• V. Kornilov, O. Boine-Frankenheim
  GSI, Darmstadt

The head-tail instability represents a potential intensity limitation for bunched beams in the synchrotrons of the FAIR project. Parametrical studies with numerical simulations over very long time scales are necessary in order to understand the effect of direct space charge, nonlinear synchrotron oscillations and image charges, which are all important in FAIR synchrotrons. Existing analytic approaches either neglect space charge or describe simplified models, which require a numerical or experimental validation. For our simulation studies we use two different computer codes, HEADTAIL and PATRIC. In this work we verify models for wake-field kicks and space-charge effect using the analytic solution for head-tail mode frequencies and growth rates from the barrier airbag model.