Bernstein Modes Research Articles

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.

Plasma wave propagation conditions analysis using the warm multi-fluid model

Although an accurate description of wave propagation and absorption in plasmas requires complicated full-wave solutions or kinetic simulations, local dispersion analysis can still be helpful to capture the main physics of wave properties. Plasma wave propagation conditions or accessibility informs whether a wave can propagate to a region, which usually depends on the wave frequency, wave vector, the local plasma density, and magnetic field. We demonstrate a warm multi-fluid eigenvalue model and a matrix approach to rapidly calculate plasma wave accessibility diagrams, where thermal effects are also included via an isotropic pressure term. All cold plasma waves, from high-frequency electron cyclotron waves, intermediate-frequency lower hybrid waves, to low-frequency ion cyclotron waves, are presented. By comparing with the kinetic model, it is interesting to find that the warm multi-fluid model, though incapable of reproducing the Bernstein modes, can provide a quick way to determine whether thermal effects are important.

Evaluation of Particle Scattering by Oxygen Ion Cyclotron Harmonic Waves in the Inner Magnetosphere

AbstractThe scattering of charged particles by oxygen ion cyclotron harmonic (OCH) waves in the inner magnetosphere is investigated by evaluating the relevant quasi‐linear diffusion coefficients. Recent studies demonstrated that OCH waves are oxygen ion Bernstein modes and their complex kinetic dispersion relation has made it challenging to assess their role in scattering charged particles. The present study calculates the quasi‐linear diffusion coefficients for the scattering of electrons and ions by OCH waves using their kinetic dispersion relation. The results show that OCH waves can effectively scatter electrons between ∼100 eV and 100s keV via Landau resonance. They are also capable of heating cold helium and oxygen ions through cyclotron resonances. Specially, it is found that the 4th harmonic of OCH waves can lead to effective heating of helium ions, while oxygen ions would interact more efficiently with lower harmonics of OCH waves.

Particle-in-cell simulations of electron–positron cyclotron maser forming pulsar radio zebras

Context. The microwave radio dynamic spectra of the Crab pulsar interpulse contain fine structures represented via narrowband quasiharmonic stripes. The pattern significantly constrains any potential emission mechanism. Similar to the zebra patterns observed, for example, in type IV solar radio bursts or decameter and kilometer Jupiter radio emission, the double plasma resonance (DPR) effect of the cyclotron maser instability may allow for interpretion of observations of pulsar radio zebras. Aims. We provide insight at kinetic microscales of the zebra structures in pulsar radio emissions originating close to or beyond the light cylinder. Methods. We present electromagnetic relativistic particle-in-cell (PIC) simulations of the electron–positron cyclotron maser for cyclotron frequency smaller than the plasma frequency. In four distinct simulation cycles, we focused on the effects of varying the plasma parameters on the instability growth rate and saturation energy. The physical parameters were the ratio between the plasma and cyclotron frequency, the density ratio of the “hot” loss-cone to the “cold” background plasma, the loss-cone characteristic velocity, and comparison with electron–proton plasma. Results. In contrast to the results obtained from electron–proton plasma simulations (for example, in solar system plasmas), we find that the pulsar electron–positron maser instability does not generate distinguishable X and Z modes. On the contrary, a singular electromagnetic XZ mode was generated in all studied configurations close to or above the plasma frequency. The highest instability growth rates were obtained for the simulations with integer plasma-to-cyclotron frequency ratios. The instability is most efficient for plasma with characteristic loss-cone velocity in the range vth = 0.2 − 0.3c. For low density ratios, the highest peak of the XZ mode is at double the frequency of the highest peak of the Bernstein modes, indicating that the radio emission is produced by a coalescence of two Bernstein modes with the same frequency and opposite wave numbers. Our estimate of the radiative flux generated from the simulation is up to ∼30 mJy from an area of 100 km2 for an observer at 1 kpc distance without the inclusion of relativistic beaming effects, which may account for multiple orders of magnitude.

