Landau Resonance Research Articles

Study of Wave‐Particle Interactions for Whistler Mode Waves at Oblique Angles by Utilizing the Gyroaveraging Method

AbstractWe investigate the properties of whistler mode wave‐particle interactions at oblique wave normal angles to the background magnetic field. We find that electromagnetic energy of waves at frequencies below half the electron cyclotron frequency can flow nearly parallel to the ambient magnetic field. We thereby confirm that the gyroaveraging method, which averages the cyclotron motion to the gyrocenter and reduces the simulation from two‐dimensional to one‐dimensional, is valid for oblique wave‐particle interaction. Multiple resonances appear for oblique propagation but not for parallel propagation. We calculate the possible range of resonances with the first‐order resonance condition as a function of electron kinetic energy and equatorial pitch angle. To reveal the physical process and the efficiency of electron acceleration by multiple resonances, we assume a simple uniform wave model with constant amplitude and frequency in space and time. We perform test particle simulations with electrons starting at specific equatorial pitch angles and kinetic energies. The simulation results show that multiple resonances contribute to acceleration and pitch angle scattering of energetic electrons. Especially, we find that electrons with energies of a few hundred keV can be accelerated efficiently to a few MeV through the n = 0 Landau resonance.

Ion acceleration and heating by kinetic Alfvén waves associated with magnetic reconnection

Our previous study on the generation and signatures of kinetic Alfvén waves (KAWs) associated with magnetic reconnection in a current sheet revealed that KAWs are a common feature during reconnection [Liang et al. J. Geophys. Res.: Space Phys. 121, 6526 (2016)]. In this paper, ion acceleration and heating by the KAWs generated during magnetic reconnection are investigated with a three-dimensional (3-D) hybrid model. It is found that in the outflow region, a fraction of inflow ions are accelerated by the KAWs generated in the leading bulge region of reconnection, and their parallel velocities gradually increase up to slightly super-Alfvénic. As a result of wave-particle interactions, an accelerated ion beam forms in the direction of the anti-parallel magnetic field, in addition to the core ion population, leading to the development of non-Maxwellian velocity distributions, which include a trapped population with parallel velocities consistent with the wave speed. The ions are heated in both parallel and perpendicular directions. In the parallel direction, the heating results from nonlinear Landau resonance of trapped ions. In the perpendicular direction, however, evidence of stochastic heating by the KAWs is found during the acceleration stage, with an increase of magnetic moment μ. The coherence in the perpendicular ion temperature T⊥ and the perpendicular electric and magnetic fields of KAWs also provides evidence for perpendicular heating by KAWs. The parallel and perpendicular heating of the accelerated beam occur simultaneously, leading to the development of temperature anisotropy with T⊥>T∥. The heating rate agrees with the damping rate of the KAWs, and the heating is dominated by the accelerated ion beam. In the later stage, with the increase of the fraction of the accelerated ions, interaction between the accelerated beam and the core population also contributes to the ion heating, ultimately leading to overlap of the beams and an overall anisotropy with T∥>T⊥.

Electrostatic and whistler instabilities excited by an electron beam

The electron beam-plasma system is ubiquitous in the space plasma environment. Here, using a Darwin particle-in-cell method, the excitation of electrostatic and whistler instabilities by a gyrating electron beam is studied in support of recent laboratory experiments. It is assumed that the total plasma frequency (ωpe) is larger than the electron cyclotron frequency (Ωe). The fast-growing electrostatic beam-mode waves saturate in a few plasma oscillations by slowing down and relaxing the electron beam parallel to the background magnetic field. Upon their saturation, the finite amplitude electrostatic beam-mode waves can resonate with the tail of the background thermal electrons and accelerate them to the beam parallel velocity. The slower-growing whistler waves are excited in primarily two resonance modes: (a) through Landau resonance due to the inverted slope of the beam electrons in the parallel velocity and (b) through cyclotron resonance by scattering electrons to both lower pitch angles and smaller energies. It is demonstrated that, for a field-aligned beam, the whistler instability can be suppressed by the electrostatic instability due to a faster energy transfer rate between the beam electrons and electrostatic waves. Such a competition of growth between whistler and electrostatic waves depends on the ratio of ωpe/Ωe. In terms of wave propagation, beam-generated electrostatic waves are confined to the beam region, whereas beam-generated whistler waves transport energy away from the beam.

