Magnetosonic Research Articles

Two-dimensional cylindrical magnetosonic shock waves in a relativistic degenerated plasma

Abstract In this paper, the characteristics of two-dimensional magnetosonic (MS) shock waves have been studied in a nonplanar relativistic degenerate collisional magnetoplasma whose constituents are non-degenerate warm ions and relativistic degenerated electrons. Employing fluid model equations for such plasma along with Maxwell equations, a set of magnetohydrodynamic (MHD) model equations is obtained. Based on the newly obtained MHD equations, a Burgers–Kadomstev–Petviashvili (Burger–KP) equation (which describes shock wave structures) is derived in cylindrical geometry using the reductive perturbation technique. The considered plasma system was investigated under the impacts of spin-magnetization, relativistic degeneracy, cylindrical geometry, and dissipation. Numerical results revealed that the relativistic degeneracy, dissipation, and electron spin-magnetization as well as nonplanar geometry significantly altered the MS shock wave properties. Interestingly, it is found that there is a change in the shock nature and emergence of new structures due to the influences of both transverse perturbation and cylindrical geometry. The implications of our investigation may be applicable to dense astrophysical environments, particularly neutron stars, and white dwarfs at which the relativistic degenerated electrons are existed.

Magnetosonic Waves Excited by Maxwellian Ring Protons in Space Plasma Environment

A comprehensive theoretical model for a homogeneous plasma system of hot, tenuous Maxwellian ring-distributed protons and the cold background of Maxwellian ions and electrons is used to study the resonant instabilities of magnetosonic (MS) waves. The perpendicular velocity integrals associated with the Maxwellian ring distribution have no analytical solution, hence, are solved numerically, while the parallel velocity integrals are solved analytically by invoking series expansion of the plasma dispersion function. For the plasma parameters relevant to Earth’s inner magnetosphere, the theoretical model generates MS waves with frequencies from 5 times the local proton cyclotron frequency to above the lower hybrid frequency for a propagation angle of 89.5°. Hydrogen (H+) band electromagnetic ion cyclotron waves are also excited by the Maxwellian ring protons for the same set of plasma parameters. A detailed analysis reveals that a sufficiently large ring velocity, as well as a smaller perpendicular and parallel thermal velocity, can enhance the MS wave growth. The study also explores the role of background plasma parameters in modulating the waves. The present theoretical model reproduces the harmonics of the MS waves observed by the Van Allen Probes in the Earth’s inner magnetosphere. Further, the model can generate MS waves in other plasma environments, e.g., Mars, where the presence of ring protons has been established by MAVEN in connection with the MS wave observations.

Reflection Coefficient for Two‐Dimensional Propagation of Fast Magnetosonic Waves Emerging One‐Dimensional Mesoscale Density Boundaries

AbstractIn recent studies, two‐dimensional propagation model of fast magnetosonic (MS) waves has been proposed to interpret the satellite observations of MS waves knocking into a density boundary. Although the theoretical model is able to capture the main properties of the two‐dimensional propagation of MS waves, quantitative description about the MS wave behaviors has not been given yet. Here, with the assumption of a parabolic function for the potential function near its minimum, we solve the wave equation only with a potential function to obtain the reflection coefficients. It is found that the wave equation with a potential function can describe the full reflection and full transmission of MS waves rather well. Furthermore, the first‐order derivative term in the wave equation is utilized to modify the reflection coefficient when the minimum of the potential function is near zero. Our result is helpful for further understanding the two‐dimensional propagation of MS waves.

