Transport equations for aeronomy

In this paper we present results for a general system of transport equations appropriate to a multi-constituent gas mixture. This system includes a continuity, momentum, internal energy, pressure tensor and heat flow equation for each species. The results can be applied to both collision dominated and collisionless plasmas with there being explicit limits derived for the validity of the various expressions. In the limit of very frequent collisions the pressure tensor and heat flow equations give the usual Navier-Stokes results for the viscous stress tensor and heat flow vector. Furthermore, the momentum equation includes thermal diffusion and thermoelectric transport coefficients equivalent to the second approximation of Chapman and Cowling. The basic system of equations has been applied to different regions of the ionosphere and neutral atmosphere. It is found that: (1) The viscous stress tensor and heat flow expressions used in previous studies of the neutral thermosphere may not be appropriate; (2) The transport coefficients normally used for mid-latitude F2-region and topside studies seem to be adequate; (3) The high speed flow of plasma in the polar topside ionosphere is likely to be strongly affected by stresses and heat flow; and (4) E- and F-region ionization at high latitudes is substantially affected by stresses and heat flow.     

Equations of anisotropic hydrodynamics for electron component of the ionospheric plasma

In this paper we have derived a set of transport equations for thermal electron component of the ionospheric plasma in the presence of an anisotropy of the electron energy distribution. Expressions are calculated in a 16-moment approximation for the moments of integrals of elastic and inelastic collisions of thermal electrons with basic neutral ionospheric components. The obtained moments determine variations of the hydrodynamical parameters, such as macroscopic velocity, pressure tensor, viscosity tensor, heat fluxes in respective equations due to collisions. The results have been obtained for an arbitrary degree of electron temperature anisotropy.     

The influence of radiometer forces on the pressure balance within the solar atmosphere

In a gas heat transport is accompanied by the transport of momentum. The momentum change that accompanies a spatial change in heat flow - this is the radiometer force - results in a pressure gradient. This effect is analogous to the radiation pressure of wavemechanical energy transport. The radiometer pressure increases with temperature and temperature gradient but is independent of the gas density. In the transition zone and in the solar corona the radiometer forces have a definite effect on the pressure balance within the solar atmosphere. In this note the relationship between the radiometer pressure and the acoustic radiation pressure in the solar atmosphere is derived.     

Acceleration of Pick-up Ions at the Solar Wind Termination Shock

It is generally accepted that pick-up ions act as a seed population for anomalous cosmic rays originating at the solar wind termination shock. We believe that the ion pre-acceleration process operating in the heliosphere up to the termination shock can be very important to inject the ions into the shock acceleration process. The pick-up ions pre-accelerated by solar wind turbulences have already a pronounced high energy tail when they reach the shock. Some fraction of these ions can experience further acceleration up to energies of anomalous cosmic rays by means of shock drift and diffusive acceleration. In the present paper the shock drift acceleration of pick-up ions suffering multiple reflection due to abrupt changes in both the strength and direction of the magnetic field through the shock is considered. The reflection process operates for high velocity particles different from the reflection by the electric cross-shock potential. During the first reflection the mean kinetic energy of pick-up ions increases by approximately a factor of 10. Reflected particles have highly anisotropic velocity distribution. Subsequent excursion of the particles in the turbulent upstream flow leads to diffusion in pitch-angle space and, as a result, the particles can return to the shock again suffering, thus, multiple encounters. In order to describe the motion of particles in the upstream and down streamparts of the flow we solve the Fokker-Plank transport equation for anisotropic velocity distribution function. This revised version was published online in July 2006 with corrections to the Cover Date.     

Solutions to bi-Maxwellian transport equations for SAR-arc conditions

We have compared solutions obtained from the bi-Maxwellian based 16-moment transport equations with those obtained from the Maxwellian based 13-moment transport equations for conditions leading to the steady state, subsonic flow of a fully-ionized electron-proton plasma along geomagnetic field lines in the vicinity of the plasmapause. The bi-Maxwellian based equations can account for large temperature anisotropies and the flow of both parallel and perpendicular thermal energy, while the Maxwellian based equations account for small temperature anisotropies and only the total heat flow. Our comparison indicates that for Stable Auroral Red arc (SAR-arc) conditions leading to strong field-aligned heat flows (temperatures of 8000 K and temperature gradients of4K. km⁻¹ at 1500 km), the bi-Maxwellian based equations predict a different thermal structure in the topside ionosphere than the less rigorous Maxwellian based equations. In particular, the bi-Maxwellian based equations predict proton and electron temperature anisotropies with T > T, while the Maxwellian based equations predict the opposite behavior for the same boundary conditions. This difference is related to the way in which the temperature anisotropies and heat flows are treated in the two formulations. For the bi-Maxwellian based equations, the inclusion of separate heat flows for parallel and perpendicular thermal energy allows for the development of a pronounced tail in both the electron and proton distribution functions, which leads to temperature anisotropies with T > T. For the Maxwellian based equations, on the other hand, the tail development is restricted because only the total heat flow is considered. Consequently, as the heat flows down, the presence of an increasing magnetic field acts to produce an anisotropy with T > T, and this process dominates tail formation for the Maxwellian based equations.     

