Numerical investigation of stability of low-current needle-to-plane negative corona discharges in air

A. Eivazpour Taher; G. V. Naidis; M. S. Benilov; N. G. C. Ferreira; P. G. C. Almeida

REVIEW 3 major objections 4 minor 49 references

Numerical investigation of stability of low-current needle-to-plane negative corona discharges in air

T0 review · 3 major / 4 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read A pulseless negative corona discharge in air can remain stable over a nearly 6 kV window immediately after ignition when the needle tip is sharp and the gap long, with the stable range growing as the electric field becomes more nonuniform.

desk verdict A useful but self-flagged extrapolation: the paper's wide pulseless windows for sharp needles are a qualitative trend, not a quantitative prediction. read the letter →

arxiv 2506.06744 v1 pith:7MRURLMI submitted 2025-06-07 physics.plasm-ph

N. G. C. Ferreira , P. G. C. Almeida , A. Eivazpour Taher , G. V. Naidis , M. S. Benilov This is my paper

classification physics.plasm-ph PACS 52.80.Hc52.65.-y

keywords negativecoronadischargeTrichelpulsespulselessregimestabilityofneedle-to-planegeometrydrift-diffusionmodelatmospheric-pressureairionizationwaves

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

This paper seeks to establish that the stationary, pulseless negative corona discharge in a needle-to-plane gap in atmospheric-pressure air is stable immediately after ignition, and that the width of that stable voltage window is controlled by the nonuniformity of the electric field. In the computed configurations the window widens from about 15 V for a blunt 100 µm tip over a 10 mm gap to nearly 6 kV and 4 µA for a sharp 2 µm tip over a 50 mm gap, so a sharp needle and a long gap should make the pulseless mode easy to observe. The paper further claims that after stability is lost the current passes through quasi-harmonic oscillations into one of three outcomes: small low-current pulses, regular Trichel pulses (the characteristic current bursts of negative corona) developing as standing waves, or Trichel pulses driven by cathode-directed ionization waves. It also proposes that the stochastic Trichel pulses reported in some experiments can be provoked by finite perturbations of an otherwise stable pulseless state. If these claims hold, the contradictory experimental reports about whether negative coronas ignite pulsed or pulseless would be resolved as a matter of geometry.

What carries the argument

The argument is carried by a two-dimensional, time-dependent drift-diffusion model of low-current discharges in atmospheric-pressure dry air: conservation and transport equations for electrons, one effective positive-ion species, and three negative-ion species ($\mathrm{O}^-$, $\mathrm{O}_2^-$, $\mathrm{O}_3^-$), coupled to the Poisson equation, with transport and kinetic coefficients treated as known functions of the local electric field and photoionization described by a three-exponential model. Stability is probed by first computing all stationary states, then applying a perturbation equal to the difference between the stationary solutions at neighbouring voltages ($\Delta U = -1$ V typically) and following the response with a time-dependent solver: a decaying perturbation marks a stable state, and the last stable state fixes the window $U_C - U_O$. The same apparatus distinguishes the three post-instability outcomes by tracking where in the gap the electron-density maximum sits and whether a space-charge sheath with an intense field maximum moves toward the cathode.

What would settle it

Record the onset voltage of the first repetitive current pulses in dry atmospheric-pressure air for needle tips of radius roughly 2, 20, and 100 µm at gaps of 10 and 50 mm: the model predicts the pulseless window grows from about 15 V for the bluntest, shortest geometry to about 6 kV for the sharpest, longest one, and that for a 125 µm hemispherical tip the stability is lost within about 1% of the inception voltage. A pulseless window much narrower or much wider than predicted, or pulses arising immediately at inception in the sharp geometry, would refute the claim that field nonuniformity controls the stability range. A second, cheaper test applies to the ionization-wave outcome: the paper's assignment of large-radius needles to that mechanism rests on trial simulations truncated before the pulses fully develop, so a complete simulation or an experiment that images a cathode-directed ionization wave preceding each Trichel pulse would settle it.