The effects of plasma density structure on the propagation of magnetosonic waves: 1-D particle-in-cell simulations

Magnetosonic (MS) waves, i.e., ion Bernstein mode waves, are one of the common plasma waves in the Earth’s magnetosphere, which are important for regulating charged particle dynamics. How MS waves propagate in the magnetosphere is critical to understanding the global distribution of the waves, but it remains unclear. Although previous studies present that MS waves can be reflected by fine-scale density structures, the dissipation of waves by background plasma has long been neglected. In this study, we perform one-dimensional (1-D) particle-in-cell (PIC) simulations to study the propagation of MS waves through density structures, where both absorption and reflection have been included. We find that absorption is as important as reflection when considering the propagation of MS waves through density structures, and both of them are strongly dependent on the shape of density structures. Specifically, the reflectivity of MS waves is positively and negatively correlated with the height and width of density structures, respectively, while the absorptivity of MS waves has a positive correlation with both the height and width of density structures. Our study demonstrates the significance of absorption during the propagation of MS waves, which may help better understand the distribution of MS waves in the Earth’s magnetosphere.

Migration of Fast Magnetosonic Waves in the Magnetosphere With a Plasmaspheric Plume

AbstractPlasmaspheric density structures are considered to control the propagation trajectories of fast magnetosonic (MS) waves in the inner magnetosphere. However, whether the plasmaspheric plume can effectively alter the propagation of MS waves remains unknown. Based on the analytical model of plasma density, ray tracing simulations are performed to investigate the propagation of exactly perpendicular MS waves in the equatorial plane in the magnetosphere containing a plasmaspheric plume. We find that plasmatrough and plume MS waves propagating toward the plasmaspheric plume can be reflected into the plasmaspheric core by the plume, then potentially migrating globally and thus quasi‐trapped inside the plasmaspheric core. The simulations also indicate that lower‐frequency MS waves approaching the plasmaspheric plume are more easily reflected and quasi‐trapped inside the plasmaspheric core. Our findings illustrate a previously unexplored way that plasmatrough MS waves could access and be trapped inside the plasmaspheric core via azimuthal plasmaspheric density structures.

Characterization of Turbulent Fluctuations in the Sub-Alfvénic Solar Wind

Parker Solar Probe (PSP) observed sub-Alfvénic solar wind intervals during encounters 8–14, and low-frequency magnetohydrodynamic (MHD) turbulence in these regions may differ from that in super-Alfvénic wind. We apply a new mode decomposition analysis to the sub-Alfvénic flow observed by PSP on 2021 April 28, identifying and characterizing entropy, magnetic islands, forward and backward Alfvén waves, including weakly/nonpropagating Alfvén vortices, forward and backward fast and slow magnetosonic (MS) modes. Density fluctuations are primarily and almost equally entropy- and backward-propagating slow MS modes. The mode decomposition provides phase information (frequency and wavenumber k) for each mode. Entropy density fluctuations have a wavenumber anisotropy of k ∥ ≫ k ⊥, whereas slow-mode density fluctuations have k ⊥ > k ∥. Magnetic field fluctuations are primarily magnetic island modes (δ B i ) with an O(1) smaller contribution from unidirectionally propagating Alfvén waves (δ B A+) giving a variance anisotropy of 〈δBi2〉/〈δBA2〉=4.1 . Incompressible magnetic fluctuations dominate compressible contributions from fast and slow MS modes. The magnetic island spectrum is Kolmogorov-like k⊥−1.6 in perpendicular wavenumber, and the unidirectional Alfvén wave spectra are k∥−1.6 and k⊥−1.5 . Fast MS modes propagate at essentially the Alfvén speed with anticorrelated transverse velocity and magnetic field fluctuations and are almost exclusively magnetic due to β p ≪ 1. Transverse velocity fluctuations are the dominant velocity component in fast MS modes, and longitudinal fluctuations dominate in slow modes. Mode decomposition is an effective tool in identifying the basic building blocks of MHD turbulence and provides detailed phase information about each of the modes.