Effects of hall current on the oscillatory MHD free-convection flow

An analysis of Hall currents and heat generation on the free-convection flow resulting from the combined effects of thermal and mass diffusion is considered. Analytical expressions for the transient velocity and transient temperature field are derived. The influence of the different parameters entering into the problem are discussed by graphs.     

Non-Maxwellian effects associated with the thermal escape of a planetary atmosphere

The velocity distribution function of a minor gaseous constituent escaping from a planetary atmosphere is perturbed from the equilibrium Maxwell-Boltzmann distribution function, There is a depletion in the high energy portion of the distribution function. The escape flux is consequently somewhat less than the Jeans flux obtained assuming complete equilibrium. The non-Maxwellian velocity distribution function for an escaping constituent is calculated with a Boltzmann equation modified by the addition of an isotropic sink term. The effects due to diffusion of particles and heat conduction are neglected. A discrete ordinate method which requires little computational time is employed in the solution of the Boltzmann equation. The corrections to the Jeans flux calculated in this way are compared with the results obtained with the Monte-Carlo techniques. The corrections for the escape of H and He from Earth, H from Mars and H₂ from Titan are calculated. The reductions in the Jeans flux are largest for a light escaping gas and for small escape parameters. The depletion of fast particles also results in the cooling of the minor component below the temperature of the background gas. This effect is also studied for the escape of H from Earth.     

Plasma transport in the topside venus ionosphere

We have studied the extent to which certain transport processes affect ion composition and heat flow in the daytime, topside Venus ionosphere. Particular attention is given to the conditions that prevailed during the Mariner 5 measurements, at which time the topside Venus ionosphere appeared to be in a state of diffusive equilibrium. We have found that the ion composition is sensitive to the ion temperature, the ion temperature gradient, and to relative drifts between the ion species of a few $\text{m}\text{sec}$. The electron density, on the other hand, is very insensitive to these parameters. As a consequence, ionospheric models of the topside Venus ionosphere are not likely to yield definitive information about the ion composition, the thermal structure or the flow conditions, since at present only electron density profiles are available for testing model predictions. We have also found that a relative drift between the ion species of a few $\text{m}\text{sec}$ induces an ion heat flow that is equivalent to a $\text{1}\text{K}\text{km}$ temperature gradient. This induced heat flow could influence the energy balance in the topside Venus ionosphere.     

A statistical theory for the decay process of weak homogeneous convective turbulence

In this paper we have derived kinetic equations for the decay of kinetic and thermal energy of a weak homogenous turbulent flow in which the fluctuating temperature field is superimposed on the eddy velocity field. Random fluctuations of velocity and temperature in a one-dimensional model have been considered on the basis of wavenumbers in Fourier space together with linearized mode approximations. Energy decay equations have been obtained in closed form, using quasi-normal approximations and the Bogoliubov expansion method. The paper also discusses the cases off=v andf=0.     

Thermal balance of the mid-latitude F2-region at night

The thermal balance of the plasma in the night-time mid-latitude F2-region is examined using solutions of the steady-state O⁺ and electron heat balance equations. The required concentrations and field-aligned velocities are obtained from a simultaneous solution of the time-dependent O⁺ continuity and momentum equations.The results demonstrate the systematic trend for the O⁺ temperature to be 10–20 K greater than the electron temperature during the night at around 300 km, as observed at St. Santin by Bauer and Mazaudier. It is shown that frictional heating between the O⁺ and neutral gases is the cause of the O⁺ temperature being greater than the electron temperature; the greater the importance of frictional heating in the thermal balance the greater is the difference in the O⁺ and electron temperatures. A study is made of the roles played in the thermal balance of the plasma by the thermal conductivity of the O⁺ and electron gases; collisional heat transfer between O⁺ electrons and neutrals; frictional heating between the O⁺ and neutral gases; and advection and convection due to field-aligned O⁺ and electron motions. The results of the study show that, at around 300 km, electron cooling by excitation of the fine structure of the ground state of atomic oxygen plays a major role in the thermal balance of the electrons and, since the temperature of the ions is little affected by this electron cooling process, in determining the difference between the ion and electron temperatures.     

Effect of general loss-cone distribution function on electrostatic ion-cyclotron instability in an inhomogeneous plasma: particle aspect analysis

The electrostatic ion-cyclotron instability (EICI) in low β (ratio of plasma to magnetic pressure), anisotropic, inhomogeneous plasma is studied by investigating the trajectories of the particles using the general loss-cone distribution function (Dory-Guest-Harris type) for the plasma ions. In particular, the role of the loss-cone feature as determined by the loss-cone indices, in driving the drift-cyclotron loss-cone (DCLC) instability is analysed. It is found that for both long and short wavelength DCLC mode the loss-cone indices and the perpendicular thermal velocity affect the dispersion equation and the growth rate of the wave by virtue of their occurrence in the temperature anisotropy. The dispersion relation for the DCLC mode derived here using the particle aspect analysis approach and the general loss-cone distribution function considers the ion diamagnetic drift and also includes the effects of the parallel propagation and the ion temperature anisotropy. It is also found that the diamagnetic drift velocity due to the density gradient of the plasma ions in the presence of the general loss-cone distribution acts as a source of free energy for the wave and leads to the generation of the DCLC instability with enhanced growth rate. The particle aspect analysis approach used to study the EICI in inhomogeneous plasma gives a fairly good explanation for the particle energisation, wave emission by the wave–particle interaction and the results obtained using this particle aspect analysis approach are in agreement with the previous theoretical findings using the kinetic approach.     

