Nonlinear Wave Growth Research Articles

Suppression of Nonlinear Chorus Wave Growth by Active Control of Gyroresonant Interactions With Electron Hole Deformation

AbstractNonlinear gyroresonant acceleration is an essential mechanism for the formation of relativistic electrons in Earth's radiation belts, yet we still have only limited knowledge of how electron motion interacts nonlinearly with plasma waves. Here we demonstrate the compelling suppression of whistler‐mode chorus emissions as a resonant wave with energetic electrons by tuning an external transmitter signal in space plasmas. Through forcible modification of electron motions via phase trapping by the external waves, the nonlinear gyroresonant current is suppressed along with the electron hole deformation. Moreover, this can decrease the population of relativistic electrons due to the lack of coherent resonant waves seen by the phase‐organized electrons. Understanding such nonlinear wave suppression effects is crucial for a potential active control of Earth's plasma environment.

Nonlinear Drift‐Bounce Resonance Between Charged Particles and Ultralow Frequency Waves

AbstractUltra‐low frequency (ULF) waves contribute significantly to the dynamic evolution of Earth's magnetosphere by accelerating and transporting charged particles within a wide energy range. A substantial excitation mechanism of these waves is their drift‐bounce resonant interactions with magnetospheric particles. Here, we extend the conventional drift‐bounce resonance theory to formulate the nonlinear particle trapping in the ULF wave‐carried potential well, which can be approximately described by a pendulum equation. We also predict the observable signatures of the nonlinear drift‐bounce resonance, and compare them with spacecraft observations. We further discuss potential drivers of the pendulum including the convection electric field and the magnetospheric dayside compression, which lead to additional particle acceleration or deceleration depending on magnetic longitude. These drivers indicate preferred regions for nonlinear ULF wave growth, which are consistent with previous statistical studies.

Observations of co-existing rising and falling tone emissions of electromagnetic ion cyclotron waves

We report observations of co-existing rising and falling tone emissions of electromagnetic ion cyclotron (EMIC) waves by THEMIS E spacecraft. The investigation of these fine structures of the EMIC waves is essential from the point of view of understanding the connection between the proton holes and the proton hills in velocity phase-space. The wave packets of rising and falling tones are tracked by Poynting vector analysis, where we observe that the rising tones are propagating northward and the falling tones are propagating southward. The nonlinear wave growth theory supports our observations. We propose a model where the proton velocity distribution function evolves through the formation of proton holes on the negative side of the distribution function and mirrored resonant protons forming proton hills on the positive side of the distribution function, allowing us to observe the co-existing rising and falling tone EMIC waves.Graphical abstract

Upstream motion of chorus wave generation: comparisons with observations

An understanding of the development of strong very low frequency chorus elements is important in the study of the rapid MeV electron acceleration observed during radiation belt recovery events. During such events, chorus elements with long-duration (20–40 ms), strong (|Bw| 0.5–2.0 nT) subpackets with smoothly varying frequency and phase capable of producing nonlinear energy gain of 1%–2% for multi-MeV seed electrons. For such strong chorus elements, we examine the consequences of an upstream motion of the chorus wave generation region using Van Allen Probes observations and nonlinear theory. For a given upstream velocity, vs, resonant electron energy (50–350 keV) and pitch angle (105–115 deg) are uniquely determined for each wave frequency. We examine the effect of an upstream vs on the inhomogeneity factor that controls wave growth. For steadily increasing upstream motion as the chorus element evolves, vs/c ranging over [-0.001, −0.065], nonlinear wave growth takes place at ≥ 50% of the theoretical maximal value during the development of the observed strong subpackets. For the cases examined, resonant electron energies and pitch angles closely match those of the observed injected electron flux enhancements responsible for chorus development and the nonlinear acceleration of MeV radiation belt electrons.

Possible Global Generation Region of Nonlinear Whistler‐Mode Chorus Emission Waves at Mercury

AbstractChorus waves are a kind of intense electromagnetic emission wave in magnetized planets and can play important roles in the kinetic electron dynamics in planetary magnetospheres. Rapid changes of the ring electron current belt in Mercury’s magnetosphere and the contribution of chorus waves have remained long‐standing scientific issues from the first Mercury flyby observations by Mariner 10 in 1970s because of the small size of the magnetosphere. Based on theoretical analyses and simulations successfully reconstructing Earth’s chorus wave properties, we report on possible generation regions of chorus waves in Mercury’s magnetosphere. The theoretical analysis for low‐temperature‐anisotropy electrons shows a clear asymmetric day–night spatial distribution of the possible chorus generation region because of the difference in the nonlinear convective wave growth along the magnetic field lines. Simulation results show a rapid enhancement of the ring electron current belt by resonant interactions with repetitive chorus waves. Our study suggests that energetic electrons in Mercury’s magnetosphere can be enhanced locally by nonlinear chorus wave–particle interactions.

