Bernstein Modes Research Articles

Nonlinear Magnetoplasmons in Strongly Coupled Yukawa Plasmas

The existence of plasma oscillations at multiples of the magnetoplasmon frequency in a strongly coupled two-dimensional magnetized Yukawa plasma is reported, based on extensive molecular dynamics simulations. These modes are the analogues of Bernstein modes which are renormalized by strong interparticle correlations. Their properties are theoretically explained by a dielectric function incorporating the combined effect of a magnetic field, strong correlations and finite temperature.

Charged particle acceleration by electron Bernstein wave in a plasma channel

AbstractA model of electron acceleration by an electron Bernstein mode in a parabolic density profile is developed. The mode has a Gaussian profile. It could be excited via the mode conversion of an electromagnetic wave or by an electron beam. As it attains a large amplitude, it axially traps electrons moving close to its parallel phase velocity, where parallel refers to the direction of static magnetic field. As the electrons are accelerated and tend to get out of phase with the wave, the transverse field of the mode enhances its energy and relativistic mass, increasing the dephasing length. The scheme can produce electron energies up to a few MeV.

Possible wave modes of wideband nonthermal continuum radiation in its source region

Nonthermal continuum (NTC) electromagnetic radiation is generated within the Earth's magnetosphere and radiated to the outer space. We present cases of a specific type of NTC, which appears as multiple wide bands on the spectrograms recorded by the Cluster spacecraft just outside the plasmapause. This NTC comes from several sources located in the plasmapause density gradient where the local upper hybrid frequency is close to the harmonics of the electron cyclotron frequency. Analysis of one of these events at the eighth harmonic frequency indicates that, in the vicinity of the source, the electric field fluctuations are polarized in the plane perpendicular to the magnetic field line. Hot‐plasma dispersion relation based on the measured electron distribution shows that the observed polarization excludes the presence the Langmuir mode and the ordinary mode. This analysis suggests that the observed waves can propagate in the L mode or, for perpendicular wave vectors, in the extraordinary Z mode or on a complex structure of hot‐plasma Bernstein modes coupled to the Z mode at the upper hybrid frequency.

Electrodynamics of plasma irregularities in the experiments with artificial clouds and jets in the ionosphere

Electric fields in the near-Earth space was studied in the experiments with artificial plasma clouds and jets in the ionosphere and magnetosphere. The development of a nonmonotonous plasma density stratification of an artificial plasma formation, with the scale of strata across the geomagnetic field reaching several meters and tens of meters, was observed. It has been indicated that the electrodynamics of plasma clouds and jets, decomposing into strata, depends on the excitation and decay of fast oscillations of the electronic plasma component against a background of slow oscillations of the ionic component at frequencies of magnetized plasma electrostatic oscillations (electrostatic Bernstein modes of the plasma electronic and ionic components and ion acoustic oscillations).

Dispersion relation and group velocity for inhomogeneous waves in a hot magnetoplasma with application to an electron-Bernstein-wave propagation experiment in a laboratory plasma

[1] Lewis and Keller (1962) derive the dispersion relation for homogeneous waves propagating in a hot magnetoplasma. Homogeneous waves are ones for which the real and imaginary parts of the wave vector, kr and ki, are parallel. In this paper a generalization to Lewis and Keller is made for inhomogeneous waves, that is, waves for which kr and ki are not parallel. If ki is assumed to be in the same plane as kr and the magnetic field H0 in the Lewis and Keller generalization, comparison can be made with the dispersion relation of Stix (1992); good agreement is found with one exception. This generalization is applied to observations of electrostatic (ES) wave propagation in a laboratory plasma. Bernstein waves propagating perpendicular to H0 are undamped. The dispersion relation for homogeneous waves indicates that severe damping should occur for propagation slightly off perpendicular. Laboratory experiments indicate that severe damping does not occur. The laboratory results can be explained if inhomogeneous waves are considered. Muldrew and Gonfalone (1974) used the dispersion equation for homogeneous waves in a hot magnetoplasma to explain the signal maxima in the pattern when electron-Bernstein waves interfere with the electromagnetic field. Good agreement is obtained when ki is small compared to kr. However, when ki becomes significant, the pattern can no longer be explained. Different approaches to explaining the results using inhomogeneous waves are presented that are superior to the one using homogeneous waves. In one approach, plasma waves with a complex wave vector can propagate without large attenuation, and propagation characteristics can be determined, by choosing the direction of ki to be a free parameter that makes Im{k · vg} = 0, or have a minimum value; k = kr + iki, vg is the complex group velocity ∂ω/∂k and ω is the real angular wave frequency. When this condition is satisfied, good agreement in the signal maxima is obtained with the laboratory experiments if the direction of energy flow in the plasma is taken to be Re{vg}. This method of calculating the interference pattern is compared with the least damped method which calculates the potential of an oscillating point charge in a plasma. Good agreement between the two methods is found if an assumption is made regarding the wave(s) interfering with the ES Bernstein mode.