A Statistical Study of Quasi‐Electrostatic Magnetosonic Waves

AbstractQuasi‐electrostatic magnetosonic (QEMS) waves have been recently reported, referring to a distinct type of magnetosonic (MS) wave with only the electric fluctuation being detectable. Here a statistical study of QEMS waves is carried out with the Van Allen Probes data. 83% of 40,466 QEMS samples are observed with plasma density ne < 20 cm−3, and intense QEMS waves tend to appear in the lower density region. QEMS waves become strong in the case of more pronounced proton rings around 10 keV and larger suprathermal proton populations. High occurrence rates and large amplitudes of QEMS waves are confined near the dayside equator (|MLAT| < 3°). The wave frequencies are typically slightly below the nth harmonic of proton gyro‐frequency, and the wave intensity gradually decreases with an increasing harmonic number n. Our results further demonstrate that low plasma densities and abundant suprathermal protons are beneficial for intensifying QEMS waves and contribute to the establishment of QEMS wave model.

Analytical Approach to Two‐Dimensional Full Reflections of Fast Magnetosonic Waves Due To Mesoscale Density Boundaries

AbstractPropagation of fast magnetosonic (MS) waves in the equatorial plane has attracted a growing attention in recent studies. Although computer simulations including ray tracing, PIC, and full wave simulations have been utilized to study the propagation of MS waves, analytical approach is needed to investigate the physics insight. In this letter, we first derive the wave equations describing the two‐dimensional propagation of MS waves under the assumption that the mesoscale density inhomogeneity is only along one dimensional. After investigating the essential role of the potential function in the wave equation for the full reflection of MS waves, we find that full reflection can occur when the minimum potential is significantly negative. Finally, we have discussed the effects of incidence angles and wave frequencies on the full reflection. Our results show that MS waves with an incidence angle or wave frequency greater than the critical value would be fully reflected.

Effects of Cold Plasma on the Mode Conversion From Fast Magnetosonic Wave to Electromagnetic Ion Cyclotron Wave in the Inner Plasmasphere

AbstractPrevious studies show that fast magnetosonic (MS) wave with frequency of tens of Hz may propagate to low L‐shells (L < 2.0) in the inner plasmasphere and mode convert to electromagnetic ion cyclotron (EMIC) wave where its wave frequency is close to the local crossover‐cutoff‐resonance frequency triplet through different propagation paths. In this study, we investigate how this mode conversion process may depend on the ion composition and electron density by full‐wave simulation with various plasma density profiles and initial wave normal angles (WNAs) of incoming MS wave from magnetic equator and a higher latitude of 15°. We find that critical fraction of minority ion (He+ or M/Q = 2 ion − D+ or He++) exists during the mode conversion, over which the conversion from MS wave to H+ band right‐handedly polarized EMIC wave starts to become negligible. This critical fraction decreases with the incident WNA of MS wave from equator. The efficiency of this conversion process also decreases with the electron density. As incoming MS is from higher latitudes off equator, optimal fraction of minority ion exists, with which the efficiency of conversion from MS wave to H+ band left‐handedly polarized EMIC wave reaches a maximum. Moreover, this maximum conversion efficiency varies with the incident WNA and may approach 100% with WNA close to 90° at the magnetic latitude of 15°. We also find that localized wave structure may be formed when the converted H+ band EMIC wave is trapped between local H+ − D+(He++) bi‐ion resonance frequency and D+(He++) − He+ left‐handed polarization cut‐off frequency with a small M/Q = 2 ion fraction and a relatively larger He+ fraction as incoming MS wave is near equator.

