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

Amudon Chingangbam; Rajaraman Ganesh; Sanjeev Kumar Pandey

REVIEW 4 major objections 4 minor 33 references

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

T0 review · 4 major / 4 minor · reviewed 2026-08-01 · deepseek-v4-flash

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Pith's one-line read This paper claims that an ion-scale density inhomogeneity suppresses the electron phase-space vortices produced by downward-chirped frequency drives in a collisionless plasma.

desk verdict New inhomogeneous-background chirp simulations are worth a look, but the headline suppression numbers compare different diagnostics and the moving-average subtraction likely removes the stationary vortex signal, so the quantitative claim does not hold as written. read the letter →

arxiv 2607.16786 v1 pith:IDZUILQF submitted 2026-07-18 physics.plasm-ph physics.comp-ph

Sanjeev Kumar Pandey , Amudon Chingangbam , Rajaraman Ganesh This is my paper · ORCID

classification physics.plasm-phphysics.comp-ph PACS 52.65.-y52.35.Fp52.35.-g

keywords phasespacevorticeschirpedfrequencydriveVlasov–PoissonsimulationelectronacousticwavesLangmuirmodesparticletrappinganduntrappingionscaleinhomogeneityBGK

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper tries to establish that a quasi-stationary ion-scale density inhomogeneity, prepared beforehand in a 1D Vlasov–Poisson plasma, changes how electrons respond to external drives whose frequency is swept downward. Across matched simulations, the inhomogeneous background makes electron phase-space vortices smaller, reduces the measured trapped-electron density at late times, and removes the multi-vortex honeycomb pattern that appears in a homogeneous plasma. The claim matters because chirp-driven vortex formation is a standard way to study nonlinear wave–particle trapping, and any background density structure—common in real plasmas—could materially weaken or redirect that trapping. If correct, laboratory and astrophysical inferences that assume a homogeneous background would need revision.

What carries the argument

The central objects are chirped external electric-field drives, applied either as a two-step process (constant-frequency electron-acoustic drive, relaxation, then downward chirp) or a one-step downward chirp, on top of a quasi-stationary ion-scale inhomogeneity of wavenumber k_eq/k_min = 2. The simulations use a 1D Vlasov–Poisson solver with kinetic ions and electrons on a periodic domain. The main diagnostic is the electron excess density fraction (EDF), a measure of local trapped-particle density; for inhomogeneous cases the paper subtracts a moving average of the electron density to remove background ion-induced oscillations before computing the fraction.

What would settle it

Re-run the two-step chirp case twice: once homogeneous and once with the ion-scale inhomogeneity, and compute the same moving-average-subtracted excess density fraction for both. If the late-time suppression (0.065 to 0.026) disappears when the diagnostics are identical, the central claim fails. A more direct check is to inspect the phase-space portraits at late times with the moving-average filter applied to the homogeneous run; if the homogeneous vortex size shrinks by a comparable factor, the filter is removing genuine trapped-particle structure.

Watch

Extended reading notes

Core claim

With identical chirp parameters, replacing a Maxwellian homogeneous background with a quasi-stationary ion-scale inhomogeneity suppresses electron phase-space vortex formation. Quantitatively, the late-time electron excess density fraction drops from 0.065 to 0.026 for the two-step chirp case and from 0.140 to 0.032 for the one-step large-vortex case. The inhomogeneous runs also show an earlier onset of Langmuir modes, stronger wave–wave mode-coupling signatures, a more discrete frequency spectrum, and complete absence of the honeycomb vortex structures seen in the homogeneous runs. The ion-scale background itself remains essentially unchanged throughout the electron-scale drive, indicating

Load-bearing premise

The suppression conclusion rests on comparing a raw electron excess density fraction in the homogeneous case with a moving-average-subtracted version in the inhomogeneous case; if that subtraction removes part of the trapped-particle signal, the reported suppression is a diagnostic artifact rather than a plasma effect.