Electron butterfly distributions at particular magnetic latitudes observed during Juno's perijove pass

AbstractWe report observations of energetic electron butterfly distributions measured in a narrow range of Jupiter's magnetic latitudes by Juno during perijove 1. The electron butterfly distributions are characterized as clear electron flux peaks at 30–80° pitch angles, compared with the 90°‐peaked pitch angle distributions of the trapped electrons. Jupiter Energetic Particle Detector Instrument measurements during the close approach to Jupiter indicate a specific electron population with butterfly distributions formed between the main auroral oval and the radiation belt. The off‐90° flux peak is most clearly observed at tens of keV energies and gradually merges toward 90° pitch angle at higher energies. By projecting the observed electron pitch angle distributions along the magnetic field line, we found that the electron butterfly distributions are observed close to their source region. The particular electron distribution is possibly formed by parallel acceleration of electrons through Landau resonance with electrostatic waves.

Nonlinear Landau resonance with localized wave pulses

AbstractWave‐particle resonant interaction is responsible for many important space plasma processes and can be formally described theoretically for two main regimes: particle scattering (quasilinear diffusion) by low‐intensity waves and particle trapping/phase bunching by sufficiently intense waves. There are important modifications of these regimes in inhomogeneous plasma systems. However, almost all theoretical results have been derived for harmonic waves and linear plasma modes. High‐resolution spacecraft measurements of spatially localized plasma waves in Earth's magnetosphere demonstrate electron acceleration attributed to the Landau resonance mechanism. In the classical mechanism, the magnitude of the electric potential determines the maximum energy gain of electrons. However, a less reported mechanism of electron acceleration becomes possible in inhomogeneous plasma and magnetic field. In this Commentary, we discuss how combination of wave localization and plasma inhomogeneity modifies the nonlinear Landau resonance. We underline the important property of this resonance: an electron energy gain depends on the gradient in wave potential and not just its magnitude. We also consider this modified resonance mechanism in context of generation of hot field‐aligned electron populations, particle transport, and energy transfer in the magnetosphere.

Nonlinear dynamics of electrons interacting with oblique whistler mode chorus in the magnetosphere

AbstractWe perform test particle simulations for relativistic electrons interacting with a whistler mode chorus packet propagating at oblique angles. By confirming that the energy transport of oblique lower band chorus is nearly along the ambient magnetic field, we apply the gyroaveraging method in calculating equations of motion of electrons. We trace evolution of a delta function of relativistic electrons in a phase space of kinetic energy and equatorial pitch angle and obtain numerical Green's functions of the chorus wave‐particle interactions. Examining the Green's functions in a wide range of kinetic energies, we find that Landau resonance can accelerate MeV electrons efficiently and that higher nth resonances such as n =− 1 and n = 2 also contribute to acceleration of electrons at high equatorial pitch angles (∼70°) and high energies (∼2 MeV). We investigate the rate of energy gain of the cyclotron resonance acceleration and the Landau resonance acceleration and find that the perpendicular component of wave electric field dominates both accelerations for MeV electrons. Furthermore, the proximity between the parallel components of Vp and Vg of oblique whistler mode waves and the nonlinear trapping condition make the interaction time of Landau resonance much longer than that of n = 1 cyclotron resonance, resulting in efficient acceleration of MeV electrons.

