Whistler wave instabilities in collisionless current sheet

Instability of whistler wave in collisionless current sheet is studied with numerical solution of the general dispersion relation obtained in Ref.[4] for the physical model A. As revealed by the results, the whistler wave can be directly absorbed by collisionless current sheets. On the neutral sheet (z/d_i = 0) oblique whistler waves over a rather wide range of wave numbers can propagate, while they are basically stable. In the ionic inertial region (z/d_i < 1), the obliquely propagating whistler wave is unstable. On the edge of the ionic inertial region (z/d_i = 1), the whistler wave is still unstable, with an increase in the growth rate, and in the frequency of the unstable wave. The growth rate is larger for the whistler wave propagating towards the neutral sheet (k_zd_i < 0) than away from the neutral sheet (k_zd_i > 0).     

Collisionless tearing modes in the presence of shear flow

Tearing modes in a plane collisionless current sheet with shear bulk flow are studied. An analytic expression for the growth rate is obtained for the case \(M^2 = (1 - \varepsilon {\text{ sech}}^m \bar z)\) , whereM is the Mach number,m the shear flow index, ε a positive constant less than unity, and \(\bar z\) the (normalized) co-ordinate normal to the current sheet. The growth rates are large and the unstable wave number domain is increased as compared to the case without flow. The relevance of these results to time-dependent reconnection processes in the Earth's magnetosphere is discussed.     

Influence of the Variations of Current Sheet Parameters on the Acceleration of Electrons

By the test particle method, we have investigated the kinematic characteristics of the electrons in the reconnecting current sheet with a guiding magnetic field B_z after they are accelerated by the supper-Dreicer electric field E_z. Firstly, the influence of the guiding magnetic field B_z on the particle acceleration is discussed under the assumption that B_z is constant in magnitude but different in orientation with respect to the electric field. In this case, the variation of the B_z direction directly leads to the variation of electron trajectories and makes electrons leave the current sheet along different paths. If B_z is parallel to E_z, the pitch angles of the accelerated electrons are close to 180°. If B_z is anti-parallel to E_z, the pitch angles of the accelerated electrons are close to 0°. The orientation of the guiding magnetic field just makes the electric field accelerate selectively the electrons in different regions, but does not change the energy distribution of electrons, and the finally derived energy spectrum is the common power-law spectrum E^?γ. In typical coronal conditions, γ is about 2.9. The further study indicates that the magnitude of γ depends on the strengths of the guiding magnetic field and reconnecting electric field, as well as the scale of the current sheet. Then, the kinematic characteristics of the accelerated electrons in the current sheet with multiple X-points and O-points are also studied. The result indicates that the existences of the X-points and O-points have the particles constrained in the accelerating region to obtain the maximum acceleration, and the final energy spectrum has the characteristics of multi-power law spectra.     

The analytic properties of the flapping current sheets in the earth magnetotail

The current sheet in Earth’s magnetotail often flaps, and the flapping waves could be induced propagating towards the dawn and dusk flanks, which could make the current sheet dynamic. To explore the dynamic characteristics of current sheet associated with the flapping motion holistically and provide reasonable physical interpretations, detailed direct calculation and analysis have been applied to one approximate analytic model of magnetic field in the flapping current sheet. The main results from the model demonstrate: (1) the magnetic fluctuation amplitude is attenuated from the center of current sheet to the lobe regions; The larger wave amplitude would induce the larger magnetic amplitude; (2) the curvature of magnetic field lines (MFLs), with maximum at the center of current sheet, is only dependent on the displacement Z along the south-north direction from the center of current sheet, regardless of the tilt of current sheet; (3) the half-thickness of neutral sheet, h, the minimum curvature radius of MFLs, R_cmin, and the tilt angle of current sheet, δ, satisfies h=R_cmin cos δ; (4) the gradient of magnetic strength forms a double-peak profile, and the peak value would be more intense if the local current sheet is more tilted; (5) current density j and its j_y, j_z components reach the extremum at the center of CS. j and j_z would be more intense if the local current sheet is more tilted, but it is not the case for j_y; and (6) the field-aligned component of current density mainly appears in the neutral sheet, and the sign of it would change alternatively as the flapping waves passing by. To check the validity of the model, one simulation on the virtual measurements has been made, and the results are in well consistence with actual observations of Cluster.     

