The Orientale basin (Figure 3.1) is located on the western limb of the Moon; most of the basin and its deposits extend over the lunar far side. The name “Orientale” (eastern) is derived from the old astronomical practice of displaying telescopic photographs of the Moon with south at the top and east-west convention derived from terrestrial coordinates. The first studies of the Orientale basin utilized Earth-based telescopic photographs; because of the basin's location on the extreme limb, these photographs were geometrically rectified at the Lunar and Planetary Laboratory (University of Arizona) to create a vertical viewing perspective (Hartmann and Kuiper, 1962). These rectified photographs also served as the primary data base for an early geological study of Orientale as the prototype lunar basin (McCauley, 1968).

Because of the spectacular success of the Lunar Orbiter spacecraft, particularly a series of high-quality photographs by Orbiter IV that provide contiguous coverage, the number of detailed geological descriptions of the Orientale basin increased dramatically in the years immediately following the Apollo missions (Hartmann and Wood, 1971; Head, 1974a; Moore et al., 1974; McCauley, 1977; Scott et al., 1977; Spudis et al., 1984b). In this chapter, I review the regional and local geology of Orientale and, in conjunction with data from photogeology and remote sensing, integrate these data into a geological model for the formation and evolution of the basin.

Regional geology of the Orientale impact site

The Orientale basin is sparsely filled by mare basalt and located in rugged highland terrain on the western limb of the Moon (Figure 3.1).

Multi-ring basins are features produced by the collision of solid bodies with the planets, so the basin problem is a subset of the more general problem of impact cratering, a vast field of study. This chapter briefly describes the impact process from theoretical considerations, from the evidence of some well studied terrestrial impact craters, and from the observed morphology of impact craters on the Moon and their systematic changes with increasing crater size.

The cratering process

Impact mechanics

Our understanding of what happens when a solid body hits a planetary surface at high speeds has increased greatly over the past 25 years. The study of the physical processes occurring during impact events is called impact mechanics. Although the details of this complex process are not understood, laboratory experiments, explosion craters, natural impact craters, and computer simulations have given us a general outline of the main stages that characterize the formation of an impact crater.

Solid bodies collide with planetary surfaces at very high speeds; such impact speeds are in the range called hypervelocity. Encounter velocities can vary from lunar escape velocity (about 2.5 km/s) at a minimum, up to many tens of kilometers per second (on the basis of velocities of bodies in heliocentric orbits). On the Moon, the mean impact velocity is about 20 km/s (Shoemaker, 1977). At the moment of contact between an impactor and a planet, the kinetic energy of the impacting body is transferred to the planetary surface target. A shock wave propagates into the target and projectile, resulting in intensive compression of both objects. In hypervelocity impacts, the quantities of energy produced greatly exceed the heat of vaporization for geological materials.

The formation of multi-ring basins dominated the early geological evolution of the Moon. The five basins described in the preceding chapters represent a spectrum of basin ages, sizes and morphologies. By comparing the similarities and differences among these basins, some general inferences may be made regarding the process of formation of multi-ring basins on the Moon. I here synthesize the information described in the previous chapters to develop a model for the formation and geological evolution of multi-ring basins on the Moon. This model is incomplete, but several puzzling aspects of basin geology can be explained satisfactorily through this approach. At various points in the following discussion, please refer to preceding sections in the text.

Composition and structure of the lunar crust

The crust of the Moon is heterogeneous on a local and a regional scale; the impact targets for lunar multi-ring basins were similarly heterogeneous. The crustal thickness at the basin target sites was widely varied, ranging from 50 km thick for parts of the Imbrium basin to over 120 km thick for the Orientale highlands (Bills and Ferrari, 1976). Moreover, lithospheric conditions during the era of basin-forming impacts changed with time in response to rapidly changing thermal conditions within the Moon 4 Ga ago (Hubbard and Minear, 1975; Solomon and Head, 1980). The older basins formed in a relatively thin, easily penetrated lithosphere that gave rise to extensive post-impact modification.

