Stability Analysis of Longitudinal Beam Dynamics using Noncanonical Hamiltonian Methods and Energy Principles

Technical Report · Tue Aug 06 04:00:00 EDT 2002

DOI:https://doi.org/10.2172/799993· OSTI ID:799993

Venturini, Marco ^[1]

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1. SLAC

In the presence of RF focusing and a purely inductive impedance bunch equilibria in the form of Haiessinski distributions--when they exist--are linearly stable. This is the case whether the potential well distortion associated with the impedance causes bunch lengthening or shortening. We provide a general proof of this fact using Hamiltonian methods and energy principles. In the presence of bunch shortening our analysis indicates that there is a critical current for linear stability. However, this threshold is identical to the critical current defining the condition for the very existence of a Haiessinski equilibrium.

• Research Organization: Stanford Linear Accelerator Center, Menlo Park, CA (US)
• Sponsoring Organization: USDOE Office of Energy Research (ER) (US)
• DOE Contract Number: AC03-76SF00515
• OSTI ID: 799993
• Report Number(s): SLAC-PUB-9351
• Country of Publication: United States
• Language: English

Related Subjects

43 PARTICLE ACCELERATORS
BEAM BUNCHING
BEAM DYNAMICS
CRITICAL CURRENT
FOCUSING
HAMILTONIANS
IMPEDANCE
RF SYSTEMS
STABILITY