Auroral ion velocity distributions using a relaxation model

For application to the auroral ionosphere we have calculated ion velocity distributions for a weakly-ionized plasma subjected to crossed electric and magnetic fields. By replacing the Boltzmann collision integral with a simple relaxation model, we have been able to obtain an exact solution to Boltzmann's equation. This solution has the advantage over a series expansion in that all the higher order velocity moments are inherent in it. The exact solution is particularly advantageous when studying large departures of the distribution from its Maxwellian form because these departures are caused by the higher velocity moments. In general, however, a simple relaxation model can only be used to obtain qualitative information on the distribution function. Consequently, we can determine when the higher order velocity moments affect the ion velocity distribution and the nature of their effect, but we cannot obtain accurate quantitative results. The higher velocity moments have their greatest effect on the distribution function above about 120 km, where the ion-neutral collision frequency is less than the ion cyclotron frequency. As the magnitude of the electric field increases, these higher moments act to decrease the number of ions at the peak of the distribution function. Peak densities are reduced by a few per cent for perpendicular electric fields of about 20 mV m^?1.     

Auroral ion velocity distributions for a polarization collision model

We have calculated the effect that convection electric fields have on the velocity distribution of auroral ions at the altitudes where the plasma is weakly-ionized and where the various ion-neutral collision frequencies are much smaller than the ion cyclotron frequencies, i.e. between about 130 and 300 km. The appropriate Boltzmann equation has been solved by expanding the ion velocity distribution function in a generalized orthogonal polynomial series about a bi-Maxwellian weight factor. We have retained enough terms in the series expansion to enable us to obtain reliable quantitative results for electric field strengths as large as 90 mV m^?1. Although we have considered a range of ion-neutral scattering mechanisms, our main emphasis has been devoted to the long-range polarization interaction. In general, we have found that to lowest order the ion velocity distribution is better represented by a two-temperature or bi-Maxwellian distribution than by a one-temperature Maxwellian, with there being different ion temperatures parallel and perpendicular to the geomagnetic field. However, the departures from this zeroth-order bi-Maxwellian distribution become significant when the ion drift velocity approaches (or exceeds) the neutral thermal speed.     

Behaviour of ion velocity distributions for a simple collision model

For application to studies of the high latitude ionosphere, we have calculated ion velocity distributions for a weekly-ionized plasma subjected to crossed electric and magnetic fields. An exact solution to Boltzmann's equation has been obtained by replacing the Boltzmann collision integral with a simple relaxation model. At altitudes above about 150 km, where the ion collision frequency is much less than the ion cyclotron frequency, the ion distribution takes the shape of a torus in velocity space for electric fields greater than 40 mV m^?1. This shape persists for 1–2 hr after application of the electric field. At altitudes where the ion collision and cyclotron frequencies are approximately equal (about 120 km), the ion velocity distribution is shaped like a bean for large electric field strengths. This bean-shaped distribution persists throughout the lifetime of ionospheric electric fileds. These highly non-Maxwellian ion velocity distributions may have an appreciable affect on the interpretation of ion temperature measurements.     

The conditions for the existence of the electric field opposite to the current along the magnetic field lines in the thin plasma

The flow of the current along the magnetic field lines in the thin plasma directed opposite to the electric field is considered. The particles moving to the equatorial plane are supposed to have mirror points above the region of absorption (the ionosphere) and the particles moving to the ionosphere are supposed to have mirror points below the region of absorption. The current, therefore, flows. The functions of the distribution of the electrons and ions are considered to be mono-energetic. The energies of the electrons and the ions and their densities on the boundary of absorption are estimated for the potential difference and for the current density which are typical for the auroral field lines.     

Location and source of ionospheric high latitude troughs

One prominent feature of the high latitude topside ionosphere is the existence of sharp latitudinal depletions in the total ion (electron) concentrations within the auroral/cusp regions. These high latitude troughs, as seen by the Bennett ion mass spectrometer observations on the satellite OGO 6 at altitudes between 400 and 1100km correspond to depletions in the atomic ions which are accompanied by localized enhancements of the minor molecular ion densities. All of the high latitude troughs traversed by OGO 6 (1969–1970) were recorded and the average invariant latitude-magnetic local time (M.L.T.) distribution was determined. The troughs on the average were found at all local times to be in the vicinity of the auroral oval and to move equatorward in response to increasing magnetic activity. The average trough location was compared to the average polar cap boundary as defined by the convection electric field reversal and the electron trapping boundary as well as to the maximum horizontal magnetic disturbance associated with the large scale field aligned currents. The high latitude troughs on the average best followed the maximum magnetic disturbance distribution. It is concluded that the troughs are the result predominantly of enhanced chemical 0⁺ losses in regions with high convection velocities.     

