Fermilab, Batavia
A purely imaginary Space Charge Impedance (SCI) is a part of the entire impedance which takes into account local electromagnetic field carried by a beam only. Such impedance is unable to cause the beam instability by itself (negative mass instability is the unique exclusion derived from a lack of longitudinal focusing in coasting beams). Real part of the impedance is just the one directly responsible for the instability, and it is generated by any retarding (wake) field. However, SCI affects on all the instability characteristics including threshold, frequency, ramp rate and shape of intra-bunch oscillations (head-tale modes). This influence can be crucially important in proton synchrotrons where SCI, typically, constitutes a significant or even dominant part of the impedance. In such conditions, the wake field can be treated as a small perturbation which controls parameters of collective beam modes at given head-tale bunch mode. This talk is designated to analyze the mentioned effects in frames of these assumptions. The emphasis is on the problem of transverse oscillations of a bunched beam.