Editorial extensions

If this is right

If the suppression is real, chirp-driven particle trapping is weaker in inhomogeneous than in homogeneous plasmas, so trapped-particle fractions inferred from homogeneous models would overestimate the energy transferred to electrons.
The honeycomb vortex pattern, predicted and seen in homogeneous simulations, is not a robust outcome: even long low-frequency chirps fail to produce it when an ion-scale background is present.
The early Langmuir mode onset in the inhomogeneous case means the energy cascade path differs, with more mode coupling and a more discrete frequency spectrum than in the homogeneous case.
The non-monotonic dependence of the trapped-electron fraction on chirp interval, seen in both homogeneous and inhomogeneous runs, means longer chirp duration does not simply imply more trapping.
The ion-scale inhomogeneity acts as a consistent suppressor: across all chirp intervals studied, the excess density fraction for the inhomogeneous case is never larger than the homogeneous counterpart.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

One extension the paper leaves implicit is a control test: applying the same moving-average subtraction to the homogeneous case and checking whether the 0.065-versus-0.026 gap survives. Without that control, part of the reported suppression could be a diagnostic artifact rather than a plasma effect.
A plausible physical mechanism not directly proven here is that the ion-scale density corrugations phase-mix or scatter resonantly trapped electrons, effectively dephasing the chirp drive and increasing late-time untrapping; this could be tested by measuring the velocity-space width of the trapped region as a function of background inhomogeneity amplitude.
The disappearance of honeycomb structures in the inhomogeneous case may connect to enhanced inverse cascading, as the paper suggests; a direct test would be to run the HC chirp on a weaker inhomogeneity (for example, k_eq/k_min = 1) and see whether the multi-vortex pattern reappears gradually.
These results suggest that in any experimental or space plasma with pre-existing density fluctuations, chirp-driven heating or particle transport will likely be less efficient than homogeneous predictions—a consequence the authors stop short of stating.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

You should know two things about this paper. First, the genuinely new material is the set of chirp-drive cases run on top of the quasi-stationary ion-scale (QSIS) background: the two-step SEAW case, the LPSV case, and the HC chirp case, each compared against a homogeneous counterpart with the same parameters. The observations that stand out are the early onset of the Langmuir mode in the QSIS cases, the absence of the honeycomb vortex pattern, and the non-monotonic response of the excess density fraction to increasing chirp interval. Those are legitimate, useful additions to the authors' earlier homogeneous work. Second, the quantitative suppression claim, which is the central advertised result, is built on a diagnostic mismatch. In Tables 1 and 2, the homogeneous EDF is reported as raw δn_e/n_e0, while the QSIS EDF is (δn_e − δn̂_e)/n_e0, where δn̂_e is a temporal moving average with an unspecified window. For a stationary BGK/PSV structure, the trapped-particle density perturbation is roughly constant in time after the drive is off. A moving average is a high-pass filter: it estimates and removes the local mean, which includes that DC signal. So the QSIS numbers at the late-time points (δ3, T2) are systematically reduced by construction. Applying the same subtraction to the homogeneous time series would also lower its EDF substantially — the 0.065 vs 0.026 comparison in Table 1 is therefore not apples-to-apples. I don't see any statement in the paper that the moving-average subtraction was applied to the homogeneous case, and the window is never given. This is a load-bearing flaw for the quantitative suppression and 'enhanced late time particle untrapping' statements in Sections 3.1 and 3.4. The qualitative claim that vortices are smaller or absent in the QSIS phase-space portraits may well be true — the figures show it visually — but the numbers reported in the tables do not support it as they stand. There are also no convergence studies, no error bars, and no code or data release; Part I, which supplies the initial QSIS state, is not available. I want to give credit where it is earned: the simulation setup is described in unusual detail, the ion distribution is shown to remain unaffected by the electron-scale drives, and the authors state energy and entropy conservation checks. The writing is straightforward and the citations to their own prior work are relevant, not padding. The issue is the diagnostic, not the simulation effort. For whom is this paper? Kinetic plasma physicists studying chirped drives, BGK modes, and phase-space vortices will find the qualitative results interesting. It deserves a serious referee — the new cases are worth scrutiny — but it needs major revision before the suppression claim can be accepted: identical diagnostics for both cases, a specified and justified filter, and ideally a convergence or resolution study. If the authors redo the comparison with the same post-processing on both sides, the conclusion may survive, but it has to be demonstrated.

