Abstract
Transverse mode coupling instability of bunched beam is investigated in the paper at different form of the bunches with space charge included. Equation of transverse motion of the bunch in parabolic potential well of synchrotron oscillations is derived and analysed. The bunch of constant density (flat bunch) is examined in detail to make comparison with the square well model. It is shown that both models result in very close instability thresholds of the flat bunch. Then different form bunches are investigated in the parabolic potential well. It is shown that decrease of the bunch r.m.s length leads to the growth of its threshold, that is the flat bunch model gives only a minimal estimation of the threshold. The results are treated in terms of Landau damping due to spread of the space charge tune shift.
Highlights
Transverse mode coupling instability (TMCI) of the bunched beam has been observed first in the electron storage ring PETRA and explained by Kohaupt [1]
Using the two-particle model, the author has shown that the instability occurs when tunes of two head-tail modes approach each other being shifted by the bunch wakefield
Being interested mainly by dependence on the TMCI threshold on the space charge (SC) tune shift at arbitrary bunch shape, we restrict ourselves to the case of zero chromaticity and constant wake: ξ 1⁄4 0, q 1⁄4 q0 1⁄4 const
Summary
The transverse mode coupling instability of a bunched beam is investigated in the paper at different forms of the bunches, with space charge included. An equation of transverse motion of the bunch in the parabolic potential well of synchrotron oscillations is derived and analyzed. The bunch of constant density (flat bunch) is examined in detail to make a comparison with the square well model. It is shown that both models result in very close instability thresholds of the flat bunch. Different form bunches are investigated in the parabolic potential well. It is shown that decrease of the bunch RMS length leads to the growth of its threshold, that is the flat bunch model gives only a minimal estimation of the threshold. The results are treated in terms of Landau damping due to a spread of the space charge tune shift
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