The Influence of Guiding Field on Low-frequency Electromagnetic Instabilities in Collisionless Current Sheets

This work investigates the effect of guiding field on low-frequency electromagnetic instabilities in collisionless current sheets using the dispersion relation obtained in the collisionless and compressible magnetohydrodynamic model. The results in the following three cases show that the guiding field can strongly affect the 3-dimensional propagating disturbed waves. (1) On the middle plane of the current sheet (z = 0), if there is no guiding field, then no instability is observed. But if there a guiding field, then instability can take place. (2) Near the middle plane of the current sheet (z = 0.2), the current sheet becomes unstable. With increasing the intensity of the guiding field, the instability grows obviously. The wave mode may be whistler or low-hybrid wave. (3) Near the edge of the current sheet (z = 0.8), the guiding field exhibits no evident effect and the unstable wave mode is a quasi-parallel whistler wave.     

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).     

Whistler wave amplitude oscillation and frequency modulation in the magnetospheric cavity

A magnetospheric cavity model is presented to explain self-pulsing and frequency modulation of ducted whistler waves associated with triggered emissions. Partial reflection of these waves at the ends of the duct suggests such a magnetospheric cavity analogous to a laser cavity.     

A note on adiabatic solutions of the one-dimensional current sheet problem

It has recently been shown that adiabatic solutions of the one-dimensional current sheet problem exist provided that magnetically trapped particles are included in the model together with the current-carrying untrapped “beam” particles. We show here that a formulation of the problem in terms of particle velocity and pitch angle is advantageous, and we derive some general properties of the solutions. In particular it is shown that there is, in general, no discontinuity in the value of the particle distribution function ? across the boundary in velocity space between “beam” and trapped particles, but that there will be a discontinuity in the gradients of ?. An example is given in which the beam population is of bi-Maxwellian form at the outer boundary of the current sheet.     

Origin of Mercury’s double magnetopause: 3D hybrid simulation study with A.I.K.E.F.

During the first and second Mercury flyby the MESSENGER spacecraft detected a dawn side double-current sheet inside the Hermean magnetosphere that was labeled the “double magnetopause” (Slavin, J.A. et al. [2008]. Science 321, 85). This double current sheet confines a region of decreased magnetic field that is referred to as Mercury’s “dayside boundary layer” (Anderson, M., Slavin, J., Horth, H. [2011]. Planet. Space Sci.). Up to the present day the double current sheet, the boundary layer and the key processes leading to their formation are not well understood. In order to advance the understanding of this region we have carried out self-consistent plasma simulations of the Hermean magnetosphere by means of the hybrid simulation code A.I.K.E.F. (Müller, J., Simon, S., Motschmann, U., Schüle, J., Glassmeier, K., Pringle, G.J. [2011]. Comput. Phys. Commun. 182, 946–966). Magnetic field and plasma results are in excellent agreement with the MESSENGER observations. In contrast to former speculations our results prove this double current sheet may exist in a pure solar wind hydrogen plasma, i.e. in the absence of any exospheric ions like sodium. Both currents are similar in orientation but the outer is stronger in intensity. While the outer current sheet can be considered the “classical” magnetopause, the inner current sheet between the magnetopause and Mercury’s surface reveals to be sustained by a diamagnetic current that originates from proton pressure gradients at Mercury’s inner magnetosphere. The pressure gradients in turn exist due to protons that are trapped on closed magnetic field lines and mirrored between north and south pole. Both, the dayside and nightside diamagnetic decreases that have been observed during the MESSENGER mission show to be direct consequences of this diamagnetic current that we label Mercury’s “boundary-layer-current“.     

Instability of a thin field-aligned electron beam in a plasma

The formulation of Elliott (1975) is recapitulated somewhat more elegantly for a monenergetic beam of “Top Hat” profile. The mode corresponding most closely to the parallel-polarized mode in a uniform beam is explored for phase velocities less than the beam velocity and frequencies between the hybrid frequencies. The mere existence of solutions indicates the possibility of instability in some real case. Solutions are found for all frequencies except for a range above the gyrofrequency, beyond which a ducted solution exists up to the plasma frequency. In the other range radiative solutions exist.The nature of the results provides a guide for several applications, but more realistic models must be specific to the application.     

