• Open Access

Modeling of second order space charge driven coherent sum and difference instabilities

Yao-Shuo Yuan, Oliver Boine-Frankenheim, and Ingo Hofmann
Phys. Rev. Accel. Beams 20, 104201 – Published 26 October 2017

Abstract

Second order coherent oscillation modes in intense particle beams play an important role for beam stability in linear or circular accelerators. In addition to the well-known second order even envelope modes and their instability, coupled even envelope modes and odd (skew) modes have recently been shown in [Phys. Plasmas 23, 090705 (2016)] to lead to parametric instabilities in periodic focusing lattices with sufficiently different tunes. While this work was partly using the usual envelope equations, partly also particle-in-cell (PIC) simulation, we revisit these modes here and show that the complete set of second order even and odd mode phenomena can be obtained in a unifying approach by using a single set of linearized rms moment equations based on “Chernin’s equations.” This has the advantage that accurate information on growth rates can be obtained and gathered in a “tune diagram.” In periodic focusing we retrieve the parametric sum instabilities of coupled even and of odd modes. The stop bands obtained from these equations are compared with results from PIC simulations for waterbag beams and found to show very good agreement. The “tilting instability” obtained in constant focusing confirms the equivalence of this method with the linearized Vlasov-Poisson system evaluated in second order.

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  • Received 20 July 2017

DOI:https://doi.org/10.1103/PhysRevAccelBeams.20.104201

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Accelerators & Beams

Authors & Affiliations

Yao-Shuo Yuan1, Oliver Boine-Frankenheim1,2, and Ingo Hofmann1,2

  • 1Technische Universität Darmstadt, Schlossgartenstrasse 8, 64289 Darmstadt, Germany
  • 2GSI Helmholtzzentrum für Schwerionenforschung GmbH, Planckstrasse 1, 64291 Darmstadt, Germany

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Vol. 20, Iss. 10 — October 2017

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