Referee Report

4 major / 4 minor

Summary. The paper reports 1D1V Vlasov-Poisson simulations of chirped-frequency electron-scale drives in a homogeneous plasma and in a plasma with a pre-existing quasi-stationary ion-scale inhomogeneity (QSIS). It claims that the QSIS background suppresses electron phase-space vortices (PSVs), causes early Langmuir-mode onset, suppresses higher-frequency spectral power, and prevents honeycomb vortex formation. The cases include a two-step SEAW+chirp drive, one-step LPSV and HC chirp drives, and a scan over chirp interval. Comparisons are made with homogeneous runs using nominally identical parameters.

Significance. The question of how pre-existing ion-scale structure modifies chirp-driven electron phase-space-hole formation is a reasonable and potentially interesting extension of earlier homogeneous studies by the same group. The manuscript has strengths: the simulation setup is described in considerable detail, the homogeneous/QSIS parameter sets are matched, a wide set of diagnostics (phase-space portraits, spectrograms, 2D power spectra, energy traces) is deployed, and the authors explicitly check energy and entropy conservation. If the suppression claim were quantitatively supported, the paper would be a useful contribution to the driven-phase-space-dynamics literature. However, the central quantitative comparison is currently built on two different diagnostics for the two cases, so the main conclusion is not yet established.

major comments (4)

[Sec. 3.1, Table 1 and Fig. 8; also Sec. 3.4, Table 2 and Fig. 19] The central suppression claim compares the raw electron excess density fraction EDF = δn_e/n_e0 for the homogeneous case with (δn_e − δ̂n_e)/n_e0 for the QSIS case, where δ̂n_e is a moving average whose window is never specified. A temporal moving average is a high-pass filter and will remove the low-frequency/DC component of the electron density perturbation, including any stationary trapped-particle (BGK/PSV) contribution. Thus the QSIS EDF values at the late-time locations (e.g., EDF|δ3 = 0.026 vs 0.065, EDF|T2 = 0.032 vs 0.140) are biased downward by construction relative to the homogeneous raw values. The statement that the two numbers support 'enhanced late time particle untrapping' is therefore not supported by the reported diagnostics. The authors must either apply the same moving-average subtraction to the homogeneous data, report raw δn_e/n_e0 for the QSIS cases, or otherwise d
[Sec. 3.1, Tables 1–2 and Fig. 20] All EDF values are evaluated at a single spatial point, x = L_max/8, with no spatial averaging, no error bars, and no check that this point is representative of the global vortex amplitude. The phase-space portraits in Figs. 4, 5, 12, and 14 show structures extending over a range of phase velocities and spatial locations, so a single-point diagnostic can depend sensitively on the chosen x and on the local phase of the BGK structure. The quantitative differences used to support the suppression claim (e.g., EDF|δ3 = 0.065 vs 0.026) need to be shown to persist under spatial averaging over the vortex region and under reasonable variation of the measurement point. Without such robustness information, the numerical values in Tables 1 and 2 cannot carry the weight of the central conclusion.
[Secs. 3.1 and 3.4 (energy conservation statements)] The paper repeatedly states that energy and entropy conservation hold for the chosen grid resolution (e.g., Sec. 3.1 and Sec. 4), but no conservation-error curves or resolution tests are shown. The central claim involves relatively small EDF differences, and the QSIS runs extend to t = 123000ω_pe^{-1}, roughly 40 times longer than the homogeneous runs. It is essential to demonstrate that 1024×6000 grid points are sufficient for the long-time QSIS runs and that the quoted EDF differences are not numerical artifacts. A convergence study with at least one coarser and one finer resolution, together with quantitative plots of relative energy and entropy conservation, should be provided.
[Sec. 3.3, Figs. 16 and 23] The HC case is the most striking qualitative claim — the authors report a complete absence of honeycomb vortices in the QSIS background. However, unlike the SEAW and LPSV cases, no EDF table is provided for the HC runs, and Fig. 23 states that a moving average δ̂n_e could not even be defined for this case. The claim therefore rests entirely on visual inspection of phase-space plots at a single late time. Given that the homogeneous HC run shows multiple small-scale vortex structures, the authors should quantify the QSIS HC suppression using a diagnostic that does not require the moving-average subtraction, for example a spatial integral of the phase-space density perturbation in the vortex region or a velocity-space measure of flattening. As it stands, the HC suppression claim is qualitative and not supported by the quantitative framework used elsewhere in the paper.

