We present an overview of the status of ongoing work on physics models describing beam matching and halo control for particle accelerators, particularly high power ion linacs. We consider moments and various new variables that more naturally describe beam halo evolution. We compute matched beams and ''mode invariants'' (analogs of moment invariants) using primarily symbolic techniques.

Chaos control refers to purposefully manipulating chaotic dynamical behaviors of some complex nonlinear systems. There exists no similar control theory-oriented book available in the market that is devoted to the subject of chaos control, written by control engineers for control engineers. World-renowned leading experts in the field provide their state-of-the-art survey about the extensive research that has been done over the last few years in this subject. The new technology of chaos control has major impact on novel engineering applications such as telecommunications, power systems, liquid mixing, internet technology, high-performance circuits and devices, biological systems modeling like the brain and the heart, and decision making. The book is not only aimed at active researchers in the field of chaos control involving control and systems engineers, theoretical and experimental physicists, and applied mathematicians, but also at a general audience in related fields.

This book contains the proceedings of the 1999 ICFA workshop on the physics of high brightness beams. The workshop took a snapshot in time of a fast moving, interdisciplinary field driven by advanced applications such as high gradient, high energy physics linear colliders, high gain free electron lasers, heavy ion fusion, and transmutation of nuclear materials. While the field of high brightness beam physics has traditionally been divided into disparate electron and heavy ion communities, the workshop brought the two types of researchers together, so that a sharing of insights and methods could be achieved. Thus, this book represents a unifying step in the development of the diverse fascinating discipline of high brightness beam physics, with its challenges rooted in collective, nonlinear particle motion and ultra-high electromagnetic energy density.

Over the last two decades, chaos in engineering systems has moved from being simply a curious phenomenon to one with real, practical significance and utility. Engineers, scientists, and mathematicians have similarly advanced from the passive role of analyzing chaos to their present, active role of controlling chaos-control directed not only at suppression, but also at exploiting its enormous potential. We now stand at the threshold of major advances in the control and synchronization of chaos for new applications across the range of engineering disciplines. Controlling Chaos and Bifurcations in Engineering Systems provides a state-of-the-art survey of the control-and anti-control-of chaos in dynamical systems. Internationally known experts in the field join forces in this volume to form this tutorial-style combination of overview and technical report on the latest advances in the theory and applications of chaos control. They detail various approaches to control and show how designers can use chaos to create a wider variety of properties and greater flexibility in the design process. Chaos control promises to have a major impact on novel time- and energy-critical engineering applications. Within this volume, readers will find many challenging problems-yet unsolved-regarding both the fundamental theory and potential applications of chaos control and anti-control. Controlling Chaos and Bifurcations in Engineering Systems will bring readers up-to-date on recent development in the field and help open the door to new advances.