Effect of two ion species on the propagation of shear Alfvén waves of small transverse scale

The results of a theoretical modeling study and experimental investigation of the propagation properties of shear Alfvén waves of small transverse scale in a plasma with two ion species are reported. In the two ion plasma, depending on the mass of the heavier species, ion kinetic effects can become prominent, and significant parallel electric fields result in electron acceleration. The theory predicts the appearance of frequency propagation gaps at the ion-ion hybrid frequency and between harmonics of the lower cyclotron frequency. Within these frequency bands spatial structures arise that mix the cone-propagation characteristics of Alfvén waves with radially expanding ion Bernstein modes. The experiments, performed at the Basic Plasma Science Facility (BaPSF) at UCLA, consist of the spatial mapping of shear waves launched by a loop antenna. Although a variety of two ion-species combinations were explored, only results from a helium-neon mix are reported. A clear signature of a shear wave propagation gap, as well as propagation between multiple harmonics, is found for this gas combination. The evanescence of shear waves beyond the reflection point at the ion-ion hybrid frequency in the presence of an axial magnetic field gradient is also documented.

Interaction of branches of magnetoplasmon spectrum in 2D systems with spin–orbit coupling

We have theoretically investigated magnetoplasma oscillations of a 2D electronic system with spin–orbit interaction (SOI) in the Bychkov–Rashba model. Accounting for SOI results in new branches of magnetoplasmons as compared with the spinless case where the Bernstein modes exist only. A remarkable feature of the problem in question is magnetic field controlled interaction of branches (multiple anticrossings). This is manifested in the spectra of plasmon absorption of electromagnetic radiation.

Warm electromagnetic lower hybrid wave dispersion relation

Lower hybrid (LH) waves can interact resonantly with both electrons and ions transferring energy between the species. For this reason the properties of LH waves are of interest. Most treatments of LH waves include either electromagnetic (EM) or warm plasma effects but not both. Here a new analytic dispersion relation for LH waves, including both EM and warm plasma effects, is derived and shown to be more consistent than the previous analytic dispersion relations with numerical results. These comparisons show a very good agreement of the real part of the frequency and reasonable agreement of the imaginary part for a wide range of parameters. It is found that ion magnetization effects, which have been neglected in all previous analytic treatments of LH waves, are surprisingly important. When ion magnetization effects become important the continuous LH mode breaks up into a series of segments of ion Bernstein modes.

Numerical and theoretical study of Bernstein modes in a magnetized quantum plasma

A numerical and theoretical study is presented for the propagation of electron Bernstein modes in a magnetized quantum plasma. The dispersion relation for electrostatic waves is derived, using a semiclassical Vlasov model for Fermi–Dirac distributed electrons. The dispersion relation is checked numerically with direct Vlasov simulations, where the wave energy is concentrated to the Bernstein modes as well as to the zero-frequency convective mode. Dispersion relations in the long wavelength limit are derived, including the upper hybrid dispersion relation for a degenerate quantum plasma.

Transport of transient solar wind particles in Earth’s cusps

An important problem in space physics still not understood well is how the solar wind enters the Earth’s magnetosphere. Evidence is presented that transient solar wind particles produced by solar disturbances can appear in the Earth’s mid-altitude (∼5RE geocentric) cusps with densities nearly equal to those in the magnetosheath. That these are magnetosheath particles is established by showing they have the same “flattop” electron distributions as magnetosheath electrons behind the bow shock. The transient ions are moving parallel to the magnetic field (B) toward Earth and often coexist with ionospheric particles that are flowing out. The accompanying waves include electromagnetic and broadband electrostatic noise emissions and Bernstein mode waves. Phase-space distributions show a mixture of hot and cold electrons and multiple ion species including field-aligned ionospheric O+ beams.

Flux averaged current drive efficiency of electron Bernstein waves

Electron Bernstein waves are of interest for heating and current drive in spherical tokamaks where the central region of the plasma is not accessible to the ordinary and extraordinary modes. In this paper we adapt an analytical theory of current drive in toroidal geometry developed by Lin-Liu et al (2003 Phys. Plasmas 10 4064) to this system. This involves taking account of the fact that the ratio of the Larmor radius to the perpendicular wavelength is not, in general, small for the Bernstein waves and also including the effects of a non-circular plasma cross section. By comparing the results with those of a full Fokker–Planck code, we demonstrate that the analytical method can yield a good approximation to the current drive efficiency in most regimes of practical interest. Since it is much less computationally demanding than using a Fokker–Planck code we suggest that it could be a useful tool for analysing experiments on Bernstein mode current drive in spherical tokamaks.