The study of magnetic reconnection in solar spicules

This work is devoted to study the magnetic reconnection instability under solar spicule conditions. Numerical study of the resistive tearing instability in a current sheet is presented by considering the magnetohydrodynamic (MHD) framework. To investigate the effect of this instability in a stratified atmosphere of solar spicules, we solve linear and non-ideal MHD equations in the x?z plane. In the linear analysis it is assumed that resistivity is only important within the current sheet, and the exponential growth of energies takes place faster as plasma resistivity increases. We are interested to see the occurrence of magnetic reconnection during the lifetime of a typical solar spicule.     

Effect of parallel electric fields on whistler mode waves in an anisotropic Jovian magnetospheric plasma

The effect of parallel electrostatic field on the amplification of whistler mode waves in an anisotropic bi-Maxwellian weakly ionized plasma for Jovian magnetospheric conditions has been carried out. The growth rate for different Jovian magnetospheric plasma parameters forL = 5.6R _j has been computed with the help of general dispersion relation for the whistler mode electromagnetic wave of a drifted bi-Maxwellian distribution function. It is observed that the growth or damping of whistler mode waves in Jovian magnetosphere is possible when the wave vector is parallel or antiparallel to the static magnetic field and the effect of this field is more pronounced at low frequency wave spectrum.     

Cross-scale coupling at a perpendicular collisionless shock

A full particle simulation study is carried out on a perpendicular collisionless shock with a relatively low Alfven Mach number (M_A = 5). Recent self-consistent hybrid and full particle simulations have demonstrated ion kinetics are essential for the non-stationarity of perpendicular collisionless shocks, which means that physical processes due to ion kinetics modify the shock jump condition for fluid plasmas. This is a cross-scale coupling between fluid dynamics and ion kinetics. On the other hand, it is not easy to study cross-scale coupling of electron kinetics with ion kinetics or fluid dynamics, because it is a heavy task to conduct large-scale full particle simulations of collisionless shocks. In the present study, we have performed a two-dimensional (2D) electromagnetic full particle simulation with a “shock-rest-frame model”. The simulation domain is taken to be larger than the ion inertial length in order to include full kinetics of both electrons and ions. The present simulation result has confirmed the transition of shock structures from the cyclic self-reformation to the quasi-stationary shock front. During the transition, electrons and ions are thermalized in the direction parallel to the shock magnetic field. Ions are thermalized by low-frequency electromagnetic waves (or rippled structures) excited by strong ion temperature anisotropy at the shock foot, while electrons are thermalized by high-frequency electromagnetic waves (or whistler mode waves) excited by electron temperature anisotropy at the shock overshoot. Ion acoustic waves are also excited at the shock overshoot where the electron parallel temperature becomes higher than the ion parallel temperature. We expect that ion acoustic waves are responsible for parallel diffusion of both electrons and ions, and that a cross-scale coupling between an ion-scale mesoscopic instability and an electron-scale microscopic instability is important for structures and dynamics of a collisionless perpendicular shock.     

Generation of 1–30 Hz waves near the plasmapause by resonant electron-instability

A generation mechanism for 1–30 Hz waves of the second category, observed near the plasmapause by Taylor and Lyons (1976), is suggested in terms of a resonant electron instability. The instability arises because of the resonant interaction between the ring current electrons outside the plasmapause and the ordinary mode drift waves. The instability can generate waves in the frequency range from 0.45 to 35.0 Hz in the region between L = 4.5 and 5.5. The instability can also explain satisfactorily the other properties such as no changes in the proton distributions, the direction of the wave magnetic field and the localization of the region of wave activity, associated with these waves.     

Radial plasma drifts deduced from VLF whistler mode signals: A modelling study

VLF whistler mode signals have previously been used to infer radial plasma drifts in the equatorial plane of the plasmasphere and the field-aligned ionosphere-protonosphere coupling fluxes. Physical models of the plasmasphere consisting of O⁺ and H⁺ ions along dipole magnetic field lines, and including radial Ez × B drifts, are applied to a mid-latitude flux tube appropriate to whistler mode signals received at Wellington, New Zealand, from the fixed frequency VLF transmitter NLK (18.6 kHz) in Seattle, U.S.A. These models are first shown to provide a good representation of the recorded Doppler shift and group delay data. They are then used to simulate the process of deducing the drifts and fluxes from the recorded data. Provided the initial whistler mode duct latitude and the ionospheric contributions are known, the drifts at the equatorial plane can be estimated to about ± 20 ms^?1 (～10–15%), and the two hemisphere ionosphere-protonosphere coupling fluxes to about ± 10¹² m^?2 s^?1 (～40%).     