Linear and nonlinear cyclotron instability and VLF emissions in the magnetosphere

A theoretical study is made of the whistler mode cyclotron instability both in linear and nonlinear regimes in conjunction with the generation of VLF emissions in the magnetosphere. For the nonlinear treatment, a well-established quasilinear method is used and some physical processes of the cyclotron instability viz. energy conservation, mechanism of instability and frequency change of the excited emissions are clarified. The results are applied to some types of the triggered VLF emissions; whistler triggered emissions and artificially stimulated emissions (ASE). It is found that whistler triggered emissions excited around the upper cutoff frequencies of whistlers may be explained by the whistler mode cyclotron instability by a model distribution function inferred from satellite data. In order to see a nonlinear evolution of the whistler mode cyclotron instability, computer simulations were carried out and it is shown that the change of frequency with time of whistler triggered emissions as well as characteristics of ASE are well explained by resonant nonlinear behaviour of whistler mode cyclotron instability considered in the present paper.     

Quasilinear effect of noise in a magnetic neutral sheet

Recent linear calculations concerning waves in a magnetic neutral sheet have been extended by a crude quasilinear treatment. By making speculative, but plausible, assumptions about the noise, a simple expression is obtained for the velocity diffusion coefficient for those electrons which move in “serpentine” orbits. With an assumption about the velocity distribution it is possible to calculate the rate of change of current density due to the noise, which is expressed as an equivalent electric field.     

Current sheet acceleration of ions in the geomagnetic tail and the properties of ion bursts observed at the lunar distance

Recent analyses of measurements obtained from the Rice University Apollo 14 SIDE on the lunar surface have revealed the frequent appearance of fast tailward-streaming ion “bursts” near the centre plane of the geomagnetic tail. In this paper the properties of these “bursts” are tested for compatibility with tail current sheet tangential stress balance conditions assuming that they are produced by current sheet acceleration of tail lobe plasma downstream and tailward of a magnetic neutral line. Calculations are performed taking the ions to be either protons or singly charged oxygen, the latter possibility being directly suggested by several recent observations. When “burst” bulk parameters are calculated by assuming that the ion distribution functions are convecting isotropic Maxwellians, the results are found to be difficult to reconcile with current sheet stress balance conditions for either protons or oxygen. Use of a different ion distribution based on theoretical expectations and observations in the near-Earth tail, however, results in number density estimates being increased by factors of around an order of magnitude. When the revised densities and ion distribution functions are taken into account, reasonable agreement between observed and expected ion bulk speeds is obtained. In some cases the agreement is better assuming oxygen ions rather than protons, but not by a large factor.     

VLF emissions and substorm activity

The resonant interaction between the whistler mode waves and the energetic electrons near the plasmapause boundary has been studied in the presence of field aligned currents which seem to exist during substorm activity. It is shown that the electrons which carry the current along the direction of the magnetic field enhance the whistler mode growth considerably if the streaming velocity is small compared to the phase velocity of the wave. It is likely that this is one of the mechanisms explaining the intense VLF emissions observed near the plasmapause during substorm activity.     

Electron acceleration within coronal loops: A wave-particle process?

A simple model as given which aims at explaining how electrons could be accelerated within solar coronal loops due to their trapping by quasi-monochromatic whistler waves.Proceedings of the Second CESRA Workshop on Particle Acceleration and Trapping in Solar Flares, held at Aubigny-sur-Nère (France), 23–26 June, 1986.     

A note on the motion of charged particles in one-dimensional magnetic current sheets

By considering the integrals of the motion of charged particles moving in one-dimensional current sheets, a simple and exact proof is given that particles which are either magnetically or electrostatically trapped about such a current sheet exhibit zero net drift. The transition to the special case of a strictly neutral sheet, a limit remaining unclear from previous studies, is also elucidated. Finally, the relationship between the results and existing self-consistent current sheet solutions is discussed.     

