1. Example: Longitudinal single bunch effects Synchrotron tune spread Synchrotron phase shift Potential well distortion Energy spread widening (microwave inst. above threshold) Bunch lengthening COLLECTIVE EFFECTS SIMPLIFIED CLASSIFICATION: Longitudinal, Transverse Single bunch, Multi-bunch

2. INGREDIENTS : Accurate modeling of the beam-wall interaction (wake-potentials or machine impedance) TOOLS AVAILABLE Haissinkii Equation (potential well distortion) Vlasov Equation (mode coupling) Simulation codes (tracking)

3. Pseudo-Green function gaussian bunches << bunch-length For LHC  = 7 cm How accurate ? Impedance frequency spectrum response to point charge excitation Pseudo-Green function with  = few mm ? Pipe cut-off Micro-density modulation? Coasting beam? Landau ….

4. How reliable are the tools ? Haissinskii equation OK Mode-coupling theory for the threshold OK,.. not for the lengthening regime Missing an analytical theory above threshold…. Tracking codes seem to be OK (CERN, SLAC, LNF…) however there is no comparison among different codes in particular for: - modeling and use of the pseudo-green function - results for different benchmark cases Similar arguments apply to the transverse case….. Finally, new dynamics of interest? Longitudinal instabilities of the square shaped beam…. Saw tooth instab.