Energy and pitch angle distributions for auroral ions using the current sheet acceleration model

Using a dipole plus tail magnetic field model, H⁺, He⁺⁺ and O ₁₆ ⁺⁶ ions are followed numerically, backward in time, from an output plane perpendicular to the axis of the geomagnetic tail, to their point of entrace to the magnetosphere as solar wind particles in the magnetosheath. An adiabatic or guiding center approximation is used in regions where the particles do not interact directly with the current sheet. A Maxwellian distribution with bulk flow is assumed for solar wind particles in the magnetosheath. Bulk velocity, density, and temperature along the magnetopause are taken from the fluid calculations of Spreiter. Using Liouville's theorem, and varying initial conditions at the output plane, the distribution function is found as a function of energy and pitch angle at the output plane. These results are then mapped to the auroral ionosphere using guiding center theory. Results show that the total precipitation rate is sufficient only for particles which enter the magnetosphere near the edges of the current sheet. Small pitch angles are favored at the output plane, but mappings to the auroral ionosphere indicate isotropic pitch angle distributions are favored with some peaking of the fluxes parallel or at other angles to the field lines. Perpendicular auroral pitch angle anisotropies are at times produced by the current sheet acceleration mechanism. Therefore, caution must be used in interpreting all such observations as ‘loss cone-trapping’ distributions. Energy spectra appear to be quite narrow for small cross-tail electric fields, and a little broader as the electric field increases. Comparisons of these results with experimental observations are presented.     

The fine structure of intensive small-scale electric and magnetic fields in the high-latitude ionosphere as observed by Intercosmos-Bulgaria 1300 satellite

The data on intensive small-scale electric fields and related transverse magnetic disturbances observed from Intercosmos-Bulgaria 1300 satellite at altitudes of 800–900 km in the auroral ionosphere are presented here. The typical time scale of the phenomena is of the order of 1 s, the amplitudes reach 250 mV m⁻¹ in electric field and up to 300 nT in magnetic field. A detailed correlation between the variations of electric and magnetic fields in such structures is shown. Some peculiarities are presented which show that the observed electric jumps are transient electromagnetic disturbances rather than steady electrostatic structures.     

Auroral ion velocity distribution function: The Boltzmann model revisited

The velocity distribution of ion populations is calculated for auroral conditions where strong convection electric fields exist. The Boltzmann equation has been solved for the E and F regions of the ionosphere where plasma is weakly dense, weakly ionized and where the ion-neutral collision frequency is small in regard to the ion cyclotron frequency. The ion distribution function has been expanded in a generalized orthogonal polynomial series about a bi-Maxwellian “temperature” varying weight function. This generalized Grad solution expansion enables us to obtain good approximations for electric field strengths as large as 75 mV m^?1 and 115 mV m^?1 respectively, for both the resonant charge exchange and the polarization collision models. The instability threshold of these distribution functions appears to be higher than the two respective electric field strengths considered above.     

EMEC instability based on kappa-Maxwellian distributed trapped electrons in auroral plasma

In space plasmas, particle distributions are often observed having high energy tails and are well fitted by kappa distribution function. However, in auroral region electrons are expected to be accelerated mainly along the magnetic field lines and one may expect Maxwellian behaviour in perpendicular direction. Therefore, in the present study propagation characteristics of electromagnetic electron cyclotron (EMEC) waves is studied by employing kappa-Maxwellian distribution function for energetic trapped electrons in auroral region. Real frequency and the growth rate expressions have been solved numerically for kappa-Maxwellian plasma and then analyzed by considering the effect of different plasma parameters for wide range of auroral altitudes. The numerical results obtained show that growth rate increases with the increase in ratio \({\omega_{pe}} / {\varOmega_{e}}\), plasma beta, temperature anisotropy \({T_{\bot}} / {T_{\parallel}}\) and trapped electron drift speed but decreases when superthermal electron population increases.     

Short-wavelength drift dissipative instability in the presence of field-aligned currents

Sharp density gradients coupled with field-aligned currents can give rise to short wavelength (?15 m) drift waves due to collisional effects in the F-region of the auroral ionosphere. In this wavelength range, ion-ion collisions at altitudes of 300–450 km render the ions unmagnetized and a field-aligned current can drive a drift wave, propagating almost transverse to the magnetic field, unstable due to the resistance in electron parallel motion arising from electron collisions.     

Thermal ion flows in the topside auroral ionosphere and the effects of low-altitude,transverse acceleration

Topside ionospheric profiles are used to study the upward field-aligned flow of thermal O⁺ at high latitudes. On the majority of the field lines outside the plasmasphere, the mean flux is approximately equal to the mean polar wind measured by spacecraft at greater altitudes. This is consistent with the theory of thermal light ion escape supported, via charge exchange, by upward O⁺ flow at lower heights. Events of larger O⁺ flow are detected at auroral latitudes and their occurrence is found to agree with that of transversely accelerated ions within the topside ionosphere and the magnetosphere. The effects of low altitude heating of O⁺ by oxygen cyclotron waves, driven by downward field-aligned currents, are considered as a possible common cause of these two types of event.     

