Structure of the Bernstein modes for large values of the plasma parameter.
Bernstein modes structure and electrostatic frequency vs wave number dispersion relation for waves propagating across magnetic field in plasma
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Bernstein modes structure and electrostatic frequency vs wave number dispersion relation for waves propagating across magnetic field in plasma
Generalized ion Bernstein modes for electrostatic wave propagation across magnetic field and not parallel to electric field in warm plasma, noting dispersion relation
Our report presents theory and numerical calculations of electrostatic Bernstein modes in an inhomogeneous cylindrical plasma column. These modes rely on finite Larmor radius effects to propagate radially across the column until they are reflected when their frequency matches the upper hybrid frequency. This reflection sets up an internal normal mode on the column and also mode-couples to the electrostatic surface cyclotron wave (which allows the normal mode to be excited and observed using external electrodes). Numerical results predicting the mode spectra, using a novel linear Vlasov code on a cylindrical grid, are presented and compared to an analytical Wentzel Kramers Brillouin (WKB) theory. A prior version of the theory [D. H. E. Dubin, Phys. Plasmas 20(4), 042120 (2013)] expanded the plasma response in powers of 1/B, approximating the local upper hybrid frequency, and consequently, its frequency predictions are spuriously shifted with respect to the numerical results presented here. A new version of the WKB theory avoids this approximation using the exact cold fluid plasma response and does a better job of reproducing the numerical frequency spectrum. The effect of multiple ion species on the mode spectrum is also reported on, to make contact with experiments that observe cyclotron modes in a multi-species pure ion plasma [M. Affolter et al., Phys. Plasmas 22(5), 055701 (2015)].
Wave dispersion across magnetic field in cold and warm collisioness Maxwellian plasma, discussing electromagnetic and electrostatic Bernstein modes
Magnetic holes (MHs) are coherent structures characterized by a strong and localized magnetic field amplitude dip, commonly observed in the heliosphere. These structures come in different sizes, from magnetohydrodynamic to kinetic scales. Subion-scale MHs are usually sustained by an electron current vortex and exhibit a strong electron temperature anisotropy, with higher temperatures perpendicular to the background magnetic field. Magnetospheric multiscale observations (MMSs) have revealed electron-scale MHs to be ubiquitous in the turbulent Earth’s magnetosheath and the solar wind, potentially playing an important role in the energy cascade and dissipation. Despite abundant observations, the origin of electron-scale MHs is still unclear and debated. In this work, we use fully kinetic simulations to investigate the role of plasma turbulence in generating electron-scale MHs. We find that the turbulence spontaneously produces electron-scale MHs via the following mechanism: first, large-scale turbulent velocity shears produce regions with high electron temperature anisotropy; these localized regions become unstable, generating oblique electron-scale whistler waves; as they propagate over the inhomogeneous turbulent background, whistler fluctuations develop an electrostatic component, turning into Bernstein-like modes; the strong electrostatic fluctuations produce current filaments that merge into an electron-scale current vortex; the resulting electron vortex locally reduces the magnetic field amplitude, finally evolving into an electron-scale MH. We show that MHs generated by this mechanism have properties consistent with MMSs and nontrivial kinetic features with a “mushroom”-shaped electron velocity distribution function. Our results have potential implications for understanding the formation and occurrence of electron-scale MHs in astrophysical turbulent and space environments, such as the Earth’s magnetosheath and the solar wind.
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In the scenario of weak turbulence, energy is believed to be cascaded from smaller to larger wave numbers and frequencies due to weak wave-wave interactions. Based on its perturbative treatment one may regard plasma turbulence as a superposition of linear modes (or normal modes) and sideband waves (or nonlinear modes). In this study, we use magnetic field and plasma measurements of nine solar wind events obtained by the Cluster spacecraft and make extensive use of a high-resolution wave vector analysis method, the Multi-point Signal Resonator technique, to find frequencies and wave vectors of discrete modes on ion kinetic scales in the plasma rest frame. The primarily unstructured wave observations in the frequency-wave number diagram are classified into three distinct linear modes (proton Bernstein modes, helium-alpha Bernstein modes, and kinetic Alfvén waves) and the sideband waves by comparing with the dispersion relations derived theoretically from linear Vlasov theory using observational values of the plasma parameter beta and the propagation angle from the mean magnetic field. About 60% of the observed discrete modes can be explained by the linear modes, primarily as the proton Bernstein and the kinetic Alfvén waves, within the frequency uncertainties, while the rest of the population (about 40%) cannot be classified as linear modes due to the large deviation from dispersion relations. We conclude that both the linear modes and sideband wave components are needed to construct the wave picture of solar wind turbulence on ion-kinetic scales.