A Triggering Process for Nonlinear EMIC Waves Driven by the Compression of the Dayside Magnetosphere

AbstractUsing the Arase and Van Allen Probes satellite observations, we investigate the nonlinear electromagnetic ion cyclotron (EMIC) rising‐tone (RT) emissions with an increase of the solar wind dynamic pressure in the dayside magnetosphere. We find that EMIC RT emissions are accompanied by the extended dayside uniform zone (DUZ) over |MLAT| < 25° due to the dayside magnetospheric compression by an increase in Pdyn. Using the observed plasma and magnetic field data, we modeled the threshold amplitude for the nonlinear EMIC waves and compared it with the observation. The small gradient of the ambient magnetic field strongly contributes to the reduction in the threshold amplitude of nonlinear wave growth compared to other parameters. When the threshold amplitude falls to comparable level of pre‐existing EMIC waves, EMIC RT emissions are immediately triggered, suggesting direct evidence that the DUZ is the preferred condition to cause the nonlinear EMIC RT emission in the dayside magnetosphere.

Chorus Wave Generation Modulated by Field Line Resonance and Mirror‐Mode ULF Waves

AbstractEarth's inner magnetosphere is a zoo of plasma waves where electromagnetic and electrostatic emissions with distinct frequencies coexist and interact. Spacecraft observations have shown that whistler‐mode chorus waves, one of the key components in the magnetospheric dynamics, are often modulated by ultralow frequency (ULF) waves. Here, we investigate the effects of two typical ULF wave modes (i.e., field line resonance and mirror mode) on the nonlinear generation process of chorus waves. We report for the first time periodic excitations of lower‐ and upper‐band chorus waves near ULF wave crests and troughs, respectively. Their anticorrelated occurrence is explained by the nonlinear theory, in which the threshold amplitude of nonlinear wave growth is modified by the ULF wave field configuration and the modulated electron distributions. In this framework, the newly observed feature of chorus wave occurrence near the ULF wave crests is attributed to the antisymmetric field profiles of mirror‐mode ULF waves, which periodically modulate the threshold amplitude by modifying the second‐order derivative of the background dipole field. In addition to the second‐order derivative, the first‐order derivative of the background magnetic field is also modulated by the ULF waves to regulate the size of the chorus wave source region.

Direct observations of energy transfer from resonant electrons to whistler-mode waves in magnetosheath of Earth

Electromagnetic whistler-mode waves in space plasmas play critical roles in collisionless energy transfer between the electrons and the electromagnetic field. Although resonant interactions have been considered as the likely generation process of the waves, observational identification has been extremely difficult due to the short time scale of resonant electron dynamics. Here we show strong nongyrotropy, which rotate with the wave, of cyclotron resonant electrons as direct evidence for the locally ongoing secular energy transfer from the resonant electrons to the whistler-mode waves using ultra-high temporal resolution data obtained by NASA’s Magnetospheric Multiscale (MMS) mission in the magnetosheath. The nongyrotropic electrons carry a resonant current, which is the energy source of the wave as predicted by the nonlinear wave growth theory. This result proves the nonlinear wave growth theory, and furthermore demonstrates that the degree of nongyrotropy, which cannot be predicted even by that nonlinear theory, can be studied by observations.

Nonlinear Wave Growth Analysis of Chorus Emissions Modulated by ULF Waves

AbstractWe present Van Allen Probes observations of periodic chorus wave emissions in the troughs of compressional ultralow frequency (ULF) waves. During this event, the spectral gap of chorus waves gradually widens as the spacecraft moves from the equatorial source region towards higher latitudes. Moreover, chorus wave intensity increases and frequency range widens after a substorm injection. We show that the periodic occurrence of chorus waves is attributed to the modulation of threshold amplitude for nonlinear growth of chorus waves by the second spatial derivative of ULF compressional magnetic field. The widening gap can be interpreted in terms of the nonlinear damping mechanism. A good agreement is also found between the nonlinear wave growth theory and the observations regarding the influence of substorm injection on the chorus. These findings support the applicability of the nonlinear theory in describing the chorus wave generation and damping, together with their modulations by ULF waves.