A short wavelength instability in the neutral sheet of the earth's geomagnetic tail

In an earlier paper, Bowers (1973), ion plasma oscillations were found to be unstable in the steady state developed by Cowley (1972) for the neutral sheet in the Earth's geomagnetic tail. In this paper a similar stability analysis is carried out but for a different steady state, suggested by Dungey, with the result that unstable waves with frequencies near the electron plasma frequency are found. In the Dungey steady state the current necessary for magnetic field reversal is carried by plasma originating from both the magnetosheath and the lobes of the tail. This modifies the steady state proposed by Alfvén and subsequently developed by Cowley in which all the current is carried by plasma from the lobes of the tail thereby fixing the cross-tail potential Φ. With magnetosheath plasma present the value of Φ is no longer fixed solely by parameters in the lobes of the tail but the cross-tail electric field is still assumed localised in the dusk region of the sheet as in the Cowley model due to the balance of charge required in the neutral sheet. The value of Φ can be expected to increase as magnetic flux is transported to the tail which inflates and causes flux annihilation because the magneto-sheath plasma in the neutral sheet has insufficient pressure to keep the two lobes of the tail apart. The Vlasov-Maxwell set of equations is perturbed and linearised enabling a critical condition for instability to be found for modes propagating across the tail. Typically, this condition requireseΦ≳KT _m whereT _m is the temperature of magnetosheath electrons. The instability occurs in the presence of cold plasma which hasE×B drifted into the neutral sheet from the lobes of the tail. This contrasts with the usual two stream instability which is stabilised by the cold plasma. Once precipitated the instability may be explosive provided current disruption occurs, for then a further increase in Φ will result which drives a greater range of wave numbers unstable thereby causing even more turbulence and an even larger cross-tail electric field. Because of this behaviour the instability may be a trigger for a substorm.     

The effect of pressure anisotropy on the equilibrium structure of magnetic current sheets

The equilibrium structure of two-dimensional magnetic current sheets is investigated for systems in which the plasma pressure dominates the bulk flow energy, as appears appropriate for the quiet time plasmasheet in the geomagnetic tail. A simple model is studied in which the field is contained between plane parallel boundaries and varies exponentially along the system, while the plasma pressure is anisotropic, the anisotropy being arbitrary but constant along the centre plane. When the field is highly inflated by the plasma current it is found that adiabatic solutions exist only when the plasma pressure is close to isotropic. For the case P_∥ > P_⊥ it is argued that a thin, non-adiabatic current layer will in general form at the sheet centre, usually embedded within a much broader adiabatic current distribution. When P_⊥ > P_∥, a broad region of very depressed fields develops about the centre of the current sheet, terminated at its outer boundary by a spike in the current density. This central region becomes unstable to the mirror mode well before the limiting adiabatic solution is reached.     

Collisionless Magnetic Reconnection in the Presence of Initial Guide Field

By using the method of 2-dimensional, 3-component full particle simulation, collisionless magnetic reconnection in the presence of various initial guide fields and the Harris current sheet with 1-dimensional initial state are studied. The results show that strong guide fields with B_z0 > 0.5B₀ can evidently alter not only the trajectory of the particles, but also the structure of the electric and velocity fields in the vicinity of the reconnection region, thereby affecting the rate of reconnection and the acceleration of electrons. The generalized Ohm's law is employed to interpret the structural characteristics of the electric fields with various guide fields. Also, via the tracing of the electron beam near he diffusion region, it is revealed that in the 2-D model, for both strong and weak guide fields, the induced electric field perpendicular to the simulation plane at the center of the diffusion region plays the major role in the acceleration of electrons. The contribution of the planar electric field outside the diffusion region is very small.     

Parallel electric field-induced instability in the magnetospheric ion-electron plasma

A complete dispersion relation for a whistler mode wave propagation in an anisotropic warm ion-electron magnetoplasma in the presence of parallel electric field using the dispersion relation for a circularly polarized wave has been derived. The dispersion relation includes the effect of anisotropy for the ion and electron velocity distribution functions. The growth rate of electron-ion cyclotron waves for different plasma parameters observed atL = 6.6R _E has been computed and the results have been discussed in detail in the light of the observed features of VLF emissions and whistlers. The role of the combination of ion-cyclotron and whistler mode electromagnetic wave propagation along the magnetic field in an anisotropic Maxwellian weakly-ionized magnetoplasma has been studied.     

