Dynamics of phase space vortices in Vlasov plasmas with ion scale inhomogeneity : II Chirped frequency drive study

Technical Summary: Dynamics of Phase Space Vortices in Vlasov Plasmas with Ion Scale Inhomogeneity: II Chirped Frequency Drive Study

Problem Statement
This study investigates the evolutionary dynamics of phase space vortices (PSVs) in collisionless, electrostatic, unbounded Vlasov plasmas when subjected to time-dependent, downward frequency chirped electric field drives. Specifically, the paper addresses how these dynamics are altered in the presence of a pre-existing quasi-stationary ion scale (QSIS) inhomogeneity. This inhomogeneity, characterized by a non-Maxwellian ion distribution, was established in a companion paper (Part I) using a constant frequency external drive. The research contrasts these inhomogeneous scenarios with homogeneous plasma counterparts using identical simulation parameters to isolate the effects of the background ion scale inhomogeneity on electron phase space dynamics, mode coupling, and particle trapping/untrapping fractions.

Methodology
The authors utilize the OpenMP Vlasov-Poisson solver (VPPM-OMP 1.0) to solve the coupled Vlasov-Poisson equations for kinetic ions and electrons in a 1D phase space $(x, v)$. The simulation domain is defined as $D = [0, L_{max}] \times [-v_{max}^e, v_{max}^e]$ with periodic boundary conditions, using a grid resolution of $N_x \times N_v = 1024 \times 6000$.

The study employs two primary methodologies for applying the external electric field drive ($E_{Chirp}^{Ext}$) on top of the QSIS background:

1. Two-Step Chirping Method: A constant frequency electron acoustic wave (EAW) drive is applied first to create a "seed" flattening in the electron distribution, followed by a relaxation period, and finally a downward frequency chirp drive ($\omega = \alpha t + \beta$).
2. One-Step Chirping Method: A downward frequency chirp drive is applied directly from the start (or after the QSIS background is established) without a prior constant frequency seed. This method is further divided into cases targeting Large Phase Space Vortex (LPSV) structures and Honeycomb (HC) transient structures.

The simulations compare two distinct scenarios:

• Homogeneous Case: Starting with a Maxwellian ion distribution.
• QSIS Inhomogeneity Case: Starting with the non-Maxwellian ion distribution generated in Part I (scale $k_{eq}/k_{min} = 2$).

Diagnostic tools include 2D $(\omega, k)$ power spectra, spectrograms, phase space portraits of electron and ion distribution functions, and quantitative analysis of electron excess density fractions (EDF) to measure trapping and untrapping dynamics.

Key Contributions and Results

• Suppression of Phase Space Vortices: A central finding is that the presence of background QSIS inhomogeneity suppresses the formation and size of electron phase space vortices compared to homogeneous cases. In the two-step chirping method, the QSIS case exhibited a reduced size of PSVs at late times. Similarly, in the one-step LPSV and HC cases, the QSIS background led to smaller vortex structures or, in the case of Honeycomb structures, a complete absence of the multi-extrema vortex formations observed in homogeneous plasmas.
• Mode Coupling and Frequency Signatures:
  • Power Spectra: In the QSIS cases, the 2D $(\omega, k)$ power spectra showed a suppression of higher frequency modes in the range $\omega/\omega_{pe} = 1.0$ to $2.0$ compared to homogeneous cases. Conversely, wave-wave mode coupling signatures were more prominent in the QSIS cases, particularly in the low-frequency range ($0 < \omega/\omega_{pe} < 1$).
  • Spectrograms: The frequency generation in QSIS cases appeared more discrete and discontinuous compared to the continuous bands seen in homogeneous cases. Specifically, the QSIS case showed a discontinuity in the frequency band around the initial chirp frequency ($\omega_c = 1.0$).
• Particle Trapping Dynamics:
  • Early Onset: In the two-step method, the QSIS inhomogeneity caused an early onset of Langmuir (LAN) mode formation and enhanced particle trapping in the separatrix region before the EAW perturbation drive ended.
  • Trapping vs. Untrapping: While initial particle trapping fractions were often higher in the QSIS separatrix regions, the relaxation phase revealed enhanced particle untrapping in homogeneous cases compared to QSIS cases. However, the net result in QSIS cases was a lower final EDF (excess density fraction), indicating a net suppression of stable vortex structures.
  • Chirp Interval Dependence: Increasing the chirp interval ($\Delta t_{Chirp}$) generally increased the size of PSVs and trapping fractions in homogeneous cases. In QSIS cases, this trend was non-monotonic, and the EDF estimates remained lower than or equal to their homogeneous counterparts across all tested intervals (50 to 600 $\omega_{pe}^{-1}$).
• Honeycomb Structure Suppression: In the Honeycomb (HC) case, the homogeneous plasma developed multiple PSVs (HCV structures) corresponding to various phase velocities. In contrast, the QSIS inhomogeneity completely suppressed the formation of these multi-extrema structures, resulting in a phase space devoid of vortex structures. The authors attribute this to the interaction between the HCV structures and the background ion scale inhomogeneity, which either suppresses their formation or accelerates inverse cascading to zero trapped particle fractions.
• Stability of Ion Background: The ion phase space structure (QSIS inhomogeneity) remained stable and unaffected by the electron-scale perturbations and chirp drives throughout the simulations.

Significance and Claims
The paper claims that the presence of ion-scale inhomogeneity fundamentally alters the kinetic response of collisionless plasmas to chirped frequency drives. Specifically, the QSIS background acts to suppress the formation of large-scale, stable phase space vortices and modifies wave-wave mode coupling interactions. The study demonstrates that while chirped drives can generate complex structures in homogeneous plasmas (such as giant vortices and honeycomb patterns), these structures are either diminished or entirely absent in the presence of ion-scale inhomogeneity.

The authors emphasize that their results provide insights into fundamental phenomena such as wave-wave mode coupling, wave-particle resonance, and collisionless turbulence in spatially non-uniform plasma systems. These findings are presented as relevant to understanding plasma dynamics in both laboratory and astrophysical contexts where spatial inhomogeneities are present. The study maintains that energy and entropy conservation were upheld in all simulations, confirming the stability and numerical accuracy of the results.