Nonlinear Wave Growth of Whistler‐Mode Hiss Emissions in a Uniform Magnetic Field

AbstractWe conduct electromagnetic particle simulations in a uniform magnetic environment to verify the nonlinear wave growth process of plasmaspheric hiss in the equatorial plasmasphere. The satisfaction of the separability criterion for coexisting multiple frequency waves in the initial stage of wavenumber‐time evolution declares that wave packets are coherent and capable of growing nonlinearly. Spatial and temporal evolutions of two typical modes located in wavenumber‐time evolution demonstrate the consistency among wave growths, frequency variations, and inhomogeneity factor S in coherent wave packets, showing that rising and falling tones occur at negative and positive S values, respectively, and an obvious wave growth happens in a reasonable range of S satisfying the second‐order resonance condition. Wave packets extracted from wave fields in space and time by a frequency band‐pass filter confirm a good agreement between the nonlinear theory and simulation results. The nonlinear growth rates of the extracted wave packets possess similar magnitudes to the growth rates of wave packets in the simulation, and they are much greater than the theoretical linear growth rate, indicating that the nonlinear process is essential in the generation of plasmaspheric hiss.

Nonlinear wave growth of whistler-mode hiss emissions in a uniform magnetic field

Nonlinear wave growth of whistler-mode hiss emissions in a uniform magnetic field

Simulation study on parametric dependence of whistler-mode hiss generation in the plasmasphere

We conduct electromagnetic particle simulations to examine the applicability of nonlinear wave growth theory to the generation process of plasmaspheric hiss. We firstly vary the gradient of the background magnetic field from a realistic model to a rather steep gradient model. Under such variation, the threshold amplitude in the nonlinear theory increases quickly and the overlap between threshold and optimum amplitude disappears correspondingly, the nonlinear process is suppressed. In the simulations, as we enlarge the gradient coefficient of the background magnetic field, waves generated near the equator do not grow through propagation. By examining the range of suitable values of inhomogeneity factor S (i.e., |S|<2), we find the generation of wave packets is limited to the equatorial region when the background field is steep, showing a good agreement with what is indicated by critical distance in the theory. We then check the dependence of generation of hiss emissions on different hot electron densities. Since the overlap between threshold and optimum amplitude vanishes, the nonlinear process is weakened when hot electron density becomes smaller. In the simulation results, we find similar wave structures in all density cases, yet with different magnitudes. The existence of suitable S values implies that the nonlinear process occurs even at a low level of hot electron density. However, by examining J_E that closely relates to the wave growth, we find energy conveyed from particles to waves is much limited in small density cases. Therefore, the nonlinear process is suppressed when hot electron density is small, which agrees with the theoretical analysis.Graphical

Multipoint Analysis of Source Regions of EMIC Waves and Rapid Growth of Subpackets

AbstractElectromagnetic Ion Cyclotron (EMIC) rising tone emissions are important in understanding the nonlinear wave evolution and interaction with the energetic particles. We present observations of rising tone emissions of EMIC waves by THEMIS A, D, and E spacecraft in the outer magnetosphere. These emissions with subpacket structures in the proton band were observed during the time interval 14:20 UT to 14:30 UT on September 9, 2010. The observed waves are left‐handed polarized with wave normal angles less than . THEMIS A was closest to the equator and was in a higher L‐shell than THEMIS E and D. The smallest radial separation is 2,000 km between THEMIS E and D spacecraft. This configuration of THEMIS allows us to investigate the subpackets of rising tone EMIC waves observed simultaneously at 14:23 UT by three spacecraft. Hilbert Huang Transformation (HHT) is applied to show the variations of the instantaneous frequency and the observed wave amplitude. The direction of energy flow is determined from the analysis of the Poynting flux. There is a rapid nonlinear growth of the EMIC subpackets within one wavelength. Subpackets are dynamic in nature as their structure changes within one wave period, which is further supported by the nonlinear wave growth theory. Optimum and threshold amplitudes for the EMIC wave growth are calculated beside the nonlinear transition time (). Observed ion energies and pitch angle spectra of the ion fluxes are consistent with the energy associated with the Landau and cyclotron resonance conditions.