Watch

Extended reading notes

Core claim

The central claim is that the stationary negative corona in the needle-to-plane geometry is stable — pulseless — immediately after ignition, in line with the earlier theory for concentric cylinders, and that stability is lost only on the rising section of the current-voltage characteristic, at a voltage $U_C$ with a current in the tens of nanoamperes to microamperes range. The paper's key numerical result is that the stability range $U_C - U_O$ depends strongly on the nonuniformity of the electric field: decreasing the tip radius from 100 µm to 2 µm or lengthening the gap from 10 mm to 50 mm widens the computed window from 15 V to 5977 V, while the stationary current-voltage curves change only slightly. Just above the stability limit the instability develops as weakly nonlinear quasi-harmonic oscillations that accumulate into low-current pulses on a virtually undisturbed field; further from the limit the classic Trichel pulses appear, with small tip radii favouring a standing-wave mechanism and large radii favouring a cathode-directed ionization wave. The paper also argues that finite perturbations of a stable pulseless state — equivalent to applied-voltage swings of order 10 V — can produce solitary Trichel pulses, which offers an explanation for the apparently stochastic pulses seen in some experiments, and it reports agreement between the computed current-voltage characteristic and stability limit and the experimental data for a 125 µm hemispherical-tip rod.

Load-bearing premise

The central claim that sharp needles and long gaps give a wide pulseless window rests on trusting the drift-diffusion local-field model at reduced electric fields above 1500 Td at the needle tip, where its transport and ionization coefficients are extrapolated beyond their known range of validity — the paper itself notes the results there can only be qualitatively correct.

Editorial extensions

If this is right

A pulseless negative corona can be observed in the laboratory without ambiguity by using a sharp needle (tip radius of a few micrometres) and a long gap: the computed stable window reaches nearly 6 kV and 4 µA, more than two orders of magnitude wider than the roughly 10 V windows found in earlier modelling.
Geometry acts on stability much more strongly than on the stationary current-voltage characteristic: changing the tip radius leaves the CVC nearly unchanged while changing the pulseless voltage window by orders of magnitude.
The loss of stability, which occurs on the rising branch of the CVC, leads to three distinct outcomes — low-current pulses immediately above the stability limit, standing-wave Trichel pulses for small tip radii, and ionization-wave Trichel pulses for large tip radii.
Stochastic Trichel pulses can arise from finite perturbations of a stable pulseless state: in the model, applied-voltage swings of order 10 V generate a solitary Trichel pulse followed by recovery to the pulseless state.
For the 125 µm hemispherical-tip rod of the long-standing experiment, the computed stability limit lies within about 1% of the inception voltage, tying the pulseless regime to the discharge state immediately above inception.

Reading between the lines

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

Extrapolating the Table 1 trend, the pulseless window should track the geometric field enhancement at the tip, so sub-micrometre tips or gaps far beyond 50 mm might push the stable range to tens of kilovolts; the paper itself does not extrapolate this far.
Because the paper concedes that the local-field model is only qualitatively correct above 1500 Td, the safest prediction is the ordering — sharper tips and longer gaps widen the window — rather than the absolute widths; an experiment with two or three tip radii would test the ordering even if the exact voltages shift.
The low-current pulse regime, a weakly nonlinear accumulation of oscillations on an almost undisturbed field, should in principle appear in other geometries (wire-cylinder, sphere-plane) near their stability limits; looking for sub-microampere pulses just above the stable range there would be a direct transfer of this prediction.
The standing-wave versus ionization-wave dichotomy is attributed to tip radius, but a more natural control variable is the ratio of the ionization-region thickness to the gap length; repeating the calculations in nitrogen or carbon dioxide, where attachment and ionization rates differ, would separate a geometric criterion from a gas-specific one.

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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

Colleague,

The thing to know: this is a competent numerical study that gives the first systematic map of where the pulseless negative corona is stable in needle-to-plane geometry, and it contains a genuinely new classification of what happens after stability is lost. But the headline quantitative result—that sharp needles give stability windows up to ~6 kV—rests on a model that the authors themselves say is only qualitatively correct at the fields near the tip. Read those numbers as a trend, not a prediction.