Parametric decay of a parallel propagating monochromatic whistler wave: Particle-in-cell simulations

In this paper, by using one-dimensional (1-D) particle-in-cell simulations, we investigate the parametric decay of a parallel propagating monochromatic whistler wave with various wave frequencies and amplitudes. The pump whistler wave can decay into a backscattered daughter whistler wave and an ion acoustic wave, and the decay instability grows more rapidly with the increase of the frequency or amplitude. When the frequency or amplitude is sufficiently large, a multiple decay process may occur, where the daughter whistler wave undergoes a secondary decay into an ion acoustic wave and a forward propagating whistler wave. We also find that during the parametric decay a considerable part of protons can be accelerated along the background magnetic field by the enhanced ion acoustic wave through the Landau resonance. The implication of the parametric decay to the evolution of whistler waves in Earth's magnetosphere is also discussed in the paper.

PROTON HEATING BY PICK-UP ION DRIVEN CYCLOTRON WAVES IN THE OUTER HELIOSPHERE: HYBRID EXPANDING BOX SIMULATIONS

ABSTRACT Using a one-dimensional hybrid expanding box model, we investigate properties of the solar wind in the outer heliosphere. We assume a proton–electron plasma with a strictly transverse ambient magnetic field and, aside from the expansion, we take into account the influence of a continuous injection of cold pick-up protons through the charge-exchange process between the solar wind protons and hydrogen of interstellar origin. The injected cold pick-up protons form a ring distribution function, which rapidly becomes unstable, and generate Alfvén cyclotron waves. The Alfvén cyclotron waves scatter pick-up protons to a spherical shell distribution function that thickens over that time owing to the expansion-driven cooling. The Alfvén cyclotron waves heat solar wind protons in the perpendicular direction (with respect to the ambient magnetic field) through cyclotron resonance. At later times, the Alfvén cyclotron waves become parametrically unstable and the generated ion-acoustic waves heat protons in the parallel direction through Landau resonance. The resulting heating of the solar wind protons is efficient on the expansion timescale.

Unraveling the excitation mechanisms of highly oblique lower band chorus waves

AbstractExcitation mechanisms of highly oblique, quasi‐electrostatic lower band chorus waves are investigated using Van Allen Probes observations near the equator of the Earth's magnetosphere. Linear growth rates are evaluated based on in situ, measured electron velocity distributions and plasma conditions and compared with simultaneously observed wave frequency spectra and wave normal angles. Accordingly, two distinct excitation mechanisms of highly oblique lower band chorus have been clearly identified for the first time. The first mechanism relies on cyclotron resonance with electrons possessing both a realistic temperature anisotropy at keV energies and a plateau at 100–500 eV in the parallel velocity distribution. The second mechanism corresponds to Landau resonance with a 100–500 eV beam. In both cases, a small low‐energy beam‐like component is necessary for suppressing an otherwise dominating Landau damping. Our new findings suggest that small variations in the electron distribution could have important impacts on energetic electron dynamics.

Upper limit of electron fluxes generated by kinetic Alfvén waves in Maxwellian plasma

AbstractWe consider electron acceleration by kinetic Alfvén waves in the equatorial inner magnetosphere and plasma sheet boundary layer. The competition between the accelerating effect of the wave parallel electric field and mirror force acting on particles in an inhomogeneous background magnetic field generates an effective potential well where electrons can be trapped and accelerated. We compare energy variations of trapped and transient resonant electrons and show that these variations almost compensate each other. Thus, energy provided to waves by transient particles is transferred to trapped particles. This effect allows waves accelerate trapped electrons without being significantly damped. Using energy balance equations, we estimate the maximum flux of electrons accelerated via trapping into Landau resonance with kinetic Alfvén waves. For a wide range of system parameters (i.e., ion to electron temperature ratio, magnetic field amplitude, and wave number and wave frequency), acceleration of trapped electrons can generate fluxes with amplitude about 5–25% of the background thermal fluxes. We determine parametric regions for the most efficient acceleration.