Propagation Characteristics and Generation Mechanism of ELF/VLF Hiss Observed at Low-latitude Ground Station (L = 1.17)

Extremely low frequency (ELF)/Very low frequency (VLF) hiss is whistler mode wave that interacts with energetic electrons in the magnetosphere. The characteristics features of ELF/VLF hiss observed at low latitude ground station Jammu (Geomag. lat. 22°16′ N, L=1.17) are reported. It is observed that most of hiss events first propagate in ducted mode along higher L-values (L = 4–5), after reaching lower edge of ionosphere excite the Earth-ionosphere waveguide and propagate towards equator to be received at low-latitude station Jammu. To understand the generation mechanism of ELF/VLF hiss, incoherent Cerenkov radiated power from the low-latitude and mid-latitude plasmasphere are evaluated. Considering this estimated power as an input for wave amplification through wave–particle interaction, the growth rate and amplification factor is evaluated which is too small to explain the observed wave intensity. It is suggested that some non-linear mechanism is responsible for the generation of ELF/VLF hiss.     

The three-dimensional geometry of the heliospheric current sheet

The three-dimensional geometry of the heliospheric current sheet seen from fixed points in interplanetary space is constructed for idealized (sinusoidal) magnetic neutral lines (equators) and for an observed magnetic equator on the basis of the “kinematic method” developed by Hakamada and Akasofu (1982). The cross-sections of the wavy current sheet at distances 1, 2 and 5 a.u. are also constructed for the idealized magnetic neutral lines.     

POLAR 5—an electron accelerator experiment within an aurora. 3. Evidence for significant spacecraft charging by an electron accelerator at ionospheric altitudes

The POLAR 5 rocket experiment carried an electron accelerator on a “daughter” payload which injected a 0,1 A beam of 10 keV electrons in a pulsed mode every 410ms. With spin and precession, injections were made over a wide range of pitch angles. Measurements from a double probe electric field instrument and from particle detectors on the “mother” payload and from a crude R.P.A. on the “daughter” payload are interpreted to indicate that the “daughter” charges to a potential between several hundred volts and 1 kV. The neutralizing return current to the “daughter” is shown to be assymetrically distributed with the majority being collected from the direction of the beam. The additional electrons necessary to neutralize the daughter are thought to be produced and heated through beam-plasma interactions postulated by Maehlum et al. (1980b) and Grandal et al. (1980) to explain the particle and optical measurements. Significant electric fields emanating from the charged “daughter” and the beam are seen at distances exceeding 100 m at the “mother” payload.     

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.     

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.     

Damping of electrostatic noise by warm auroral electrons

Cyclotron damping by warm electrons limits the amplitude of high frequency electrostatic waves propagating in discrete auroral arcs. The effect of this damping on whistler VLF hissupper hybrid noise and Bernstein modes is examined by calculating temporal growth rates and power flux intensities of amplified noise produced by precipitating electrons. The auroral electrons are described by a realistic distribution function. The effect of varying ionospheric conditions is also considered. Whistler mode noise is found to be less sensitive to the warm electron model than the upper hybrid mode. Bernstein modes are rapidly absorbed by the ionospheric and warm electrons. The difference in the peak power flux of the whistler and upper hybrid modes is indicative of the local value of the ratio of electron plasma frequency to electron gyrofrequency. For peak upper hybrid noise to exceed peak whistler noisethis ratio should be greater than 1. Ionospheric electron temperature has little effect on the spectrum, and intense narrow beams in the distribution function should be most effective at producing high noise levels for a given warm electron model.     

Plasma-sheet dynamics and magnetospheric substorms

We present a conceptual model of the formation of the plasma sheet and of its dynamical behavior in association with magnetospheric substorms. We assume that plasma mantle particles $\text{E}\text{～}\text{×}\text{B}\text{～}$ drift toward the current sheet in the center of the tail where they are accelerated by magnetic-field annihilation to form the plasma sheet. Because of the velocity-dependent access of mantle particles to the current sheet, we argue that the convection electric field and the corresponding rate of field annihilation decrease with increasing radial distance. As a consequence, there exists no steady-state configuration for the plasma sheet, which must instead shrink continuously in thickness until the near-earth portion of the current sheet is disrupted by the formation of a magnetic neutral line. The current-sheet disruption launches a large-amplitude hydromagnetic wave which is largely reflected from the ionosphere. The reflected wave sets the neutral line in motion away from the earth; the neutral line comes to rest at a distance (which we estimate to be a few hundred earth radii) where the incoming mantle particles enter the current sheet at the local Alfvén velocity. At this “Alfvén point” reconnection ceases and the thinning of the plasma sheet begins again. Within this model, the magnetospheric substorm (which is associated with the current-sheet disruption) is a cyclical phenomenon whose frequency is proportional to the rate of convection in the magnetospheric tail.