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On the evolution of a large-amplitude, weakly-collisional electron plasma wave

A. S. Joglekar, A. G. R. Thomas

Abstract

Vlasov-Poisson-Fokker-Planck (VPFP) simulations of large-amplitude electron plasma waves, where the bounce frequency is much larger than the collision frequency, $ω_B \gg ν_\text{ee}$, show that the evolution of these waves exhibits three phases; I. A short-lived trapping phase during which collisional effects are minimal. II. A long-lived detrapping phase during which collisional effects are most influential. III. A short-lived Landau damping phase where the effect of collisions becomes minimal again. While the dispersion relation during the trapping and Landau damping phase is well known, the wave behavior during the detrapping phase is not as well understood. The simulations show that during the detrapping phase, the interplay between weak electron-electron collisions and strong wave-electron interactions results in an increasing frequency shift further from the linear root, $ω_\text{EPW}$. At the conclusion of the detrapping phase, the distribution function is nearly Maxwellian, the frequency shift rapidly diminishes, and the wave damps at a larger rate than the Landau damping rate. Empirical fits to the damping rates, frequency shift enhancement rate, and the lifetime of the plasma waves are provided as functions of collision frequency, wavenumber, and wave amplitude.

On the evolution of a large-amplitude, weakly-collisional electron plasma wave

Abstract

Vlasov-Poisson-Fokker-Planck (VPFP) simulations of large-amplitude electron plasma waves, where the bounce frequency is much larger than the collision frequency, , show that the evolution of these waves exhibits three phases; I. A short-lived trapping phase during which collisional effects are minimal. II. A long-lived detrapping phase during which collisional effects are most influential. III. A short-lived Landau damping phase where the effect of collisions becomes minimal again. While the dispersion relation during the trapping and Landau damping phase is well known, the wave behavior during the detrapping phase is not as well understood. The simulations show that during the detrapping phase, the interplay between weak electron-electron collisions and strong wave-electron interactions results in an increasing frequency shift further from the linear root, . At the conclusion of the detrapping phase, the distribution function is nearly Maxwellian, the frequency shift rapidly diminishes, and the wave damps at a larger rate than the Landau damping rate. Empirical fits to the damping rates, frequency shift enhancement rate, and the lifetime of the plasma waves are provided as functions of collision frequency, wavenumber, and wave amplitude.
Paper Structure (17 sections, 10 equations, 11 figures, 3 tables)

This paper contains 17 sections, 10 equations, 11 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Simulation Configuration
  3. Overall Wave Dynamics
  4. Physical Mechanism for Frequency Shift Enhancement
  5. Phase I: Trapping and Plateau Formation
  6. Phase Space Evolution
  7. Wave Evolution and Nonlinear Frequency Shift
  8. Physical Mechanism for the Nonlinear Frequency Shift
  9. Phase II: Quasi-Steady Collisional Phase
  10. Phase Space Evolution
  11. Wave Amplitude and Frequency Evolution
  12. Physical Mechanism for Frequency Shift Enhancement
  13. Summary of Phase II Dynamics
  14. Phase III: Return to Landau Damping
  15. Distribution Function Thermalization
  16. ...and 2 more sections

Figures (11)

  • Figure 1: The envelope amplitude of the external forcing term over time. This value is then multiplied by $\sin(k x - \omega_{EPW} t)$ to give the external forcing term on the spacetime grid.
  • Figure 2: a) Wave amplitude, b) spatially-averaged distribution function and c) wave oscillation frequency are plotted during three distinct phases of wave evolution.
  • Figure 3: The evolution of the contributions to the susceptibility function
  • Figure 4: Phase space portrait at $t=650\omega_{pe}^{-1}$, shortly after the drive is turned off, for Simulation A and B.
  • Figure 5: The evolution of the (a) wave amplitude (b) and instantaneous frequency during Phase I for Simulation A and B. The dashed line in (b) indicates the linear frequency.
  • ...and 6 more figures