Shear Bernstein modes in a two-dimensional electron liquid

Shear Bernstein modes in a two-dimensional electron liquid

Oblique Bernstein wave propagation in electron‐ion plasma with electron quantization effects

AbstractWe have studied the role of electron quantization effects on the dispersion characteristics of the oblique electron Bernstein wave (EBW) in an electron‐ion plasma using Vlasov‐Poisson model. Our analysis shows that large thermal effects (as compared to quantization effects) give rise to the usual classical results while in the limit of strong magnetic field, the dispersion characteristics changes. The existence of a quantum Bernstein mode has been proposed which appears purely due to the electron quantization effects. The damping of the oblique EBW has also been analyzed in detail and we found that the magnitude of the damping of the wave decreases as we decrease the obliqueness parameter (parallel to perpendicular wavenumber ratio) which agrees with the earlier theoretical and experimental findings. Moreover, the strong quantization effects () also tend to suppress the damping of EBW which contributes to the stabilization of the waves. The present findings are relevant to the laboratory laser‐produced plasmas where strong external magnetic fields exist, and also to the dense astrophysical plasma environments.

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.

Electron distribution-controlled electron cyclotron harmonic wave generation in the magnetosphere

Electron cyclotron harmonic (ECH) waves, contributing significantly to magnetospheric dynamics, usually appear as a series of harmonics between the multiples of electron gyrofrequency. Previous studies have demonstrated that ECH waves are the electron Bernstein mode excited by the electron loss cone distribution. To investigate how the electron distribution controls the frequency and wave normal angle of excited ECH waves, we derive a concise analytic formula for ECH growth rates using the bi-Maxwellian distribution. Parametric studies show that the expansion of the loss cone size could effectively enlarge ECH growth rates and move the peak growth rates to a smaller wave number k (higher frequency) region, while the deepening of the loss cone can only increase the growth rates. It is also found that the growth rate pattern in the k space exhibits different trends on the two sides of 1.5 fce because the dominant resonance orders on the two sides are different. This study further develops our understanding of the generation mechanism of ECH waves.

Dynamic structure factor and excitation spectrum of the one‐component plasma: The case of weak to moderate magnetization

AbstractMagnetized plasmas are well known to exhibit a rich spectrum of collective modes. Here, we focus on the density modes in dense or cold plasmas, where strong coupling effects alter the mode spectrum known from traditional weakly coupled plasmas. In particular, we study the dynamic structure factor (DSF) of the magnetized one‐component plasma with molecular dynamics simulations. Extending our previous results (H. Kählert and M. Bonitz, Phys. Rev. Research 2022, 4, 013197), it is shown that Bernstein modes can be observed in the weakly magnetized regime, where they are found below the upper hybrid frequency, provided the coupling strength is sufficiently low. We investigate the DSF for a variety of different wave numbers and plasma parameters and show that even small magnetization can give rise to a strong zero‐frequency mode perpendicular to the magnetic field and change the dispersion as well as the damping of the upper hybrid mode.

Ballistic-to-hydrodynamic transition and collective modes for two-dimensional electron systems in magnetic field

The recent demonstrations of viscous hydrodynamic electron flow in two-dimensional electron systems poses serious questions to the validity of existing transport theories, including the ballistic model, the collision-induced and collisionless hydrodynamics. While the theories of transport at hydrodynamic-to-ballistic crossover for free 2d electrons are well established, the same is not true for electrons in magnetic fields. In this work, we develop an analytically solvable model describing the transition from ballistic to hydrodynamic transport with changing the strength of electron-electron collisions in magnetic fields. Within this model, we find an expression for the high-frequency non-local conductivity tensor of 2d electrons. It is valid at arbitrary relation between frequency of external field $\omega$, the cyclotron frequency $\omega_c$, and the frequency of e-e collisions $\tau^{-1}_{ee}$. We use the obtained expression to study the transformation of 2d magnetoplasmon modes at hydrodynamic-to-ballistic crossover. In the true hydrodynamic regime, $\omega\tau_{ee} \ll 1$, the 2DES supports a single magnetoplasmon mode that is not split at cyclotron harmonics. In the ballistic regime, $\omega\tau_{ee} \gg 1$, the plasmon dispersion develops splittings at cyclotron harmonics, forming the Bernstein modes. A formal long-wavelength expansion of kinetic equations ("collisionless hydrodynamics") predicts the first splitting of plasmon dispersion at $\omega\approx 2\omega_c$. Still, such expansion fails to predict the zero and negative group velocity sections of true magnetoplasmon dispersion, for which the full kinetic model is required.

