Whistler Mode Instability Research Articles

Linear analysis of whistler mode instability in anisotropic q-nonextensive distributed plasmas: a numerical approach

Due to the occurrence of nonextensive particle distributions in different space plasma environments, an analytical and numerical studies of electron temperature anisotropy-driven whistler instability (WI) in the nonextensive magnetized plasma are performed within the framework of kinetic theory for both superextensive (q < 1) and subextensive (q > 1) cases. By taking the nonextensive character of electrons into account (distinguished to nearly all existing studies), the dispersion relation for WI is derived and solved numerically to examine the characteristics of growth rate against the allowed domain of wave number. The effect of various physical parameters such as electron plasma beta , temperature anisotropy (Λ e ), and nonextensivity (q) on the growth rate and frequency of whistler mode are investigated. The growth rate of WI displays a significant dependence on these parameters, i.e. the growth rate increases by taking smaller values of nonextensive parameter q and for the large initial electron plasma beta and temperature anisotropy magnitudes. It is observed that the variation in the frequency of whistler mode is more sensitive to the temperature anisotropy (Λ e ) compared with other physical parameters, i.e. plasma beta and nonextensivity. The present findings also validate the large impact of electron temperature anisotropy on altering the dispersion properties of whistler mode. A detailed comparison of parametric dependence of the growth rate of WI for both superextensive and subextensive plasmas is also presented. Furthermore, a comparative analysis of whistler mode instability in anisotropic q-nonextensive and bi-Maxwellian plasmas is also the part of our present findings.

Impact of hot injected beam on whistler mode with alternating electric field (AC) in the magnetosphere of Saturn

Whistlers are believed to be generated by its own and responsible to evolve dynamical properties of magnetized planetary environment. Growing whistler instability can cause other uncertainties in the magnetosphere and evident to be generated by mean of injection events and temperature variance in plasma environment. In this paper the empirical dispersion relation has developed for parallel propagating whistler mode instability in an infinite saturnian magneto plasma in the presence of perpendicular electric field for ring distribution function having non-monotonous nature. Method of characteristics solutions alongside kinetic approach found to be most suitable in order to achieve perturbed plasma states. The perturbed and unperturbed particle trajectories have taken into consideration to determine perturbed distribution function. A remarkable growth rate expression with added hot plasma injection has been calculated in inner magnetosphere near 6.18 Rs. The results obtained using demonstrative value of the parameters suited to the Saturnian magnetosphere have been computed and discussed. Pressure (Temperature) anisotropy is found to be a peculiar source of free energy for whistler mode instability. The AC frequency irrespective of its magnitude, affects the growth rate significantly. The bulk of energetic hot electrons injection influences the growth rate by increasing its peak value. The result obtained provide the important view of wave particle interaction and useful to analyze the VLF emissions observed over a wide frequency range.

Influence of Kappa Distributions on the Whistler Mode Instability

AbstractKappa distributions possess an enhanced high‐energy tail characterized by a spectral index κ. Here we consider how kappa distributions influence the whistler mode instability. In a relativistic regime, we analyze the effects of the bi‐kappa and kappa loss‐cone distributions on the linear and nonlinear growth of whistler mode waves. We find that for κ = 2, the linear growth rate corresponding to the bi‐kappa distribution exceeds that for a bi‐Maxwellian distribution (κ = ∞) for electron anisotropies less than a critical value. The threshold wave amplitude for nonlinear growth corresponding to a hot injected bi‐kappa distribution can be sensitively dependent on the value of κ, but also depends crucially on the electron anisotropy, parallel hot electron temperature, and wave frequency. We plot time profiles of the wave magnetic field, frequency, total nonlinear growth rate and local nonlinear growth rate, and examine how these depend on κ. The sweep (chirp) rates of the whistler mode chorus waves are found to be in the range of observed values, for the adopted plasma parameters. For a given value of the loss‐cone parameter σ, realistic whistler mode wave profiles may only exist for a restricted range of κ. For example, for σ ≥ 4, realistic wave profiles require κ ≥ 4 as well as a sufficiently large anisotropy. In summary, this new study finds that the influence of kappa distributions on the whistler mode instability is complex, not least because the instability depends on several system parameters as well as κ.

