The 13-moment system of transport equations was presented in Chapter 3 and several associated sets of collision terms were derived in Chapter 4. These 13-moment transport equations, in combination with the Maxwell equations for the electric and magnetic fields, are very general and can be applied to describe a wide range of plasma flows in the ionospheres. However, the complete system of equations for a multi-species plasma is difficult to solve under most circumstances, and therefore, simplified sets of transport equations have been used over the years. The simplified sets of equations that are based on the assumption of collision dominance were presented in Chapter 5. In this chapter, certain simplified transport equations are derived in which the plasma is treated as a single conducting fluid, rather than a mixture of individual plasma species. These single-fluid transport equations, along with the Maxwell equations, are known as the single-fluid magnetohydrodynamic (MHD) equations.

The outline of this chapter is as follows. First, the single-fluid transport equations are derived from the 13-moment system of equations. Subsequently, a generalized Ohm's law is derived for a fully ionized plasma. This naturally leads to simplifications that yield the classical set of MHD equations. The classical MHD equations are then applied to important specific cases, including a discussion of pressure balance, the diffusion of a magnetic field into a plasma, the concept of a B field frozen in a plasma, the derivation of the spiral magnetic field associated with rotating magnetized bodies, and the derivation of the double-adiabatic energy equations for a collisionless anisotropic plasma. These topics are followed by a derivation of the MHD waves and shocks that can exist in a plasma.

A wide variety of plasma flows can be found in the various planetary ionospheres. For example, gentle near-equilibrium flows occur in the terrestrial ionosphere at mid-latitudes, while highly nonequilibrium flow conditions exist in the terrestrial polar wind and in the Venus ionosphere near the solar terminator. The highly nonequilibrium flows are generally characterized by large temperature differences between the interacting species, by flow speeds approaching and exceeding thermal speeds, and by flow conditions changing from collision-dominated to collisionless regimes. In an effort to model the various ionospheric flow conditions, several different mathematical approaches have been used, including collision-dominated and collisionless transport equations, kinetic and semikinetic models, and macroscopic particle-in-cell techniques. However, the transport equation approach has received the most attention, primarily because it can handle most of the flow conditions encountered in planetary ionospheres. Therefore, the main focus of this chapter is on transport theory, although other mathematical approaches are briefly discussed at the end of the chapter. Typically, numerous assumptions are made to simplify the transport equations before they are applied, and therefore, it is instructive to trace the derivation of the various sets of transport equations in order to establish their intrinsic strengths and limitations. Before diving into the rigorous derivation of the transport equations, it is useful to review the simple derivation of the continuity equation given in Appendix N.

Boltzmann equation

The Boltzmann equation is not only the starting point for the derivation of the different sets of transport equations but also forms the basis for the kinetic and semikinetic theories. With Boltzmann's approach, one is not interested in the motion of individual particles in the gas, but instead with the distribution of particles.

Plasma waves are prevalent throughout the ionospheres. The waves can just have fluctuating electric fields or they can have both fluctuating electric and magnetic fields. Also, the wave amplitudes can be either small or large, depending on the circumstances. Small amplitude waves do not appreciably affect the plasma, and in many situations they can be used as a diagnostic of physical processes that are operating in the plasma. Large amplitude waves, on the other hand, can have a significant effect on the plasma dynamics and energetics. In general, there is a myriad of waves that can propagate in a plasma, and it is not possible, or warranted, to give a detailed discussion here. Instead, the focus in this chapter is on just the fundamental wave modes that can propagate in both magnetized and unmagnetized plasmas. First, the general characteristics of waves are presented. This is followed by a discussion of small amplitude waves in both unmagnetized and magnetized plasmas, including high frequency (electron) waves and low frequency (ion) waves. Next, the effect that collisions have on the waves is illustrated, and this is followed by a presentation of wave excitation mechanisms (plasma instabilities). Finally, large amplitude shock waves and double layers are discussed.

General wave properties

Many types of waves can exist in the plasma environments that characterize the ionospheres. Hence, it is useful to first introduce some common wave nomenclature before discussing the various wave types. It is also useful to distinguish between background plasma properties and wave induced properties. In what follows, subscript 0 designates background plasma properties, and subscript 1 designates both the wave and the perturbed plasma properties associated with the wave.