The Serenitatis basin is on the near side of the Moon, east of Mare Imbrium and north of Mare Tranquillitatis (Figure 1.1). The basin is almost completely flooded by mare basalts (Figure 6.1) and displays a mascon gravity anomaly (Sjogren et al., 1974). The Serenitatis basin was recognized as multi-ring in the studies of Hartmann and Kuiper (1962), Baldwin (1963), Hartmann and Wood (1971) and during systematic geological mapping of the Moon (Wilhelms and McCauley, 1971). Because of the large amount of mare flooding and generally degraded appearance of the basin, Serenitatis was once considered to be one of the oldest basins on the Moon (Hartmann and Wood, 1971; Wilhelms and McCauley, 1971). This view has changed, primarily because of ages obtained for some Apollo 17 samples considered to represent impact melt of the Serenitatis basin (James et al., 1978; Wilhelms, 1987). I will describe the regional geology of the Serenitatis basin and some aspects of Apollo 17 site geology that relate to problems in the interpretation of its formation and subsequent evolution.

Regional geological setting and basin definition

The Serenitatis basin is close to the Imbrium basin and the effects of Imbrium on the morphologic evolution of Serenitatis have been significant. Most interpretations of basin geology rely on the well exposed highlands to the east of Mare Serenitatis (Figure 6.1). Thus, the morphological data available for interpreting the geology of the Serenitatis basin are limited compared with those for some of the other basins described in this book.

The Imbrium basin (Figure 7.1) is probably the most studied multi-ring basin on the Moon. Prominently located on the lunar near side, west of Mare Serenitatis and east of the large maria Oceanus Procellarum (Figure 1.1), the Imbrium basin first attracted the attention of G.K. Gilbert (1893) in his historic analysis of lunar craters. Gilbert recognized the extensive pattern of radial texture associated with Imbrium and postulated that Mare Imbrium had formed by the collision of a large meteorite with the Moon. The impact origin of the Imbrium basin was also recognized by Dietz (1946), Baldwin (1949; 1963), Urey (1952), and Hartmann and Kuiper (1962). The landmark paper of Shoemaker and Hackman (1962) proposed a global stratigraphic system for the Moon based on the deposition of ejecta from the Imbrium basin as a marker horizon. The Imbrium impact was considered such a key event in lunar geological history that two Apollo missions (Apollo 14 and 15) were sent to landing sites specifically chosen to address problems of Imbrium basin geology.

Regional geology and setting

Imbrium is one of the youngest major basins on the Moon, but extensively flooded by mare basalt (Figure 7.1). Even so, as one of the largest lunar basins (main topographic rim 1160 km in diameter), it has an ejecta blanket so extensive that almost all of the near side may be dated relatively with respect to the time of the Imbrium impact (Wilhelms, 1970).

The formation of multi-ring basins was an important process in the early histories of Solar System bodies. Thus, study of basins on the other planets potentially can give us insight into the early geological evolution of the planets. Although occurring on all of the terrestrial planets, the most and best preserved basins occur on planets that display remnants of their early crusts, i.e., Mercury, Mars, and the icy satellites of Jupiter and Saturn. In this chapter, I discuss the geology of basins found on the terrestrial planets in relation to the geological model for basin formation and development on the Moon discussed above.

Earth

Most of the recognized impact structures on the Earth are either simple, bowlshaped craters or complex craters displaying central peaks (Grieve and Robertson, 1979; Masaitis et al., 1980; Grieve, 1987). However, several of Earth's larger craters have multiple rings; seventeen craters display at least two rings (Table 9.1; Pike, 1985 and references therein). The paucity of terrestrial multi-ring basins doubtless reflects the relatively youthful average surface age of the Earth, as compared with the more primitive terrestrial planets, such as Mercury and Mars.

Impact craters of the Earth show the morphological transitions with increasing size, as do craters on the planets, but changes in form occur at different diameters (Pike, 1985). Complex craters on the Earth range in size from about 4 km to about 25 km in diameter.

Large solar flares are probably the most spectacular eruptive events in cosmical plasmas. Though rather weak in absolute magnitude compared for instance with the enormous energies set free in a supernova explosion, they outshine all other cosmic events for a terrestrial observer. According to the generally accepted picture, a flare constitutes a sudden release of magnetic energy stored in the corona and is therefore primarily an MHD process, though the various nonthermal channels of energy dissipation and deposition, which give rise to the richness of the observations, require a framework broader than MHD theory.

