Introduction

The differences between the E and D regions in middle latitudes hold also at high latitude. The E region is characterized by relatively simple photochemistry and high electrical conductivity, whereas the D region below it has a complex and less well-known chemistry, the electric currents and plasma motions being inhibited by the higher atmospheric pressure. What they have in common at high latitude is the importance of ionization by energetic particles. Typical spectra include particles with energies such that they are stopped and ionize in both regions, the lower energies (for example, electrons of a few kilo-electron volts) affecting the E region and the higher ones (e.g. electrons with energies of tens of kilo-electron volts) penetrating into region D. Figure 7.1 shows electron-density profiles between 65 and 110 km due to representative spectra of ionizing electrons incident on the atmosphere from above. Increasing the characteristic energy of the spectrum lowers the peak of the layer, increasing the electron density in the D region but reducing it in the E region.

At middle latitude the D region's role in radio propagation is a secondary one. The main parameters of HF propagation are determined by the E and the F regions, and the D region acts mainly as an absorbing layer, reducing the strength of the signal but seldom preventing communications for any long period. At high latitude the D region may be much enhanced and then absorption becomes a considerable problem.

Introduction

Propagation of radio waves from ELF to UHF frequencies via the high latitude ionosphere is sometimes radically different from propagation at middle and low latitudes. This is primarily due to the fact that the magnetic field-lines at “corrected geomagnetic latitudes” greater than ∼60° allow solar and magnetospheric particles and plasma to penetrate into the ionosphere. This results in the creation of many large-magnitude irregularities with scale sizes from meters to kilometers, most of which are aligned with the geomagnetic field in the auroral E and F regions. There are also sun-aligned arcs plus patches and blobs of ionization in the polar F region. Because of the extremely wide variation in ionospheric characteristics at high latitudes, this chapter contains many examples of actual propagation behavior.

In contrast, it should also be mentioned that there is a wide spectrum of lessintense ionospheric irregularities in the mid-latitude ionosphere. Since most antennas used for communication and ionospheric sounding up until the 1960s had rather large antenna half-power beamwidths (typically 50° × 50° in azimuth and elevation), these small irregularities were not observed. Starting in the early 1960s, several very-high-resolution HF backscatter sounders were constructed and employed in ionospheric research (see descriptions of the systems and results by Croft, 1968, and Hunsucker, 1991, Ch. 4). These systems revealed a plethora of echoes from irregularities, mostly of meter wavelengths.

This book is in a sense a sequel to my previous book Nonlinear Magnetohydrodynamics, which contained a chapter on magnetic reconnection. Judging from many discussions it appeared that it was this chapter that was particularly appreciated. The plan to write a full monograph on this topic actually took a concrete shape during a stay at the National Institute for Fusion Science at Nagoya, where I found the time to work out the basic conception of the book. It became clear that resistive theory, to which most of the previous work was restricted, including that chapter of my previous book, covers only a particular aspect of this multifaceted subject and not even the most interesting one, in view of the various applications, both in fusion plasma devices and in astrophysical plasmas, where collisionless effects tend to dominate over resistivity.

While resistive reconnection theory had reached a certain level of maturity and completion about a decade ago (few theories are really complete before becoming obsolete), the understanding of collisionless reconnection processes has shown a rapid development during the past five years or so. The book therefore consists of two main parts, chapters 3–5 deal with resistive theory, while chapters 6–8 give an overview of the present understanding of collisionless reconnection processes. I mainly emphasize the reconnection mechanisms, which operate under the different plasma conditions, to explain the apparent paradox that formally very weak effects in Ohm's law account for the rapid dynamic time-scales suggested by the observations.

Since the early 1950s, when magnetohydrodynamics – MHD in short – became an established theory and along with it the concept of a “frozenin” magnetic field within an electrically conducting fluid, the problem of how magnetic field energy could be released in such a fluid has been generally acknowledged. In the early days the major impetus came from solar physics. Estimates readily showed that the energies associated with eruptive processes, notably flares, can only be stored in the coronal magnetic field, all other energy sources being by far too weak. On the other hand the high temperature in the corona, which makes the coronal plasma a particularly good electrical conductor, appeared to preclude any fast magnetic change involving diffusion. For a coronal electron temperature Te ～ 106 K the magnetic diffusivity is η ～ 104 cm2/s, hence field diffusion in a region of diameter L ～ 104 km as typically involved in a flare would require a time-scale τη = L2/η ～ 1014 s, whereas the observed flash phase of a flare takes less than ～ 103 s.

