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Formulation of nonlinear chromaticity in circular accelerators by canonical perturbation method
1SPring-8, Mikazuki, Sayo-gun, Hyogo 679-5198, Japan. takao@spring8.or.jp
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 31, 2005
Summary
This study simplifies calculating nonlinear chromaticity in circular accelerators using the canonical perturbation method. This approach directly links tune shift to the perturbation Hamiltonian for easier analysis.
Area of Science:
- Accelerator physics
- Particle beam dynamics
Background:
- Nonlinear chromaticity is crucial for stable particle beams in accelerators.
- Calculating nonlinear chromaticity traditionally involves complex methods.
Purpose of the Study:
- To present a simplified formulation for nonlinear chromaticity in circular accelerators.
- To utilize the canonical perturbation method for this formulation.
Main Methods:
- Applying the canonical perturbation method.
- Relating tune shift directly to the perturbation Hamiltonian.
- Deriving an integral representation for nonlinear chromaticity.
Main Results:
- A simplified calculation of nonlinear chromaticity is achieved.
- The canonical perturbation method proves effective for this analysis.
- An integral representation for nonlinear chromaticity is obtained.
Conclusions:
- The canonical perturbation method offers a more straightforward approach to nonlinear chromaticity.
- The derived integral representation can be extended to higher orders for more precise accelerator modeling.
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