Parameter scans and accuracy estimates of the dynamical aperture of the CERN LHC

Techniques to make use of large distributed computing facilities allow for denser parameter scans of the dynamic aperture, i.e., the domain in phase space where bounded single-particle motion prevails. Moreover, one can also increase the number of 'seeds' each of which represents a possible realization of multipolar components around the machine. In this paper the dependence of the dynamic aperture on the step size of the grid of initial conditions and on the number of seeds is studied. Estimates on the accuracy of the dynamic aperture are derived and the definition of an improved protocol for numerical simulations is presented.