Excitation of extremely low-frequency chorus emissions: The role of background plasma density

Low-frequency chorus emissions have recently attracted much attention due to the suggestion that they may play important roles in the dynamics of the Van Allen Belts. However, the mechanism (s) generating these low-frequency chorus emissions have not been well understood. . In this letter, we report an interesting case in which background plasma density lowered the lower cutoff frequency of chorus emissions from above 0.1 fce (typical ordinary chorus) to 0.02 fce (extremely low-frequency chorus). Those extremely low-frequency chorus waves were observed in a rather dense plasma, where the number density Ne was found to be several times larger than has been associated with observations of ordinary chorus waves. For suprathermal electrons whose free energy is supplied by anisotropic temperatures, linear growth rates (calculated using in-situ plasma parameters measured by the Van Allen Probes) show that whistler mode instability can occur at frequencies below 0.1 fce when the background plasma density Ne increases. Especially when Ne reaches 90 cm–3 or more, the lowest unstable frequency can extend to 0.02 fce or even less, which is consistent with satellite observations. Therefore, our results demonstrate that a dense background plasma could play an essential role in the excitation of extremely low-frequency chorus waves by controlling the wave growth rates.

Nonlinear Evolution of Counter‐Propagating Whistler Mode Waves Excited by Anisotropic Electrons Within the Equatorial Source Region: 1‐D PIC Simulations

AbstractNonlinear physical processes related to whistler mode waves are attracting more and more attention for their significant role in reshaping whistler mode spectra in the Earth's magnetosphere. Using a 1‐D particle‐in‐cell simulation model, we have investigated the nonlinear evolution of parallel counter‐propagating whistler mode waves excited by anisotropic electrons within the equatorial source region. In our simulations, after the linear phase of whistler mode instability, the strong electrostatic standing structures along the background magnetic field will be formed, resulting from the coupling between excited counter‐propagating whistler mode waves. The wave numbers of electrostatic standing structures are about twice those of whistler mode waves generated by anisotropic hot electrons. Moreover, these electrostatic standing structures can further be coupled with either parallel or antiparallel propagating whistler mode waves to excite high‐k modes in this plasma system. Compared with excited whistler mode waves, these high‐k modes typically have 3 times wave number, same frequency, and about 2 orders of magnitude smaller amplitude. Our study may provide a fresh view on the evolution of whistler mode waves within their equatorial source regions in the Earth's magnetosphere.

On the conditions for nonlinear growth in magnetospheric chorus and triggered emissions

The nonlinear whistler mode instability associated with magnetospheric chorus and VLF triggered emissions continues to be poorly understood. Following up on formulations of other authors, an analytical exploration of the stability of the phenomenon from a new vantage point is given. This exploration derives an additional requirement on the anisotropy of the energetic electron distribution relative to the linear treatment of the instability, and shows that the nonlinear instability is most favorable to increasing growth rate when electrons become initially trapped in the wave potential of a constant frequency wave. These results imply that the initiation of the nonlinear instability at the equator requires a positive frequency sweep rate, while the initiation of the instability by a constant frequency triggering wave must occur at a location downstream of the geomagnetic equator.

On the ordinary mode and whistler mode instabilities in the degenerate anisotropic plasmas

Employing Vlasov-Maxwell set of equations, we have investigated the O-mode and whistler mode instability in a degenerate anisotropic magnetoplasma environment and compared the results to those reported for classical plasmas. We propose the excitation of a new banded type of instability for the O-mode case, which grows at some particular values of temperature anisotropy and external magnetic field. For the case of whistler wave, we observe instability saturation mechanism similar to the case of classical plasmas. The existence of both O-mode and whistler mode instability has been observed only for some specific range of unstable wavenumbers. The possible excitation of such instabilities in solid state plasma has been discussed, particularly for semiconductor and semimetal plasmas.

Whistler mode instability and pitch-angle diffusion near Ganymede

The present study is aimed at resolving the issue of pitch-angle diffusion by whistler mode waves near Ganymede and to understand the interaction of Ganymede with magnetosphere of Jupiter. A new electron distribution function, which is a combination of Maxwellian and kappa loss-cone distribution, is used to calculate whistler mode wave growth rates. The distribution function is fitted to observed distribution near Ganymede. Wave growth rates have been used to obtain bounce-averaged pitch-angle diffusion coefficients along the field line connecting Ganymede and Jupiter. Variations of electron density and magnetic field along the particle bounce trajectory and a non dipolar field have been taken into account. Pitch-angle variation of diffusion coefficients is parameterized in a simple form ~Dο(sinα)p. Do is diffusion coefficient (independent of pitch angle). The calculated energy dependence of diffusion coefficients (Do) is in good agreement with observed energy dependence of coefficient Do. Wave magnetic field ~16pT is required to match observed and calculated diffusion coefficients. The exponent p takes values from ~1 to 4 for electron energies 15keV to 1MeV, respectively. It is found that contribution of Ganymede interaction region to pitch-angle scattering is quite small (~4% to 20%). Further analysis of Galileo energetic particle detector (EPD) and plasma wave data or new particle and wave data near Ganymede from JUNO mission to Jupiter are necessary to confirm the findings of present work.

