Large-amplitude Whistler Waves Research Articles

Large Amplitude Whistler Waves in Earth's Plasmasphere and Plasmaspheric Plumes

AbstractWhistler mode waves in the plasmasphere and plumes drive significant losses of energetic electrons from the Earth's radiation belts into the upper atmosphere. In this study, we conducted a survey of amplitude‐dependent whistler wave properties and analyzed their associated background plasma conditions and electron fluxes in the plasmasphere and plumes. Our findings indicate that extremely large amplitude (>400 pT) whistler waves (a) tend to occur at L > 4 over the midnight‐dawn‐noon sectors and have small wave normal angles; (b) are more likely to occur during active geomagnetic conditions associated with higher fluxes of anisotropic electrons at 10 s keV energies; and (c) tend to occur at higher latitudes up to 20° with increasing amplitude. These results suggest that extremely large amplitude whistler waves in the plasmasphere and plumes could be generated locally by injected electrons during substorms and further amplified when propagating to higher latitudes.

Excitation characterization of whistler waves and electrostatic oscillation in asymmetric magnetic reconnection

Utilizing the 2.5D Particle-in-Cell (PIC) method, we observe that large-amplitude whistler waves are present near the separatrix on the magnetospheric side and in the outflow region during asymmetric magnetic reconnection. Minimum variance analyses confirm their quasi-parallel and anti-parallel propagation to the background magnetic field, respectively, and their accuracy is validated through parallel Poynting fluxes (S∥). The excited whistler waves have intermittent property due to the evolution and movement of the reconnection layer. Wave-Particle Interaction Analysis (WPIA) reveals a pronounced energy conversion between the waves and electrons. Our simulation results demonstrate that whistler waves near the separatrix are excited by the cyclotron resonance duo to the instability of electron beam by analyzing the electron velocity distribution functions (VDFs). Meanwhile, the electrostatic oscillation is generated by the positive parallel drift of electron beam. However, the whistler waves in the outflow region are excited by the Landau resonance duo to anisotropic instability distributions of electron beam-mode.

Beam-driven whistler mode nonlinear saturation and turbulence in the magnetopause

This work presents a model to understand the generation of whistler turbulence in the magnetic reconnection region of magnetopause by the energetic electron beams (generated by magnetic reconnection process) as observed by magnetospheric multiscale mission [Zhao et al., J. Geophys. Res.: Space Phys. 126, e2020JA028525 (2021)]. In this model, the magnetic reconnection process has been replaced by the energetic electron beam source. Hence, the beam-driven whistler-mode dynamical equation has been set up by anticipating that it will grow from noise level due to beam energy and then will attain large amplitude such that nonlinear effects due to ponderomotive force will lead to the localization of whistler waves, and finally, this will lead to the turbulent state. For this, a non-linear two-dimensional fluid model is developed in which nonlinear interaction between high-frequency whistler wave and low-frequency ion acoustic wave (IAW) is pertinent to the magnetopause region. Due to large-amplitude whistler waves, ponderomotive force components emerge, which are included in IAW's nonlinear dynamics. The system of the dimensionless equations consists of the dynamics of whistler wave and IAW, and this has been solved by the numerical method. The results of the simulation show that the whistler's temporal evolution results in localized structures that eventually lead to turbulence. The relevance of the present investigation to the recent observations has also been pointed out.

Analysis of multiscale structures at the quasi-perpendicular Venus bow shock

Context. Solar Orbiter is a European Space Agency mission with a suite of in situ and remote sensing instruments to investigate the physical processes across the inner heliosphere. During the mission, the spacecraft is expected to perform multiple Venus gravity assist maneuvers while providing measurements of the Venusian plasma environment. The first of these occurred on 27 December 2020, in which the spacecraft measured the regions such as the distant and near Venus magnetotail, magnetosheath, and bow shock. Aims. This study aims to investigate the outbound Venus bow shock crossing measured by Solar Orbiter during the first flyby. We study the complex features of the bow shock traversal in which multiple large amplitude magnetic field and density structures were observed as well as higher frequency waves. Our aim is to understand the physical mechanisms responsible for these high amplitude structures, characterize the higher frequency waves, determine the source of the waves, and put these results into context with terrestrial bow shock observations. Methods. High cadence magnetic field, electric field, and electron density measurements were employed to characterize the properties of the large amplitude structures and identify the relevant physical process. Minimum variance analysis, theoretical shock descriptions, coherency analysis, and singular value decomposition were used to study the properties of the higher frequency waves to compare and identify the wave mode. Results. The non-planar features of the bow shock are consistent with shock rippling and/or large amplitude whistler waves. Higher frequency waves are identified as whistler-mode waves, but their properties across the shock imply they may be generated by electron beams and temperature anisotropies. Conclusions. The Venus bow shock at a moderately high Mach number (∼5) in the quasi-perpendicular regime exhibits complex features similar to the Earth’s bow shock at comparable Mach numbers. The study highlights the need to be able to distinguish between large amplitude waves and spatial structures such as shock rippling. The simultaneous high frequency observations also demonstrate the complex nature of energy dissipation at the shock and the important question of understanding cross-scale coupling in these complex regions. These observations will be important to interpreting future planetary missions and additional gravity assist maneuvers.

