This book aims to coherently present applications of group analysis to integro-differential equations in an accessible way. The book will be useful to both physicists and mathematicians interested in general methods to investigate nonlinear problems using symmetries.

James L. Burch·C. Philippe Escoubet Originally published in the journal Space Science Reviews, Volume 145, Nos 1–2, 1–2. DOI: 10. 1007/s11214-009-9532-7 © Springer Science+Business Media B. V. 2009 The IMAGE and CLUSTER spacecraft have revolutionized our understanding of the inner magnetosphere and in particular the plasmasphere. Before launch, the plasmasphere was not a prime objective of the CLUSTER mission. In fact, CLUSTER might not have ever observed this region because a few years before the CLUSTER launch (at the beginning of the 1990s), it was proposed to raise the perigee of the orbit to 8 Earth radii to make multipoint measu- ments in the current disruption region in the tail. Because of ground segment constraints, this proposal did not materialize. In view of the great depth and breadth of plasmaspheric research and numerous papers published on the plasmasphere since the CLUSTER launch, this choice certainly was a judicious one. The fact that the plasmasphere was one of the prime targets in the inner magnetosphere for IMAGE provided a unique opportunity to make great strides using the new and comp- mentary measurements of the two missions. IMAGE, with sensitive EUV cameras, could for the rst time make global images of the plasmasphere and show its great variability d- ing storm-time. CLUSTER, with four-spacecraft, could analyze in situ spatial and temporal structures at the plasmapause that are particularly important in such a dynamic system.

Magnetohydrodynamics, or MHD, is a theoretical way of describing the statics and dynamics of electrically conducting uids. The most important of these uids occurring in both nature and the laboratory are ionized gases, called plasmas. These have the simultaneous properties of conducting electricity and being electrically charge neutral on almost all length scales. The study of these gases is called plasma physics. MHD is the poor cousin of plasma physics. It is the simplest theory of plasma dynamics. In most introductory courses, it is usually afforded a short chapter or lecture at most: Alfven ´ waves, the kink mode, and that is it. (Now, on to Landau damping!) In advanced plasma courses, such as those dealing with waves or kinetic theory, it is given an even more cursory treatment, a brief mention on the way to things more profound and interesting. (It is just MHD! Besides, real plasma phy- cists do kinetic theory!) Nonetheless, MHD is an indispensable tool in all applications of plasma physics.

This book contains contributions to the 172. WE-Heraeus-Seminar “Atoms and Molecules in Strong External Fields,” which took place April 7–11 1997 at the Phys- zentrum Bad Honnef (Germany). The designation “strong fields” applies to external static magnetic, and/or electric fields that are sufficiently intense to cause alterations in the atomic or molecular str- ture and dynamics. The specific topics treated are the behavior and properties of atoms in strong static fields, the fundamental aspects and electronic structure of molecules in strong magnetic fields, the dynamics and aspects of chaos in highly excited R- berg atoms in external fields, matter in the atmosphere of astrophysical objects (white dwarfs, neutron stars), and quantum nanostructures in strong magnetic fields. It is obvious that the elaboration of the corresponding properties in these regimes causes the greatest difficulties, and is incomplete even today. Present-day technology has made it possible for many research groups to study the behavior of matter in strong external fields, both experimentally and theore- cally, where the phrase “experimentally” includes the astronomical observations. - derstanding these systems requires the development of modern theories and powerful computational techniques. Interdisciplinary collaborations will be helpful and useful in developing more efficient methods to understand these important systems. Hence the idea was to bring together people from different fields like atomic and molecular physics, theoretical chemistry, astrophysics and all those colleagues interested in aspects of few-body systems in external fields.

