Circular modes, beam adapters, and their applications in beam optics

Area of Science:

• Charged particle beam optics
• Accelerator physics
• Geometric optics

Background:

• Conventional beam optics often uses planar (elliptical) modes.
• Rotation-invariant transformations are crucial for certain beam manipulations.
• Existing methods lack efficient ways to convert between planar and circular beam modes.

Purpose of the Study:

• To introduce and describe novel transformers for converting charged particle beams between planar and circular transverse modes.
• To establish a connection between these transformations and canonical angular momentum preserving mappings.
• To explore the implementation and applications of these beam adapters.

Main Methods:

• Development of planar-to-circular and circular-to-planar beam transformers based on circular and planar modes.
• Parametrization of circular modes and transformations analogous to Courant-Snyder forms.
• Implementation using skew quadrupole magnets.
• Analysis of beam matching and solenoid configurations.

Main Results:

• Demonstrated equivalence between a group of circular mode transformations and canonical angular momentum preserving mappings.
• Introduction of "beam adapters" for mode conversion.
• Successful implementation of transformers using skew quadrupole blocks.
• Consideration of various matching scenarios for beams, adapters, and solenoids.

Conclusions:

• The developed beam adapters provide an effective means for mode conversion in charged particle beams.
• These methods offer versatile applications in circular colliders, linear colliders, electron cooling, and ionization cooling.
• The framework extends standard beam optics to include circular modes and their transformations.