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Perturbative formulation for nonlinear chromaticity of circular accelerators.

Masaru Takao1, Hitoshi Tanaka, Kouichi Soutome

  • 1SPring-8, Mikazuki, Sayo-gun, Hyogo 679-5198, Japan. takao@spring8.or.jp

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|August 25, 2004
PubMed
Summary

We derived a new formula for nonlinear chromaticity in particle accelerators. This formula accurately predicts accelerator performance, matching measurements at the SPring-8 storage ring.

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Area of Science:

  • Accelerator Physics
  • Particle Dynamics
  • Nonlinear Optics

Background:

  • Nonlinear chromaticity is crucial for particle dynamics in strong focusing circular accelerators, especially at far off-momentum.
  • Understanding nonlinear chromaticity impacts accelerator performance and stability.

Purpose of the Study:

  • To derive an exact perturbative formula for the nonlinear dispersion function in ring accelerators.
  • To obtain higher-order expressions for nonlinear chromaticity up to the third order.

Main Methods:

  • Derivation of the exact perturbative formula for the nonlinear dispersion function.
  • Development of higher-order expressions for nonlinear chromaticity using the derived dispersion function formula.
  • Numerical estimation of nonlinear chromaticity for the SPring-8 storage ring.

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Main Results:

  • An exact perturbative formula for the nonlinear dispersion function was derived, including explicit higher-order terms.
  • Higher-order expressions for nonlinear chromaticity up to the third order were obtained.
  • Numerical estimation of nonlinear chromaticity for the SPring-8 storage ring showed good agreement with experimental measurements.

Conclusions:

  • The derived formulas provide accurate predictions for nonlinear chromaticity.
  • The findings are validated by experimental data from the SPring-8 storage ring.
  • This work contributes to a better understanding and control of particle dynamics in accelerators.