Broadening of cyclotron resonance conditions in the relativistic interaction of an intense laser with overdense plasmas.

The interaction of dense plasmas with an intense laser under a strong external magnetic field has been investigated. When the cyclotron frequency for the ambient magnetic field is higher than the laser frequency, the laser's electromagnetic field is converted to the whistler mode that propagates along the field line. Because of the nature of the whistler wave, the laser light penetrates into dense plasmas with no cutoff density, and produces superthermal electrons through cyclotron resonance. It is found that the cyclotron resonance absorption occurs effectively under the broadened conditions, or a wider range of the external field, which is caused by the presence of relativistic electrons accelerated by the laser field. The upper limit of the ambient field for the resonance increases in proportion to the square root of the relativistic laser intensity. The propagation of a large-amplitude whistler wave could raise the possibility for plasma heating and particle acceleration deep inside dense plasmas.

ON THE CONNECTION BETWEEN MICROBURSTS AND NONLINEAR ELECTRONIC STRUCTURES IN PLANETARY RADIATION BELTS

ABSTRACT Using a dynamical-system approach, we have investigated the efficiency of large-amplitude whistler waves for causing microburst precipitation in planetary radiation belts by modeling the microburst energy and particle fluxes produced as a result of nonlinear wave–particle interactions. We show that wave parameters, consistent with large-amplitude oblique whistlers, can commonly generate microbursts of electrons with hundreds of keV-energies as a result of Landau trapping. Relativistic microbursts (>1 MeV) can also be generated by a similar mechanism, but require waves with large propagation angles θ kB > 50 ° ?> and phase-speeds v Φ ≥ c / 9 ?> . Using our result for precipitating density and energy fluxes, we argue that holes in the distribution function of electrons near the magnetic mirror point can result in the generation of double layers and electron solitary holes consistent in scales (of the order of Debye lengths) to nonlinear structures observed in the radiation belts by the Van Allen Probes. Our results indicate a relationship between nonlinear electrostatic and electromagnetic structures in the dynamics of planetary radiation belts and their role in the cyclical production of energetic electrons ( E ≥ 100 ?> keV) on kinetic timescales, which is much faster than previously inferred.

Electron scattering and nonlinear trapping by oblique whistler waves: The critical wave intensity for nonlinear effects

In this paper, we consider high-energy electron scattering and nonlinear trapping by oblique whistler waves via the Landau resonance. We use recent spacecraft observations in the radiation belts to construct the whistler wave model. The main purpose of the paper is to provide an estimate of the critical wave amplitude for which the nonlinear wave-particle resonant interaction becomes more important than particle scattering. To this aim, we derive an analytical expression describing the particle scattering by large amplitude whistler waves and compare the corresponding effect with the nonlinear particle acceleration due to trapping. The latter is much more rare but the corresponding change of energy is substantially larger than energy jumps due to scattering. We show that for reasonable wave amplitudes ∼10–100 mV/m of strong whistlers, the nonlinear effects are more important than the linear and nonlinear scattering for electrons with energies ∼10–50 keV. We test the dependencies of the critical wave amplitude on system parameters (background plasma density, wave frequency, etc.). We discuss the role of obtained results for the theoretical description of the nonlinear wave amplification in radiation belts.

The importance of amplitude modulation in nonlinear interactions between electrons and large amplitude whistler waves

The effects of amplitude modulation on nonlinear interactions between a parallel propagating whistler wave and electrons in a dipole field are investigated in this work using a test particle code. Here we first use the test particle simulation to validate a previous single-wave nonlinear theory. Then we adopt a simple two-wave model to represent the recently observed amplitude modulation of a whistler wave field. By varying the frequency spacing between the two waves, we investigate the effects of different modulation frequencies on the nonlinear interactions. We demonstrate that when the resonance overlap condition is satisfied, the resulting change in the electron pitch angle and energy could be very different from what has been predicted by ideal single-wave nonlinear theories. Using a previously observed probability distribution of the subpacket modulation frequency of a chorus event, we obtain the probability distribution of different types of electron response. Our results indicate that the observed subpacket distribution produces particle responses in both non-overlapping and overlapping regimes. Our results suggest that the observed amplitude modulation should be considered when quantitatively treating interactions between electrons and recently observed large amplitude whistler waves or chorus waves.