Oblique propagating whistler mode wave with parallel AC electric field at magnetosphere of Uranus

Oblique propagating electromagnetic whistler mode instability has been studied having a k vector at angle to ambient magnetic field for bi-Maxwellian distribution function with parallel AC electric field in the magnetosphere of Uranus. The dispersion relation and growth rate have been calculated for plasma parameters suited to the magnetosphere of Uranus by using the method of characteristic solutions and kinetic approach. The effect of AC electric field and temperature anisotropy for oblique propagating electromagnetic whistler mode instability has been reported and discussed in the ‘results and discussion section. The comparisons have been made with observations made by Voyager 2. It is found that whistler mode emissions observed at lower radial distances cannot reproduce in our calculations. The present studies should be helpful in making estimates on the scattering properties of whistler mode waves and, thus, contribute to a better understanding of auroral activity in the planetary atmosphere.

Whistler-mode instability in magnetospheres of Uranus and Neptune

Whistler-mode instability in the magnetospheres of the outer planets Uranus and Neptune is investigated using an anisotropic kappa loss-cone distribution and comparisons have been made with the observations made by Voyager 2. Normalized temporal growth rates have been evaluated numerically at two representative radial distances at each planet. Parametric studies have been performed by changing plasma parameters: cold and hot electron densities, hot electron temperature and temperature anisotropy. It is found that whistler-mode emissions observed at lower radial distances cannot be reproduced in our calculations. Electron pitch-angle diffusion and energy diffusion coefficients have been obtained using the calculated growth rates. The present calculations show that electrons of energy above about 20 keV may be able to precipitate into the planetary atmospheres of both planets. Present studies should be helpful in making estimates on scattering properties of whistler-mode waves and thus contribute to a better understanding of the auroral activity in the planetary atmospheres.

Study of whistler mode instability in Saturn's magnetosphere

Abstract. A dispersion relation for parallel propagating whistler mode waves has been applied to the magnetosphere of Saturn and comparisons have been made with the observations made by Voyager and Cassini. The effect of hot (suprathermal) electron-density, temperature, temperature anisotropy, and the spectral index parameter, κ, on the temporal growth rate of the whistler mode emission is studied. A good agreement is found with observations. Electron pitch angle and energy diffusion coefficients have been obtained using the calculated temporal growth rates.

Excitation of oblique whistler waves in magnetosphere and in interplanetary space at 1 A.U.

The oblique whistler waves have been studied having k vector at an angle to magnetic field for a generalized distribution function reducible to bi-maxwellian and loss-cone. The dispersion relation and growth rate have been obtained for oblique whistler mode instability incorporating the trajectory of the particles, in the presence of perpendicular a-c electric field by method of characteristic solutions. The effects of distribution function and beam effect have been discussed for the space plasma at magnetospheric height and at 1 A.U. The results are compared with satellite observations and reported results obtained by other techniques. Excitation of two separate, but simultaneous left hand polarized whistler mode at 1 A.U. by electron been are demonstrated.

Effect of Cold Plasma Injection on Whistler Mode Instability Triggered by Perpendicular Ac Electric Field at Uranus

The effect of cold plasma injection on whistler mode instability has been studied separately for a bi-Maxwellian and a loss-cone hackground plasma with perpendicular AC electric field. The cold plasma is described by a simple Maxwellian distribution, whereas a generalized distribution function with index j that reduces to a bi-Maxwellian for j = 0 and to a loss-cone for j = 1 has been derived for a plasma in the presence of a perpendicular AC electric field, to form a hot/warm background. The dispersion relation is obtained using the method of characteristic solutions and kinetic approach. An expression for the growth rate of a system with added cold plasma injection has been calculated. Results of sample theoretical calculations for representative values of parameters suited to the magnetosphere of Uranus has been obtained. The salient features of the analysis and the results obtained in both cases have been compared and discussed. It is inferred that it is not the magnitude but the frequency of the AC field which influences the growth rate and a loss-cone background plasma has a triggering effect on the growth rate, increasing the value of the real frequency and maximum growth rate by an order of magnitude. These results may go a long way to enable one to get a better understanding of whistlers and diagnostics of plasma parameters in the Uranian magnetosphere.

