Introduction to particle accelerators Walter Scandale CERN - AT department Lecce, 17 June 2006

Particle accelerators are black boxes producing Introductory remarks Particle accelerators are black boxes producing either flux of particles impinging on a fixed target or debris of interactions emerging from colliding particles In trying to clarify what the black boxes are one can list the technological problems describe the basic physics and mathematics involved Most of the phenomena in a particle accelerator can be described in terms of classical mechanics and electro-dynamics, using a little bit of restricted relativity However there will be complications: in an accelerator there are many non-linear phenomena (stability of motion, chaotic single-particle trajectories) there are many particles interacting to each other and with a complex surroundings the available instrumentation will only provide observables averaged over large ensembles of particles In two hours we can only fly over the problems just to have an overview of them

Inventory of synchrotron components

Bending magnet Efficient use of the current -> small gap height Field quality -> determined by the pole shape Field saturation -> 2 Tesla BEarth = 3 10-5 Tesla B > 2 Tesla -> use superconducting magnets BLHC = 8.4 Tesla

Quadrupole magnet Vertical focusing Horizontal defocusing g=gradient [T/m]

Alternate gradient focusing QF QD

Mechanical analogy for alternate gradient

Basic 2-D equation of motion in a dipolar field

Basic 2D equation of motion

Basic 2D equation of motion FODO structure Periodic envelop Cos-like trajectory Sin-like trajectory Multi-turn trajectory

Longitudinal stability Momentum compaction

Chromaticity and sextupole magnet Dispersion orbit

Chromaticity correction and non-linear resonance

Emittance

Synchrotron radiation

Synchrotron radiation and beam size Adiabatic damping Synchrotron light emission

Effect of synchrotron light

Collective effects

Instabilities and feedback

Space charge

Beam size

Fixed target versus collider rings Advantage Collider Bruno Touschek

Lepton versus hadron colliders -> (At the parton level ) ->