Weakly relativistic dielectric tensor for arbitrary wavenumbers

The validity of Shkarofsky’s dielectric tensor is extended by taking the strictly weakly relativistic limit and removing, when possible, assumptions on the wavenumbers along and across the ambient magnetic field, k∥ and k⊥. An approximation of the time integral is retained, but is shown to be valid under more benign assumptions than those of quasiperpendicular incidence and small Larmor radius. The increased generality with respect to k∥ permits to handle cases of comparable Doppler and relativistic widths of electron cyclotron resonances. The tensor also suits Bernstein waves, as it captures both their natural large k⊥ and the finite k∥ that is typical of some mode conversions, or acquired as a consequence of the large k⊥ when propagating in curved magnetic fields. Finally, relativistic corrections to the optimal angle for the ordinary-extraordinary Bernstein mode conversion are presented.

Magnetized Plasma in Polar Semiconductors

Plasma excitations in solids have been intensively studied already at the time of the 1960’s. A significant interest was focused on doped polar semiconductors. In these systems, the nowadays text-book effect of coupling between plasmons and optical phonon modes can be clearly observed as demonstrated, for example, by the pioneering work of Mooradian and Wright [1] on inelastic light scattering in n-type GaAs samples. The properties of a plasma subjected to a static magnetic field are significantly modified. A magnetic field B applied to a metallic system introduces a characteristic frequency, namely the cyclotron frequency ωc =eB/m of motion of the carriers (with an effective mass m) in the plane perpendicular to the field direction. In polar-semiconductor plasmas, by changing the magnetic field the cyclotron frequency ωc can be made comparable to all important frequencies of the system, namely the plasma frequency ωp and the frequencies of longitudinal (LO) and transverse (TO) optical phonons. The physics of coupled plasmon phonon modes under these particular and interesting conditions has never been fully explored in Raman scattering experiments in 3D systems. On the other hand, there exist a number of works, concerning both Raman scattering and far-infrared magneto-spectroscopy which address the issue of coupling between the electronic and phonon excitations in twodimensional semiconductor structures. The physics of low energy excitations in these structures is far more complex because of the modification of the energy spectrum due to effects of spatial confinement. The results of high-magmetic-field (up to 28T) inelastic light scattering studies on coupled plasmon-LO-phonon modes in bulk, degenerate n-type GaAs will be presented. [2] The data analysis implies the use of a standard dielectric function approach. Results obtained for samples with high electron concentration are well understood. A strong interaction of coupled LO-phonon-plasmon modes with the collective cyclotron resonance excitations (Bernstein modes) is observed. In samples with lower electron concentration, an unexpected Raman scattering signal in the vicinity of the undressed optical phonon is observed at high magnetic fields. A field induced metal-insulator transition is shown to be observable in Raman scattering experiments in samples with lowest electron concentration. The plasmon-phonon modes which are characteristic of the metallic state are replaced by intradonor excitations in the case of the insulating state. It is very interesting, that the resonant magnetopolaron effect reflecting the interaction between the LO phonon and the 1s-2p intradonor excitation is observed in the insulating state but no coupling between LO-phonon and cyclotron resonance excitations is seen in the metallic state. This result allows us to discuss some aspects of an apparent controversy existing in two-dimensional systems regarding the fundamental problem of Frohlich interaction: whether it manifests itself as a resonant repulsion between the cyclotron resonance and LO-phononlike modes for a two-dimensional electron gas, or not.

Parametric excitation of electron Bernstein waves by radio waves in the ionosphere and its possible consequence for airglow

A high power radio wave, launched into the polar ionosphere at angle θ with the earth's magnetic field from a ground-based transmitter in the vicinity of twice the electron cyclotron frequency (2.75 MHz), is reported to create an airglow at an effective radiated power (ERP) = 10 MW. We interpret this result as a consequence of parametric decay of the radio wave into an electron Bernstein wave (EBW) and an ion acoustic wave (IAW). The oscillatory velocity of electrons due to the pump couples with the density perturbation due to the IAW to produce a current, driving the Bernstein mode. The latter, in connection with the pump, exerts a ponderomotive force on electrons, driving the IAW. The growth rate of the parametric instability is maximum for θ = 0. At the same time, for any given value of θ, the growth rate increases with and attains a maximum around b ∼ 2, then falls gradually. The EBW produces energetic electrons via cyclotron damping. These electrons collide with the neutral atoms of the plasma to excite them to higher energy states. As the excited atoms return to lower energy states, they radiate in the visible.