What is new and good: the geometry dependence of the stability range (from 15 V at R=100 µm to ~6 kV at R=2 µm), the identification of low-current periodic pulses as a distinct instability outcome, and the demonstration that finite perturbations of a stable state can trigger solitary 'stochastic' Trichel pulses. The internal consistency checks are reassuring: Table 2 shows the stability range changes little when the perturbation amplitude is varied from 1 to 5 V, and the computed CVC matches Bandel's 1951 experiment over 10 pA to 10 µA. The authors also state the model's high-field limitation plainly, which is more than many papers do.

Where it is soft: the stability boundary is set by space-charge dynamics within tens of micrometres of the tip, and in every computed case the reduced field there exceeds 1500 Td—beyond the range where the drift-diffusion local-field approximation is valid. The transport and ionization coefficients have to be extrapolated past their validated range, and the stability windows for the sharpest needles are exactly what those extrapolations produce. The one experimental comparison is for R=125 µm, d=20 mm, where the predicted window is only 37 V, so the wide-window claim for sharp needles is not experimentally checked. No code or data are shipped, so independent numerical reproduction isn't possible from the paper alone.

The qualitative conclusions—pulseless discharge exists after ignition, stability range grows with field nonuniformity, and three distinct instability outcomes exist—are probably robust. The specific numbers for sharp needles should be treated as a testable hypothesis until confirmed by experiment or by a model with a better high-field electron description.

This paper is for corona experimentalists and modellers. It deserves a serious referee; the limitations are real but acknowledged, and the work moves the field forward. My recommendation: send to peer review, and push the authors to frame the sharp-needle wide-window prediction as an extrapolation and to seek direct experimental confirmation.

Referee Report

3 major / 4 minor

Summary. This paper reports a numerical study of the stability of low-current negative corona discharges in a needle-to-plane geometry in atmospheric-pressure air. The model is a two-dimensional drift-diffusion local-field model with three negative-ion species and photoionization, solved with COMSOL. For nine configurations varying the needle tip radius and gap length, the authors compute stationary current-voltage characteristics and then test stability by imposing voltage perturbations and following the time evolution. They find that the stationary (pulseless) corona is stable immediately after ignition, with a voltage stability range that increases strongly as the field nonuniformity increases, from 15 V for R = 100 μm and d = 10 mm to 5977 V for R = 2 μm and d = 50 mm (Table 1). After loss of stability, the simulations produce three distinct outcomes: low-current pulses, Trichel pulses via a standing-wave mechanism, and Trichel pulses via ionization waves. The paper also reports that sufficiently large finite perturbations of a stable state can produce a solitary stochastic-looking Trichel pulse. The computed current-voltage characteristic and the location of the stability limit are compared with the classic Bandel experiment for R = 125 μm and d = 20 mm, with good agreement in the current range 10 pA to 10 μA.

Significance. If the quantitative predictions hold, the paper would resolve the contradictory experimental reports about whether negative coronas ignite in a pulseless mode by identifying a wide, experimentally accessible voltage window for sharp needles and long gaps. The work is a natural extension of the authors' earlier theory and modeling of concentric-cylinder coronas, and it provides a plausible mechanism for stochastic Trichel pulses. Strengths include the absence of fitted parameters (the illustrative photoemission fit is confined to a side discussion), the perturbation-amplitude check in Table 2, and the successful comparison with Bandel's experiment over five decades of current. However, the central quantitative claim—the wide stability window for sharp needles—rests entirely on a local-field drift-diffusion model in a regime where the authors themselves state the model is only qualitatively correct, and this limitation is not reflected in the presentation of Table 1 and the conclusions.

major comments (3)

