We review our recent work on methods to study stability in nonlinear mechanics, especially for the problems of particle accelerators, and compare our ideas to those of other authors. We emphasize methods that (a) show promise as practical design tools, (b) are effective when the nonlinearity is large, and (c) have a strong theoretical basis. TABLE OF CONTENTS

This Focus Issue presents a collection of papers originating from the workshop Methods of Chaos Detection and Predictability: Theory and Applications held at the Max Planck Institute for the Physics of Complex Systems in Dresden, June 17-21, 2013. The main aim of this interdisciplinary workshop was to review comprehensively the theory and numerical implementation of the existing methods of chao...

Interactions of ultrahigh energy neutrinos of cosmological origin in large volumes of dense, radio-transparent media can be detected via coherent Cherenkov emission from accompanying electromagnetic showers. Antarctic ice meets the requirements for an e cient detection medium for a radio frequency neutrino telescope. We carefully estimate the sensitivity of realistic antennas embedded deep in t...

A class of nonrelativistic particle accelerators in which the majority of particles gain energy at an exponential rate is constructed. The class includes ergodic billiards with a piston that moves adiabatically and is removed adiabatically in a periodic fashion. The phenomenon is robust: deformations that keep the chaotic character of the billiard retain the exponential energy growth. The growt...

The motion of beams in particle accelerators is dominated by a plethora of non-linear effects, which can enhance chaotic motion and limit their performance. The application of advanced non-linear dynamics methods for detecting and correcting these effects and thereby increasing the region of beam stability plays an essential role during the accelerator design phase but also their operation. Aft...

We recall the motivation for research in high-gradient acceleration and the problems posed by a compact collider. We summarize the phenomena known to appear in operation of a solid-state structure with large fields, and research relevant to the question of the ultimate gradient. We take note of new concepts, and examine one in detail, a miniature particle accelerator based on an active millimet...

Compared to conventional particle accelerators, plasmas can sustain accelerating fields that are thousands of times higher. To exploit this ability, massively parallel SciDAC particle simulations provide physical insight into the development of next-generation accelerators that use laser-driven plasma waves. These plasmabased accelerators offer a path to more compact, ultra-fast particle and ra...

Ancient Greeks and Indians had the conception of atoms. They thought and debated in great lengths about the fundamental constituents of matter. They were limited in what they can do, besides talking, due to the paucity of Particle Accelarators. In the last few decades, this has been rectified. We have many particle accelerators. Particle accelerators are what Feynman described as smashing swiss...