Consequences of the direct space charge effect for dynamic aperture and beam tail formation in the LHC

The direct space charge detuning at the centre of a nominal LHC proton bunch is about 10^-3 at injection energy. Owing to their slow synchrotron motion, particles with small betatron amplitudes sample a varying electric charge density within the bunch and thus experience a tune modulation at twice the 66 Hz synchrotron frequency. In conjunction with magnet nonlinearities, such tune modulation may give rise to particle diffusion to large betatron amplitudes and eventually to particle loss. Coherent quadrupole oscillations, caused, e.g., by injection mismatch, resonantly perturb the single-particle motion via the space-charge force, and can cause a rapid growth in the transverse amplitude. Using the results of numerical and analytical investigations, we show that these space-charge effects alone will not affect the LHC performance