[Section 3.2, after Figure 6] The manuscript states that the reduced electric field at the needle exceeds 1500 Td in all cases and that 'the computation results can only be qualitatively correct here' because the electron distribution function becomes strongly anisotropic. This is a direct admission that the local-field drift-diffusion model is quantitatively invalid in the very region that controls the stability boundary: the space-charge dynamics and ionization balance within tens of micrometers of the tip (Figures 5 and 6). The stability ranges in Table 1, especially UC - UO = 5977 V for R = 2 μm, are therefore quantitative predictions made with a model outside its stated domain of validity. The paper should either (i) explicitly reframe the sharp-needle stability windows as qualitative trends, (ii) support them with a model that is valid at >1500 Td (e.g., a kinetic or hybrid scheme), or (iii) provide experimental corroboration for a sharp-needle configuration. As written, the abstract and conclusions present the 5977 V window as a quantitative result, which is inconsistent with the stated model limitation.
[Section 5, Figure 10] The only quantitative experimental comparison is for R = 125 μm and d = 20 mm (configuration 9), where the computed stability range is just 37 V. This comparison validates the current-voltage characteristic and shows that the stability limit lies very close to inception for that geometry, but it does not test the paper's central predictive claim that sharp needles (R = 2–10 μm) give wide pulseless windows of hundreds to thousands of volts. The authors should either obtain or identify an experiment with a sharp, well-characterized needle, or clearly limit the claim of wide stability windows to a qualitative prediction until such data exist.
[Section 4, Figure 9] The conclusion that stochastic Trichel pulses arise from finite (non-small) fluctuations of a pulseless discharge is based on a single demonstrative example: one stable state, one perturbation amplitude of -10 V, and one -2 V control. While the idea is plausible and hints at a mechanism, the 'insight into stochastic Trichel pulses' claimed in the abstract would be considerably strengthened by a systematic scan over perturbation amplitudes, durations, and possibly spatial forms, and by checking whether the resulting solitary pulses reproduce the observed statistics or intermittency. As it stands, the claim is under-supported as a general explanation.

minor comments (4)

[Abstract] There is a typo: 'stedy-state' should be 'steady-state'.
[References] Reference [2] contains 'Electrical Goronas' (should be 'Coronas'), and references [22] and [23] contain OCR artifacts such as 'Gonf. Phenom.', 'fhe Netherlands', 'fhe plasma road', and 'morkshop'. These should be corrected.
[Section 3.2, paragraph on Figure 6] The notation 'nA+' and 'nA-' for ion densities is introduced without a formal definition in that paragraph; a brief parenthetical definition would improve readability.
[Section 2, Table 1] The caption states 'against perturbations with AU = -1 V', but the symbol should be ΔU (Delta U), not 'AU'. The same symbol appears in Section 3.2 and Table 2.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the stability ranges and pulse outcomes are obtained by direct time-dependent solution of a parameter-free drift-diffusion model, not by fitting the predicted quantities.

full rationale

The paper's central quantitative claims—the pulseless stability window UC−UO and the three instability outcomes—are generated by solving the drift-diffusion equations for charged particles together with Poisson's equation using transport and kinetic coefficients tabulated as functions of the local electric field, then applying time-dependent perturbations to stationary states. No target quantity (UC, IC, or the stability window) is used as an input or fitted parameter; the same stationary solver and perturbation procedure are applied uniformly to all nine geometries. The secondary emission coefficient is prescribed, not adjusted to reproduce stability data. The only parameter adjusted to experiment is the illustrative 3 pA photoemission current in Section 5, which the authors explicitly label 'for illustrative purposes' and which does not enter the main stability calculations (the values with and without it, UC=3496 V vs 3500 V, are essentially unchanged). The agreement with the Bandel experiment validates the computed CVC and the proximity of the stability limit to inception in a configuration where the predicted window is small, rather than being used to construct the wide windows claimed for sharp needles. Self-citations to [21] and [25] supply the underlying theory and numerical model, but the present stability boundaries are computed in this paper from the model's own time evolution, so those citations are not load-bearing in the sense of replacing an independent derivation. The paper itself flags the local-field model's limited quantitative validity above 1500 Td near the tip; that is a correctness and validity limitation, not circularity, because it concerns extrapolation of physical coefficients rather than a quantity defined in terms of the result being predicted. No step was found in which a prediction reduces by construction to an input.