He2+ HEATING VIA PARAMETRIC INSTABILITIES OF PARALLEL PROPAGATING ALFVÉN WAVES WITH AN INCOHERENT SPECTRUM

ABSTRACT The preferential heating of heavy ions in the solar corona and solar wind has been a long-standing hot topic. In this paper we use a one-dimensional hybrid simulation model to investigate the heating of He2+ particles during the parametric instabilities of parallel propagating Alfvén waves with an incoherent spectrum. The evolution of the parametric instabilities has two stages and involves the heavy ion heating during the entire evolution. In the first stage, the density fluctuations are generated by the modulation of the pump Alfvén waves with a spectrum, which then results in rapid coupling with the pump Alfvén waves and the cascade of the magnetic fluctuations. In the second stage, each pump Alfvén wave decays into a forward density mode and a backward daughter Alfvén mode, which is similar to that of a monochromatic pump Alfvén wave. In both stages the perpendicular heating of He2+ particles occurs. This is caused by the cyclotron resonance between He2+ particles and the high-frequency magnetic fluctuations, whereas the Landau resonance between He2+ particles and the density fluctuations leads to the parallel heating of He2+ particles. The influence of the drift velocity between the protons and the He2+ particles on the heating of He2+ particles is also discussed in this paper.

Observational evidence of generation mechanisms for very oblique lower band chorus using THEMIS waveform data

AbstractChorus waves are intense coherent whistler mode waves with frequency chirping which play a dual role in both loss and acceleration of radiation belt electrons in the Earth's magnetosphere. Although the generation of parallel chorus waves has been extensively studied by means of theory, simulations, and observations, the generation mechanism of very oblique chorus waves still remains a mystery. In this study, we have analyzed hundreds of very oblique discrete (rising or falling tone) lower band chorus events collected from 7 years of Time History of Events and Macroscale Interactions during Substorms (THEMIS) waveform data to investigate their potential generation mechanisms. Comparisons between wave normal angles directly measured onboard THEMIS in the dawn‐day sector at L = 5–9 and inferred from theoretical models on the basis of measured wave characteristics (frequency sweep rate, mean frequency, and amplitude) show that these very oblique waves are more commonly generated through cyclotron resonance with anisotropic electron streams. However, a second generation mechanism via Landau resonance with low‐energy electron beams seems to be also operating on the nightside at L < 6.7 and at all local times at L > 8.5. Moreover, very oblique lower band chorus waves with large frequency chirping rates or small magnetic field amplitudes are more likely excited via cyclotron resonance, while waves with small frequency chirping rates or large magnetic field amplitudes are preferentially generated through Landau resonance. This comprehensive statistical study provides interesting insight into the possible generation mechanisms of very oblique lower band chorus waves in the Earth's magnetosphere.

KINETIC SIMULATION OF SLOW MAGNETOSONIC WAVES AND QUASI-PERIODIC UPFLOWS IN THE SOLAR CORONA

ABSTRACT Quasi-periodic disturbances of emission-line parameters are frequently observed in the corona. These disturbances propagate upward along the magnetic field with speeds of ∼100 km s−1. This phenomenon has been interpreted as evidence of the propagation of slow magnetosonic waves or has been argued to be a signature of intermittent outflows superposed on the background plasmas. Here we aim to present a new “wave + flow” model to interpret these observations. In our scenario, the oscillatory motion is a slow-mode wave, and the flow is associated with a beam created by the wave–particle interaction owing to Landau resonance. With the help of a kinetic model, we simulate the propagation of slow-mode waves and the generation of beam flows. We find that weak periodic beam flows can be generated by to Landau resonance in the solar corona, and the phase with the strongest blueward asymmetry is ahead of that with the strongest blueshift by about 1/4 period. We also find that the slow wave damps to the level of 1/e after the transit time of two wave periods, owing to Landau damping and Coulomb collisions in our simulation. This damping timescale is similar to that resulting from thermal conduction in the MHD regime. The beam flow is weakened/attenuated with increasing wave period and decreasing wave amplitude since Coulomb collisions become more and more dominant over the wave action. We suggest that this “wave + flow” kinetic model provides an alternative explanation for the observed quasi-periodic propagating perturbations in various parameters in the solar corona.

