Landau Resonant Interaction Research Articles

Nonlinear Landau resonant interaction between whistler waves and electrons: Excitation of electron-acoustic waves

Electron-acoustic waves (EAWs) as well as electron-acoustic solitary structures play a crucial role in thermalization and acceleration of electron populations in Earth's magnetosphere. These waves are often observed in association with whistler-mode waves, but the detailed mechanism of EAW and whistler wave coupling is not yet revealed. We investigate the excitation mechanism of EAWs and their potential relation to whistler waves using particle-in-cell simulations. Whistler waves are first excited by electrons with a temperature anisotropy perpendicular to the background magnetic field. Electrons trapped by these whistler waves through nonlinear Landau resonance form localized field-aligned beams, which subsequently excite EAWs. By comparing the growth rate of EAWs and the phase mixing rate of trapped electron beams, we obtain the critical condition for EAW excitation, which is consistent with our simulation results across a wide region in parameter space. These results are expected to be useful in the interpretation of concurrent observations of whistler-mode waves and nonlinear solitary structures and may also have important implications for investigation of cross-scale energy transfer in the near-Earth space environment.

Electron Heat Flux Instabilities in the Inner Heliosphere: Radial Distribution and Implication on the Evolution of the Electron Velocity Distribution Function

Abstract This Letter investigates the electron heat flux instability using the radial models of the magnetic field and plasma parameters in the inner heliosphere. Our results show that both the electron acoustic wave and the oblique whistler wave are unstable in the regime with large relative drift speed (ΔV e ) between electron beam and core populations. Landau-resonant interactions of electron acoustic waves increase the electron parallel temperature that would lead to suppressing the electron acoustic instability and amplifying the growth of oblique whistler waves. Therefore, we propose that the electron heat flux can effectively drive oblique whistler waves in an anisotropic electron velocity distribution function. This study also finds that lower-hybrid waves and oblique Alfvén waves can be triggered in the solar atmosphere, and that the former instability is much stronger than the latter. Moreover, we clarify that the excitation of lower-hybrid waves mainly results from the transit-time interaction of beaming electrons with resonant velocities v ∥ ∼ ω/k ∥, where ω and k ∥ are the wave frequency and parallel wavenumber, respectively. In addition, this study shows that the instability of quasi-parallel whistler waves can dominate the regime with medium ΔV e at the heliocentric distance nearly larger than 10 times of the solar radius.

Gap formation around <em>Ω</em><sub>e</sub>/2 and generation of low-band whistler waves by Landau-resonant electrons in the magnetosphere: Predictions from dispersion theory

In this paper we show that two significant phenomena of magnetospheric chorus emission can be explained by the participation of beam-like electron structures, created by Landau-resonant interaction with growing oblique whistler waves. The first concerns the widely observed spectral gap near half the electron cyclotron frequency Ωe; the second is related to the observation of very obliquely propagating lower-band waves that cannot be directly generated by temperature anisotropy. Concerning the gap, kinetic dispersion theory reveals that interference of the beam-related cyclotron mode ω~Ωe-kVb with the conventional whistler mode leads to mode splitting and the appearance of a ‘forbidden’ area in the ω-k space. Thereby the beam velocity Vb appears as an essential parameter. It is directly related to the phase velocity of the most unstable whistler wave mode, which is close to VAe/2 for sufficiently hot electrons (VAe is the electron Alfven velocity). To clarify the second point, we show that Landau-resonant beams with Vb < VAe/2, which arise in cold plasmas from unstable upper-band waves, are able to generate lower-band whistler mode waves at very oblique propagation (θ ≥ 60°). Our studies demonstrate the important role of Landau-resonant electrons in nonlinear whistler wave generation in the magnetosphere.

Combined Scattering of Radiation Belt Electrons Caused by Landau and Bounce Resonant Interactions With Magnetosonic Waves

AbstractWe develop a full relativistic test particle code to model the combined electron scattering effect of Landau and bounce resonances with magnetosonic waves. Test particle simulations of magnetosonic wave‐electron interactions indicate that the two resonances coexist to affect radiation belt electrons at different energies and pitch angles, and the resultant combined pitch angle scattering and energy diffusion can reach the rates of ~10−4 and ~10‐5 s, respectively, for electrons ~40–500 keV at pitch angles ~ 70 ° – 80° for the given wave model (~200 pT) inside the plasmapause at L = 4.5. Comparisons with the quasi‐linear theory results show that the test particle combined scattering rates are generally an order of magnitude weaker, possibly because the electrons are moved out of the Landau resonance by the advective effect of the bounce resonance. Our investigation demonstrates that the Landau and bounce resonances with magnetosonic waves cannot be treated independently or additively in terms of quasi‐linear theory to simulate the associated radiation belt electron dynamics.

