It is determined by the average of the scattering rate around the ring
In fact, since the momentum acceptance for scattering with energy gain may be different from that for scattering with energy loss, the lifetime must be computed by taking into account the positive and negative momentum acceptances, i.e.
A formula for the local scattering rate, given by Bruck, is
where the function F is given by
A more accurate formula, valid in a wider range of conditions is derived by Piwinski.
Momentum acceptance calculation
Calculation in beam dynamics codes
In order to compute the Touschek lifetime for a real storage ring, one needs a beam dynamics code. The Piwinski formula may be used together with the Elegant code for example.
- "C. Bernardini et al. – Lifetime and beam size in a Storage Ring".
- Henri Bruck – Los Alamos Scientific Laboratory, p303-308.
- "A. Piwinski, The Touschek Effect in Strong Focusing Storage Rings".
- "Belgroune et. al., Refined Tracking Procedure For The Soleil Energy Acceptance Calculation".
- "Elegant code, Touschek Lifetime function".