The ARCS 3 sounding rocket experiment used two argon guns oriented parallel and perpendicular to the geomagnetic field. The parameters of this experiment have been used in a series of particle simulations in order to interpret ion beam interaction with the multispecies ionospheric plasma. Along with the lower hybrid mode between the electron and the hydrogen gyrofrequencies, ion-ion hybrid modes between the hydrogen and helium gyrofrequencies and between the helium and oxygen gyrofrequencies are identified in the simulations. Besides these cold plasma modes, warm Bernstein modes of the respective ion species are identified. The parallel argon beam injections excite lower hybrid waves perpendicular to the magnetic field because of the finite thermal spread of the parallel beam. Perpendicular ion heating of background hydrogen, helium, and oxygen is comparable in the simulations. Comparisons are made with the wave and particle data from the ARCS 3 rocket experiment.
The dissipation of solar wind turbulence at kinetic scales is believed to be important for the heating of the corona and for accelerating the wind. The linear Vlasov kinetic theory is a useful tool for identifying various wave modes, including kinetic Alfvén, fast magnetosonic/whistler, and ion-acoustic (or kinetic slow), and their possible roles in the dissipation. However, the kinetic mode structure in the vicinity of ion-cyclotron modes is not clearly understood. The present paper aims to further elucidate the structure of these low-frequency waves by introducing discrete particle effects through hybrid simulations and Klimontovich formalism of spontaneous emission theory. The theory and simulation of spontaneously emitted low-frequency fluctuations are employed to identify and distinguish the detailed mode structures associated with ion-Bernstein modes versus quasi-modes. The spontaneous emission theory and simulation also confirm the findings of the Vlasov theory in that the kinetic Alfvén waves can be defined over a wide range of frequencies, including the proton cyclotron frequency and its harmonics, especially for high-beta plasmas. This implies that these low-frequency modes may play predominant roles even in the fully kinetic description of kinetic scale turbulence and dissipation despite the fact that cyclotron harmonic and Bernstein modes may also play important roles in wave–particle interactions.
The dissipation of solar wind turbulence at kinetic scales is believed to be important for the heating of the corona and for accelerating the wind. The linear Vlasov kinetic theory is a useful tool for identifying various wave modes, including kinetic Alfven, fast magnetosonic/whistler, and ion-acoustic (or kinetic slow), and their possible roles in the dissipation. However, the kinetic mode structure in the vicinity of ion-cyclotron modes is not clearly understood. The present paper aims to further elucidate the structure of these low-frequency waves by introducing discrete particle effects through hybrid simulations and Klimontovich formalism of spontaneous emission theory. The theory and simulation of spontaneously emitted low-frequency fluctuations are employed to identify and distinguish the detailed mode structures associated with ion-Bernstein modes versus quasi-modes. The spontaneous emission theory and simulation also confirm the findings of the Vlasov theory in that the kinetic Alfven waves can be defined over a wide range of frequencies, including the proton cyclotron frequency and its harmonics, especially for high-beta plasmas. This implies that these low-frequency modes may play predominant roles even in the fully kinetic description of kinetic scale turbulence and dissipation despite the fact that cyclotron harmonic and Bernstein modes may also play important roles in wave-particle interactions.
One of the mechanisms for generating electromagnetic plasma waves (Z-mode and LO-mode) is mode conversion from electrostatic waves into electromagnetic waves in inhomogeneous plasma. Herein, we study a condition required for mode conversion of electrostatic waves propagating purely perpendicular to the ambient magnetic field, by numerically solving the full dispersion relation. An approximate model is derived describing the coupling between electrostatic waves (hot plasma Bernstein mode) and Z-mode waves at the upper hybrid frequency. The model is used to study conditions required for mode conversion from electrostatic waves (electrostatic electron cyclotron harmonic waves, including Bernstein mode) into electromagnetic plasma waves (LO-mode). It is shown that for mode conversion to occur in inhomogeneous plasma, the angle between the boundary surface and the magnetic field vector should be within a specific range. The range of the angle depends on the norm of the k vector of waves at the site of mode conversion in the inhomogeneous region. The present study reveals that inhomogeneity alone is not a sufficient condition for mode conversion from electrostatic waves to electromagnetic plasma waves and that the angle between the magnetic field and the density gradient plays an important role in the conversion process.
A study of the ELF plasma wave environment of the cold Io torus in Jupiter's magnetosphere is made. Voyager 1 data are presented which show three distinct types of electrostatic ion waves occurring there: the Buchsbaum ion-ion mode just below the proton cyclotron frequency f(cp), hydrogen Bernstein modes at (n + 1/2) f(cp), and lower hybrid waves near f(LHR). The presence of these waves at their characteristic frequencies is consistent with a predominantly heavy ion plasma composed of singly ionized sulfur and oxygen ions along with a small admixture of protons. The hydrogen Bernstein modes are tightly confined to the magnetic equator, occurring within + or - 4 deg of it, while the Buchsbaum mode is localized to the dense heavy ion plasma of the cold torus near the centrifugal equator. A general theory for excitation of the waves based on the ion pickup process is developed.