Whistler Mode Instability in a Lorentzian (κ) Magnetoplasma in the Presence of Perpendicular A.C. Electric Field and Cold Plasma Injection

The dielectric tensor, modified plasma dispersion function and dispersion relation for Whistler mode instability in an infinite magnetoplasma are obtained in the case of cold plasma injection to background hot anisotropic generalized bi-Lorentzian (κ) plasma in the presence of external perpendicular a.c. electric field. The method of characteristics solutions using perturbed and unperturbed particle trajectories have been used to determine the perturbed distribution function. Integrals and modified plasma dispersion function Zκ *(ξ ) are reduced in power series expansion form. Numerical methods using computer technique have been used to obtained temporal growth rate for magnetospheric plasma at geostationary height. The bi-Lorentzian (κ) plasma is reducible to various forms of distribution function by changing the spectral index κ. The results of bi-Lorentzian (κ) plasma are compared with those of bi-Maxwellian plasma. It has been found that the addition of cold plasma injection gives different frequency spectra. The a.c. frequency of moderate amplitude increases the growth rate and instability in K space to lower range. Growth rate maximum is not affected by a.c. frequencies. However, it shifts the maximum to lower K space in both cases, rather than on the variation of the magnitude. Thus a physical situation like this may explain emission of various high frequency whistler emissions by cold plasma injection. The potential application of controlled plasma experiments in the laboratory and for planetary atmosphere are indicated.

Enhanced whistler‐mode emissions: Signatures of interchange motion in the Io torus

During the Galileo inbound pass through the Io torus the plasma wave instrument detected intervals of enhanced whistler‐mode emissions. Over two of these intervals in the inner torus (L &lt; 6.5), for which energetic particle data is also available, the flux and pitch angle anisotropy of resonant electrons exhibited a simultaneous enhancement consistent with inward adiabatic transport from a source region in the outer torus. The enhanced electromagnetic emissions are interpreted as a modulation of cyclotron whistler‐mode instability above the normal marginally stable state of the plasma. This suggests that the enhanced emissions are a sensitive indicator of rapid inward transport associated with interchange motions in the Io torus.

Generation of whistler emissions by injection of hot electrons in the presence of a perpendicular Ac electric field

The dispersion for the whistler mode instability in an infinite magnetoplasma in the presence of a perpendicular electric field for a loss cone type distribution function having an anisotropic temperature is obtained. The method of characteristics solutions using the perturbed and unperturbed particle trajectories have been used to determine the perturbed distribution function. Growth rates for various strengths of the loss cone index have been determined. The effect of injection of hot energetic particles of solar wind origin having a positive slope and a loss cone index j=1 has been evaluated. The ac frequency, rather than its magnitude, affects the growth rate and shifts the maxima to a higher or frequency range, modifying the resonance conditions of charged particles. The injection of a higher number of energetic hot electrons affects the growth rate significantly, decreasing the maxima by an order of magnitude and shifting them to a lower frequency or ranges in contrast to cold plasma injection results. This result is of importance in explaining the observed VLF emissions over a wide frequency range.

One‐ and two‐dimensional simulations of whistler mode waves in an anisotropic plasma