Effects of Hall current and rotation

Effects of Hall current and rotation on the flow of electrically conducting rarefied gas due to combined buoyant effects of thermal and mass diffusion, past an infinite porous plate in the presence of transverse magnetic have been investigated. The equations governing the flow problem have been solved and the profiles are shown on graphs. Effects ofm (Hall parameter) andE (Ekman number) on velocity are discussed.     

Heat and mass transfer in rotating fluid with Hall current,I

Hall effects on the hydromagnetic free convection resulting from the combined effects of thermal and mass diffusion of an electrically conducting liquid past an infinite vertical porous plate in a rotating system have been analysed. The expressions for the mean velocity, mean temperature in the boundary layer and the mean skin friction, the mean rate of heat transfer on the plate are derived. The effects of magnetic parameterM, Hall parameterm, Schmidt number Sc, and Ekman numberE on the flow field, are discussed with the help of graphs and tables.     

Propagation of Extremely Low Frequency Waves Through the Ionosphere

The propagation features of extremely low frequency electromagnetic waves through the multicomponent ionospheric plasma are studied. It is shown that at relatively lower frequencies refractive index for right hand mode is higher than the left-hand mode, which is reversed at higher frequencies. The thermal temperature of plasma particle causes decrease in phase and group velocities of both right and left-hand modes. The crossover frequencies for different plasma models are computed and variation with ion concentration and thermal velocity is studied. Explicit expression for group velocity and travel time has been derived and studied numerically. Finally, we have presented simulation of the ion whistler spectrograms for Hydrogen, Helium and Oxygen ions present in the ionospheric plasma. The results are compared with the experimentally detected hydrogen and helium ion whistlers. The importance of the present study in the exploration of ionospheric plasma is illustrated.     

Rotating motion in solar surges

The line-of-sight velocity field of the solar limb surge of 1980 Oct 11, observed at Yunnan Observatory, showed a rotating motion. The velocity of rotation and the true ascending speed of the surge were determined from H observations. We also found an accompanying expansion at several tens of km/s and the presence of a pulsed phenomenon with a period of a few minutes at the root of the surge. We point out that the steep density gradient between the surge plasma and its surrounding atmosphere causes double-pole diffusion, and the electric field generated by the double-pole diffusion causes electric drift of the surge plasma, hence the rotation.     

Heat and mass transfer of an oscillatory flow with Hall current,II

An analysis of Hall current on the combined effects of thermal and mass diffusion of an electrically conducting liquid past an infinite vertical porous plate is performed. Analytical expressions for the transient velocity, the transient temperature in the boundary layer and the skin-friction on the plate are derived. The effects of various parameters on the velocity, temperature, shearing stresses and rate of heat transfer are shown by graphs and tables.     

Mulit-ion plasmas in astrophysics

An isothermal hydrodynamic model of the motions of a multi-ion plasma in a gravitational field is developed and the properties of the flow are discussed for the case of major astrophysical interest in which the gas undergoes a subsonic-supersonic transition. It is shown that the existence of critical points thorough which the plasma has to pass will determine a large number of the plasma parameters, especially the temperature of the minor ions. The equation of motion of a two ion gas (hydrogen-helium) are solved numerically and yield the interesting result that the bulk velocity of the plasma constituents are not equal at 1 AU.Operated by the Association of Universities for Research in Astronomy, under contract with the National Science Foundation.     

On the propagation of hydromagnetic waves in a plasma of thermal and suprathermal components

The propagation of MHD waves is studied when two ideal fluids, thermal and suprathermal gases, coupled by magnetic field are moving with the steady flow velocity. The fluids move independently in a direction perpendicular to the magnetic field but gets coupled along the field. Due to the presence of flow in suprathermal and thermal fluids there appears forward and backward waves. All the forward and backward modes propagate in such a way that their rate of change of phase speed with the thermal Mach number is same. It is also found that besides the usual hydromagnetic modes there appears a suprathermal mode which propagates with faster speed. Surface waves are also examined on an interface formed with composite plasma (suprathermal and thermal gases) on one side and the other is a non-magnetized plasma. In this case, the modes obtained are two or three depending on whether the sound velocity in thermal gas is equal to or greater than the sound velocity in suprathermal gas. The results lead to the conclusion that the interaction of thermal and suprathermal components may lead to the occurrence of an additional mode called suprathermal mode whose phase velocity is higher than all the other modes.