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Scientific Information Service CERN
Publication date
2016
fields
Physics
and research's language is
English
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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 several unwanted phenomena related to beam dynamics, such as energy loss, shift of the synchronous phase and frequency, shift of the betatron frequencies, and instabilities. We will discuss in this lecture the main feature of space charge effects in high-energy storage rings as well as in low-energy linacs and transport lines.
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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.
A brief historical review is presented of progressing understanding of transverse coherent instabilities of charged particles beams in circular machines when both Coulomb and wake fields are important. The paper relates to a talk given at ICFA Workshop on Mitigation of Coherent Beam Instabilities in Particle Accelerators, 23-27 September 2019 in Zermatt, Switzerland.
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.
Linear gas stoppers are widely used to convert high-energy, rare-isotope beams and reaction products into low-energy beams with small transverse emittance and energy spread. Stopping of the high-energy ions is achieved through interaction with a buffer gas, typically helium, generating large quantities of He$^+$/e$^-$ pairs. The Advanced Cryogenic Gas Stopper (ACGS) was designed for fast, efficient stopping and extraction of high-intensity, rare-isotope beams. As part of the design process, a comprehensive particle-in-cell code was developed to optimize the transport and extraction of rare isotopes from the ACGS in the presence of space charge, including He$^+$/e$^-$ dynamics, buffer gas interactions including gas flow, RF carpets, and ion extraction through a nozzle or orifice. Details of the simulations are presented together with comparison to experiment when available.
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.
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