minor comments (4)

[General] There are numerous typos and grammatical errors throughout (e.g., 'cirpped' in Eq. (2), 'pressence' in Sec. 3.1, 'asymptotic decrease' phrasing in Sec. 3.3). The paper would benefit from a careful proofreading pass.
[Fig. 6 caption] The caption reads 'Phase space portrait of ion distribution function f_e(x,v)' but the figure shows ions; the distribution function label should be f_i(x,v), not f_e(x,v).
[Sec. 3.4, Fig. 19 caption and Table 2] The table uses T1 and T2 for the two temporal locations, while the Fig. 19 caption refers to ψ1; this notation should be unified. Also, in Table 2 the homogeneous column header 'Position' is unexplained — it presumably lists the chirp interval, not a spatial position.
[Sec. 3.1, Fig. 8 discussion] The moving-average quantity δ̂n_e is introduced in the text and figure but never defined formally (window length, type of average, and whether it is centered or causal). This definition is necessary for reproducibility and is directly relevant to the diagnostic used in the main claim.

Circularity Check

2 steps flagged · score 6.0 of 10

QSIS suppression is quantified with a background-subtracted residual, while the homogeneous comparison uses raw EDF; the reported suppression is partly built into the diagnostic.

fitted input called prediction [Sec. 3.1, Table 1 and Fig. 8]
"In order to quantify our argument, in Table 1, we have tabulated the electron excess density fraction [EDF : δn_e/n_e0, defined in the companion paper Part I] for the homogeneous case alongwith the difference of electron EDF and moving average δ̂n_e value i.e (δn_e − δ̂n_e)/n_e0 for the QSIS inhomogeneity case ... EDF|Homo_δ3 = 0.065 and EDF|QSIS_δ3 = 0.026 supporting our earlier argument of suppression of PSV formation in the electron phase space due to enhanced late time particle untrapping in the pressence of background QSIS inhomogeneity."

The two columns in Table 1 are not the same observable. The homogeneous value is the raw electron excess density δn_e/n_e0, while the QSIS value is the residual (δn_e − δ̂n_e)/n_e0 after subtracting an unspecified temporal moving average δ̂n_e from the same δn_e signal. A temporal moving average is a high-pass filter: after the chirp drive is off, a stationary trapped-particle (BGK/PSV) density offset contributes to δ̂n_e and is removed by the subtraction. Hence EDF|QSIS is biased toward zero by construction relative to EDF|Homo, regardless of the actual vortex amplitude. The quantitative suppression statement therefore reduces to the choice of diagnostic rather than to a measured plasma property.
fitted input called prediction [Sec. 3.4, Table 2 and Fig. 19]
"we have tabulated the electron excess density fraction [EDF : δn_e/n_e0, defined in the companion paper Part I] for the homogeneous case alongwith the difference of electron EDF and moving average δ̂n_e value i.e (δn_e − δ̂n_e)/n_e0 for the QSIS inhomogeneity case ... At T2 temporal location, we have observed greater relaxation in the QSIS EDF estimates when compared to the homogeneous case i.e EDF|Homo_T2 = 0.140 and EDF|QSIS_T2 = 0.032 supporting our argument of suppression of PSV formation in the electron phase space due to enhanced late time particle untrapping in the presence of backgroun"