Large-amplitude whistler waves and electron acceleration

[1] A recent observation shows that large-amplitude whistler waves propagating obliquely with respect to the ambient magnetic field may be responsible for energizing the radiation belt electrons to relativistic energies (MeV) within a time scale as short as a fraction of a second. Test-particle simulations available in the literature invariably adopt simple model wave forms for the oblique whistlers, such that rigorous analysis of these waves have not been performed to this date. The present Letter solves fully nonlinear cold electron fluid equation for obliquely propagating large-amplitude whistlers. Relativistic test particle simulation is then performed over these exact wave solutions, and it is shown that a population of initially low energy electrons can be accelerated to (10) MeV energies, within a few seconds time scale.

Physics of neutralization of intense high-energy ion beam pulses by electrons

Neutralization and focusing of intense charged particle beam pulses by electrons form the basis for a wide range of applications to high energy accelerators and colliders, heavy ion fusion, and astrophysics. For example, for ballistic propagation of intense ion beam pulses, background plasma can be used to effectively neutralize the beam charge and current, so that the self-electric and self-magnetic fields do not affect the ballistic propagation of the beam. From the practical perspective of designing advanced plasma sources for beam neutralization, a robust theory should be able to predict the self-electric and self-magnetic fields during beam propagation through the background plasma. The major scaling relations for the self-electric and self-magnetic fields of intense ion charge bunches propagating through background plasma have been determined taking into account the effects of transients during beam entry into the plasma, the excitation of collective plasma waves, the effects of gas ionization, finite electron temperature, and applied solenoidal and dipole magnetic fields. Accounting for plasma production by gas ionization yields a larger self-magnetic field of the ion beam compared to the case without ionization, and a wake of current density and self-magnetic field perturbations is generated behind the beam pulse. A solenoidal magnetic field can be applied for controlling the beam propagation. Making use of theoretical models and advanced numerical simulations, it is shown that even a small applied magnetic field of about 100 G can strongly affect the beam neutralization. It has also been demonstrated that in the presence of an applied magnetic field the ion beam pulse can excite large-amplitude whistler waves, thereby producing a complex structure of self-electric and self-magnetic fields. The presence of an applied solenoidal magnetic field may also cause a strong enhancement of the radial self-electric field of the beam pulse propagating through the background plasma. If controlled, this physical effect can be used for optimized beam transport over long distances.

Whistler wave excitation and effects of self-focusing on ion beam propagation through a background plasma along a solenoidal magnetic field

This paper extends studies of ion beam transport through a background plasma along a solenoidal magnetic field by Kaganovich et al. [Phys. Plasmas 15, 103108 (2008)] to the important regime of moderate magnetic field strength satisfying ωce>2βbωpe. Here, ωce and ωpe are the electron cyclotron frequency and electron plasma frequency, respectively, and βb=vb/c is the directed ion beam velocity normalized to the speed of light. The electromagnetic field perturbations excited by the ion beam pulse in this regime are calculated analytically and verified by comparison with the numerical simulations. The degrees of beam charge neutralization and current neutralization are estimated, and the transverse component of the Lorentz force associated with the excited electromagnetic field is calculated. It is found that the plasma response to the ion beam pulse is significantly different depending on whether the value of the solenoidal magnetic field is below or above the threshold value specified by ωcecr=2βbωpe, and corresponding to the resonant excitation of large-amplitude whistler waves. The use of intense whistler wave excitations for diagnostic purposes is also discussed.

Whistler wave stabilization/destabilization of drift waves in a plasma cylinder

The nonlinear coupling of a large amplitude whistler wave with low frequency drift waves in an inhomogeneous magnetized plasma cylinder is investigated. The coupling produces whistler wave sidebands. The pump and sidebands exert a ponderomotive force on electrons causing a frequency shift in the drift wave, leading to its stabilization/destabilization, depending on the relative wave numbers of the interacting waves as well as with whistler pump power. The whistler wave stabilizes the drift wave for K0z < 2.9 × 102 and destabilizes for K0z > 2.9 × 102, with K0z = k0zc/ωci, where k0z is the wave number of the whistler pump, c is the velocity of light and ωci is the ion cyclotron frequency. The whistler pump power above 5 MW also stabilizes the drift wave.