Dynamics of dust-ion acoustic cnoidal and solitary pulses in a magnetized collisional complex plasma

ABSTRACT The diagnostic of magnetized radio frequency complex plasma via probing techniques and spectroscopy is challenging. However, a self-excited dust ion acoustic waves (DIAWs) have been observed employing laser scattering. Inspired by the current high enthusiasm for the theoretical description of complex plasma, we study the propagation of DIAWs in a three-dimensional collisional and magnetized dusty plasma medium. We consider the fluid model for dust and ion particles, while we neglect the inertia of electrons considering the Boltzmann distribution. A linear dispersion relation is obtained and a nonlinear modified Zakharov–Kuznetsov equation is derived utilizing the reductive perturbation technique. The effects of ion-neutral and dust-neutral collisions on the dynamics of the nonlinear DIAWs are considered. The phase portrait analysis and numerical illustration of a rarefactive DIA cnoidal waves and solitons are also presented. Our findings agree with experimental observations by Choudhary M, Bergert R, Mitic S, and Thomas MH. [Influence of external magnetic field on dust acoustic waves in a capacitive rf discharge. Contrib Plasma Phys. 2020;60:e201900115] as the growth of nonlinear periodic waves is recorded when the magnetic field is roughly 0.05 T and vanishes when the magnetic field is close to 0.1 T. Moreover, the model reveals that the electrostatic cnoidal and soliton waves propagate with low frequencies up to 140 Hz.

Background Parameter Effects on Linear–Nonlinear Chorus Wave Growth in the Planetary Magnetosphere

Abstract We investigate the effects of the background dipole magnetic field and cold electron number density on the linear and nonlinear growth of whistler-mode chorus waves for a region of relatively small anisotropy (A T ) in Saturn’s inner magnetosphere. The linear and nonlinear features of wave growth rate and associated frequency at L = 6 are presented in detail. Although a large anisotropy is generally in favor of linear and nonlinear wave growth, the nonlinear wave growth for a small anisotropy can still be generated. All cases show a small threshold for wave amplitudes , which compromises the requirement to trigger the nonlinear wave growth, but the comparisons also clearly indicate the important transition process from the linear phase to the nonlinear phase. After checking the variation of the calculation time steps depending on the chosen electron number density N c and background magnetic field B c , respectively, a large N c can promote the nonlinear wave growth, but a large B c works against it. Our results present how these parameters really affect the generations of linear and nonlinear wave growth quantitatively. This could be significant to further understand the monumental importance of whistler-mode chorus waves and the corresponding wave–particle interactions in the planetary magnetosphere.

The Impenetrable Barrier: Suppression of Chorus Wave Growth by VLF Transmitters

AbstractRapid radiation belt recovery following storm time depletion involves local acceleration of multi‐MeV electrons in nonlinear interactions with VLF chorus waves. Previous studies of an apparent impenetrable barrier at L ~ 2.8 focused on diffusion and precipitation loss mechanisms for an explanation of the sharp reduction of multi‐MeV electron fluxes earthward of L ~ 3. Van Allen Probes observations for cases when the plasmasphere is contracted earthward of L ~ 3 indicate that strong coherent signals from VLF transmitters can play significant roles in the suppression of nonlinear chorus wave growth earthward of L ~ 3. As a result, local nonlinear acceleration of hundreds of keV electrons to MeV energies does not occur in this region. During the recovery of the outer radiation belt when the plasmasphere is significantly contracted, the suppression of chorus wave growth and local acceleration by the action of the transmitter waves at the outer edge of the VLF bubble contributes to the sharp inner edge of the new MeV electron population and the formation of the impenetrable barrier at L ~ 2.8.

Particle Simulation of the Generation of Plasmaspheric Hiss

AbstractWe have conducted a one‐dimensional electromagnetic particle simulation with a parabolic magnetic field to reproduce whistler‐mode hiss emissions in the plasmasphere. We assume a bi‐Maxwellian distribution with temperature anisotropy for energetic electrons injected into the plasmasphere and find that hiss emissions are generated with spectrum characteristics typical of those observed by spacecraft near the magnetic equator. The hiss emissions contain fine structures involving rising tone and falling tone elements with variation in frequencies. The amplitude profile of the spectra agrees with the optimum wave amplitude derived from the nonlinear wave growth theory. The simulation demonstrates that hiss emissions are generated locally near the magnetic equator through linear and nonlinear interactions with energetic electrons with temperature anisotropy. The coherent hiss emissions efficiently scatter resonant electrons of 2.5–80 keV into the loss cone.