Bounce Resonance Scattering of Radiation Belt Electrons by Low‐Frequency Hiss: Comparison With Cyclotron and Landau Resonances

AbstractBounce resonant interactions with magnetospheric waves have been proposed as an important contributing mechanism for scattering near‐equatorially mirroring electrons by violating the second adiabatic invariant associated with the electron bounce motion along a geomagnetic field line. This study demonstrates that low‐frequency plasmaspheric hiss with significant wave power below 100 Hz can bounce resonate efficiently with radiation belt electrons. By performing quantitative calculations of pitch angle scattering rates, we show that low‐frequency hiss‐induced bounce resonant scattering of electrons has a strong dependence on equatorial pitch angle αeq. For electrons with αeq close to 90°, the timescale associated with bounce resonance scattering can be comparable to or even less than 1 h. Cyclotron and Landau resonant interactions between low‐frequency hiss and electrons are also investigated for comparisons. It is found that while the bounce and Landau resonances are responsible for the diffusive transport of near‐equatorially mirroring electrons to lower αeq, pitch angle scattering by cyclotron resonance could take over to further diffuse electrons into the atmosphere. Bounce resonance provides a more efficient pitch angle scattering mechanism of relativistic (≥1 MeV) electrons than Landau resonance due to the stronger scattering rates and broader resonance coverage of αeq, thereby demonstrating that bounce resonance scattering by low‐frequency hiss can contribute importantly to the evolution of the electron pitch angle distribution and the loss of radiation belt electrons.

Nonlinear local parallel acceleration of electrons through Landau trapping by oblique whistler mode waves in the outer radiation belt

AbstractSimultaneous observations of electron velocity distributions and chorus waves by the Van Allen Probe B are analyzed to identify long‐lasting (more than 6 h) signatures of electron Landau resonant interactions with oblique chorus waves in the outer radiation belt. Such Landau resonant interactions result in the trapping of ∼1–10 keV electrons and their acceleration up to 100–300 keV. This kind of process becomes important for oblique whistler mode waves having a significant electric field component along the background magnetic field. In the inhomogeneous geomagnetic field, such resonant interactions then lead to the formation of a plateau in the parallel (with respect to the geomagnetic field) velocity distribution due to trapping of electrons into the wave effective potential. We demonstrate that the electron energy corresponding to the observed plateau remains in very good agreement with the energy required for Landau resonant interaction with the simultaneously measured oblique chorus waves over 6 h and a wide range of L shells (from 4 to 6) in the outer belt. The efficient parallel acceleration modifies electron pitch angle distributions at energies ∼50–200 keV, allowing us to distinguish the energized population. The observed energy range and the density of accelerated electrons are in reasonable agreement with test particle numerical simulations.

Interactions between magnetosonic waves and radiation belt electrons: Comparisons of quasi‐linear calculations with test particle simulations

AbstractQuasi‐linear theory (QLT) has been commonly used to study the Landau resonant interaction between radiation belt electrons and magnetosonic (MS) waves. However, the long‐parallel wavelengths of MS waves can exceed their narrow spatial confinement and cause a transit‐time effect during interactions with electrons. We perform a careful investigation to validate the applicability of QLT to interactions between MS waves, which have a distribution in frequency and wave normal angle, and radiation belt electrons using test particle simulations. We show agreement between these two methods for scattering rate of intense MS waves at L = 4.5 inside the plasmapause, but find a significant inconsistency for MS waves outside the plasmapause, due to the broad transit‐time region in (Ek,α) space. Consequently, we introduce a particle‐independent criterion to justify the validity of QLT for MS waves: the wave spatial confinement should be longer than two parallel wavelengths.

Signatures of electron Landau resonant interactions with chorus waves from THEMIS observations

AbstractSimultaneous observations of electron phase space density (PSD) and chorus waves for more than 4 years by the Time History of Events and Macroscale Interactions during Substorms (THEMIS) are analyzed to identify signatures of the electron Landau resonant interactions with chorus waves in the radiation belts. Chorus waves play an important role in the radiation belt dynamics by effectively interacting with electrons. Landau resonant interactions arise when the waves are not exactly parallel propagating. Such interactions lead to “plateaus” along v∥ in the electron velocity distributions, where v∥is the parallel (with respect to the background magnetic field) component of the electron velocity. The analyzed electron PSDs often demonstrate local minima in the derivative of the velocity distribution along v∥ near the Landau resonant velocity calculated from the simultaneous in situ wave observations. These minima are, therefore, direct signatures and solid evidence of the electron Landau resonant interactions with chorus waves.

