Abstract
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 strong space charge (SSC) type. For the former, the threshold value of the wake tune shift is asymptotically proportional to the SC tune shift, as it was first observed twenty years ago by M. Blaskiewicz for exponential wakes. For the latter, the threshold value of the wake tune shift is asymptotically inversely proportional to the SC, as it was shown by one of the authors. In the presented studies of various wakes, potential wells, and bunch distributions, the second type of instability was always observed for cosine wakes; it was also seen for the sine wakes in the case of a bunch within a square potential well. The vanishing TMCI was observed for all other wakes and distributions we discuss in this paper: always for the negative wakes, and always, except the cosine wake, for parabolic potential wells. At the end of this paper, we consider high-frequency broadband wake, suggested as a model impedance for CERN SPS ring. As expected, TMCI is of the vanishing type in this case. Thus, SPS Q26 instability, observed at strong SC almost with the same bunch parameters as it would be observed without SC, cannot be TMCI.
Highlights
The problems of coherent beam stability are known to be hard when the beam space charge (SC) has to be taken into account, which is necessary for low- and medium-energy hadron rings
As it was pointed out at the beginning of this article, for the vanishing type of transverse mode coupling instability (TMCI), there is always an absolute threshold of the wake amplitude, such that the beam is stable for any number of particles as soon as the wake is below its absolute threshold value
We investigated transverse mode coupling thresholds for various space charge, wakes, potential wells and bunch distribution functions
Summary
The University of Chicago, 5801 S Ellis Avenue, Chicago, Illinois 60637, USA (Received 19 December 2017; published 11 October 2018). There are only two types of TMCI with respect to SC: the vanishing type and the strong space charge (SSC) type. For the former, the threshold value of the wake tune shift is asymptotically proportional to the SC tune shift, as it was first observed twenty years ago by M. In the presented studies of various wakes, potential wells, and bunch distributions, the second type of instability was always observed for cosine wakes; it was seen for the sine wakes in the case of a bunch within a square potential well. The vanishing TMCI was observed for all other wakes and distributions we discuss in this paper: always for the negative wakes, and always, except the cosine wake, for parabolic potential wells. SPS Q26 instability, observed at strong SC almost with the same bunch parameters as it would be observed without SC, cannot be TMCI
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