+ ions and fundamental mode poloidal Alfvén waves detected near the magnetic equator at L ∼ 5.7. Results obtained from simulations reproduce important features of the observations, including a substantial enhancement of the differential flux between ∼20 and 40° pitch angle for ion energies between ∼90 and 220 keV and an absence of flux modulations at 90°. The numerical results confirm predictions of drift‐bounce resonance theory and show good quantitative agreement with observations of modulations in differential flux produced by ultralow‐frequency waves.

Microwave fields driven domain wall motions in antiferromagnetic nanowires

In this work, we study the microwave field driven domain wall (DW) motion in an antiferromagnetic nanowire, using the numerical calculations based on a classical Heisenberg spin model with the biaxial magnetic anisotropy. We show that a proper combination of a static magnetic field plus an oscillating field perpendicular to the nanowire axis is sufficient to drive the DW propagation along the nanowire. More importantly, the drift velocity at the resonance frequency is comparable to that induced by temperature gradients, suggesting that microwave field can be a very promising tool to control DW motions in antiferromagnetic nanostructures. The dependences of resonance frequency and drift velocity on the static and oscillating fields, the axial anisotropy, and the damping constant are discussed in details. Furthermore, the optimal orientations of the field are also numerically determined and explained. This work provides useful information for the spin dynamics in antiferromagnetic nanostructures for spintronics applications.

Rapid Enhancements of the Seed Populations in the Heart of the Earth's Outer Radiation Belt: A Multicase Study

AbstractTo better understand rapid enhancements of the seed populations (hundreds of keV electrons) in the heart of the Earth's outer radiation belt (L* ~ 3.5–5.0) during different geomagnetic activities, we investigate three enhancement events measured by Van Allen Probes in detail. Observations of the fluxes and the pitch angle distributions of energetic electrons are analyzed to determine rapid enhancements of the seed populations. Our study shows that three specified processes associated with substorm electron injections can lead to rapid enhancements of the seed populations, and the electron energy increases up to 342 keV. In the first process, substorm electron injections accompanied by the transient and intense substorm electric fields can directly lead to rapid enhancements of the seed populations in the heart of the outer radiation belt. In the second process, the substorm injected electrons are first trapped in the outer radiation belt and subsequently transported into L* < 4.5 by the convection electric field. In the third process, the lower energy electrons are first injected at L* ~ 5.3 and then undergo drift resonance with ultralow‐frequency waves. These accelerated electrons by ultralow‐frequency waves are further transported into L* < 4.5 due to the convection electric field. This process is consistent with the radial diffusion. Our results suggest that these specified processes are important for understanding the dynamics of the seed populations in the heart of the outer radiation belt.

Electromagnetic banana kinetic equation and its applications in tokamaks

A banana kinetic equation in tokamaks that includes effects of the finite banana width is derived for the electromagnetic waves with frequencies lower than the gyro-frequency and the bounce frequency of the trapped particles. The radial wavelengths are assumed to be either comparable to or shorter than the banana width, but much wider than the gyro-radius. One of the consequences of the banana kinetics is that the parallel component of the vector potential is not annihilated by the orbit averaging process and appears in the banana kinetic equation. The equation is solved to calculate the neoclassical quasilinear transport fluxes in the superbanana plateau regime caused by electromagnetic waves. The transport fluxes can be used to model electromagnetic wave and the chaotic magnetic field induced thermal particle or energetic alpha particle losses in tokamaks. It is shown that the parallel component of the vector potential enhances losses when it is the sole transport mechanism. In particular, the fact that the drift resonance can cause significant transport losses in the chaotic magnetic field in the hitherto unknown low collisionality regimes is emphasized.

Influence of Acousto-Optic Resonances in Electro-Optical Modulator on Fiber Optic Gyro Performance and Method for Its Compensation

The electro-optical modulator is one of the most important parts of the fiber optic gyroscope. Unfortunately, the integral implementation of the modulator has a number of undesirable effects such as parasitic amplitude modulation, phase drift, and acousto-optical resonance effects. Influence of the first two effects on the gyroscope operation has been described in a number of works, but at the moment, there are no published papers aimed at investigating the relationship between the presence of acousto-optic resonances in modulators and changes in the performance of a fiber optic gyroscope. There are several design solutions that provide damping of undesired acoustic waves in electro-optical modulators. However, the use of these solutions requires a method to estimate their effectiveness. The main purpose of the article is to describe such a method and to evaluate the correctness of its application. We also offer an additional way to reverse the effect of the mentioned resonant effects on the characteristics of the fiber gyroscope.