Nonlinear generation of ion loss-cone waves by electrostatic turbulence in the magnetosphere

Effects of plasma turbulence on the stability of electrostatic ion loss-cone waves are examined. The turbulence is assumed to be electrostatic with frequencies near 1.5 times the electron gyrofrequency and the frequencies of the generated waves are below the ion plasma frequency ω_pi>. A nonlinear growth rate of the order of 10^?2ω_pi may be obtained, when the amplitude of the turbulence is 20 mV/m. This is comparable to previously found growth rates of the linear ion loss-cone instability, in a plasma with large pitch angle anisotropy. Bounce averaged pitch angle diffusion coefficients are also presented for different models of the ion loss-cone wave spectrum.     

Gradients and thermal effects on ring current loss-cone instability

The proton ring current is found to become unstable to a flute-type loss cone mode in the presence of inhomogeneities in the background plasma. Larger growth rates poleward of the equator are expected when the finite temperature of the electrons is taken into account.     

Low-frequency electric field fluctuations excited by ring current protons

Energetic protons haying ring type distributions are shown to generate low-frequency electrostatic waves, propagating nearly transverse to the geomagnetic field lines, in the ring current region by exciting Mode 1 arid Mode 2 nonresonant instabilities and a resonant instability. Mode 1 nonresonant instability has frequencies around ~4 Hz with transverse wavelengths of ~(8–80) km, and it is likely to occur in the region L = (7–8). Mode 2 nonresonant instability can generate frequencies ~(850–1450) Hz with transverse wavelengths ~(2–20) km. The typical frequencies and transverse wavelengths associated with the resonant instability are (950–1250) Hz and (30–65) km. Both the Mode 2 nonresonant instability and the resonant instability can occur in the ring current region with L = (4–6). The low-frequency modes driven by energetic protons could attain maximum saturation electric field amplitude varying from 0.8 mV/m to 70 mV/m. It is suggested that the turbulence produced by the low-frequency modes may cause pitch angle scattering of ring current protons in the region outside the plasmapause resulting in the ring current decay.     

Electron surfing acceleration by electrostatic waves in current sheet

The electron surfing acceleration in the current sheet with perpendicular propagating electrostatic waves is studied using analytical theories and test particle simulations. The trapped electron moving with the phase velocity v _p of wave may be accelerated effectively in the outflow direction by force until the electron is de-trapped from the wave potential. A criterion K>0 for the electron surfing acceleration is obtained. The electron will escape from the boundary of current sheet quickly, if this criterion does not hold. The maximum velocity of surfing acceleration is about the same as the electric drift velocity. Superposed longitudinal magnetic field along the wave propagation is favorable for the electron surfing acceleration in the current sheet.      

On the modulational instability of electrostatic ion cyclotron waves

The instability of electrostatic ion cyclotron waves to low frequency density modulations is considered and nonlinear equations are derived which describe its development in terms of a coherent four wave interaction. A dispersion relation for the linear phase of the instability is obtained and threshold conditions for marginal stability determined. It is shown, using data from recent optical observations, that the conditions necessary for the instability to occur in the auroral plasma would probably be satisfied and that modulational frequencies in agreement with the observations are obtained for plausible wave amplitudes. The nonlinear development of the instability is then studied and it is shown that substantial modulation can occur. It is suggested therefore that this instability could lead to the development of a strongly turbulent state.     

Optical detection of electrostatic ion cyclotron waves in the auroral plasma

Spectral analysis of recent photometric observations has revealed the existence of narrow frequency band pulsations in the brightness of some auroras. Peaks in the power spectra, between 25 and 32 Hz have been observed. We suggest that these observations are associated with electrostatic ion cyclotron waves, which are excited when the relative drift between ions and electrons due to field aligned (Birkeland) currents, exceeds a certain critical value.     

Pitch-angle scattering of energetic protons in the magnetotail current sheet as the dominant source of their isotropic precipitation into the nightside ionosphere

Characteristics of the nightside isotropic precipitation of energetic protons during a period of 4 quiet days has been studied using data from the ESRO 1A satellite. The observed features of the equatorward precipitation boundary (its thickness, energy dependence, dynamics, dependence of its latitudinal position on the magnetic field at the geosynchronous orbit, etc.) were found to be in good agreement with calculations based on recent magnetospheric magnetic field models. We argue that the mechanism of non-adiabatic pitchangle scattering in the equatorial current sheet is a dominant source of isotropic precipitation of energetic protons observed in the nightside auroral zone. Observations of the isotropic precipitation boundary can be used for monitoring the changes in the magnetotail current intensity.     

