ABSTRACT
After introducing the concept of luminosity in fixed target experiments, the energy loss due to ionization is discussed and the Bethe-Bloch equation derived, followed by a discussion of transverse scattering in targets and how it affects the emittance and lifetime of beams. In the next sections are dedicated to colliding beams. Their luminosities are determined for general beam sizes and reductions due to the hour-glass effects and crossing angles are addressed. The electro-magnetic fields caused by the colliding beams, squeezed to very small transverse sizes, deect the particles and affect their betatron motion. The field is linear in the center of the beam and causes the so-called incoherent tune shift. But also the beam centroid experiences a kick that causes two colliding bunches to perform coherent oscillations, which are analyzed with a simple Matlab model. Likewise, a Matlab simulation to analyze colliding beams in linear colliders is introduced. There, the fields are so strong, that the beams mutually focus and disrupt each other and even emit synchrotron radiation, so-called beamstrahlung.
