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Recursive solution for beam dynamics of periodic focusing channels
1Argonne National Laboratory, 9700 South Cass Avenue, Argonne, Illinois 60439, USA.
Summary
We developed a recursive analysis for beam dynamics in periodic focusing channels. This method aids in understanding orbit stability and envelope functions for advanced accelerator designs, including muon ionization cooling.
Area of Science:
- Accelerator Physics
- Beam Dynamics
- Particle Accelerators
Background:
- Periodic focusing channels are crucial for particle accelerators.
- Understanding beam dynamics is essential for accelerator performance.
- Extended focusing elements present analytical challenges.
Purpose of the Study:
- To present a novel recursive analysis for beam dynamics in periodic focusing channels.
- To derive formulas for orbit stability and the envelope function.
- To provide tools for analytical and numerical studies of advanced focusing systems.
Main Methods:
- Fourier analysis of the focusing function.
- Recursive mathematical formulation.
- Derivation of analytical expressions for beam parameters.
Main Results:
- Formulas for orbit stability derived.
- Formulas for the envelope function derived.
- The analysis is applicable to extended focusing elements.
Conclusions:
- The recursive analysis offers a valuable method for studying beam dynamics.
- Results are useful for numerical calculations and analytical insights.
- Potential applications in muon ionization cooling channels are highlighted.