Beta function (accelerator physics)


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
Typically, separate beta functions are used for two perpendicular directions in the plane transverse to the beam direction.
The beta function is one of the Twiss parameters.

Beta star

The value of the beta function at an interaction point is referred to as beta star.
The beta function is typically adjusted to have a local minimum at such points. Assuming that this point is
in a drift space, one can show that the evolution of the beta function around the
minimum point is given by:
where z is the distance along the nominal beam direction from the minimum point.
This implies that the smaller the beam size at the interaction
point, the faster the rise of the beta function when going away from the interaction point.
In practice, the aperture of the beam line elements around the interaction point
limit how small beta star can be made.