Since the early days of modem physics spectroscopic techniques have been employed as a powerful tool to assess existing theoretical models and to uncover novel phenomena that promote the development of new concepts. Conventionally, the system to be probed is prepared in a well-defined state. Upon a controlled perturbation one measures then the spectrum of a single particle (electron, photon, etc.) emitted from the probe. The analysis of this single particle spectrum yields a wealth of important information on the properties of the system, such as optical and magnetic behaviour. Therefore, such analysis is nowadays a standard tool to investigate and characterize a variety of materials. However, it was clear at a very early stage that real physical compounds consist of many coupled particles that may be excited simultaneously in response to an external perturbation. Yet, the simultaneous (coincident) detection of two or more excited species proved to be a serious technical obstacle, in particular for extended electronic systems such as surfaces. In recent years, however, coincidence techniques have progressed so far as to image the multi-particle excitation spectrum in an impressive detail. Correspondingly, many-body theoretical concepts have been put forward to interpret the experimental findings and to direct future experimental research. This book gives a snapshot of the present status of multi-particle coincidence studies both from a theoretical and an experimental point of view. It also includes selected topical review articles that highlight the achievements and the power of coincident techniques.

The recent developement of high power lasers, delivering femtosecond pulses of 20 2 intensities up to 10 W/cm , has led to the discovery of new phenomena in laser interactions with matter. At these enormous laser intensities, atoms, and molecules are exposed to extreme conditions and new phenomena occur, such as the very rapid multi photon ionization of atomic systems, the emission by these systems of very high order harmonics of the exciting laser light, the Coulomb explosion of molecules, and the acceleration of electrons close to the velocity of light. These phenomena generate new behaviour of bulk matter in intense laser fields, with great potential for wide ranging applications which include the study of ultra-fast processes, the development of high-frequency lasers, and the investigation of the properties of plasmas and condensed matter under extreme conditions of temperature and pressure. In particular, the concept of the "fast ignitor" approach to inertial confinement fusion (ICF) has been proposed, which is based on the separation of the compression and the ignition phases in laser-driven ICF. The aim of this course on "Atom, Solids and Plasmas in Super-Intense Laser fields" was to bring together senior researchers and students in atomic and molecular physics, laser physics, condensed matter and plasma physics, in order to review recent developments in high-intensity laser-matter interactions. The course was held at the Ettore Majorana International Centre for Scientific Culture in Erice from July 8 to July 14,2000.

This text is an introduction to the physics of collisional plasmas, as opposed to plasmas in space. It is intended for graduate students in physics and engineering . The first chapter introduces with progressively increasing detail, the fundamental concepts of plasma physic. The motion of individual charged particles in various configurations of electric and magnetic fields is detailed in the second chapter while the third chapter considers the collective motion of the plasma particles described according to a hydrodynamic model. The fourth chapter is most original in that it introduces a general approach to energy balance, valid for all types of discharges comprising direct current(DC) and high frequency (HF) discharges, including an applied static magnetic field. The basic concepts required in this fourth chapter have been progressively introduced in the previous chapters.

In this undergraduate textbook, now in its 2nd edition, the author develops the quantum theory from first principles based on very simple experiments: a photon traveling through beam splitters to detectors, an electron moving through magnetic fields, and an atom emitting radiation. From the physical description of these experiments follows a natural mathematical description in terms of matrices and complex numbers.

An outgrowth of a workshop held by the Community of European Solar Radio Astronomers (CESRA), this volume collects reviews on current research and perspectives on the variable solar corona: high-energy particles, large-scale disturbances such as mass ejections and waves, and radio diagnostics of the coronal plasma. Multiwavelength observations of the Sun with radio instruments and recent space missions are drawn on extensively, as well as input from neighbouring fields e.g. solar wind, Earth's bow shock. Recent developments are discussed alongside key developments in this rapidly evolving field.

This Springer Handbook of Atomic, Molecular, and Optical Physics comprises a comprehensive reference source that unifies the entire fields of atomic, molecular, and optical (AMO) physics, assembling the principal ideas, techniques and results of the field from atomic spectroscopy to applications in comets. Its 92 chapters are written by over 100 authors, all leaders in their respective disciplines.