Since the major part of this book is concerned primarily with phenomena in laboratory plasmas, it seems to be convenient for the generally interested reader to find a somewhat broader introduction to this astrophysical topic. The engine driving the magnetic activity in the solar atmosphere is turbulent convection in the solar interior. Section 10.1 therefore gives an overview of our present understanding of the convection zone, in particular magnetoconvection. In section 10.2 we consider the solar atmosphere, its mean stratification, the process of magnetic flux emergence from the convection zone and the magnetic structures in the corona, in particular in active regions. In section 10.3 we then focus in on the MHD modelling of the flare phenomenon.

Ordinary nonmagnetic fluids are known to become turbulent at sufficiently high Reynolds numbers and a similar behavior is expected for electrically conducting magnetized fluids, though direct experimental evidence is scarce. Some confusion may arise, however, owing to the convention, widespread in the fusion research community, of calling the Lundquist number S = LvA/η the magnetic Reynolds number, the latter being correctly defined by Rm = Lv/η, where v is some average fluid velocity. S ≫ 1 simply means that the resistivity is small, while the system may well be nonturbulent, or even static corresponding to Rm ≃ 0. S is an important theoretical parameter characterizing growth rates of possible resistive instabilities. But only when large fluid velocities are generated in the nonlinear phase of an instability or by some external stirring Rm can become large, making the system prone to turbulence. MHD turbulence can thus be expected only in strongly dynamic systems, e.g. disruptive processes in tokamaks or flares in the solar atmosphere.

Though the behavior at Reynolds numbers close to the critical value, where the transition from laminar flow to turbulence occurs, has recently attracted much attention, the strongest interest is in the high-Reynolds-number regime, where turbulence is fully developed, which is characteristic of most turbulent fluids in nature.

Tokamaks constitute the best plasma physics laboratory available today. The largest devices (e.g. JET and DIII-D) confine plasmas of considerable volume (many m3), high densities (ne ∼ 1020 m-3) and high temperatures (Te ∼ 10 keV) under quasi-stationary conditions (for an introduction to the general physics of tokamaks see Wesson, 1987). Tokamak plasmas exhibit a rich variety of MHD phenomena, being investigated by numerous diagnostic tools with high spatial and temporal resolution, which make theoretical interpretation a challenging task.

Particularly conspicuous MHD effects are the different kinds of disruptive events which affect global plasma confinement more or less severely. In this chapter we consider the three most important disruptive processes. Section 8.1 deals with the sawtooth oscillation, a quasi-periodic internal relaxation process, which is observed in most tokamak discharges. Their main effect is to limit the central temperature increase, generating a more uniform average temperature distribution. They also have the beneficial effect of preventing the central accumulation of impurity ions.

Section 8.2 considers major disruptions, which constitute the most violent processes in a tokamak plasma. Disruptions occur when certain limits in the plasma parameters are exceeded, causing loss of a large fraction of the plasma energy, which often leads to the termination of the discharge.

Plasma physics has sometimes been called the science of instabilities. In fact during the last three decades of plasma research, stability theory was probably the most intensively studied field. The reason for this widespread activity is the empirical finding that in general plasmas, especially those generated in laboratory devices, are not quiescent but spontaneously develop rapid dynamics which often tend to terminate the plasma discharge. MHD instabilities are considered as particularly dangerous because they usually involve large-scale motions and short time scales. Though a realistic picture of dynamic plasma processes requires a nonlinear theory, the knowledge of the basic linear instability is usually a very helpful starting point, in particular since linear theory has a solid mathematical foundation.

The organization of the chapter is as follows. Section 4.1 presents the linearized MHD equations. In section 4.2 we consider the simplest case of linear eigenmodes, waves in a homogeneous plasma. The energy principle is introduced in section 4.3. In section 4.4 we then derive in some detail the theory of eigenmodes in a circular cylindrical pinch, which contains many qualitative features of geometrically more complicated configurations. In section 4.5 this theory is applied to the cylindrical tokamak model. The influence of toroidicity, which most severely affects the n = 1 mode, is discussed briefly in section 4.6.

