Nonlinear spherical gravitational downfall of gas onto a solid ball: analytic and numerical results

The process of downfall of initially homogeneous gas onto a solid ball due to the ball's gravity (relevant in astrophysical situations) is studied with a combination of analytic and numerical methods. The initial explicit solution soon becomes discontinuous and gives rise to a shock wave. Afterwards, there is a crossover between two intermediate asymptotic similarity regimes, where the shock wave propagates outwards according to two self-similar laws, initially accelerating and eventually decelerating and vanishing, leading to a static state. The numerical study allows one to investigate in detail this dynamical problem and its time evolution, verifying and complementing the analytic results on the initial solution, intermediate self-similar laws and static long-term solution.Comment: 19 pages, 10 PS figures (some large

Emittance growth for the LHC beams due to head-on beam-beam interaction and ground motion

The influence of ground motion on the LHC beam is estimated applying the existing theories of particle diffusion due to a weak-strong beam-beam collision with random offset at the interaction point. Noise at odd harmonics of the betatron frequency contributes significantly to particle diffusion. The spectrum of the random offset, as obtained from the ground motion spectrum at the LHC site, shows a fast fall-off with frequency and the amplitude is very small even at the first harmonic. They find that the head-on beam-beam force in the weak-strong approximation and ground motion by themselves do not induce significant diffusion over the lifetime of the beam