Modeling the Propagation of Fast Magnetosonic Waves and Their Conversion to Electromagnetic Ion Cyclotron Waves at Low L Shells

AbstractThe propagation of fast magnetosonic (MS) waves from high to extremely low L shells and their conversion into electromagnetic ion cyclotron (EMIC) waves is investigated with a ray tracing model and a full‐wave model. The ray tracing simulations show that MS waves in the vicinity of the local crossover frequency at low L shells have a latitudinal range from to with wave normal angles from to , both of which provide the opportunity for their mode conversion to EMIC waves. Results from ray tracing are fed into the full‐wave model as initial conditions. The full‐wave simulations show that the incoming MS waves with small () and intermediate () wave normal angles may be efficiently converted to right‐handedly polarized band EMIC waves, which may be further converted to right‐handedly polarized band EMIC waves or to guided left‐handedly polarized band EMIC waves through bi‐ion resonance reflection and polarization reversal. With intermediate () or larger wave normal angles, via polarization reversal and left‐handed polarization cut‐off reflection, the incoming MS waves may be efficiently converted to guided left‐handedly polarized band EMIC waves and the optimal wave normal angles corresponding to the maximum conversion efficiencies decrease with magnetic latitudes. Our study verifies the mode conversion mechanism of MS waves to EMIC waves proposed with a previous ray tracing study and examines the dependence of the efficiency of the wave energy transfer on the magnetic latitudes and wave normal angles, which may help to understand the wave properties and distribution of MS and EMIC waves observed at extremely low L shells.

Simultaneous Observation of Whistler‐Mode Chorus and Fast Magnetosonic Waves During the Magnetic Peak in the Inner Magnetosphere

AbstractSimultaneous observations of whistler‐mode chorus and magnetosonic (MS) waves are reported within a magnetic peak in the inner magnetosphere for the first time. During the magnetic peak, Van Allen Probe A observes flux enhancements of both ring current electrons and relativistic electrons, while medium‐energy proton fluxes are reduced but high‐energy proton fluxes are raised. Those flux variations of ring current particles are almost concentrated in the perpendicular direction of the background magnetic field, leading to enhancements of the electron temperature anisotropy and a positive gradient of proton velocity distributions. The calculated linear growth rates show that unstable electrons with temperature anisotropic instabilities and unstable protons with ring distribution during the magnetic peak structure can provide free energy for the excitation of whistler‐mode chorus and MS waves, respectively. Our findings suggest that injected particles encountering the magnetic peak structure may form more complex unstable electron and ion distributions driving multiple instabilities simultaneously.

Expected EMIC Wave Generation and Unexpected MS Wave Disruption in a Magnetic Dip

AbstractMagnetic dip plays a potentially important role in the ring‐current‐radiation‐belt‐coupling. Here, we report a proton‐driven magnetic dip event accompanied by the expected generation of electromagnetic ion cyclotron (EMIC) wave and the unexpected disruption of fast magnetosonic (MS) wave observed by the Van Allen Probe B on 03 November 2015. The effect of magnetic dip on the EMIC wave generation and MS wave propagation is analyzed. The analysis of EMIC wave instability demonstrates that EMIC waves are more easily excited in the magnetic dip. Moreover, the cold plasma density shows a highly positive correlation with the magnetic field fluctuation, and they are closely related to the disappearance of MS wave during the magnetic dip structure, which is confirmed by theoretical estimation. Our results indicate that magnetic dip may play different roles in the activities of EMIC and MS waves, which has rarely been discussed before.

Scattering of Radiation Belt Electrons by Fast Magnetosonic Waves: Considering the Kinetic Effects

AbstractWhen assessing the scattering of radiation belt electrons by fast magnetosonic (MS) waves, it is traditionally assumed that the waves follow the MS/whistler branch of the cold plasma dispersion relation (CPDR) in magnetohydrodynamics. However, MS waves are essentially ion Bernstein modes following a distinct kinetic dispersion relation. This study calculates the MS wave‐induced electron diffusion rates with the kinetic dispersion relation for the first time and compares the results with that obtained with the CPDR. It is found that the kinetic effects lead to a lower minimum resonant energy around 100 eV and a broader resonant pitch angle range. Kinetic effects also result in power spectral density attenuation when transforming wave frequency spectra into wavenumber spectra, so the diffusion rates are overall smaller than the ones obtained using the CPDR. Our results demonstrate that kinetic effects can significantly affect the role that MS waves play in the radiation belt dynamics.

