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 eect 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 eects 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.
Dierent techniques are appropriate for dierent cases.