Narrowband Spikes Observed During the 13 June 2012 Flare in the 800 – 2000 MHz Range

Narrowband (∼5 MHz) and short-lived (∼0.01 s) spikes with three different distributions in the 800 – 2000 MHz radio spectrum of the 13 June 2012 flare are detected and analyzed. We designate them as SB (spikes distributed in a broad band or bands), SZ (spikes distributed in zebra-like bands) and SBN (spikes distributed in broad and narrow bands). On analyzing AIA/SDO images of the active region NOAA 11504, a rough correspondence between groups of the spikes observed at 1000 MHz and peaks in the time profiles of AIA channels taken from the flare subarea close to the leading sunspot is found. Among the types of spikes the SZ type is the most interesting because it resembles zebras. Therefore, using autocorrelation and crosscorrelation methods we compare SZ and SBN spikes with the typical zebra observed in the same frequency range. While the ratio of SZ band frequencies with their frequency separation (220 MHz) is about 4, 5, and 6, in the zebra the frequency stripe separation is about 24 MHz and the ratio is around 50. Moreover, the bandwidth of SZ bands, which consists of clouds of narrowband spikes, is much broader than that of zebra stripes. This comparison indicates that SZ spikes are generated in a different way from the zebra, but in a similar way to SBN spikes. We successfully fit the SZ band frequencies by the Bernstein modes. Based on this fitting we interpret SZ and SBN spikes as those generated in the model of Bernstein modes. Thus, the magnetic field and plasma density in the SZ spike source are estimated to be about 79 G and 8.4 × 109 cm−3, respectively.

Dynamic structure factor of the magnetized one-component plasma: Crossover from weak to strong coupling

Plasmas in strong magnetic fields have been mainly studied in two distinct limiting cases---that of weak and strong nonideality with very different physical properties. While the former is well described by the familiar theory of Braginskii, the latter regime is closer to the behavior of a Coulomb liquid. Here we study in detail the transition between both regimes. We focus on the evolution of the dynamic structure factor of the magnetized one-component plasma from weak to strong coupling, which is studied with first-principle molecular dynamics simulations. The simulations show the vanishing of Bernstein modes and the emergence of higher harmonics of the upper hybrid mode across the magnetic field, a redistribution of spectral power between the two main collective modes under oblique angles, and a suppression of plasmon damping along the magnetic field. Comparison with results from various models, including the random phase approximation, a Mermin-type dielectric function, and the quasilocalized charge approximation show that none of the theories is capable of reproducing the crossover that occurs when the coupling parameter is on the order of unity. The findings are relevant to the scattering spectra, stopping power, and transport coefficients of correlated magnetized plasmas.

Cyclotron resonance overtones and near-field magnetoabsorption via terahertz Bernstein modes in graphene

Two-dimensional electron systems subjected to a perpendicular magnetic field absorb electromagnetic radiation via cyclotron resonance (CR). Here we report a qualitative deviation from this well-known behaviour in graphene. Our measurements of the terahertz photoresponse reveal a resonant burst at the main overtone of the CR that exceeds the signal detected at the position of the ordinary CR. The dependencies of photoresponse on the magnetic field, doping level and sample geometry suggest that the origin of this anomaly lies in the near-field magnetoabsorption facilitated by the Bernstein modes—ultraslow magnetoplasmonic excitations reshaped by non-local electron dynamics. Close to CR harmonics, these modes are characterized by a flat dispersion and diverging plasmonic density of states that amplify radiation absorption. Besides carrying fundamental interest, our results show that radiation absorption via non-local collective modes can facilitate a strong photoresponse—a behaviour potentially useful for infrared and terahertz technology. Electrons in an external magnetic field absorb electromagnetic radiation via cyclotron resonance. Deviations from this behaviour in the form of overtone resonances due to ultraslow magnetoplasmonic excitations are now reported for graphene.

