Sideband growth rates for differentiable and discontinuous distribution functions

Area of Science:

• Plasma Physics
• Nonlinear Waves
• Beam-Plasma Interactions

Background:

• Nonlinear electron plasma waves (EPWs) can exhibit instability due to sideband growth.
• Understanding EPW stability is crucial for various plasma phenomena and applications.
• Existing theories often struggle with discontinuous electron distribution functions.

Purpose of the Study:

• To theoretically investigate the stability of nonlinear electron plasma waves (EPWs).
• To analyze the growth of longitudinal sidebands and the unstable spectrum.
• To develop a theory applicable to a wider range of electron distribution functions, including discontinuous ones.

Main Methods:

• Theoretical calculation of sideband growth rates and unstable spectrum.
• Inclusion of exact nonlinear electron orbits within the EPW.
• Comparison of theoretical results with previous theories and Vlasov simulations.

Main Results:

• The theory accurately predicts sideband growth rates and spectra for differentiable electron distributions.
• The developed theory extends to discontinuous electron distribution functions, relevant to stimulated Raman scattering.
• The study discusses the impact of discontinuities on the unstable spectrum and linear approximation validity.

Conclusions:

• The new theoretical framework provides a more comprehensive understanding of nonlinear EPW stability.
• The theory's applicability to discontinuous distributions addresses a significant challenge in kinetic code simulations.
• This work advances the analysis of wave-particle interactions in plasmas, particularly concerning EPW dynamics.