Confirmation of quasi‐perpendicular shock reformation in two‐dimensional hybrid simulations

Shock reformation involves regions of a shock undergoing periodic collapse and redevelopment on a time scale close to the ion cyclotron period. Reformation is often observed in one‐dimensional (1‐D) hybrid and particle in cell (PIC) simulations of quasi‐perpendicular collisionless shocks provided the Alfvén Mach number MA and ion plasma beta βi are sufficiently high and low, respectively. Initial 2‐D PIC simulations showed some evidence for shock reformation, with ion reflection providing the main energy dissipation mechanism, while recent spacecraft observations showed a reforming shock with large amplitude whistler waves in the foot region. While recent spacecraft observations showed an case with reforming shock crossing with whistler waves dominated in the foot region. However, recent 2‐D hybrid and PIC simulations suggest that reformation does not occur in exactly perpendicular 2‐D shocks. This paper re‐examines shock reformation in quasi‐perpendicular shocks using 1‐D and 2‐D hybrid simulations. We find that 2‐D quasi‐perpendicular shocks (θbn = 85°) indeed undergo cyclic reformation providing MA and βi are high and low enough, respectively. For low MA ≤ 4, 2‐D quasi‐perpendicular shocks are found to be quasi‐stationary, despite 1‐D simulations predicting reformation, confirming and extending recent work for perpendicular 2‐D shocks. The dynamics of reformation are quite different in 2‐D than in 1‐D: in 2‐D large amplitude whistler waves grow in the shock foot, have amplitudes of order the downstream magnetic field, and affect the reformation. The whistlers have almost zero phase speeds in the shock frame and oblique wave vectors with respect to the upstream magnetic field. The predicted reformation period increases in 2‐D compared with 1‐D and increases nonlinearly as MA decreases towards the reformation threshold.

Emission of nonlinear whistler waves at the front of perpendicular supercritical shocks: Hybrid versus full particle simulations

New behavior of strictly perpendicular shocks in supercritical regime is analyzed with the help of both two‐dimensional (2‐D) hybrid and full particle electromagnetic simulations. Surprisingly, in both simulation cases, the shock front region appears to be dominated by emission of coherent large amplitude whistler waves for some plasma conditions and shock regimes. These whistler waves are oblique with respect to the shock normal as well as to the upstream magnetic field and are phase‐standing in the shock rest frame. A parametric study shows that these whistler waves are emitted in 2‐D perpendicular shocks and, simultaneously, the self‐reformation of the shock front associated with reflected ions disappears; the 2‐D shock front is almost quasi‐stationary. In contrast, both corresponding one‐dimensional (1‐D) hybrid and full particle simulations performed in similar plasma and Mach regime conditions show that the self‐reformation takes place for 1‐D perpendicular shock. These results indicate that the emission of these 2‐D whistler waves can inhibit the self‐reformation in 2‐D shocks. Possible generating mechanisms of these waves emissions and comparison with previous works are discussed.

Amplification of Whistler Waves for the Precipitation of Trapped Relativistic Electrons in the Magnetosphere

Energetic electrons trapped in the radiation belts undergo bounce motion about the geomagnetic equator. The behaviors of the trajectories of these electrons interacting with a large amplitude whistler wave are explored, with the electron energy and wave amplitude as variable parameters. A surface of section technique is used to examine the chaoticity of the system graphically. The wave amplitude required causing an electron trajectory to become chaotic decreases with increasing electron energy. Once the trajectory of an electron becomes chaotic, it can wander into the loss cone and subsequently precipitates into the ionosphere and/or the upper atmosphere. This chaotic scattering process requires a threshold field for the commencement of chaotic behavior in the electron trajectories. Therefore, a loss-cone negative mass instability process to amplify whistler waves by electrons in the bulk of the energy distribution is also studied. The numerical results show that the injected whistler waves can be amplified by more than 20 dB, agreeing with the experimental results. This amplification process reduces considerably the required field intensity of injected whistler wave for the purpose of precipitating those tail electrons in the megaelectronvolt range.