Multiband Electrostatic Waves below and above the Electron Cyclotron Frequency in the Near-Sun Solar Wind

Abstract Using the Parker Solar Probe measurements, this Letter reports two new types of multiband electrostatic waves in and near the heliospheric current sheet. They are classified into the f < f ce and f > f ce multiband electrostatic waves, in which most (or all) of the bands in the former type are lower than f ce, and all of the bands in the latter type are higher than f ce, where f and f ce denotes the wave frequency and the electron cyclotron frequency, respectively. This Letter also exhibits observational evidence of the existence of nonlinear wave–wave interactions of both types of electrostatic waves. In particular, the f > f ce multiband electrostatic waves are found to be modulated in the presence of low-frequency oblique ion-scale waves. According to the observed frequency distribution, this Letter proposes that the mode nature of the f < f ce multiband electrostatic waves could be the oblique ion acoustic wave or the lower-hybrid wave, and the f > f ce multiband electrostatic waves are the electron Bernstein mode wave. These findings provide a challenge to understand the complex electron and ion dynamical processes in and near the heliospheric current sheet.

Observation and Fully Thermal Simulation of Quasi‐Electrostatic Magnetosonic Waves

AbstractMagnetosonic (MS) waves are generally considered as electromagnetic harmonic fluctuations below the lower hybrid frequency. Here we present a correlated observation of proton ring‐like distribution and low harmonic magnetosonic waves with undetectable magnetic components (called QEMS). We conduct fully thermal simulations (WHAMP) to investigate the wave properties. The calculated growth rates can reproduce the observed spectral characteristics and demonstrate that the QEMS waves are excited as ion Bernstein modes by proton ring‐like distribution. The ratios between the wave electric and magnetic amplitudes E/B given by WHAMP indicate that the magnetic spectral densities are below the instrument noise level, and the ratios are ∼7–80 times larger than the wave phase speeds Vph, suggesting that the QEMS waves are essentially quasi‐electrostatic, not just visually quasi‐electrostatic due to the measurement limit. This study provides further insights into the QEMS natures.

Geomagnetic field impacts on second harmonic generation during high power radio wave-ionosphere interaction

Contained herein are results from an experimental study of geomagnetic field (B0) impacts on second harmonic generation (SHG) during the interaction of high power, high frequency radio waves with the ionosphere. These magnetic field effects on SHG are assessed by (1) considering the proximity of the pump frequency to the electron gyroharmonic frequency and (2) considering the pump antenna beam angle relative to the geomagnetic field direction. The observations show evidence of ion Bernstein mode wave-mixing processes in stimulated electromagnetic emissions (SEEs) simultaneously near the pump wave frequency (f0) and its second harmonic (2f0). In an experiment performed at the High Frequency Active Auroral Research Program (HAARP) facility, the transmit antenna beam was either oriented along or tilted away from B0, and f0 was stepped near the second harmonic of the electron gyrofrequency (2fce). SEEs ordered by the oxygen ion gyrofrequency (fci) are observed in spectra near 2f0 for: (1) a B0-oriented antenna beam when f0≈2fce and (2) f0<2fce, when the beam is tilted away, but not beyond a maximum angle from B0. The observations motivate further studies to develop SHG into important diagnostics for the modified ionosphere.