In Situ Observations of Lower Hybrid Drift Waves at the Inner Edge of the Ring Current by the Van Allen Probe‐A

AbstractIn the magnetosphere of the Earth, lower hybrid drift (LHD) waves effectively cause plasma diffusion and couple well to both electrons and ions. LHD waves have the characteristics of linear polarization and highly oblique propagation with frequencies near the lower hybrid resonance frequency, which is similar to the characteristics of high‐frequency magnetosonic (MS) waves. The existence of diamagnetic drift at the inner edge of the ring current provides free energy for the excitation of LHD waves, while the free energy to generate MS waves are provided by proton ring distribution. Here, we report on a typical case of LHD waves which was excited by LHD instability. Different from the global distribution of high‐frequency MS waves, statistical results indicate that most LHD waves have a uniform distribution over all MLTs except the noon sector inside the plasmapause. Besides, the occurrence of LHD waves reaches a maximum in the dusk sector outside the plasmapause.

Combined Scattering of Concurrent Unusual High‐Frequency EMIC Waves and MS Waves on Radiation Belt Electrons

AbstractWe report a concurrent event of unusual high‐frequency Electromagnetic ion cyclotron (EMIC) and Magnetosonic (MS) waves in correspondence with butterfly distributions for sub‐MeV electrons and flux decay of MeV electrons, observed by Van Allen Probe A on 16 October 2017. The scattering effects are quantitatively investigated by test particle simulations. The results indicate that the unusual EMIC waves mainly scatter electrons from hundreds of keV to several MeV at pitch angles <60° while the MS waves mainly influence sub‐MeV and MeV electrons at pitch angles >60°. Their combined scattering effects are suitably analyzed to be justified as the linear superposition of the effect induced by each wave mode. The Fokker‐Planck simulations exhibit the formation of butterfly pitch angle distributions for sub‐MeV electrons and the obvious flux decay for electrons ∼1.8 MeV at all pitch angles, showing similar variation trends to the observations. Our study suggests that the occurrence of the two waves can significantly influence the electrons over the whole pitch angle range, which can help us better understand the radiation belt dynamics.

A Statistical Study of Pancake Pitch Angle Distribution of Low‐Energy Protons and Their Correlation With Magnetosonic Waves

AbstractWe performed a statistical study of the proton pancake pitch angle distributions (PADs) at the energy from 10 to 300 eV with the Helium Oxygen Proton Electron instrument on board the Van Allen Probes. The occurrence rate of low energy proton pancake PADs and their dependence on the energy, L shell, magnetic local time (MLT) and AL* index are analyzed. The results indicate that: (a) the occurrence rate of pancake PADs decreases as the proton energy increases; (b) under active geomagnetic activities (AL* < −300 nT), pancake PADs preferentially occur in the dayside; (c) under weak geomagnetic activities (AL* > −100 nT), the occurrence rate of pancake PADs has little dependence on MLT. We further discuss the contribution of magnetosonic (MS) waves on the formation of proton pancake PADs at low energy. The strong correlation between the occurrence of pancake PADs and the appearance of MS waves indicates that MS waves contribute to the formation of low energy proton pancake PADs. Moreover, the proton diffusion coefficients caused by MS waves suggest that MS waves can cause the proton heating at low energies in high density regions.

Fast Magnetosonic Waves in a Dipolarizing Flux Bundle Inside the Geosynchronous Orbit

AbstractAlthough commonly observed in the inner magnetosphere, fast magnetosonic (MS) waves are often owe to be excited by those proton rings resulting from the so‐called energy‐dependent drift path of ring current protons. In this letter, we report an interesting MS wave event in a dipolarizing flux bundle (DFB) observed by the Van Allen Probe A. In the DFB, perpendicular proton fluxes are found depleted at low and intermediate energies, while enhanced at high energies, which should be attributed to proton accelerations by DFB. As a result, proton ring could be locally formed. Using the observed plasma environment parameters and the modeled proton distributions, we have calculated the linear growth rates for MS waves and found that these MS waves might be locally excited. Our results provide insight into the generation of MS waves in a DFB, and provide a new channel to excite MS waves in the inner magnetosphere.