Electromagnetic particle simulation of the effect of toroidicity on linear mode conversion and absorption of lower hybrid waves

Effects of toroidicity on linear mode conversion and absorption of lower hybrid (LH) waves in fusion plasmas have been studied using electromagnetic particle simulation. The simulation confirms that the toroidicity induces an upshift of parallel refractive index when LH waves propagate from the tokamak edge toward the core, which affects the radial position for the mode conversion between slow and fast LH waves. Furthermore, moving LH antenna launch position from low field side toward high field side leads to a larger upshift of the parallel refractive index, which helps the slow LH wave penetration into the tokamak core. The broadening of the poloidal spectrum of the wave-packet due to wave diffraction is also verified in the simulation. Both the upshift and broadening effects of the parallel spectrum of the wave-packet modify the parallel phase velocity and thus the linear absorption of LH waves by electron Landau resonance.

Equatorial electron loss by double resonance with oblique and parallel intense chorus waves

AbstractPuzzling satellite observations of butterfly pitch angle distributions and rapid dropouts of 30–150 keV electrons are widespread in the Earth's radiation belts. Several mechanisms have been proposed to explain these observations, such as enhanced outward radial diffusion combined with magnetopause shadowing or scattering by intense magnetosonic waves, but their effectiveness is mainly limited to storm times. Moreover, the scattering of 30–150 keV electrons via cyclotron resonance with intense parallel chorus waves should be limited to particles with equatorial pitch angle smaller than 70°–75°, leaving unaffected a large portion of the population. In this paper, we investigate the possible effects of oblique whistler mode waves, noting, in particular, that Landau resonance with very oblique waves can occur up to ∼89°. We demonstrate that such very oblique chorus waves with realistic amplitudes can very efficiently nonlinearly transport nearly equatorially mirroring electrons toward smaller pitch angles where nonlinear scattering (phase bunching) via cyclotron resonance with quasi‐parallel waves can take over and quickly send them to much lower pitch angles <40°. The proposed double resonance mechanism could therefore explain the formation of butterfly pitch angle distributions as well as contribute to some fast dropouts of 30–150 keV electrons occurring during moderate geomagnetic disturbances at L = 4–6. Since 30–150 keV electrons represent a seed population for a further acceleration to relativistic energies by intense parallel chorus waves during storms or substorms, the proposed mechanism may have important consequences on the dynamics of 100 keV to MeV electron fluxes in the radiation belts.

Nonlinear Landau resonant scattering of near equatorially mirroring radiation belt electrons by oblique EMIC waves

AbstractIn response to solar wind disturbances, radiation belt (a few hundreds of keV to several MeV) electron fluxes can be depleted significantly over the entire equatorial pitch angle range. The frequently mentioned cyclotron resonant scattering is applicable only for electrons mirroring off the equator. Here we propose a new physical mechanism, nonlinear Landau resonance with oblique electromagnetic ion cyclotron (EMIC) waves, to effectively scatter the near equatorially mirroring electrons. Our test particle simulations show that the nonlinear Landau trapping can occur over a wide energy range and yield the net decrease in equatorial pitch angle Δαeq≈10° within several seconds. Our parametric studies further reveal that this nonlinear Landau‐trapping process is favored by a low plasma density, an intense wave field, a high wave frequency close to ion gyrofrequencies, and a large wave normal angle.

Wave–particle resonance condition test for ion-kinetic waves in the solar wind

Abstract. Conditions for the Landau and cyclotron resonances are tested for 543 waves (identified as local peaks in the energy spectra) in the magnetic field fluctuations of the solar wind measured by the Cluster spacecraft on a tetrahedral scale of 100 km. The resonance parameters are evaluated using the frequencies in the plasma rest frame, the parallel components of the wavevectors, the ion cyclotron frequency, and the ion thermal speed. The observed waves show a character of the sideband waves associated with the ion Bernstein mode, and are in a weak agreement with the fundamental electron cyclotron resonance in spite of the ion-kinetic scales. The electron cyclotron resonance is likely taking place in solar wind turbulence near 1 AU (astronomical unit).

