title: Space-Charge Structural Instabilities and Resonances in High-Intensity Beams.
abstract: The existence of a structural resonance stop band caused by space charge in high-current beams, where the resonance frequency is associated with 90° phase advance per focusing period, is well known and alternatively referred to in the literature as envelope instability or as fourth-order resonance. We show, however, that this stop band is actually a coincidence of a structural fourth-order resonance and the much stronger envelope instability as competing mechanisms--depending on the time scale and initial matching. A similar complexity of behavior--dependent on the distribution function--is also found between a third-order instability and a sixth-order resonance in a 60° stop band. We claim that these findings are a generic property of high-intensity beams in periodic focusing; they also allow a reinterpretation of the 90° linear accelerator stop band previously observed experimentally at the UNILAC accelerator.
authors.affiliation: GSI Helmholtzzentrum für Schwerionenforschung GmbH, Planckstrasse 1, 64291 Darmstadt, Germany.|Technische Universität Darmstadt, Schlossgartenstrasse 8, 64289 Darmstadt, Germany.
authors.forename: Ingo
authors.initials: I
authors.lastname: Hofmann
authors.affiliation: GSI Helmholtzzentrum für Schwerionenforschung GmbH, Planckstrasse 1, 64291 Darmstadt, Germany.|Technische Universität Darmstadt, Schlossgartenstrasse 8, 64289 Darmstadt, Germany.
authors.forename: Oliver
authors.initials: O
authors.lastname: Boine-Frankenheim