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Beam Dynamics in High Energy Particle Accelerators

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Given a beam of charged particles in an accelerator, the challenge for the accelerator physicist is to explain and control the behaviour of that beam. Beam dynamics provides the tools for describing and understanding the particle motion. The electromagnetic elds that determine the dynamics may arise from components such as multipole magnets or radiofrequency cavities, from stray particles in the vacuum chamber, from the beam itself or from other beams of particles in the accelerator. An understanding of the elds generated by these sources and their e ect on the beam dynamics is needed for the design, commissioning and operation of an accelerator.

In calculating the motion of particles in an accelerator, the rst step is to select the appropriate physical principles. Here, we appear to be in good shape, since nearly all the important features of beam dynamics can be described and explained using physical laws that have been known for more than a century. In particular, the electromagnetic elds in a beam line must satisfy Maxwell's equations, and the motion of a charged particle through those elds is determined by Hamilton's equations, with an appropriate (relativistic) Hamiltonian. There are certainly some aspects of beam behaviour that give glimpses beyond the regime of purely classical physics: these include the quantum excitation of particle oscillations in a storage ring from synchrotron radiation and e ects associated with spin polarisation. But from rather few basic ingredients, there results a rather impressive and somewhat daunting diversity of phenomena. Furthermore, many of the problems that occur in practical situations are rather di- cult to solve. Much of the discussion in this book concerns techniques for nding approximate solutions, with certain desirable properties, to the classical equations of motion in various situations in accelerator beam lines. Di erent techniques are appropriate for di erent cases.
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