This repeats the same unequal diagnostic for the LPSV chirp cases: the homogeneous EDF is the raw δn_e/n_e0, while the QSIS EDF is the residual after subtracting the moving average δ̂n_e. The claimed suppression at T2 (0.140 vs 0.032) is therefore not a comparison of equivalent trapped-particle fractions; the QSIS number is the portion of the signal left after the temporally varying baseline is removed. The same reduction applies to Fig. 20, where the 'EDF : (δn_e − δ̂n_e)/n_e0' curve is plotted against the raw homogeneous curve. The conclusion 'QSIS inhomogeneity suppresses PSV formation' is supported only if one first assumes that δ̂n_e contains no trapped-particle signal, which is precisely the point at issue.

full rationale

The paper's central quantitative claim—suppression of chirp-driven electron phase-space vortices by QSIS inhomogeneity—rests on Tables 1 and 2, which compare raw δn_e/n_e0 for homogeneous runs with (δn_e − δ̂n_e)/n_e0 for QSIS runs. The moving average δ̂n_e is chosen ad hoc (no window is specified) and applied only to the QSIS cases; because it is a temporal high-pass filter, it removes any quasi-stationary trapped-particle offset that constitutes the late-time BGK/PSV signal at a fixed point. Thus the reported residual amplitudes (e.g., 0.026 vs 0.065 at δ3; 0.032 vs 0.140 at T2) are lower partly by construction, not solely by plasma physics. This is a fitted-input-called-prediction circularity: the detector is fit to each QSIS time series and then used as the measure of trapping. Independent observations (spectral suppression, absence of HC vortices in phase-space portraits) may still support a weaker statement, and the self-citations to Part I and Refs. [9,10] are not themselves load-bearing in a circular way. But the quantitative suppression claim as presented is not self-contained, so the score is 6 rather than 0.

Assumptions & free parameters 6 free parameters · 4 assumptions · 0 invented entities

The paper introduces no new physical entities. Its central claims rest mainly on simulation control parameters and on a hand-chosen moving-average background subtraction for the QSIS cases, plus the inherited QSIS state from Part I. The ledger is dominated by unverified inherited and ad hoc choices rather than new theoretical postulates.

free parameters (6)

Moving-average background δn̂_e = unspecified window/filter
Ad hoc subtraction used only for QSIS EDF estimates; directly sets the residual amplitude and hence the suppression claim. The averaging window is never defined (Sec. 3.1, Fig. 8).
Chirp coefficients α and β (two-step/LPSV) = α=-5.0e-3, β=2.0
Set the downward frequency sweep from ω_c=1.0; chosen by hand and not scanned.
Chirp coefficient α (HC chirp) = α=-2.0e-3
Sets sweep from ω_2=0.8 to ω_1=0.4; chosen by hand.
Chirp intervals Δt_Chirp = 50–400 (LPSV), 100–600 (HC)
Scanned to produce the non-monotonic trapping fraction response; conclusions depend on this scan.
Drive amplitudes E_D^c and E_P^0 = 0.025
Small-amplitude choices carried over from Part I; they set the trapping strength but are not fitted to data.
Background QSIS parameters = k_eq/k_min=2, ω_IA=0.0202
Inherited from Part I without re-derivation or independent validation in this paper.

assumptions (4)

domain assumption The 1D Vlasov-Poisson system with periodic boundaries is an adequate model for the claimed physics.
Used throughout (Sec. 2); standard but limiting: no collisions, no magnetic field, 1D geometry.
domain assumption The QSIS inhomogeneity from Part I is quasi-stationary and unaffected by the electron-scale chirp drives.
Asserted from Figs. 6 and 13; Part I is not available to audit the equilibrium construction.
domain assumption The VPPM-OMP solver conserves energy and entropy sufficiently at 1024×6000 grid resolution.
Claimed in Secs. 3.4 and 4, but no conservation-error plots or convergence study are provided.
ad hoc to paper Subtracting a moving average δn̂_e isolates the physically meaningful trapped-particle fraction in the QSIS background.
Introduced in Sec. 3.1 specifically for QSIS cases; no independent validation, and the homogeneous comparison uses the unsubtracted signal.