Coherent Capillary Wave Structure Revealed by ISS Experiments for Spontaneous Nozzle Jet Disintegration

A series of International Space Station (ISS) experiments were conducted to observe the disintegration feature of a water jet issued from an orifice/nozzle into atmospheric air. The purpose was to validate our proposal that any laminar liquid jet can spontaneously disintegrate by its own self-destabilizing loop formed along the jet. This paper reports the experiment results focusing on a water jet issued from a nozzle with a radius 0.4 mm and length 120 mm, in which the parabolic velocity profile relaxes toward that of a plug flow along the jet. As predicted in our proposal, the nozzle jet had a two-valued breakup distance in a certain jet issue speed range and exhibited hysteresis behaviors, indicating that the jet disintegration state is determined by past jet disintegration history. Analyses of video images suggest the establishment of a coherent capillary wave structure in the steady jet disintegration state. New fundamental theories were developed to examine the underlying physics involved. The short-length breakup mode was confirmed to essentially follow the same self-destabilizing mechanism as that of the plug flow jet, in which the upstream propagating capillary wave produced by the release of surface energy due to jet tip contraction or nonlinear unstable wave growth is reflected at the orifice, and becomes the unstable wave responsible for jet disintegration. In the long-length breakup mode, the velocity profile relaxation plays a role equivalent to an orifice and the average nozzle jet length is expressed as the sum of the velocity profile relaxation length and average orifice jet length at large jet issue speeds. This paper focuses on the coherent capillary wave structure of long-length breakup mode.

Nonlinear Wave Growth Analysis of Whistler‐Mode Chorus Generation Regions Based on Coupled MHD and Advection Simulation of the Inner Magnetosphere

AbstractWe show the regions where nonlinear growth of whistler‐mode chorus waves is preferred to occur in the inner magnetosphere. A global magnetohydrodynamics (MHD) simulation was used to obtain large‐scale electric and magnetic fields under the southward interplanetary magnetic field condition. With the electric and magnetic fields obtained by the MHD simulation, we ran a comprehensive inner magnetosphere‐ionosphere model to solve the evolution of phase space density of electrons. Hot electrons originating from the tail region drift sunward and penetrate deep into the inner region due to a combination of convection and substorm‐associated electric fields. Cold electrons also drift sunward, resulting in a contraction of the plasmasphere. We obtained the following results. (1) The whistler waves can first grow due to the linear mechanism (pitch angle anisotropy) in the premidnight‐prenoon region outside the plasmapause, followed by rapid, nonlinear mechanism accompanied with rising‐tone chorus elements. (2) When the solar wind speed is high, the whistler waves grow more efficiently due to linear and nonlinear mechanisms over a wider area because of deep penetration of hot electrons and the large contraction of the plasmasphere. This is consistent with the observation that the outer belt electrons increase for the fast solar wind. (3) For slow solar wind, the linear growth is mostly suppressed, but the nonlinear growth can still take place when external seed waves are present. This may explain the persistence of dawn chorus and large‐amplitude chorus waves that are often observed in the premidnight‐postdawn region in relatively weak geomagnetic activities.

Evaluation of Plasma Properties From Chorus Waves Observed at the Generation Region

AbstractIn this study we present an inversion method which provides thermal plasma population parameters from characteristics of chorus emissions only. Our ultimate goal is to apply this method to ground‐based data in order to derive the lower‐energy boundary condition for many radiation belt models. The first step is to test the chorus inversion method on in situ data of the Van Allen Probes in the generation region. The density and thermal velocity of energetic electrons (few kiloelectron volts to 100 keV) are derived from frequency sweep rate and starting frequencies of chorus emissions through analysis of wave data from the Electric and Magnetic Field Instrument Suite and Integrated Science on board the Van Allen Probes. The nonlinear wave growth theory of Omura and Nunn (2011, https://doi.org/10.1029/2010JA016280) serves as the basis for our inversion method, assuming that the triggering wave is originated by the linear cyclotron instability. We present 16 consecutive rising‐tone emissions recorded in the generation region between 11 and 12 UT on 14 November 2012. The results of the inversion are compared with density and thermal velocities (parallel and perpendicular) of energetic electrons derived from the unidirectional flux data of the Helium, Oxygen, Proton, and Electron instrument, showing a good agreement: The normalized root‐mean‐square deviation between the measured and predicted values are less than ∼15%. We found that the theoretical amplitudes are consistent with the measured ones. The relation between linear and nonlinear wave growth agrees with our basic assumption; namely, linear growth is a preceding process of nonlinear wave growth. We analyze electron distributions at the relativistic resonant energy ranges.