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The head-tail modes are described for the space charge tune shift significantly exceeding the synchrotron tune. A general equation for the modes is derived. The spatial shapes of the modes, their frequencies, and coherent growth rates are explored. The Landau damping rates are also found. The suppression of the transverse mode coupling instability by the space charge is explained.
Longitudinal collective modes of a bunched beam with a repulsive inductive impedance (the space charge below transition or the chamber inductance above it) are analytically described by means of reduction of the linearized Vlasov equation to a parame
The space charge forces are those generated directly by the charge distribution, with the inclusion of the image charges and currents due to the interaction of the beam with a perfectly conducting smooth pipe. Space charge forces are responsible for
Transverse mode-coupling instability (TMCI) is known to limit bunch intensity. Since space charge (SC) changes coherent spectra, it affects the TMCI threshold. Generally, there are only two types of TMCI with respect to SC: the vanishing type and the
Coulomb fields of charged particle beams in circular machines determine, together with wake fields, modes of the collective beam oscillations, both for transverse and longitudinal degrees of freedom. Recent progress in these two areas of beam dynamics is discussed.
Space-charge-induced emittance growth is a big con-cern for designing low energy and high intensity linacs. The Equipartitioning Principle was introduced to mini-mize space-charge-induced emittance growth by remov-ing free energy between the transver