Electron precipitation caused by chaotic motion in the magnetosphere due to large‐amplitude whistler waves

In the magnetosphere, energetic electrons in the radiation belts are trapped by Earth's magnetic field and undergo bounce motion about the geomagnetic equator. When a large‐amplitude whistler wave is present, the motion of the electrons becomes perturbed. It is shown that the nonlinear interaction due to the spatial dependence of the field quantities causes the motion of some of the trapped particles to become chaotic. Contrary to considering a gyroresonant interaction, this chaotic scattering does not have a directional preference and may therefore offer a plausible explanation of the simultaneous observation of the electron precipitation into the upper atmosphere at geomagnetically conjugate regions due to a single lightning flash [Burgess and Inan, 1990]. After simplifying the dipole configuration of the geomagnetic field, a Hamiltonian formulation is used to study the dynamics of a single, trapped electron on the L = 3 shell, subjected to a large amplitude 13.7 kHz whistler wave. A canonical transformation is introduced to remove the time dependence from the test electron's Hamiltonian. The chaotic behavior of the electron motion is investigated with surface of section and Lyapunov exponent techniques. To show that this chaotic behavior can lead to particle precipitation, the temporal evolution of the equatorial pitch angle of the electron is computed. Considering electrons with an initial pitch angle of 88°, the results are found to be qualitatively independent of the bounce frequency. They show that the equatorial pitch angle of a chaotic electron varies wildly and often dips below 25°, the minimum loss cone angle one would expect to find for a charged particle in the magnetosphere. Therefore the electrons may escape the geomagnetic trap and be precipitated into the upper atmosphere.

Excitation of whistler waves driven by an electron temperature anisotropy

A 3-D particle simulation of excitation of whistler waves driven by an electron temperature anisotropy (T ⊥ > T ∥) is presented. Results show that whistler waves can have appreciable growth driven by the anisotropy. The maximum intensity of the excited whistler waves increases as a quadratic function of the anisotropy. Due to the presence of a threshold, one needs a relatively large electron temperature anisotropy above threshold to generate large-amplitude whistler waves. The average amplitude of turbulence in the context of whistler waves is up to as large as about 1% of the ambient magnetic field when T ⊥/T ∥. The total energy density of the whistler turbulence is adequate for production of relativistic electrons in solar flares through stochastic acceleration.

Quasi-parallel collisionless shocks

The magnetic field and plasma data from the ISEE 1, 2, and 3 spacecraft have greatly increased our knowledge of the quasi-parallel collisionless shock in space. Hybrid-code simulations have provided us with valuable insights into the physics of the quasi-parallel shock. Unfortunately, theoretical understanding of the nonlinear physics of the quasi-parallel shock is still in a qualitative stage of development. Generation of large-amplitude whistler waves and hydromagnetic waves observed in the quasi-parallel shock has been discussed either in terms of linear instabilities or qualitative nonlinear arguments. It appears that the ion reflection, ion heating, and leakage of the shock-heated downstream ions at the quasi-parallel shock can all be explained in terms of nonadiabatic scatterings of ions by the large-amplitude whistler-magnetosonic waves with frequencies near the ion gyrofrequency and wavelength near the ion inertial length. The nonadiabatic scattering is defined by the non-conservation of the magnetic moment. Future study of the quasi-parallel shock should focus on developing quantitative theoretical models for the nonlinear physical processes fundamental to the quasi-parallel shock.

Parametric decay of a whistler wave at the difference frequency of two electromagnetic waves in a plasma

A large-amplitude whistler wave excited at the difference frequency of two high-frequency electromagnetic pump waves is shown to decay parametrically into a lower-hybrid wave (LHW) and a low-frequency ion–Bernstein wave (IBW) in a collisionless magnetized multi-ion-species plasma,. A nonlinear dispersion relation describing this parametric interaction process is derived. The low-frequency ponderomotive force along the direction of the external magnetic field leads to the dominant coupling. Possible applications to ion heating in the ionosphere, in the earth's magnetosphere and in laboratory plasmas are discussed.

Test particle simulation study of whistler wave packets observed near comet Giacobini‐Zinner

In order to study nonlinear interactions of water group ions with large amplitude whistler wave packets detected at the leading edge of steepened magnetosonic waves observed near comet Giacobini‐Zinner, we carried out test particle simulations of water ion interactions with a model wave based on the G‐Z data. As the model wave, we adopted a linearly polarized magnetosonic (MS) wave as the trailing portion of the wave, and circularly polarized whistler waves in the leading edge of the wave. Both the MS and whistler waves are a priori assumed to have large amplitudes. We found that some of the water ions are decelerated in the steepened portion of the magnetosonic wave to the resonance velocity with the whistler wave packets. Through resonance and related nonlinear interaction with the large amplitude whistler waves, the water ions become trapped by the whistler wave packet. An energy balance calculation demonstrates that the trapped ions do lose their kinetic energy during the trapped motion in the whistler wave packet. It is thus demonstrated that the nonlinear trapping motion in the wave structure leads to the effective energy transfer from the water group ions to the whistler wave packets in the leading edge of the steepened MHD waves.