Neutral atmospheres play a crucial role with regard to the formation, dynamics, and energetics of ionospheres, and therefore, an understanding of ionospheric behavior requires a knowledge of atmospheric behavior. A general description of the atmospheres that give rise to the ionospheres was given in Chapter 2. In this chapter, the processes that operate in upper atmospheres are described, and the equations presented have general applicability. However, the discussion of specifics is mainly directed toward the terrestrial upper atmosphere (see Chapter 2 for a limited description of other solar system neutral atmospheres) because our knowledge of this atmosphere is much more extensive than that for all of the other atmospheres (i.e., other planets, moons, and comets).

Typically, the lower domain of an upper atmosphere is turbulent, and the various atomic and molecular species are thoroughly mixed. However, as altitude increases, molecular diffusion rapidly becomes important and a diffusive separation of the various neutral species occurs. For Earth, this diffusive separation region extends from about 110 to 500 km, and most of the ionosphere and atmosphere interactions occur in this region. At higher altitudes the collisional mean-free-path becomes very long and the neutral particles basically follow ballistic trajectories. For the case of light neutrals, such as hydrogen and helium, and more energetic heavier gases, some of the ballistic trajectories can lead to the escape of particles from the atmosphere.

The topics in this chapter progress from the main processes that operate in the diffusive separation region of an upper atmosphere to the escape of atoms from the top of the atmosphere. First, atmospheric rotation is discussed because it has a significant effect on the horizontal flow of an atmosphere.

This chapter describes the various measurement techniques that are directly applicable to the determination of ionospheric parameters. This discussion is restricted to the most commonly used methods, which measure the thermal plasma densities, temperatures, and velocities, as well as magnetic fields (currents). In general, these techniques can be grouped as remote or direct (in situ) ones. Topics related to direct measurement techniques are described in the first five sections and the rest of the chapter deals with remote sensing. The remote, radio sensing methods rely on the fact that the ionospheric plasma is a dispersive media (Section 6.8) while the relevant radar measurements use the reflective properties of the plasma. The direct in situ measurement techniques discussed here are restricted to those that are applicable to altitudes where the mean-free-path is greater than the characteristic dimension of the instrument.

Spacecraft potential

In situ measurements of ionospheric densities and temperatures are based on the laboratory technique developed and discussed by Irving Langmuir and co-workers over eighty years ago. These so-called Langmuir probes, or retarding potential analyzers (RPAs), have been used for many years in laboratory plasmas before they were adopted for space applications. On a rocket or a satellite, the voltage applied to an instrument has to be driven against the potential of the vehicle, and therefore, it is appropriate to begin with a discussion of the factors that affect the value of this potential. The equilibrium potential is the one that a floating (conducting) body immersed in a plasma acquires in order to cause the net collected current to be zero.

The magnetosphere–ionosphere–atmosphere system at high latitudes is strongly coupled via electric fields, particle precipitation, field-aligned currents, heat flows, and frictional interactions, as shown schematically in Figure 12.1. Electric fields of magnetospheric origin induce a large-scale motion of the high-latitude ionosphere, which affects the electron density morphology. As the plasma drifts through the neutrals, the ion temperature is raised owing to ion–neutral frictional heating. The elevated ion temperature then alters the ion chemical reaction rates, topside plasma scale heights, and ion composition. Also, particle precipitation in the auroral oval acts to produce enhanced ionization rates and elevated electron temperatures, which affect the ion and electron densities and temperatures. These ionospheric changes, in turn, have a significant effect on the thermospheric structure, circulation, and composition. At F region altitudes, the neutral atmosphere tends to follow, but lags behind, the convecting ionospheric plasma. The resulting ion–neutral frictional heating induces vertical winds and O/N2 composition changes. These atmospheric changes then affect the ionospheric densities and temperatures.

The ionosphere–thermosphere system also has a significant effect on the magnetosphere. Precipitating auroral electrons produce conductivity enhancements, which can modify the convection electric field, large-scale current systems, and the electrodynamics of the magnetosphere–ionosphere system as a whole. Also, once the thermosphere is set into motion by convection electric fields, the large inertia of the neutral atmosphere will act to produce dynamo electric fields whenever the magnetosphere tries to change its electrodynamic state. Additional feedback mechanisms exist on polar cap and auroral field lines via a direct flow of plasma from the ionosphere to the magnetosphere.

The 13-moment system of transport equations was introduced in Chapter 3 and several associated sets of collision terms were derived in Chapter 4. However, a rigorous application of the 13-moment system of equations for a multi-species plasma is rather difficult and it has been a common practice to use significantly simplified equation sets to study ionospheric behavior. The focus of this chapter is to describe, in some detail, the transport equations that are appropriate under different ionospheric conditions. The description includes a clear presentation of the major assumptions and approximations needed to derive the various simplified sets of equations so that potential users know the limited range of their applicability.

