Nonlinear Dynamics in Particle AcceleratorsThis book is an introductory course to accelerator physics at the level of graduate students. It has been written for a large audience which includes users of accelerator facilities, accelerator physicists and engineers, and undergraduates aiming to learn the basic principles of construction, operation and applications of accelerators.The new concepts of dynamical systems developed in the last twenty years give the theoretical setting to analyse the stability of particle beams in accelerator. In this book a common language to both accelerator physics and dynamical systems is integrated and developed, aiming to eliminate the difficulties faced by accelerator physicists, engineers and applied mathematicians when they try to join efforts in the attempt to control the nonlinearities disturbing particle beams. |
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alternating gradient amplitude analyze Ap/ps beam line beta function calculated CERN charged particle closed orbit coefficients constant coordinates Courant and Snyder cyclotron cyclotron radius defined defocusing quadrupoles design orbit differential equation dipoles dynamic aperture eigenvalues electrons emittance energy equations of motion FD cell Fermilab Figure focusing Hénon map Hill equation horizontal and vertical hyperbolic fixed points initial conditions integer Introducing layout length longitudinal machine magnetic field MapH MapV matrix monodromy matrix natural chromaticity normal form obtain off-momentum oscillations parameters period phase advance phase space Poincaré map protons quadrupolar quadrupoles resonance RF-cavity rotation number sextupolar sextupoles Snyder functions solutions stability straight sections strength synchronous particle synchrotron radiation test particle thin lens thin lens approximation trajectory transverse motion transverse plane tune shift unstable fixed points unstable manifolds vacuum chamber values variable vector field zero