Some aspects of electric field mapping in the auroral ionosphere

The mapping of the spectra of electrostatic field below 300 km altitude is theoretically calculated for a horizontally stratified auroral ionosphere. Perpendicular electric fields of large scale size are the same for different altitudes of the ionosphere. However, electric fields of small scale size vary with altitude and decrease drastically when the scale size is smaller than a certain value which depends on altitude. These results are similar to those observed by satellites above 300 km altitude. In the case of a homogeneous anisotropic ionosphere, analytical results are obtained for the penetration of electric field into the ionosphere as a function of wavenumber. The “smoothing” of the electric field when penetrating a horizontally stratified ionosphere is demonstrated. The smallest possible scale of parallel electric field structure within the ionosphere is found. Also presented is a method of finding the smallest horizontal length with which the electric field can penetrate the ionosphere with little distortion. For an average conductivity model, this length is found to be about 1 km. Finally, the mapping of packets of electric field to the ground is constructed.     

Incoherent scatter spectrum of ionospheric plasma with an anisotropic temperature ion distribution

The expression of anisotropic temperature ion distribution function under the 13-moment approximation is obtained by solving a set of moment equations based on the Boltzmann equation for a relaxation collision model and with consideration of the anisotropic temperature ion distribution. And the incoherent scatter spectrum with an anisotropic temperature ion distribution is simulated in different directions based on the electromagnetic radiation theory of Sheffield. The effects of different electrical field strengths, ratios of electron temperature to ion temperature, and ion-neutral collision frequencies on the incoherent scatter spectrum are all discussed. Finally, the value of theoretical simulation is compared with the measured value of incoherent scattering spectrum. The result show that the incoherent scatter spectrum of ions seriously deviates from the form of the Maxwellian distribution in the equilibrium state. This phenomenon can be attributed to the effects of anisotropic temperature ion distribution, the larger convection electric field, and other factors in high latitude ionosphere.     

Low density regions observed at high altitudes and their connection with equatorial spread F

Observations from the high resolution spherical electrostatic analyzer experiment aboard ISIS 1 have been used to study large amplitude irregularities at low latitudes in the tipside ionosphere. The irregularities appeared as plasma depletions near the magnetic equator and were observed up to satellite apogee (3500 km). The altitude local time distribution of the depletions was such that those at altitudes greater than 2000 km were found only in the post-midnight sector. This result agrees with the predictions of a model for plasma bubbles drifting under the influence of gravity-buoyancy forces. Evidence is presented that the initial steep gradients observed at low altitudes are reduced by anomalous diffusion due to drift waves.     

Field-aligned currents and parallel electric field potential drops at Mars. Scaling from the Earth’ aurora

The observations of electron inverted ‘V’ structures by the MGS and MEX spacecraft, their resemblance to similar events in the auroral regions of the Earth, and the discovery of strong localized magnetic field sources of the crustal origin on Mars, raised hypotheses on the existence of Martian aurora produced by electron acceleration in parallel electric fields. Following the theory of this type of structures on Earth we perform a scaling analysis to the Martian conditions. Similar to the Earth, upward field-aligned currents necessary for the generation of parallel potential drops and peaked electron distributions can arise, for example, on the boundary between ‘closed’ and ‘open’ crustal field lines due to shears of the flow velocity of the magnetosheath or magnetospheric plasmas. A steady-state configuration assumes a closure of these currents in the Martian ionosphere. Due to much smaller magnetic fields as compared to the Earth case, the ionospheric Pedersen conductivity is much higher on Mars and auroral field tubes with parallel potential drops and relatively small cross scales to be adjusted to the scales of the localized crustal patches may appear only if the magnetosphere and ionosphere are decoupled by a zone with a strong E_∥. Another scenario suggests a periodic short-circuit of the magnetospheric electric fields by a coupling with the conducting ionosphere.     

Electromagnetic Ion Cyclotron Waves in Multi-Ions Hot Anisotropic Plasma in Auroral Acceleration Region-Particle Aspect Approach

Using particle aspect approach, the effect of multi-ions densities on the dispersion relation, growth rate, perpendicular resonant energy and growth length of electromagnetic ion cyclotron wave with general loss-cone distribution function in hot anisotropic multi-ion plasma is presented for auroral acceleration region. It is observed that higher He⁺ and O⁺ ions densities enhance the wave frequency closer to the H⁺ ion cyclotron frequency and growth rate of the wave. The differential heating of He⁺ ions perpendicular to the magnetic field is enhanced at higher densities of He⁺ ions. The waves require longer distances to achieve observable amplitude by wave-particle interactions mechanism as predicted by growth length. It is also found that electron thermal anisotropy of the background plasma enhances the growth rate and reduces the growth length of multi-ions plasma. These results are determined for auroral acceleration region.     