The equation sets discussed in this chapter are based on the assumption of collision dominance, for which the species velocity distribution functions are close to drifting Maxwellians. This assumption implies that the stress and heat flow terms in the 13-moment expression of the velocity distribution (3.49) are small. Simplified equations are derived for different levels of ionization, including weakly, partially, and fully ionized plasmas. A weakly ionized plasma is one in which Coulomb collisions can be neglected and only ion–neutral and electron–neutral collisions need to be considered. In a partially ionized plasma, collisions between ions, electrons, and neutrals have to be accounted for. Finally, in a fully ionized plasma, ion and electron collisions with neutrals are negligible. Note that in the last case, neutral particles can still be present, and in many fully ionized plasmas the neutrals are much more abundant than the charged particles. The plasma is fully ionized in the collisional sense because of the long-range nature of Coulomb interactions.

Chemical processes are of major importance in determining the equilibrium distribution of ions in planetary ionospheres, even though photoionization and, in some cases, impact ionization are responsible for the initial creation of the electron–ion pairs. This is particularly apparent for the ionospheres of Venus and Mars because they determine the dominant ion species (Sections 13.2 and 13.3). The major neutral constituent in the thermosphere of both Venus and Mars is CO2, and yet the major ion is O+2, as a result of ion–neutral chemistry. Therefore, a thorough knowledge of the controlling chemical processes is necessary for a proper understanding of ionospheric structure and behavior. The dividing line between chemical and physical processes is somewhat artificial and often determined by semantics. In this chapter the discussion centers on reactions involving ions, electrons, and neutral constituents; photoionization and impact ionization are discussed in Chapter 9.

Chemical kinetics

The area of science concerned with the study of chemical reactions is known as chemical kinetics. This branch of science examines the reaction processes from various points of view. A chemical reaction in which the phase of the reactant does not change is called a homogeneous reaction, whereas a chemical process in which different phases are involved is referred to as a heterogeneous reaction. In the context of atmospheric chemistry, heterogeneous reactions involve surfaces and are significant in some of the lower atmospheric chemical processes (e.g., the Antarctic ozone hole), but do not play an important role in ionospheric chemistry.

Introduction

Empirical models of the Venus and terrestrial upper atmospheres have been developed. Tables K.1 and K.2 provide representative values of the Venus neutral temperature and densities for noon and midnight conditions, respectively. The values are from the Venus International Reference Atmosphere (VIRA) model. Representative neutral temperatures and densities for the Earth's thermosphere are given in Tables K.3 to K.6. The tables provide typical values at noon and midnight for both solar maximum and minimum conditions, and for quiet geomagnetic activity. The neutral parameters are from the Mass Spectrometer and Incoherent Scatter (MSIS) empirical model.

The latest version of the MSIS empirical model covers both the lower and upper atmosphere and includes diurnal, semi-diurnal, and terdiurnal migrating tidal modes. A reference atmosphere for Mars that is based on measurements has not been developed. However, an engineering-level Mars atmosphere model that is based on models is available.

This chapter summarizes our current understanding of the various ionospheres in the solar system. The order of presentation of the planetary ionospheres follows their position with respect to the Sun, that is, it starts with Mercury and ends with Pluto. The amount of information currently available varies widely, from a reasonably good description for Venus to just a basic guess for Pluto. In the last section of this chapter, the ionospheres of the various moons and that of Comet Halley are described. Here again the existing data are limited, with the exception of Titan, which is currently undergoing extensive exploration by the Cassini Orbiter.

Mercury

Mercury does not have a conventional gravitationally bound atmosphere, as indicated in Section 2.4. The plasma population caused by photo and impact ionization of the neutral constituents, which is present in the neutral exosphere, is an ion exosphere, not a true ionosphere. No quantitative calculations of the plasma densities have been carried out to date. The global Na+ production rate was estimated to be a few times 1023 ions s−1, but no other studies have been published and there are no observations concerning the thermal plasma densities. The Messenger spacecraft is currently on its way and will be placed in orbit around Mercury in 2011. Our understanding of Mercury's environment will increase significantly with data from a successful Messenger mission.

Venus

Of all the nonterrestrial thermospheres and ionospheres in the solar system, those of Venus have been the most studied and best understood, mainly because of the Pioneer Venus Orbiter (PVO) spacecraft, which made measurements over the 14-year period from 1978 to 1992.