Absorption of Microwave Radiation by Two-Dimensional Electron Systems Associated with the Excitation of Dimensional Bernstein Mode Resonances

Absorption of Microwave Radiation by Two-Dimensional Electron Systems Associated with the Excitation of Dimensional Bernstein Mode Resonances

The Magnetized Vlasov–Ampère System and the Bernstein–Landau Paradox

We study the Bernstein–Landau paradox in the collisionless motion of an electrostatic plasma in the presence of a constant external magnetic field. The Bernstein–Landau paradox consists in that in the presence of the magnetic field, the electric field and the charge density fluctuation have an oscillatory behavior in time. This is radically different from Landau damping, in the case without magnetic field, where the electric field tends to zero for large times. We consider this problem from a new point of view. Instead of analyzing the linear magnetized Vlasov–Poisson system, as it is usually done, we study the linear magnetized Vlasov–Ampère system. We formulate the magnetized Vlasov–Ampère system as a Schrödinger equation with a selfadjoint magnetized Vlasov–Ampère operator in the Hilbert space of states with finite energy. The magnetized Vlasov–Ampère operator has a complete set of orthonormal eigenfunctions, that include the Bernstein modes. The expansion of the solution of the magnetized Vlasov–Ampère system in the eigenfunctions shows the oscillatory behavior in time. We prove the convergence of the expansion under optimal conditions, assuming only that the initial state has finite energy. This solves a problem that was recently posed in the literature. The Bernstein modes are not complete. To have a complete system it is necessary to add eigenfunctions that are associated with eigenvalues at all the integer multiples of the cyclotron frequency. These special plasma oscillations actually exist on their own, without the excitation of the other modes. In the limit when the magnetic fields goes to zero the spectrum of the magnetized Vlasov–Ampère operator changes drastically from pure point to absolutely continuous in the orthogonal complement to its kernel, due to a sharp change on its domain. This explains the Bernstein–Landau paradox. Furthermore, we present numerical simulations that illustrate the Bernstein–Landau paradox. In Appendix 2 we provide exact formulas for a family of time-independent solutions.

Narrowband Spikes Observed during the 2013 November 7 Flare

Abstract Narrowband spikes have been observed in solar flares for several decades. However, their exact origin is still discussed. To contribute to understanding of these spikes, we analyze the narrowband spikes observed in the 800–2000 MHz range during the impulsive phase of the 2013 November 7 flare. In the radio spectrum, the spikes started with typical broadband clouds of spikes, and then their distribution in frequencies changed into unique, very narrow bands having noninteger frequency ratios. We successfully fitted frequencies of these narrow spike bands by those, calculating dispersion branches and growth rates of the Bernstein modes. For comparison, we also analyzed the model where the narrow bands of spikes are generated at the upper-hybrid frequencies. Using both models, we estimated the plasma density and magnetic field in spike sources. Then, the models are discussed, and arguments in favor of the model with the Bernstein modes are presented. Analyzing frequency profiles of this spike event by the Fourier method, we found the power-law spectra with the power-law indices varying in the −0.8 to −2.75 interval. Because at some times this power-law index was close to the Kolmogorov spectral index (−5/3), we propose that the spikes are generated through the Bernstein modes in turbulent plasma reconnection outflows or directly in the turbulent magnetic reconnection of solar flares.

Vlasov simulation of electrons in the context of hybrid global models: an eVlasiator approach

Abstract. Modern investigations of dynamical space plasma systems such as magnetically complicated topologies within the Earth's magnetosphere make great use of supercomputer models as well as spacecraft observations. Space plasma simulations can be used to investigate energy transfer, acceleration, and plasma flows on both global and local scales. Simulation of global magnetospheric dynamics requires spatial and temporal scales currently achievable through magnetohydrodynamics or hybrid-kinetic simulations, which approximate electron dynamics as a charge-neutralizing fluid. We introduce a novel method for Vlasov-simulating electrons in the context of a hybrid-kinetic framework in order to examine the energization processes of magnetospheric electrons. Our extension of the Vlasiator hybrid-Vlasov code utilizes the global simulation dynamics of the hybrid method whilst modelling snapshots of electron dynamics on global spatial scales and temporal scales suitable for electron physics. Our eVlasiator model is shown to be stable both for single-cell and small-scale domains, and the solver successfully models Langmuir waves and Bernstein modes. We simulate a small test-case section of the near-Earth magnetotail plasma sheet region, reproducing a number of electron distribution function features found in spacecraft measurements.