Cold electron heating by EMIC waves in the plasmaspheric plume with observations of the Cluster satellite

We report in situ observations by the Cluster spacecraft of plasmaspheric electron heating in the plasmaspheric plume. Electron heating events were accompanied by enhancements of electromagnetic ion cyclotron (EMIC) waves in the increased density ducts on the negative density gradient side for two substructures of the plasmaspheric plume. Electron heating is much stronger for the pitch angle of 0° and 180° than for the pitch angle of 90°. Theoretical calculations of the Landau resonant interaction between electrons and observed EMIC waves demonstrate that Landau damping of oblique EMIC waves is a reasonable candidate to heat cold electrons in the presence of O + ions in the outer boundary of the plasmaspheric plume. Therefore, this observation is considered in situ evidence of plasmaspheric electron heating through Landau damping of EMIC waves in plasmaspheric plumes.

A stochastic mechanism of electron heating

Due to Landau resonant interaction with lower hybrid waves in the lower hybrid current drive scheme part of electrons are accelerated and, as a result of this, a tail of energetic electrons is formed on the electron distribution function. The same situation takes place in the problem of type III radio bursts when the suprathermal burst electrons acquire a plateau distribution due to excitation of plasma waves in the solar wind plasma. These distributions are unstable with respect to the cyclotron excitation of waves at anomalous Doppler resonance (“fan” instability). In this case, the tail electrons interact simultaneously with both (i) waves that accelerate or decelerate them (Čerenkov resonance) and (ii) waves excited in the process of the fan instability that led to their pitch angle diffusion. Because velocity diffusion lines of electrons formed due to heir interaction with each type of waves intersect, this interaction can lead not only to pitch angle diffusion but also to heating of electrons mainly in perpendicular direction. We investigated this mechanism of electron heating and studied the temporal evolution of the electron temperature and the energy of excited waves. Our results show significant enhancement of the electron perpendicular temperature T⊥ due to this stochastic heating mechanism.

Resonant enhancement of relativistic electron fluxes during geomagnetically active periods

Abstract. The strong increase in the flux of relativistic electrons during the recovery phase of magnetic storms and during other active periods is investigated with the help of Hamiltonian formalism and simulations of test electrons which interact with whistler waves. The intensity of the whistler waves is enhanced significantly due to injection of 10-100 keV electrons during the substorm. Electrons which drift in the gradient and curvature of the magnetic field generate the rising tones of VLF whistler chorus. The seed population of relativistic electrons which bounce along the inhomogeneous magnetic field, interacts resonantly with the whistler waves. Whistler wave propagating obliquely to the magnetic field can interact with energetic electrons through Landau, cyclotron, and higher harmonic resonant interactions when the Doppler-shifted wave frequency equals any (positive or negative) integer multiple of the local relativistic gyrofrequency. Because the gyroradius of a relativistic electron may be the order of or greater than the perpendicular wavelength, numerous cyclotron, harmonics can contribute to the resonant interaction which breaks down the adiabatic invariant. A similar process diffuses the pitch angle leading to electron precipitation. The irreversible changes in the adiabatic invariant depend on the relative phase between the wave and the electron, and successive resonant interactions result in electrons undergoing a random walk in energy and pitch angle. This resonant process may contribute to the 10-100 fold increase of the relativistic electron flux in the outer radiation belt, and constitute an interesting relation between substorm-generated waves and enhancements in fluxes of relativistic electrons during geomagnetic storms and other active periods.Key words. Magnetospheric physics (energetic particles · trapped; plasma waves and instabilities; storms and substorms)

Resonant enhancement of relativistic electron fluxes during geomagnetically active periods