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Cite this review

Pith. "Pith review of Dynamics of phase space vortices in Vlasov plasmas with ion scale inhomogeneity : II Chirped frequency drive study." pith.science (2026). https://pith.science/paper/IDZUILQF

@misc{pith2026260716786,
  author       = {Pith},
  title        = {Pith review of: Dynamics of phase space vortices in Vlasov plasmas with ion scale inhomogeneity : II Chirped frequency drive study},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/IDZUILQF}},
  note         = {Machine review of arXiv:2607.16786}
}

read the original abstract

In Part I of the companion paper [Ref Part I], we have extensively discussed about the creation of quasi-stationary ion scale (QSIS) inhomogeneity using a constant frequency external drive at ion-acoustic time scales, resulting in ion trapped particle instability (ITPI), wave-wave mode coupling interaction and energy cascading. QSIS thus formed is perturbed by applying small amplitude electron acoustic (EA) mode leading to the several key plasma response features. In this Part II, using electrostatic, unbounded, OpenMP Vlasov-Poisson solver i.e VPPM-OMP 1.0, we have investigated the formation of various phase space vortices (PSV) (generated using two step or one step time dependent downward frequency chirping drives) in the presence of background QSIS inhomogeneity obtained in Part I. In addition, we have also performed one to one comparison of individual cases with their homogeneous counterparts with exact simulation parameters. In presence of QSIS inhomogeneity, we have observed interesting phenomenon such as early onset of Langmuir (LAN) mode, suppression of PSV sizes, omission of PSVs when compared to the homogeneous cases. Also, for different two step or one step downward chirp perturbation cases, particle trapping or untrapping fractions and its response to the increasing chirp intervals are respectively reported.

Figures

Figures reproduced from arXiv: 2607.16786 by the authors.

**Figure 1.** A cartoon figure of frequency versus time i.e (ω, t) showing frequency turn on-off of an external electric field drive. Each (a) and (b) cases correspond to two step and one step frequency chirping methodologies respectively. In (a) i.e two step chirping process, constant frequency EAW drive [ω P EA] is applied from t1 < t < t2 and downward chirped frequency [ω = αt + β] drive is applied from t3 < t < t4 where (α, β… view at source ↗

**Figure 2.** 2D (ω, k) power spectrum plot of (a) Homogeneous + EAW perturbation + Chirp [top and bottom left] and (b) QSIS inhomogeneity + EAW perturbation + Chirp [top and bottom right] driven plasma cases with perturbation interval ∆t P EA = 1000 ω −1 pe , ω P EA = 0.624, EP 0 = 0.025, kp/kmin = 1, kc/kmin = 1, ED c = 0.025 and chirp interval ∆tChirp = 250 ω −1 pe . Comparing (a) and (b), we can observe the supression of high… view at source ↗

**Figure 3.** Spectogram plot i.e variation of the generated frequency (ω/ωpe) with respect to simulation time for (a) Homogeneous ∆tChirp = 400 ω −1 pe + EAW perturbation + Chirp and (b) QSIS inhomogeneity + EAW perturbation + Chirp driven plasma cases with perturbation interval ∆t P EA = 1000 ω −1 pe , ω P EA = 0.624, EP 0 = 0.025, kp/kmin = 1, kc/kmin = 1, ED c = 0.025 and chirp interval ∆tChirp = 250 ω −1 pe respectively. Bot… view at source ↗

Figures from the paper (20 more)

**Figure 4.** Figure 4: Phase space portrait of electron distribution function fe(x, v) at different times i.e (a) t = 0 ω −1 pe , (b) t = 1000 ω −1 pe , (c) t = 2000 ω −1 pe and (d) t = 3000 ω −1 pe for Homogeneous + EAW perturbation + Chirp case with perturbation interval ∆t P EA = 1000 ω −…