Formation of energetic electron butterfly distributions by magnetosonic waves via Landau resonance

AbstractRadiation belt electrons can exhibit different types of pitch angle distributions in response to various magnetospheric processes. Butterfly distributions, characterized by flux minima at pitch angles around 90°, are broadly observed in both the outer and inner belts and the slot region. Butterfly distributions close to the outer magnetospheric boundary have been attributed to drift shell splitting and losses to the magnetopause. However, their occurrence in the inner belt and the slot region has hitherto not been resolved. By analyzing the particle and wave data collected by the Van Allen Probes during a geomagnetic storm, we combine test particle calculations and Fokker‐Planck simulations to reveal that scattering by equatorial magnetosonic waves is a significant cause for the formation of energetic electron butterfly distributions in the inner magnetosphere. Another event shows that a large‐amplitude magnetosonic wave in the outer belt can create electron butterfly distributions in just a few minutes.

Banded structures in electron pitch angle diffusion coefficients from resonant wave-particle interactions

Electron pitch angle (Dαα) and momentum (Dpp) diffusion coefficients have been calculated due to resonant interactions with electrostatic electron cyclotron harmonic (ECH) and whistler mode chorus waves. Calculations have been performed at two spatial locations L = 4.6 and 6.8 for electron energies ≤10 keV. Landau (n = 0) resonance and cyclotron harmonic resonances n = ±1, ±2, … ±5 have been included in the calculations. It is found that diffusion coefficient versus pitch angle (α) profiles show large dips and oscillations or banded structures. The structures are more pronounced for ECH and lower band chorus (LBC) and particularly at location 4.6. Calculations of diffusion coefficients have also been performed for individual resonances. It is noticed that the main contribution of ECH waves in pitch angle diffusion coefficient is due to resonances n = +1 and n = +2. A major contribution to momentum diffusion coefficients appears from n = +2. However, the banded structures in Dαα and Dpp coefficients appear only in the profile of diffusion coefficients for n = +2. The contribution of other resonances to diffusion coefficients is found to be, in general, quite small or even negligible. For LBC and upper band chorus waves, the banded structures appear only in Landau resonance. The Dpp diffusion coefficient for ECH waves is one to two orders smaller than Dαα coefficients. For chorus waves, Dpp coefficients are about an order of magnitude smaller than Dαα coefficients for the case n ≠ 0. In case of Landau resonance, the values of Dpp coefficient are generally larger than the values of Dαα coefficients particularly at lower energies. As an aid to the interpretation of results, we have also determined the resonant frequencies. For ECH waves, resonant frequencies have been estimated for wave normal angle 89° and harmonic resonances n = +1, +2, and +3, whereas for whistler mode waves, the frequencies have been calculated for angle 10° and Landau resonance. Further, in ECH waves, the banded structures appear for electron energies ≥1 keV, and for whistler mode chorus waves, structures appear for energies >2 keV at L = 4.6 and above 200 eV for L = 6.8. The results obtained in the present work will be helpful in the study of diffusion curves and will have important consequences for diffuse aurora and pancake distributions.

Ultrarelativistic electron butterfly distributions created by parallel acceleration due to magnetosonic waves

AbstractThe Van Allen Probe observations during the recovery phase of a large storm that occurred on 17 March 2015 showed that the ultrarelativistic electrons at the inner boundary of the outer radiation belt (L* = 2.6–3.7) exhibited butterfly pitch angle distributions, while the inner belt and the slot region also showed evidence of sub‐MeV electron butterfly distributions. Strong magnetosonic waves were observed in the same regions and at the same time periods as these butterfly distributions. Moreover, when these magnetosonic waves extended to higher altitudes (L* = 4.1), the butterfly distributions also extended to the same region. Combining test particle calculations and Fokker‐Planck diffusion simulations, we successfully reproduced the formation of the ultrarelativistic electron butterfly distributions, which primarily result from parallel acceleration caused by Landau resonance with magnetosonic waves. The coexistence of ultrarelativistic electron butterfly distributions with magnetosonic waves was also observed in the 24 June 2015 storm, providing further support that the magnetosonic waves play a key role in forming butterfly distributions.