On the stability and evolution of stationary whistler turbulence

It is shown that stationary turbulence consisting of an ensemble of small amplitude whistler wave packets becomes unstable against adiabatic perturbations. The rate of increase of the purely growing instability is presented. A stationary non-linear BGK solution for the whistler electric fields is obtained.     

Generation of intermediate drift bursts in solar type IV radio continua through coupling of whistlers and Langmuir waves

The possible generation of intermediate drift bursts in type IV dm continua through coupling between whistler waves, traveling along the magnetic field, and Langmuir waves, excited by a loss-cone instability in the source region, is elaborated. We investigate the generation, propagation and coupling of whistlers. It is shown that the superposition of an isotropic background plasma of 10⁶K and a loss-cone distribution of fast electrons is unstable for whistler waves if the loss-cone aperture 2α is sufficiently large (sec α?4); a typical value of the excited frequencies is 0.1 ω _ce (ω _ce is the angular electron cyclotron frequency). The whistlers can travel upwards through the source region of the continuum along the magnetic field direction with velocities of 21.5–28 v _A (v _A is the Alfvén velocity). Coupling of the whistlers with Langmuir waves into escaping electromagnetic waves can lead to the observed intermediate drift bursts, if the Langmuir waves have phase velocities around the velocity of light. In our model the instantaneous bandwith of the fibers corresponds to a frequency of 0.1–0.5 ω _ce and leads to estimates of the magnetic field strength in the source region. These estimates are in good agreement with those derived from the observed drift rate, corresponding to 21.5–28 v _A, if we use a simple hydrostatic density model.     

Enhanced energetic electron intensities at 100 km altitude and a whistler propagating through the plasmasphere

During the flight of a Petrel rocket, instrumented by the SRC Radio and Space Research Station with Geiger counters and launched westwards from South Uist, Outer Hebrides, Scotland (L=3.38), a transient increase was observed in the intensity of energetic electrons having pitch angles between 60 and 120°. The increase, by a factor of 20 above the quasi-steady intensity observed throughout the remainder of the flight, occurred in 0.8 sec and was simultaneous for both >45 keV and >110 keV electrons. Recorded ～0.5 sec later, on the ground, was a two-hop whistler. During the enhanced electron intensity event, the entire duration of which was ～6 sec, the four-, six- and eight-hop whistlers were also received. From an analysis of the whistlers' spectrogram, it is concluded that the whistlers were ducted through the magnetosphere along the L=3.3 ±0.1 field line; the electron density in the equatorial plane is found to be 330 ±10 cm^?3, a value characteristic of conditions within the plasmapause. It is suggested that these temporally and/or spatially associated phenomena, rather than arising by a chance coincidence, were the result of a gyroresonant interaction between energetic electrons and whistler mode waves moving in opposite directions. For gyroresonance on this field line at the equator, the parallel component of energy of the electrons is 25 keV at 3 kHz in the whistler band, or 100 keV at 1 kHz below it. It is suggested that a magnetospheric event occurred, causing both sudden enhanced electron precipitation and favourable conditions for the propagation and/or amplification of whistlers. A possible explanation is that energetic electrons, having a sufficiently anisotropic distribution function and associated with those injected during an earlier auroral substorm, become unstable via the transverse resonance instability when they drift into the plasmasphere, a region of high density thermal plasma.     

Magnetic instability in a rotating layer at highly eccentric positions of the critical level

