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Oscillating Coulomb chain in a storage ring.

H Okamoto¹, Y Yuri, K Okabe

¹Department of Quantum Matter, Graduate School of Advanced Sciences of Matter, Hiroshima University, 1-3-1 Kagamiyama, Higashi-Hiroshima 739-8530, Japan.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|June 6, 2003

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A crystalline beam in a storage ring exhibits complex oscillations when subjected to radio-frequency force, due to momentum dispersion. This study details the oscillation patterns and stability of such beams.

Area of Science:

Beam dynamics
Particle accelerators
Condensed matter physics

Background:

Bunched one-dimensional crystalline beams, or Coulomb chains, are fundamental components in particle accelerators.
Understanding their dynamic behavior under external forces is crucial for accelerator performance and stability.
Previous studies have not fully captured the complex oscillations induced by momentum dispersion.

Purpose of the Study:

To theoretically investigate the dynamic behavior of a bunched one-dimensional crystalline beam.
To analyze the complex periodic oscillations induced by longitudinal radio-frequency (RF) force in the presence of momentum dispersion.
To predict oscillation patterns in arbitrary lattice structures and discuss beam features.

Main Methods:

Theoretical derivation of equations of motion for the crystalline beam.

Related Experiment Videos

Analysis of the effects of momentum dispersion and RF force.

Confirmation of theoretical predictions using multiparticle simulations.

Main Results:

The study demonstrates that momentum dispersion causes complex periodic oscillations in crystalline beams exposed to RF force.
Derived equations accurately predict oscillation patterns for arbitrary lattice structures.
Multiparticle simulations validate the theoretical framework.

Conclusions:

The theoretical model provides a comprehensive understanding of oscillating crystalline beams.
Key features like lattice-parameter dependence, stability, and critical line density are elucidated.
This research contributes to the design and optimization of particle storage rings.