Self-consistent linear analysis of slow cyclotron and Cherenkov instabilities

Area of Science:

• Plasma physics
• Beam-plasma interactions
• Electromagnetic wave propagation

Background:

• Electron beams interacting with electromagnetic fields can exhibit instabilities.
• Understanding these instabilities is crucial for applications like free-electron lasers and particle accelerators.
• Previous analyses often simplified system geometries or boundary conditions.

Purpose of the Study:

• To self-consistently analyze slow cyclotron and Cherenkov instabilities.
• To investigate these instabilities in both unbounded and cylindrical slow wave systems.
• To compare the temporal growth rates of these instabilities.

Main Methods:

• Self-consistent analysis of electron beams propagating in guiding magnetic fields.
• Derivation of wave equations and application of the Altar-Appelton-Hartree equation.
• Superposition of plane normal modes to obtain axisymmetric modes for cylindrical systems.
• Calculation and comparison of temporal growth rates for identified instabilities.

Main Results:

• Two electromagnetic modes were identified in the electron beam.
• For unbounded systems, slow cyclotron and Cherenkov instabilities arise from coupling with X and O modes.
• For cylindrical systems, axisymmetric hybrid EH and HE modes exhibit both instabilities.
• Temporal growth rates were calculated for all identified instabilities.

Conclusions:

• Slow cyclotron and Cherenkov instabilities are prevalent in both unbounded and cylindrical slow wave systems.
• The analysis provides a comprehensive understanding of beam-plasma instabilities in different geometries.
• The findings are relevant for optimizing devices relying on controlled beam-plasma interactions.