Magnetohydrodynamics (MHD) describes the macroscopic behavior of electrically conducting fluids, notably of plasmas. However, in contrast to what the name seems to indicate, work in MHD has usually little to do with dynamics, or at least has had so in the past. In fact, most MHD studies of plasmas deal with magnetostatic configurations. This is not only a question of convenience — powerful mathematical methods have been developed in magnetostatic equilibrium theory — but is also based on fundamental properties of magnetized plasmas. While in hydrodynamics of nonconducting fluids static configurations are boringly simple and interesting phenomena are in general only caused by sufficiently rapid fluid motions, conducting fluids are often confined by strong magnetic fields for times which are long compared with typical flow decay times, so that the effects of fluid dynamics are weak, giving rise to quasistatic magnetic field configurations. Such configurations may appear in a bewildering variety of shapes generated by the particular boundary conditions, e.g. the external coils in laboratory experiments or the “foot point” flux distributions in the solar photosphere, and their study is both necessary and rewarding.

In addition to finding the appropriate equilibrium solutions one must also determine their stability properties, since in the real world only stable equilibria exist.

Magnetohydrodynamics (MHD) is the macroscopic theory of electrically conducting fluids, providing a powerful and practical theoretical framework for describing both laboratory and astrophysical plasmas. Most textbooks and monographs on the topic, however, concentrate on two particular aspects, magnetostatic equilibria and linear stability theory, while nonlinear effects, i.e. real magnetohydrodynamics, are considered only briefly if at all. I have therefore felt the need for a book with a special focus on the nonlinear aspects of the theory for some time.

In contrast to linear theory which, in particular in the limit of ideal MHD, rests on mathematically solid ground, nonlinear theory means adventures in a, mathematically speaking, hostile world, where few things can be proved rigorously. While in linear stability analysis numerical calculations are mainly quantitative evaluations, they obtain a different character in the study of nonlinear phenomena, which are often even qualitatively unknown. Hence this book frequently refers to results from numerical simulations, as a glance at the various illustrations reveals, but consideration is focused on the physics rather than the numerics.

In spite of the numerous references to the literature the book is essentially self-contained. Even the individual chapters can be studied quite independently as introductions to or current overviews of their particular topics.

There is hardly a term in plasma physics exhibiting more scents, facets and also ambiguities than does magnetic reconnection or, simply, reconnection. It is even sometimes used with a touch of magic. The basic picture underlying the idea of reconnection is that of two field lines (thin flux tubes, properly speaking) being carried along with the fluid owing to the property of flux conservation until they come close together at some point, where by the effect of finite resistivity they are cut and reconnected in a different way. Though this is a localized process, it may fundamentally change the global field line connection as indicated in Fig. 6.1, permitting fluid motions which would be inhibited in the absence of such local decoupling of fluid and magnetic field. Almost all nonlinear processes in magnetized conducting fluids involve reconnection, which may be called the essence of nonlinear MHD.

Because of the omnipresence of finite resistivity in real systems resistive diffusion takes place everywhere in the plasma, though usually at a slow rate. Reconnection theory is concerned with the problem of fast reconnection in order to explain how in certain dynamic processes very small values of the resistivity allow the rapid release of a large amount of free magnetic energy, as observed for instance in tokamak disruptions or solar flares.

The study of linear stability of plasmas had for a long period been carried by the conception that only stable configurations can exist in nature, since instability would lead to destruction of the equilibrium and loss of plasma confinement, which would be the faster the larger the growth rate. Statements like: “all plasmas (meaning real inhomogeneous plasma configurations) are unstable”, sometimes pronounced by plasma theoreticians in the heyday of instability theory, seemed to imply that magnetic fusion research is basically a futile endeavor. The development in experimental plasma physics during the past two decades proved this conception thoroughly wrong. Tokamak discharges may exist, well confined, in spite of the presence of instabilities, which often lead only to a slight change of the plasma profiles and a certain increase of plasma and energy transport (and which may even have beneficial effects such as the removal of impurities by the sawtooth process). Thus in order to judge the effect of an instability it is evidently necessary to calculate or at least estimate its nonlinear behavior, in particular the saturation level. It will turn out that linear mode properties, in particular growth rates, often have little to say about the nonlinear behavior.

As a general rule an instability is found to be the more “dangerous”, i.e. its effect on the plasma configuration is the more detrimental, the longer the wavelength (global modes).