Some ideas concerning the problem of anomalous polar E region heating due to Farley-Buneman turbulence

The energetics of the excitation of the Farley-Buneman instability is considered, which is recently observed in the auroral and equatorial E regions of the Earth's ionosphere at altitudes between 100 km and 120 km. In the magnetic field of the Earth the Farley-Buneman instability is excited under the condition of a strong enough external electric field in the case of ion-neutral collisions with frequencies much larger than the ion gyrofrequency and electron-neutral collisions with frequencies much below the electron gyrofrequency. It is shown that the linear increase of the wave amplitudes is caused by a small disbalance between the processes of nonlinear energy pumping into the wave from an external electric field and the energy loss because of the collisions of the electrons and ions with the neutral particles. During the nonlinear energy pumping energy of the external electric field is transferred into a nonlinear current of second order, which is connected with the oscillating motion of the electrons in the wave. The oscillating electron motion takes place perpendicular to wave propagation. From the estimations follows that the energy pumped into a Farley-Buneman wave during one period of pulsation is much larger than the wave energy itself. A new and simply to understand derivation of the anomalous diffusion coefficient is presented, related to the study of the behaviour of a test wave with frequency much above the frequencies of the Farley-Buneman turbulence in developed stage can cause an additional macroscopic nonlinear Pedersen current directed along the external electric field. It is found that the nonlinear Pedersen current can reach the order of the usual Pedersen current and should contribute to the effective heating of the ionospheric plasma.     

Thermal response properties of the Earth's ionospheric plasma

The thermal response of the Earth's ionospheric plasma is calculated for various suddenly applied electron and ion heat sources. The time-dependent coupled electron and ion energy equations are solved by a semi-automatic computational scheme that employs Newton's method for coupled vector systems of non-linear parabolic (second order) partial differential equations in one spatial dimension. First, the electron and composite ion energy equations along a geomagnetic field line are solved with respect to a variety of ionospheric heat sources that include: thermal conduction in the daytime ionosphere; heating by electric fields acting perpendicular to the geomagnetic field line; and heating within a stable auroral red are (SAR-arc). The energy equations are then extended to resolve differential temperature profiles, first for two separate ion species (H⁺, O⁺) and then for four separate ion species (H⁺, He⁺, N⁺, O⁺) in addition to the electron temperature. The electron and individual ion temperatures are calculated for conditions within a night-time SAR-arc excited by heat flowing from the magnetosphere into the ionosphere, and also for typical midlatitude daytime ionospheric conditions. It is shown that in the lower ionosphere all ion species have the same temperature; however, in the topside ionosphere above about 400 km, ion species can display differential temperatures depending upon the balance between thermal conduction, heating by collision with electrons, cooling by collisions with the neutrals, and energy transfer by inter-ion collisions. Both the time evolution and steady-state distribution of such ion temperature differentials are discussed.The results show that below 300km both the electrons and ions respond rapidly (<30s) to variations in direct thermal forcing. Above 600 km the electrons and ions display quite different times to reach steady state, depending on the electron density: when the electron density is low the electrons reach steady state temperatures in 30 s, but typically require 700 s when the density is high; the ions, on the other hand, reach steady state in 700 s when the density is high, and 1500–2500 s when the density is low. Between 300 and 600 km, a variety of thermal structures can exist, depending upon the electron density and the type of thermal forcing; however steady state is generally reached in 200–1000 s.     

Polar magnetic substorms

From the world distribution of geomagnetic disturbance, the connection between the electric current in the ionosphere, the field-aligned current and asymmetric equatorial ringcurrent in the magnetosphere is discussed. The partial ring-current in the afternoon-evening region, whose intensity is closely correlated with the AE-index, usually develops and decays earlier than the symmetric ring-current in the course of magnetic storms. The partial ringcurrent seems to have a direct connection with the positive geomagnetic bay in high latitudes in the evening hours through the ionizing effect of the particles leaking from the partial ringcurrent. The dawn-to-dusk electric field in the magnetospheric tail is transferred to the polar ionosphere, producing there the twin vortex Hall current responsible for polar cap geomagnetic variation. The magnetic effect of the associated Pedersen current in the ionosphere is shown to be small but still worth considering. The electrojet near midnight along the auroral oval is thought to appear when the electric conductivity of the ionosphere is locally increased under the presence of large scale dawn-to-dusk electric field. The occasional appearance of a localized abnormal geomagnetic disturbance with reversed direction near the geomagnetic pole seems to suggest the occasional reversal of electric field near the outer surface of the magnetospheric tail, especially when the interplanetary magnetic field is northward.