Assumptions & free parameters 2 free parameters · 5 assumptions · 0 invented entities

All inputs to the central claim come from a pre-existing model and physical constants; the only adjustable numbers are the secondary emission coefficient and an illustrative photoemission current. No new particles, forces, or conserved quantities are introduced.

free parameters (2)

Secondary electron emission coefficient = 2e-4
Set as a constant in the cathode boundary condition (Section 2); no sensitivity study is reported, and it affects both the current level and the stability limit.
Photoemission current for illustrative low-current fit = 3 pA
Used in Section 5 to reproduce the low-current branch of Bandel's current-voltage characteristic; declared illustrative and not used for the main stability-range predictions.

assumptions (5)

domain assumption Drift-diffusion approximation and local-field transport/kinetic coefficients are valid for the plasma description
Invoked throughout the model (Section 2); explicitly violated at E/N above 1500 Td near the needle (Section 3.2), so it is a load-bearing assumption.
domain assumption The five charged species (electrons, one effective positive ion, O-, O2-, O3-) and the three-exponential photoionization model capture the essential corona chemistry in dry air
Model description in Section 2; the effective positive-ion species is a lumped representation, and no validation of the chemistry subset is given in this paper.
domain assumption The stability test by applying a finite voltage perturbation Delta U and observing decay or growth determines stability of the stationary state
Sections 3 and 4; presumably approximating linear stability, with amplitude checks in Table 2, but no eigenvalue analysis is performed in this work.
domain assumption Gas temperature is 300 K and convective motion of neutral gas is negligible
Section 2, justified for low currents; if heating were significant, the stability windows could change.
standard math The stationary-state current-voltage characteristic has a unique solution path and the inception voltage is correctly identified by the resonance method
Relies on the bifurcation methodology of reference [25] Section IV A, not re-derived here.

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Cite this review

Pith. "Pith review of Numerical investigation of stability of low-current needle-to-plane negative corona discharges in air." pith.science (2026). https://pith.science/paper/7MRURLMI

@misc{pith2026250606744,
  author       = {Pith},
  title        = {Pith review of: Numerical investigation of stability of low-current needle-to-plane negative corona discharges in air},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/7MRURLMI}},
  note         = {Machine review of arXiv:2506.06744}
}

read the original abstract

Negative DC corona discharges are known for their self-pulsing regime: the Trichel pulses. In some works, pulsed regimes, stochastic or periodic, have been observed immediately upon the inception of the discharge, while in other works the discharge was found to be ignited in a stedy-state (pulseless) mode, with the Trichel pulses developing at higher voltages. Recent theoretical and modelling work showed that the stationary negative corona between concentric cylinders in atmospheric-pressure air is stable immediately after the ignition. The pulseless mode was found also in the modelling of the needle-to-plane geometry, however in a quite narrow voltage range. This work studies conditions for a pulseless negative corona discharge in a needle-to-plane geometry to occur over a wide range of voltages, which will facilitate its unambiguous observation in the experiment. After the negative corona loses stability, the current evolution shows, after a small region of quasi-harmonic oscillations, pulses. These can be of small amplitude or regular Trichel pulses, which develop via standing-wave or ionization-wave mechanisms. Modelling results agree with available experimental data, both for the current-voltage characteristics and the stability limit of the pulseless negative corona discharge. An insight is given into stochastic Trichel pulses, which have been observed in experiments under certain conditions.

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Reference graph

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Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.

[1] [1]

H. W. Bandel, Phys. Rev. 84, 92 (1951)

work page 1951

[2] [2]

L. B. Loeb, Electrical Goronas (University of California Press, Berkely, 1965)

work page 1965

[3] [3]

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work page 1968

[4] [4]

S. Chen, R. G. W. van den Berg, and S. Nijdam, Plasma Sources Sci. Technol. 27, 055021 (2018)

work page 2018

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