The beta function in accelerator physics is a function related to the transverse size of the particle beam at the location s along the nominal beam trajectory. It is related to the transverse beam size as follows: where * is the location along the nominal beam trajectory * the beam is assumed to have a Gaussian shape in the transverse direction * is the width of this Gaussian * is the beam emittance which is normally constant along the trajectory The beta function is one of the Twiss parameters (also called Courant-Snyder functions).