This study follows the numerical results presented in Marsenić & Ševčík (2010) that explored the influence of the critical level position on stability of a system. The model was a horizontal fluid layer between z = ±0.5d rotating with an angular velocity Ω = Ω₀ ž about the vertical axis z . The fluid was considered to be inviscid, finitely electrically conducting and incompressible and was permeated by a horizontal magnetic field B ₀ = ℬ︁₀B₀(z) y̌ , where ℬ︁₀ was the magnitude of the field and the function B₀(z) = tanh [γ (z –z₀)]. When γ is large, the field gradient is concentrated near z = z₀, the critical level, the field being almost homogeneous elsewhere. In this way it controls the width of the magnetic shear layer associated with the current sheet. It was found that at conditions when the magnetic field gradient was large enough (γ = O (10)) and the critical level was placed close enough to the (bottom) perfectly conducting boundary (z₀ < –0.388d for γ = 80), magnetically driven convection appeared localized to a close neighbourhood of the critical level – the so called critical layer. Based on the circumstances of its rise and its properties it was identified with the resistive tearing‐mode instability. This paper presents an analytical treatment of the problem assuming γ ≥ 1. The approach consists in separation of the computational domain into an outer region where the diffusionless limit (Elsasser number Λ → ∞) applies and an inner region (the critical layer) of finite conductivity. According to the tearing‐mode theory in classical systems, the solution in the inner region is sought as long‐wavelength with respect to the width of the critical layer. The obtained solution shows features similar to the one obtained numerically and confirmed relevance of the simplifying physical assumptions made in each region. The convection in the critical layer is strictly conditioned by a sharp magnetic shear. If the shear region is removed by further positioning of the critical level towards the perfectly conducting boundary, the localized convection disappears. It is in compliance with the fact that the system is stabilised by a perfectly conducting boundary with respect to the tearing mode. Stability is then checked numerically in the layer bounded by perfectly conducting boundaries where the critical point of the magnetic field lies on one of them. The existence of a magnetically driven instability is confirmed. Depending on the value γ, it may rise as a stationary convection (for γ < 1.5) or as a wave which for γ > 16 exhibits similarity properties (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The ducting of wave energy by field-aligned current sheets

A theoretical treatment of the modes of oscillation of an idealized current sheet (in which there is no perpendicular temperature) is given. For the simple case of a monoenergetic current sheet computational results are presented. These results indicate the existence of two types of ducted mode which may have relevance to observation. The first of these is a ducted “whistler” mode and the second occurs at somewhat higher frequencies and at phase velocities comparable with the streaming velocity of the current carriers in the sheet region. A simple explanation of how the ducted “whistler” mode can arise is given.     

Comments on the proton whistler generation process

The problem of the propagation of an electromagnetic wave originating for instance in a lightning flash through the ionospheric medium is analysed in order to understand the formation at high ionospheric altitudes of the so-called proton whistler. It is shown that the accessibility of the hydrodynamic (or kinetic) proton resonance at the satellite altitude requires that a mode conversion process must take place slightly above the transition region separating the one ion (O⁺) from the two ion (O⁺ + H⁺) component plasmas. Moreover, the transformation conditions in the wave conversion region imply that the magnetic field should be (almost) perpendicular to the density gradient. Otherwise, the incident electromagnetic wave will never reach the satellite altitude in the frequency range of the proton whistler. However, some former proton whistler theories have postulated that the signal is the result of simple ionospheric propagation effects, in contradiction with the above results. These former proton whistler theories are reviewed and it is shown that the basic flaw in these theories lies in that the incident electromagnetic wave has been supposed from the beginning to have reached the high ionospheric altitudes where is located the satellite without being influenced by the lower ionospheric layers. Some various aspects, like the high variability of the wave electric to magnetic field ratio and the harmonics bands as observed by Injun are analysed in the light of the obtained results. Finally, numerical solutions of the wave dispersion relation for both the fast hydrodynamic mode (the extraordinary mode) and the slow ion kinetic mode are presented which shows that a coupling process between the two modes may take place at various frequencies between the O⁺ and the H⁺ gyrofrequencies.     

Drift instabilities associated with the particles in ring current and inner edge of plasma sheet

Electromagnetic waves propagating transverse to the magnetic field, containing inhomogenous and loss cone plasma, may become unstable due to the excitation of resonant proton, resonant electron and drift cyclotron instabilities. Resonant proton instability gets excited in inhomogenous plasma, irrespective of the presence of temperature anisotropy, loss cone or temperature gradient. However, the growth rate of this instability is much smaller than the other two instabilities. The maximum growth rates of resonant electron instability are enhanced with the increase of loss cone index, gradients in transverse temperature and magnetic field, and with the decrease of temperature anisotropy and gradients in density and parallel temperature. The drift cyclotron instability exists in a bounded range of wave numbers and its growth rate increases with the increase of electron temperature, density and magnetic field gradient, and with the decrease of proton temperature and temperature anisotropy. In the region of ring current for beyond plasmapause the resonant proton and resonant electron instabilities have the characterstic frequencies around 0.1Ω_p and growth rates ~10^?6Ω_p and 10^?3Ω_p, respectively. In the ring current region the drift cyclotron instability is not excited whereas in the plasma sheet region the frequency and growth rate of this instability are around Ω_p and 10^?2Ω_p, respectively. These instabilities can accelerate the ring current particles along the magnetic field lines and dump them into the auroral region.