Parametric up-conversion of an electron Bernstein mode by a relativistic electron beam in a plasma

A relativistic electron beam, propagating with velocity v0b‖ẑ in a magnetized plasma, parametrically up-converts a pre-existing electron Bernstein wave (ω0,k0) into electromagnetic radiation when k0∙v0b<0. The Bernstein wave couples with a negative energy space-charge mode (ω,k) to produce a frequency up-converted sideband electromagnetic wave. The sideband and the Bernstein wave exert a ponderomotive force, driving space-charge mode. In the Compton regime, the growth rate of the parametric instability scales as two-third power of the pump amplitude, whereas in the Raman regime, it goes linearly.

Study of nonlinear interaction of waves through plasma-maser in magnetosphere plasma

A theoretical study is made on the generation mechanism of electrostatic Bernstein mode wave in the presence of electromagnetic Kinetic Alfven wave turbulence in magnetized inhomogeneous plasma on the basis of plasma-maser interaction. It is shown that a test high-frequency electrostatic Bernstein mode wave is unstable in the presence of low-frequency Kinetic Alfven wave turbulence. Because of the universal existence of the Kinetic Alfven waves in large-scale plasmas, the result has potential importance in space and astrophysical radiation process. The growth rate of the test high-frequency Bernstein mode wave is obtained with the involvement of spatial density gradient parameter. A comparative study on the role of density gradient in the generation of Bernstein mode on the basis of plasma-maser effect is presented.

Bernstein mode generated anomalous resistivity in a current carrying plasma focusing cell

The influence of microinstabilities and turbulence on the resistivity of plasma filled electron beam focusing cells is presented. Using a particle-in-cell simulation code, we have observed the onset of anomalous resistivity for low plasma densities and large embedded magnetic fields. The enhanced resistivity results from wave-particle interactions due to the saturation of the ion Bernstein mode instability in the current-carrying plasma. The growth rate of the mode scales with the relative drift speed between the electrons and ions. Here the scaling of the instability derived from simulation and theory and its impact on the operation of a plasma focusing cell for electron beam driven radiography are discussed. Enhanced resistivity up to 70 times larger than the classical Spitzer value is calculated for relevant plasma parameters.

Instabilities driven by ion shell distributions observed by Cluster in the midaltitude plasma sheet boundary layer

Cluster observations in the near‐Earth plasma sheet boundary layer (PSBL) region have shown the presence of ion shell distributions related to velocity‐dispersed ion structures (VDIS) coincident with electrostatic emissions. We have examined ion shell instabilities in the presence of a cold ion and electron background using linear theory and particle in cell simulations. Linear theory shows that the shell instability is only excited when a cold ion background is present, generating a broad range of ion cyclotron harmonics. Numerical simulations confirm that ion Bernstein modes are preferentially excited transverse to the ambient magnetic field, along with a lower level of wave power at oblique angles. The background ions are heated primarily in the transverse direction because of a linear nonstochastic ion cyclotron heating mechanism, and overall saturation of the instability occurs because of thermalization of the shell combined with heating of the background ions and electrons. Comparison with Cluster observations shows that observed electrostatic waves with a spectrum from a few Hz to several hundred Hz is in good agreement with that expected from the shell instability. The cold background ions are observed to have a temperature anisotropy with T⊥ > T∥, while electrons are observed to have T∥ > T⊥, also in qualitative agreement with the shell instability. The wave‐particle effects due to the shell instability in the near‐Earth PSBL could have important consequences for auroral potential structure at lower altitudes and may cause the gaps in VDIS structure leading to beamlets.

Study of plasma–maser instability in an inhomogeneous plasma

The plasma–maser, an interesting nonlinear process in plasmas, is an effective means of energy up-conversion in frequency from low-frequency turbulence to a high-frequency wave. A theoretical study is made of the amplification mechanism of an electrostatic Bernstein mode wave in presence of Langmuir wave turbulence in a magnetized inhomogeneous plasma on the basis of a plasma–maser interaction. It is shown that a test high-frequency electrostatic Bernstein mode wave is unstable in the presence of low-frequency Langmuir wave turbulence. The growth rate of a test high-frequency Bernstein mode wave is calculated with the involvement of a spatial density gradient parameter. A comparative study on the role of density gradient in the generation of the Bernstein mode on the basis of the plasma–maser effect is presented.

Bernstein mode coupling to cyclotron harmonic radiation in a plasma

An electron Bernstein wave in the presence of an ion-acoustic wave of suitable wave number converts itself into cyclotron harmonic electromagnetic radiation in a plasma. The Bernstein wave imparts oscillatory velocity to electrons that couples with the density perturbation associated with the sound wave to produce a nonlinear current, driving the electromagnetic wave at sum (or difference) frequency. Conversely a large amplitude electromagnetic wave at a cyclotron harmonic can parametrically excite an electron Bernstein wave that may effectively heat the electrons.