On the Instability of a Coasting Beam

Technical Report · Thu Jan 01 04:00:00 EST 1959

DOI:https://doi.org/10.2172/4275987· OSTI ID:4275987

Nielsen, C. E. ^[1]; Sessler, A. M. ^[2]

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1. European Organization for Nuclear Research (CERN), Geneva (Switzerland)
2. The Ohio State Univ., Columbus, OH (United States)

The time-dependent Boltzmann equation is used to study longitudinal motion of particles in a circulating beam of particles. The equation is linearized about the stationary solution corresponding to a coasting beam of almost monoenergetic particles to determine the effect of small density fluctuations. An integral equation is obtained and solved, leading to a dispersion relation quite similar to that well known in the theory of plasma oscillations. It is shown that if the accelerator is operating above the transition energy, then the motion can be unstable. Expressions are given for the rate of growth of longitudinal waves, and it is shown that if the unperturbed beam satisfies certain criteria, then the motion is either stable or it grows at such a slow rate as to be of no consequence. Numerical examples for MURA particle accelerators show that essentially there is stability.

• Research Organization: Midwestern Universities Research Association (MURA), Madison, WI (United States)
• Sponsoring Organization: US Atomic Energy Commission (AEC); National Science Foundation (NSF)
• NSA Number: NSA-13-005625
• OSTI ID: 4275987
• Report Number(s): MURA--441
• Country of Publication: United States
• Language: English

Related Subjects

43 PARTICLE ACCELERATORS
ACCELERATORS
BEAMS
BOLTZMANN EQUATION
CHARGED PARTICLES
DENSITY
DIFFERENTIAL EQUATIONS
ENERGY
EQUATIONS
INTEGRALS
MOTION
NUMERICALS
OSCILLATIONS
PLASMA
STABILITY
VARIATIONS