We present results from self‐consistent, one‐ and two‐dimensional, electromagnetic simulations of the electron whistler mode instability relevant to the near‐Earth nightside plasma sheet region during geomagnetically disturbed times. Specifically, we study the evolution of energetic, anisotropic (T⊥ &gt; T∥) electron distributions that are injected into the nightside ring current region at geomagnetically disturbed times, the resulting growth of electron whistler mode waves, and subsequent electron pitch angle diffusion via electron whistler wave‐particle interactions. Growth of whistler mode waves from an initial pitch angle anisotropy (T⊥ ≈ 4 T∥) is studied in the strong pitch angle diffusion regime (defined as having scattering times much shorter than a typical electron bounce time in the near Earth's dipolar field). The quasi‐linear and subsequent nonlinear evolution of waves and the corresponding migration of electrons in velocity space is followed over timescales such that ion motion may be neglected. Our simulations contain wave frequencies and growth rates that are a significant fraction of the electron gyrofrequency (ω ∼ 0.5ωce, γ ∼ 0.1ωce being typical) and the simultaneous evolution of waves propagating both parallel and nonparallel to the ambient magnetic field direction. Effects due to these are not usually accounted for in applications of quasi‐linear theory to the problem of electron whistler wave‐particle interactions, so that our self‐consistent simulations of the electron whistler instability provide an important insight into the applicability of quasi‐linear theory to the velocity space diffusion of electrons due to electron whistler wave‐particle interactions. We examine the dependence of whistler mode wave growth rates, nonlinear wave mode saturation, and pitch angle diffusion rates on the β value of the hot electron species which contains the resonant population, and we compare the differences between results of one‐ and two‐dimensional simulations. In general, we have found significantly larger average growth rates in a one‐dimensional than in a two‐dimensional geometry, by up to a factor of ∼2–3, with the difference between such growth rates becoming larger as β increases. As a result, we find pitch angle diffusion rates are significantly larger (by up to a factor of ∼10) in a one‐dimensional geometry, and pitch angle diffusion rates increase as β increases. During the early wave growth period of the instability, pitch angle diffusion rates Dα have been found to scale to magnetic wave energy Bw², approximately Dα ∝ Bw². We also show that in the self‐consistently evolved system (containing several wave modes), the pitch angle diffusion is still consistent with a usual quasi‐linear approach in which resonant particles are taken to diffuse along surfaces of constant wave frame energy.

An assessment of plasma instabilities or planetary lightning as a source for the VLF bursts detected at Venus

VLF signals detected in the nightside ionosphere of Venus have generally been attributed to atmospheric lightning. However it has recently been suggested that these bursts could be generated by either whistler-mode or lower hybrid drift instabilities. It has previously been shown that the growth rate for whistler-mode instabilities in the nightside ionosphere is too small for appreciable growth at altitudes < 200 km, where the VLF burst rate is highest. We show that the bursts are usually observed in regions of low electron β, where whistler-mode attenuation is small. We further show that many of the bursts are detected in regions of high collision frequency, which stabilizes the lower hybrid drift instability. Lastly, the waves are also detected in regions where the wavelength required for Doppler-shift of lower hybrid waves to 100 Hz is shorter than the electron Larmor radius, which also argues against a lower hybrid drift instability. Planetary lightning is consequently a more likely source for the VLF bursts.

Whistler mode waves in the Jovian magnetosheath

During the Ulysses flyby of Jupiter in February 1992, the spacecraft traversed the Jovian magnetosheath for a few hours during the inbound pass and for a few days during the outbound pass. Burstlike electromagnetic waves at frequencies of ∼0.1‐0.4 of the local electron cyclotron frequency have been observed by the Unified Radio and Plasma Wave (URAP) experiment. The waves were more often observed in the regions which were probably the outer or middle magnetosheath, especially near the bow shock, and rarely seen in the magnetosphere/magnetosheath boundary layer. The propagation angles of the waves are estimated by comparing the measurements of the wave electric and magnetic fields in the spacecraft spin plane with the corresponding values calculated using the cold plasma dispersion relation under local field and plasma conditions. It is found that the waves propagate obliquely with wave angles between ∼30° and 50°. These waves are likely to be the whistler mode waves which are excited by suprathermal electrons with a few hundred eV and a slight anisotropy (T⊥/T∥ ∼1.1‐1.5). They are probably similar in nature to the lion roars observed in the Earth's magnetosheath. Signature of coupling between the mirror mode and the whistler mode have also been observed. The plasma conditions which favor the excitation of the whistler mode instability during the wave events exist as observed by the plasma experiment of Ulysses.

Electron beam excitation of upstream waves in the whistler mode frequency range

We examine whistler mode instabilities arising from electron beams in interplanetary space at 1 AU. Both parallel and obliquely propagating solutions are considered. We demonstrate that the generation of two simultaneous whistler mode waves is possible, and even reasonably likely, for beam parameters frequently encountered upstream of the Earth's bow shock and at interplanetary shocks. We also explore the generation of left‐hand polarized waves at whistler mode frequencies under these same conditions. We offer both parametric variations derived from numerical solutions of the various instabilities as well as an analytical treatment of the problem which succeeds in unifying the various numerical results.