Competitive Influences of Different Plasma Waves on the Pitch Angle Distribution of Energetic Electrons Inside and Outside Plasmasphere

AbstractBy analyzing the Van Allen Probe B observations and 2‐D simulations, we found that the competitive influences of different plasma waves on the pitch angle distribution of energetic electrons (hundreds of keV) depend on density of ambient plasmas and relative intensity of waves. In the high‐density plasmasphere (>70 cm−3), plasmaspheric hiss is able to effectively remove small pitch angle electrons (<60°), while the participation of intense magnetosonic (MS) waves merely increases part of large pitch angle electrons (>60°). The combined diffusions by the two waves create pancake‐like electron pitch angle distributions in the high‐density region. Outside the plasmapause, the same‐intensity MS waves and weak exohiss waves mainly reduce large pitch angle electrons and thus create butterfly‐like pitch angle distributions in the low‐density trough (<70 cm−3). These results indicate that energetic electrons could have different pitch angle distributions under similar wave environments but different plasma densities.

Global Distribution of Concurrent EMIC Waves and Magnetosonic Waves: A Survey of Van Allen Probes Observations

AbstractRecent studies have reported the simultaneous observation of Magnetosonic (MS) waves and Electromagnetic ion cyclotron (EMIC) waves. In this study, a detailed survey of the concurrent EMIC waves and MS waves is performed using the Van Allen Probes observations from 2012 to 2017. The results suggest that most of the concurrent EMIC waves and MS waves are H+ band EMIC waves and MS waves. The favorable geomagnetic conditions for the concurrent EMIC waves and MS waves are AE* ≥ 500 nT inside the plasmapause and AE* ≥ 100 nT outside the plasmapause. Although EMIC waves are generally stronger than MS waves, stronger MS waves than EMIC waves are more likely to occur during moderate and active geomagnetic times. Our study is consistent with the most recent research, and provides more detailed information that helps us to deepen our understanding of the concurrent EMIC waves and MS waves.

Simultaneous occurrence of four magnetospheric wave modes and the resultant combined scattering effect on radiation belt electrons

We report a representative concurrent event of four wave modes at <italic>L</italic> ≈ 5.0, including electrostatic electron cyclotron harmonic (ECH) waves, exohiss, magnetosonic (MS) waves, and electromagnetic ion cyclotron (EMIC) waves, based on the observations from Van Allen Probe A on October 15, 2015. The diffusion coefficients induced by these waves are calculated by using both the Full Diffusion Code and test particle simulations. Moreover, the scattering effects of these waves on energetic electrons are simulated by using a two-dimensional Fokker–Planck diffusion model. The results show that ECH waves mainly scatter low-pitch-angle (&lt; 20°) electrons at 0.1–10 keV; exohiss can significantly scatter hundreds of kiloelectron volt electrons to form a reversed energy spectrum; MS waves mainly affect high-pitch-angle electrons (&gt; 60°); and EMIC waves scatter only &gt; 5 MeV electrons. The combined scattering effects of exohiss and MS waves are stronger than those of exohiss alone. The top-hat pitch angle distributions produced by exohiss are relaxed after adding the effect of MS waves. Because the energies of electrons scattered by ECH waves and EMIC waves are much lower and higher than those scattered by exohiss and MS waves, respectively, the combined scattering effects with the addition of ECH and EMIC waves show little difference from the results for the combination of MS waves and exohiss. These results suggest that distinct wave modes can occur simultaneously and scatter electrons in combination or individually, which requires careful consideration in future global simulations of the complex dynamics of radiation belt energetic electrons.