<strong class="journal-contentHeaderColor">Abstract.</strong> The strong increase in the flux of relativistic electrons during the recovery phase of magnetic storms and during other active periods is investigated with the help of Hamiltonian formalism and simulations of test electrons which interact with whistler waves. The intensity of the whistler waves is enhanced significantly due to injection of 10-100 keV electrons during the substorm. Electrons which drift in the gradient and curvature of the magnetic field generate the rising tones of VLF whistler chorus. The seed population of relativistic electrons which bounce along the inhomogeneous magnetic field, interacts resonantly with the whistler waves. Whistler wave propagating obliquely to the magnetic field can interact with energetic electrons through Landau, cyclotron, and higher harmonic resonant interactions when the Doppler-shifted wave frequency equals any (positive or negative) integer multiple of the local relativistic gyrofrequency. Because the gyroradius of a relativistic electron may be the order of or greater than the perpendicular wavelength, numerous cyclotron, harmonics can contribute to the resonant interaction which breaks down the adiabatic invariant. A similar process diffuses the pitch angle leading to electron precipitation. The irreversible changes in the adiabatic invariant depend on the relative phase between the wave and the electron, and successive resonant interactions result in electrons undergoing a random walk in energy and pitch angle. This resonant process may contribute to the 10-100 fold increase of the relativistic electron flux in the outer radiation belt, and constitute an interesting relation between substorm-generated waves and enhancements in fluxes of relativistic electrons during geomagnetic storms and other active periods.<br><br><b>Key words.</b> Magnetospheric physics (energetic particles · trapped; plasma waves and instabilities; storms and substorms)

Auroral beam‐plasma interactions: Particle correlator investigations

Plasma wave instabilities may occur above discrete auroral arcs where the natural accelerated auroral electron component meets the cold ionospheric plasma. These wave‐particle interactions were studied on the CAESAR II rocket by measuring the modulations in energetic electron flux in the frequency ranges 0–10 kHz and 0–10 MHz. Near apogee (700 km) a strong modulation of 7.5 keV electrons at 1.4 MHz (≈ fuh) was observed where df(υ)/dυ was positive, just below the auroral beam velocity. The measurement is shown to be consistent with instabilities driven by both Landau and cyclotron resonant interactions with upper hybrid waves, and also with the earlier observation of modulations at 2.65 MHz ( ≈ fuh) seen on a low altitude rocket E2‐B (apogee 230 km).

Nonlinear pitch angle scattering and trapping of energetic particles during Landau resonance interactions with whistler mode waves

The time averaged equations of motion derived by Inan and Tkalcevic (1982) are used in a test particle study of Landau resonant interactions of whistler mode waves and energetic particles in the magnetopshere. By computing individual particle trajectories it is shown that the pitch angle scattering and energy exchange is significantly different for the two classes of particles, trapped and untrapped. The trapped particles are characterized by a bounded phase variation, whereas the nontrapped particles exhibit unbounded phase variation. The threshold wave electric field intensities necessary for trapping are determined. Full distribution test particle simulation is carried out to determine the precipitated electron flux that would be induced as a result of these interactions. It is shown that for typical parameters the resulting precipitation fluxes for Landau resonance interactions are much smaller than those induced in gyroresonance interactions, even for wave field intensities that are much higher than the trapping threshold.

Analysis of chorus emissions at Jupiter

On the Voyager 1 inbound pass through the Jovian magnetosphere, the frequent acquisition of wide band data from the plasma wave instrument has permitted a quasi‐continuous survey of the waves which occur in the frequency band below the electron cyclotron frequency, the chorus band. Structured, rising frequency chorus was observed just outside the dense Io plasma torus but inside the low‐density middle magnetosphere. A quasi‐continuous, very narrow band emission occurred just above one‐half the electron cyclotron frequency. Power spectra, which were constructed from the wide band data, showed that the half‐cyclotron emission is unaffected by the simultaneous occurrence of chorus at lower frequencies and is separated from the chorus by a deep spectral gap just below one‐half the cyclotron frequency. Within the rising chorus band, a hisslike emission was observed which consisted of two quasi‐continuous, very narrow band tones located near the upper and lower frequency limits of the rising chorus band. Sequential power spectra showed that these twin‐frequency tones persisted during rising chorus bursts. Chorus occurs in the spatial regions where whistlers have cyclotron resonant interactions with the suprathermal population of ∼keV electrons. A possible interpretation of the twin tones is that these signals are electrostatic or resonance cone whistlers. Growth rate calculations show that the electrostatic whistler is destabilized by a loss cone distribution with the same pitch angle anisotropy which is needed to excite the electromagnetic chorus whistlers. A speculative hypothesis is presented to explain the half‐cyclotron emission. The Landau absorption of oblique chorus whistlers results in the spectral gap just below one‐half the cyclotron frequency and in the formation of a quasi‐linear plateau in the parallel velocity distribution of the suprathermal electrons. The plateau alters the Landau and cyclotron resonant interactions and permits the unstable growth of electrostatic and electromagnetic whistlers in a narrow range just above one‐half the cyclotron frequency.

Unified theory of SAR arc formation at the plasmapause

Stable auroral red arcs generation at plasmapause from ion cyclotron wave turbulent dissipation of ring current proton energy