Radiation production and energy deposition by ring current protons precipitated into the mid-latitude upper atmosphere

In the present paper the radiation production and energy deposition by ring current protons precipitated along magnetic field lines into the mid-latitude upper atmosphere is investigated. Specifically, we are interested in protons lost from the ring current by plasma instabilities. We first determine the magnitude and sharpness of the atmospheric loss cone. We then study the behavior of the precipitated hydrogen particles in the denser atmosphere using a Monte Carlo calculation. It is found that the energy deposition and radiation production will critically depend on how far the ring current protons diffuse into the loss cone before being neutralized in the atmosphere; this in turn will depend on the strength of the plasma turbulence in the ring current belt region.     

Effects of convection electric field on the distribution of ring current type protons

The topology of the boundaries of penetration (or inversely the boundaries of the forbidden regions) of 90° pitch angle equatorial protons with energies less than 100 keV are explored for an equatorial convection E-field which is directed in general from dawn to dusk. Due to the dependence of drift path on energy (or magnetic moment) complex structural features are expected in the proton energy spectra detected on satellites since the penetration distance of a proton is not a monotonically increasing or decreasing function of energy. During a storm when the convection E is enhanced, model calculations predict elongations of the forbidden regions analogous to plasmatail extensions of the plasmasphere. Following a reduction in the convection field, spiral-structured forbidden regions can occur. Structural features inherent to large scale convection field changes may be seen in the noselike proton spectrograms observed near dusk by instrumentation on the satellite Explorer 45 (S³) (Smith and Hoffman, 1974). These nose events are modelled by using an electric field model developed originally by Volland (1973). The strength of the field is related to K_p through night-time equatorial plasmapause measurements.     

Localised compressional hydromagnetic waves in the magnetospheric ring current

It is shown that the field line resonance phenomenon that occurs for quasi-transverse signals in a non-uniform cold plasma generally occurs for disturbances with a compressional magnetic component in a hot plasma like the ring current. The equations describing such localised signals are derived and discussed in various limits. It is pointed out that recent observations of low frequency compressional oscillations on spacecraft may be an example of such localised signals.     

Effect of general loss-cone distribution function on the shear-driven electrostatic ion-cyclotron instability

The shear-driven electrostatic ion-cyclotron instability (EICI) is studied using the loss-cone distribution function by particle aspect analysis. The effect of the loss-cone distribution on the dispersion relation and growth rate of weak shear-driven EICI is studied. The whole plasma is considered to consist of resonant and non-resonant particles. The wave is assumed to propagate obliquely to the static magnetic field. It is found that the frequency of the EICI is Doppler shifted due to the transverse inhomogeneous flow in the direction of the magnetic field. It is also found that for anisotropic plasma the critical velocity shear needed to excite EICI depends upon the loss-cone distribution index (J). With the increasing values the loss-cone distribution indices (J), the critical value of normalized velocity shear needed to generate EICI in anisotropic plasma, decreases and is of the order of the weak shear. The loss-cone distribution acts as a source of free energy and generates the weak shear-driven EICI at longer perpendicular perturbations. It also lowers the transverse and parallel energy of the resonant ions. The study may explain the frequently observed EICI in the auroral acceleration region.     

Pitch-angle distributions in and near the loss cone of (100–350) keV protons

The pitch-angle distributions in and near the loss cone, of ～ (100–200) and ～ (200–350) keV protons observed by the ESRO IB satellite during the period 7–15 October 1969 are presented. The data include periods of relative quiet as well as more disturbed geomagnetic conditions. Spatial characteristics and dynamics of the protons, both on the night-and dayside of the Earth are described. The actual pitch-angle distribution is interpreted as produced by wave-particle interactions, and the diffusion coefficient and lifetime against pitch angle scattering have been estimated from existing theories. During slightly disturbed conditions, the observations suggest an average random walk in pitch angle made by a particle during a crossing of the diffusion region of about one half of the loss cone half angle for 4 ? L ? 6. The lifetime against pitch angle scattering into the loss cone is found to be somewhat less than the charge exchange lifetime for these (100–350) keV protons. The spectral density of interacting waves is tentatively estimated to about 0·1 $\text{γ}{}^2\text{Hz}$, and compares with estimates arrived at from completely different approaches.     