We report the results of a direct comparison between different kinetic models of collisionless plasma turbulence in two spatial dimensions. The models considered include a first-principles fully kinetic (FK) description, two widely used reduced models (gyrokinetic (GK) and hybrid-kinetic (HK) with fluid electrons), and a novel reduced gyrokinetic approach (KREHM). Two different ion beta (β{sub i}) regimes are considered: 0.1 and 0.5. For β{sub i}=0.5, good agreement between the GK and FK models is found at scales ranging from the ion to the electron gyroradius, thus providing firm evidence for a kinetic Alfvén cascade scenario. In the same range, the HK model produces shallower spectral slopes, presumably due to the lack of electron Landau damping. For β{sub i}=0.1, a detailed analysis of spectral ratios reveals a slight disagreement between the GK and FK descriptions at kinetic scales, even though kinetic Alfvén fluctuations likely still play a significant role. The discrepancy can be traced back to scales above the ion gyroradius, where the FK and HK results seem to suggest the presence of fast magnetosonic and ion Bernstein modes in both plasma beta regimes, but with a more notable deviation from GK in the low-beta case. The identified practical limits and strengths of reduced-kinetic approximations, compared here against the FK model on a case-by-case basis, may provide valuable insight into the main kinetic effects at play in turbulent collisionless plasmas, such as the solar wind.
Voyager 2 observations of electrostatic electron and ion harmonic waves in Neptune's magnetosphere are addressed. A model of electron Bernstein modes generated by a loss cone distribution of superthermal electrons is scaled to Neptune parameters and a comparison of theory with the observed electron flux shows good agreement. A model of proton Bernstein modes generated by a ring distribution of Tritonogenic nitrogen ions is also investigated and satisfactory agreement with the data are obtained compatible with known properties of the magnetosphere. The success of the model in accounting for electrostatic emission observed by Voyager over a wide range of sampled parameters recommends its general applicability to planetary magnetospheres.
The evolution of the ion-scale plasma turbulence in the inner heliosphere is studied by associating the plasma parameters for hybrid-code turbulence simulations to the radial distance from the Sun via a Solar wind model based mapping procedure. Using a mapping based on a one-dimensional solar wind expansion model, the resulting ion-kinetic scale turbulence is related to the solar wind distance from the Sun. For this purpose the mapping is carried out for various values of ion beta that correspond to the heliocentric distance. It is shown that the relevant normal modes such as ion cyclotron and ion Bernstein modes will occur first at radial distances of about 0.2–0.3 AU, i.e., near the Mercury orbit. This finding can be used as a reference, a prediction to guide the in situ measurements to be performed by the upcoming Solar Orbiter and Solar Probe Plus missions. Furthermore, a radial dependence of the wave-vector anisotropy was obtained. For astrophysical objects this means that the spatial scales of filamentary structures in interstellar media or astrophysical jets can be predicted for photometric observations.
The effects of thermal motions on the cyclotron radiation from test particles gyrating in a homogeneous magnetoplasma are studied. These effects take care of all singularities that exist in the theory of cyclotron radiation in cold magnetoplasma - e.g., the divergence in energy loss for small particle energies. Around the hybrid frequencies thermal corrections become of dominant importance. At these frequencies cold-plasma theory breaks down. Thermal effects arise in two ways: by modifying the wave modes known from cold plasma theory, and by the introduction of a new longitudinal wave mode, known as the Bernstein mode. All wave modes are damped (in stable plasmas).
Two recent sounding rocket experiments have yielded VLF wave data with spectral structures ordered by the hydrogen gyrofrequency. The spectral structures occur near and above the lower hybrid frequency in association with auroral hiss. These structures are observed within and near regions of auroral electron precipitation and transverse ion acceleration. They are accompanied by auroral hiss but are anticorrelated with spectral peaks at the lower hybrid frequency. They are typically found above 500 km altitude, have no measurable magnetic component, and are at least occasionally short wavelength. Because the spectral structures appear to be electrostatic, are ordered by the hydrogen gyrofrequency, and are short wavelength, the structures are interpreted as modes which connect the lower hybrid mode with the hydrogen Bernstein modes. A study of the plasma wave mode structure in the vicinity of the lower hybrid frequency is presented to substantiate this interpretation. These results imply that these waves are a common feature of the auroral zone ionsphere above 500 km altitude and exist any time that auroral hiss exists. The absence of previous satellite observations of this phenomenon can be explained by Doppler broadening.
The characteristics of the maser emission from a driven system where energetic electrons continue to flow through the source region is investigated using electronic particle simulations. It is shown that, under appropriate conditions, the maser can efficiently radiate a significant portion of the energy of the fast electrons in a very short time. The radiation is emitted in pulses even though the flow of electrons through the system is at a constant rate. The mission of these pulses is proposed as the source of the fine structure. Under other conditions the dominant maser emission changes from fundamental x-mode to either fundamental z-mode or to electrostatic upper hybrid or Bernstein modes. The bulk of the emission from the maser instability cannot propagate across field lines in this regime, and hence strong local plasma heating is expected, with little energy transport across the magnetic field lines.