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Area of Science:

  • Beam Physics
  • Particle Accelerators
  • Plasma Physics

Background:

  • Space charge effects in high-current beams are known to cause resonance stop bands.
  • These stop bands are often associated with 90° phase advance and referred to as envelope instability or fourth-order resonance.

Purpose of the Study:

  • To investigate the complex interplay between structural resonance and envelope instability in high-current beams.
  • To clarify the nature of the 90° stop band in periodic focusing systems.
  • To explore similar phenomena in 60° stop bands.

Main Methods:

  • Theoretical analysis of space charge effects in periodic focusing.
  • Investigating the dependence on time scale and initial beam matching.
  • Examining the influence of the distribution function on instability and resonance.

Main Results:

  • The 90° stop band is a coincidence of fourth-order resonance and envelope instability, with their dominance depending on beam parameters.
  • A similar complex behavior is observed in the 60° stop band involving third-order instability and sixth-order resonance.
  • These findings are generic properties of high-intensity beams in periodic focusing.

Conclusions:

  • The observed stop bands are a result of competing mechanisms, not a single phenomenon.
  • The study provides a reinterpretation of experimental results from accelerators like UNILAC.
  • Understanding these complex interactions is crucial for designing and operating high-intensity beam systems.