Beam lifetime ($\tau =-N/\dot{N}$)

The inverse fractional particle-loss rate of a stored beam. A constant rate gives $N(t)=N_0{e}^{-t/\tau }$; density-dependent losses can make the instantaneous lifetime vary. At fixed revolution frequency, a calibrated beam-current measurement follows the same population decay, provided injection is absent or separately accounted for.

Intra-bunch Coulomb scattering can transfer transverse momentum into longitudinal momentum changes large enough to exceed a storage ring's accepted momentum range. This produces particle losses and a density-dependent contribution to the beam lifetime.