Sixth-order resonance of high-intensity linear accelerators

Area of Science:

• Particle Accelerator Physics
• Beam Dynamics

Background:

• Space charge effects are critical in high-intensity beams.
• Understanding resonances is crucial for beam stability and emittance preservation.

Purpose of the Study:

• Investigate the manifestation and impact of the sixth-order (6σ=720°) resonance in linear accelerators.
• Determine the conditions under which this resonance occurs and its effect on beam emittance.

Main Methods:

• Utilized simulation studies to observe emittance growth and phase space structures.
• Performed frequency analysis and resonance crossing studies for verification.
• Applied canonical perturbation theory to identify the origins of the resonance.

Main Results:

• The sixth-order resonance (6σ=720°) is observed for depressed phase advance per cell (σ) below 120°.
• Significant emittance growth and a sixfold resonance structure in phase space were simulated.
• The 6σ resonance arises from perturbations of 2:1 and 4:1 space charge resonances; the 6:1 resonance is weak.

Conclusions:

• The 6σ=720° resonance is a significant factor impacting beam quality in linear accelerators under specific phase advance conditions.
• Emittance growth due to this resonance can be mitigated by operating above σ=120°.
• Canonical perturbation analysis successfully explains the mechanism of the 6σ resonance.