Some implications of low altitude observations of isotropic precipitation of ring current protons beyond the plasmapause

The precipitation patterns of 6 keV protons at 10° and 80° pitch angles have been mapped at altitudes <1500 km from the ESRO 1A and 1B spacecraft. Equatorward of the trapping boundary, a region of isotropic precipitation, bounded on its equatorward border by a region of anisotropic (depleted loss cone) precipitation, is always observed. The latitudinal location of this transition appears to be nearly spatially coincident with the plasmapause. Similar precipitation patterns are shown to exist for higher energy protons. The general absence of enhanced precipitation at the plasmapause suggests that the inner boundary of the ring current is not usually produced by an enhanced proton pitch angle diffusion process. The isotropic precipitation observed beyond the plasmapause is most consistent with the occurence of an electrostatic instability throughout the ring current zone. It is doubtful whether the proposed cold Li plasma seeding experiments beyond the plasmapause could significantly increase the observed natural proton precipitation rates.     

A further search on waves generated by solar energetic protons

It has been suggested that in the interplanetary medium Alfvén waves may be significantly amplified or damped during large solar proton events. This implies the increase or decrease of the ambient magnetic fluctuations in concurrence with the presence of the streaming particles, that we have analysed in a first study at times of eight proton events observed by Helios spacecraft (Valdés-Galicia and Alexander, 1997). However, it is not possible with interplanetary magnetic field measurements only to distinguish between waves moving away or towards the Sun in the frame of reference of the spacecraft. Plasma data for these eight events have now been made available to us and hence the energetic content of inward and outward propagating waves may be found, which is an important aid in our search for signatures left by the energetic protons. In the present work we incorporate the new information into the analyses of those events that in our first study showed more favourable evidence and therefore try to give a more definite answer as to whether it might be observed. The new results do not reinforce the evidence of our previous work, as they seem to be mildly consistent with the presence of the proton self-generated waves in just one of the three cases studied.     

Coronal heating by ion acoustic waves

A quantitative study is made based on the suggestion that coronal heating results from Landau damping of ion acoustic waves. It is shown that both ions and electrons are heated by nonlinear saturation of ion acoustic instability. Ions are heated more rapidly than the electrons.     

Current interruption in a collisionless plasma by non-linear electrostatic waves

The existence of current-interrupting non-linear electrostatic waves in the form of negative solitons is demonstrated. Self-consistent, non-linear electrostatic potentials are constructed assuming that a current may be interrupted by trapping current-carrying electrons in such a potential. A significant fraction of the current-carrying electrons is trapped by the potential if the electron thermal velocity is much less than the electron streaming velocity. In one class of solutions, the negative solitons, the current may be reduced to a fourth of its initial value in the limit of high ion-electron temperature ratio.     

Trapping of electromagnetic waves by nonlinear resonant interactions with ion sound waves

Resonant wave-wave interaction among one ion sound wave and two electro-magnetic waves in an isotropic plasma is studied. The emphasis is on the possibility of trapping the electromagnetic wave. Equations for the three-wave system are derived. One particularly interesting case is that for which the frequency of ion sound wave is much less than the frequency of electromagnetic waves. For this case it is shown that energy exchange takes place only between the two high frequency waves. The ion sound wave does not participate in the energy exchange process but acts as a kind of catalyst for the interaction. Simple solutions are obtained. It is found that the electromagnetic energy is trapped within a certain spatial region. The trapping width is found to depend, among other parameters, on the magnitude of ion sound wave perturbation. Possible application of the theory to topside ionospheric observations of field-aligned propagation is discussed.     

Excitation of plasma waves in the ionosphere caused by atmospheric acoustic waves

The transformation of atmospheric acoustic waves into plasma waves in the ionosphere is investigated. The transformation mechanism is based on plasma wave exitation by growing acoustic waves, when a frequency/wavelength matching situation is reached. The interaction of acoustic and plasma waves occurs through collisions of neutral particles with ions. For the case of ion-sound waves, oscillations on ion cyclotron frequency and Alfvén waves is considered. A peculiarity of Alfvén waves is the wide frequency band which may be stimulated through wave-wave interaction.     

Acceleration of pickup interstellar protons by shock waves in corotating solar wind regions

It follows from numerous measurements of the differential fluxes of energetic charged particles in corotating interaction regions between solar wind streams with different speeds that the spectra of particles accelerated by reverse shocks are harder than those of particles accelerated by forward shocks. The measurements cannot be explained in terms of the theory of diffusive acceleration (first-order Fermi acceleration). We show that the measurements can be easily explained in terms of the theory of drift acceleration of charged particles by shock waves with allowance made for their multiple scattering from the front.