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Time-asymptotic wave propagation in collisionless plasmas
Carlo Lancellotti1, J J Dorning
1Department of Mathematics, City University of New York-CSI, Staten Island, New York 10314, USA.
Summary
This study reveals a critical amplitude threshold in nonlinear plasma waves. Below this threshold, waves decay; above it, they evolve into complex, persistent wave states due to particle trapping.
Area of Science:
- Plasma Physics
- Nonlinear Dynamics
- Wave Propagation
Background:
- Understanding wave propagation in plasmas is crucial for fusion energy and astrophysics.
- Collisionless plasmas exhibit complex behaviors governed by kinetic effects.
Purpose of the Study:
- To systematically investigate nonlinear longitudinal wave propagation in collisionless plasmas.
- To identify the conditions leading to wave damping versus persistent nonlinear wave states.
Main Methods:
- Decomposition of electric fields into transient and time-asymptotic parts.
- Utilizing Vlasov equation and Hamiltonian perturbation theory for analysis.
- Linearizing Vlasov equation and integrating along nonlinear characteristics.
Main Results:
- Time-asymptotic wave amplitudes satisfy nonlinear algebraic equations.
- A critical initial amplitude threshold determines wave behavior.
- Nonlinear particle trapping leads to nonzero multiple-traveling-wave states above the threshold.
Conclusions:
- Theoretical framework explains the transition from Landau damping to nonlinear wave states.
- Results clarify discrepancies in large-scale numerical plasma simulations.
- Provides insights into the stability of spatially uniform plasma equilibria.