  The subject of this introductory course is transverse dynamics of charged
particle beams in linear approximation. Starting with a discussion of the most
important types of magnets and defining their multipole strengths, the
linearized equations of motion of charged particles in static magnetic fields
are derived using an orthogonal reference frame following the design orbit.
Analytical solutions are determined for linear elements of a typical beam
transfer line (drift, dipole and quadrupole magnets), and stepwise combined by
introducing the matrix formalism in which each element's contribution is
represented by a single transfer matrix. Application of this formalism allows
to calculate single particle's trajectories in linear approximation. After
introducing the beam emittance as the area occupied by a particle beam in phase
space, a linear treatment of transverse beam dynamics based on appropriately
defined optical functions is introduced. The formalism is applied to the
concepts of both weak and strong focusing, in particular discussing the
properties of the widely-used FODO cell. Specific characteristics of transverse
beam dynamics in periodic systems like circular accelerators are studied in
detail, emphazising the effects of linear field errors on orbit stability and
introducing the phenomena of optical resonances. Finally, the dynamics of
off-momentum particles is presented, introducing dispersion functions and
explaining effects like chromaticity.