**Figure 5.** Figure 5: Phase space portrait of electron distribution function fe(x, v) at different times i.e (a) t = 0 ω −1 pe , (b) t = 1000 ω −1 pe , (c) t = 2000 ω −1 pe and (d) t = 3000 ω −1 pe for QSIS inhomogeneity + EAW perturbation + Chirp case with perturbation interval ∆t P EA = 1…

**Figure 6.** Figure 6: Phase space portrait of ion distribution function fe(x, v) at different times i.e (a) t = 120000 ω −1 pe , (b) t = 121000 ω −1 pe , (c) t = 122000 ω −1 pe and (d) t = 123000 ω −1 pe for QSIS inhomogeneity + EAW perturbation + Chirp case with perturbation interval ∆t P …

**Figure 7.** Figure 7: Spatially averaged ion and electron distribution function plots at end times i.e (a) ˆfi(vi , t) and (b) ˆfe(ve, t) [defined in Sec. 3 of the companion paper Part I] of both Homogeneous and QSIS inhomogeneity + EAW perturbation + Chirp driven plasma cases with perturba…

**Figure 8.** Figure 8: Temporal evolution of (a) homogeneous case excess density fraction (EDF) of electrons i.e δne/ne0 at x = Lmax/8, (b) electron EDF at x = Lmax/8, ion density ni(x = Lmax/8, t) and moving average variation δnˆe, (c) difference of electron EDF and moving average values i.…

**Figure 9.** Figure 9: Relative total, potential and kinetic energies (∆T E, ∆P E, ∆KE) [defined in Sec. 3 of the companion paper Part I] signatures with respect to time for (a) Homogeneous + EAW perturbation + Chirp and (b) QSIS inhomogeneity + EAW perturbation + Chirp driven plasma cases w…

**Figure 10.** Figure 10: 2D (ω, k) power spectrum plot of (a) Homogeneous + LPSV Chrip [top and bottom left] and (b) QSIS inhomogeneity + LPSV chirp [top and bottom right] driven plasma cases with inhomogeneity scale keq/kmin = 2, kc/kmin = 1, ED c = 0.025 and chirp interval ∆tChirp = 250 ω −…

**Figure 11.** Figure 11: Spectogram plot for (a) Homogeneous + LPSV Chirp and (b) QSIS inhomogeneity + LPSV Chirp driven plasma cases with inhomogeneity scale keq/kmin = 2, kc/kmin = 1, ED c = 0.025 and chirp interval ∆tChirp = 250 ω −1 pe . From (a) and (b), we can see the continous and disc…

**Figure 12.** Figure 12: Phase space portrait of electron distribution function fe(x, v) at different times i.e (a) t = 0 ω −1 pe , (b) t = 120400 ω −1 pe , (c) t = 121000 ω −1 pe and (d) t = 122000 ω −1 pe for QSIS inhomogeneity + LPSV Chirp case with inhomogeneity scale keq/kmin = 2,kc/kmin…

**Figure 13.** Figure 13: Phase space portrait of ion distribution function fi(x, v) at different times i.e (a) t = 0 ω −1 pe , (b) t = 120400 ω −1 pe , (c) t = 121000 ω −1 pe and (d) t = 122000 ω −1 pe for QSIS inhomogeneity + LPSV Chirp case with inhomogeneity scale keq/kmin = 2, kc/kmin = 1…

**Figure 14.** Figure 14: Phase space portrait of electron distribution function fe(x, v) at different times i.e (a) t = 0 ω −1 pe , (b) t = 400 ω −1 pe , (c) t = 1000 ω −1 pe and (d) t = 2000 ω −1 pe for Homogeneous + LPSV Chirp case with kc/kmin = 1, ED c = 0.025 chirp interval ∆tChirp = 250…