It had, however, soon been realized that the discrepancy is not quite as bad as this. Contrary to magnetic diffusion in a solid conductor, a fluid is stirred into motion by the change of the magnetic field. As it carries along the frozen-in field, it may generate steep field gradients typically located in sheet-like structures, and hence lead to much shorter diffusion times.

The magnetosphere is the cosmic plasma laboratory nearest to the Earth, which is therefore accessible to detailed ground and in-situ observations. It is, loosely speaking, a magnetic cavity generated by the interaction of the solar wind with the Earth's dipole field, which shields the Earth from direct bombardment by high-energy particles. This shield is, however, rather leaky, allowing solar-wind plasma to penetrate into the magnetosphere, which gives rise to a variety of different phenomena, the most spectacular being the aurora. The leakiness is mainly due to large-scale reconnection processes occurring at the front and in the tail of the magnetosphere. These processes form the main topic of this chapter.

The magnetosphere has a complex onion-like structure consisting of various plasma layers of distinctly different properties separated by rather sharp boundary surfaces. In section 8.1 we give a brief overview of the main features and outline the mechanisms leading to this layered structure. For a more detailed introduction to magnetospheric physics see, e.g., Baumjohann & Treumann (1996).

Reconnection is believed to be the main mechanism responsible for the magnetic processes observed in the magnetosphere, commonly called geomagnetic activity. The basic model of magnetospheric reconnection and plasma convection has been proposed by Dungey (1961) and this is considered in section 8.2. Reconnection of the dipole field (which is essentially oriented northward) with a southward component of the interplanetary field opens the magnetic cavity. The reconnected field lines are swept along by the solar wind to the nightside, until the increasing magnetic tension leads to a second reconnection process in the tail, reclosing the dipole field lines, which then contract back toward the Earth.

It thus appears that a long-standing riddle has now been solved. Fast quasi-Alfvénic magnetic reconnection may occur under rather general conditions with a rate rather independent of the particular reconnection physics, both in high- and low-β plasmas. Ironically, the case of stationary resistive MHD, which has been regarded as the most natural framework of reconnection theory, does not allow fast merging. The pecularities of resistive reconnection have been the origin of the long controversy dividing the community into two camps, the adherents of the Petschek model and those of the Sweet-Parker model emphasizing current sheets. Actually, physical conditions for a stationary high-Lundquist number MHD model to apply are rarely satisfied, neither in nature nor in laboratory plasmas. Either the plasma is strongly resistive, which often implies relatively low S or, at large S-value, collisionless effects are more important than resistivity. In addition, the plasma behavior is usually highly nonstationary, sometimes fully turbulent, and such a system allows fast reconnection even in resistive MHD. It is true that the usual quasi-stationary 2D models for collisionless reconnection are also highly idealized, far from real plasma conditions. Real plasmas which tend to exhibit a whole maze of fluctuations, but these do not seem to control the reconnection rate.

A concept which had also polarized the community, the distinction between driven and spontaneous reconnection, has to a good deal lost its significance. It is true that in many cases an external driving agent can be identified.

In an electrically conducting magnetized plasma even slow motions do not, in general, preserve a smooth magnetic field, but give rise to sheetlike tangential field discontinuities, called current sheets. These are the natural loci of magnetic reconnection. In this chapter we consider the properties of current sheets and reconnection via current sheets in the traditional framework of resistive magnetohydrodynamics (MHD). This restriction is justified, since macroscopic current sheets mostly occur, when the reconnection process R in Ohm's law (2.1) is dissipative. Collisionless reconnection processes, which are treated in chapters 6 and 7, usually give rise to microcurrent sheets.

The chapter starts with a brief introduction to MHD theory, discussing the basic equations, magnetostatic equilibria, and linear MHD waves. In low-β plasmas it is often convenient to eliminate the fast compressional MHD wave by using a reduced set of equations. In section 3.2 we first consider the conditions under which a current sheet arises and how it is formed by rapid thinning, which continues until finite resistivity leads to a stationary sheet configuration. Then the structure of a resistive current sheet, called a Sweet–Parker sheet (Sweet, 1958; Parker, 1963), is analyzed. While the global properties of such sheets follow from the basic conservation laws, the detailed structure requires a more specific analysis. Section 3.3 deals with the role of current sheets as centers of reconnection in a magnetic configuration. Syrovatskii (1971) has developed a simple and elegant theory of current sheets which captures many features of the fully dynamic resistive theory, in particular the complicated structure of the sheet edges, the so-called Y-points.