DYNAMIC APERTURE EXTRAPOLATION IN THE PRESENCE OF TUNE MODULATION

In hadron colliders, such as the Large Hadron Collider (LHC) to be bui lt at CERN, the long-term stability of the single-particle motion is m ostly determined by the field-shape quality of the superconducting mag nets. The mechanism of particle loss may be largely enhanced by modula tion of betatron tunes, induced either by synchrobetatron coupling (vi a the residual uncorrected chromaticity), or by unavoidable power supp ly ripple, This harmful effect is first investigated in a simple dynam ical system model, the Henon map with modulated Linear frequencies. Th en a realistic accelerator model describing the injection optics of th e LHC lattice is analyzed. Orbital data obtained with long-term tracki ng simulations (10(5)-10(7) turns) are post-processed to obtain the dy namic aperture. It turns out that the dynamic aperture can be interpol ated using a simple empirical formula, as it decays proportionally to a power of the inverse logarithm of the number of turns. Furthermore, the extrapolation of tracking data at 10(5) turns gives reliable estim ates of the dynamic aperture for 10(7) turns, which represent the expe cted duration of the LHC injection plateau.