**Figure 15.** Figure 15: Spectogram plot for (a) Homogeneous + HC Chirp and (b) QSIS inhomogeneity + HC Chirp driven plasma cases with inhomogeneity scale keq/kmin = 2, chirp interval ∆tChirp = 400 ω −1 pe , ED c = 0.025, chirp drive scale kc/kmin = 1. From (a) and (b), we can observe the gen…

**Figure 16.** Figure 16: Phase space portrait of late time electron distribution function fe(x, v) for (a) Homogeneous + HC chirp and (b) QSIS inhomogeneity + HC Chirp cases with inhomogeneity scale keq/kmin = 2, chirp interval ∆tChirp = 400 ω −1 pe , ED c = 0.025, chirp drive scale kc/kmin =…

**Figure 17.** Figure 17: Phase space portrait of electron distribution function fe(x, v, t = 2000 ω −1 pe ) at different chirping intervals i.e (a) ∆tChirp = 50 ω −1 pe , (b) ∆tChirp = 100 ω −1 pe , (c) ∆tChirp = 150 ω −1 pe , (d) ∆tChirp = 200 ω −1 pe , (e) ∆tChirp = 300 ω −1 pe and (f) ∆tCh…

**Figure 18.** Figure 18: Phase space portrait of electron distribution function fe(x, v, t = 120000 ω −1 pe ) at different chirping intervals i.e (a) ∆tChirp = 50 ω −1 pe , (b) ∆tChirp = 100 ω −1 pe , (c) ∆tChirp = 150 ω −1 pe , (d) ∆tChirp = 200 ω −1 pe , (e) ∆tChirp = 300 ω −1 pe and (f) ∆t…

**Figure 19.** Figure 19: Temporal evolution of (a) homogeneous case excess density fraction (EDF) of electrons i.e δne/ne0 at x = Lmax/8, (b) electron EDF at x = Lmax/8, ion density ni(x = Lmax/8, t) and moving average variation δnˆe, (c) difference of electron EDF and moving average values i…

**Figure 20.** Figure 20: Variation of the difference of electron EDF and moving average values i.e EDF : (δne−δnˆe)/ne0 at x = Lmax/8 for LPSV + QSIS inhomogeneous case and EDF : δne/ne0 at x = Lmax/8 for LPSV + homogeneous case with respect to LPSV chirp intervals ∆tChirp with keq/kmin = 2, …

**Figure 21.** Figure 21: Phase space portrait of electron distribution function fe(x, v, t = 3000 ω −1 pe ) at different chirping intervals i.e (a) ∆tChirp = 100 ω −1 pe , (b) ∆tChirp = 200 ω −1 pe , (c) ∆tChirp = 300 ω −1 pe , (d) ∆tChirp = 400 ω −1 pe , (e) ∆tChirp = 500 ω −1 pe and (f) ∆tC…

**Figure 22.** Figure 22: Phase space portrait of electron distribution function fe(x, v, t = 123000 ω −1 pe ) at different chirping intervals i.e (a) ∆tChirp = 100 ω −1 pe , (b) ∆tChirp = 200 ω −1 pe , (c) ∆tChirp = 300 ω −1 pe , (d) ∆tChirp = 400 ω −1 pe , (e) ∆tChirp = 500 ω −1 pe and (f) ∆…

**Figure 23.** Figure 23: Temporal evolution of (a) homogeneous case excess density fraction (EDF) of electrons i.e δne/ne0 at x = Lmax/8, (b) electron EDF at x = Lmax/8, ion density ni(x = Lmax/8, t), (c) electric field variation at x = Lmax/8 for both homogeneous and QSIS inhomogeneity + HC …

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Bernstein I B, Greene J M and Kruskal M D 1957Phys. Rev.108(3) 546–550 URL https://link.aps.org/doi/10.1103/PhysRev.108.546

doi:10.1103/physrev.108.546

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O’Neil T 1965The Physics of Fluids82255–2262 (Preprint https://aip.scitation.org/doi/pdf/10.1063/1.1761193) URL https://aip.scitation.org/doi/abs/10.1063/1.1761193

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work page doi:10.1063/1.5024376