Trichel: Science Contrarian review (Step 2)

Reviewer role: judge by experimental evidence, not consensus. Tags: [read] from the documents, [web] with URL, [memory] with confidence, [calc] my own arithmetic. Source folder: one paper only, Sattari, Castle, Adamiak, ESA 2010 paper K4 (15 pp., full text, no source gap). Nothing by G. W. Trichel is in the folder; statements about his 1938 work rest on this paper's description [read: p.1-2], on the Investigator's finds, or on [memory].

Inputs read: facts.json, claims.md, the deep read (both parts), the paper text (introduction, conclusions, Table 1), sites.md and all eight research notes, and the downloaded Sattari 2011 thesis (checked passages: Table 7.1, Ch. 8.2) [read: thesis text].

Short answer

This is not an "inventor vs. mainstream" project. Trichel pulses are a textbook phenomenon, observed by many groups since 1938. The folder holds a modelling paper that is itself mainstream. The contrarian questions are therefore different: (1) is the mechanism in claim 2 actually established by experiment, or only by models whose checks are weak? (2) does the model's "success" (claims 3-5) survive scrutiny of the data it was compared with? On (2) I found something Step 1 did not: the paper's "experimental" column looks like Lama and Gallo's empirical law evaluated with the wrong onset voltage (see Section "A new finding"). That undercuts the "underestimates by 50%" claim as a statement about physics.

Corrections to Step 1

1. Claim 5 / Table 1 reading. Step 1 accepted the experimental column (21.85, 13.32, 9.09, 5.07 us) as Lama and Gallo's measurements. The Investigator showed the same authors' thesis uses different reference values (11.3, 8.1, 6.1, 4.8 us at 7-10 kV) [read: thesis Table 7.1] and flips the sign of the error. I confirmed the thesis table and, further, that the thesis values are exactly Lama and Gallo's published law (below). Step 1 should treat the ESA experimental column as unverified.
2. Ionization formula. Step 1 flagged "4.493" as a likely misprint. Confirmed 449.3 in the authors' thesis, p.91 [web: Investigator, research/2026-10-04-uwo-scholaris.md]. Remaining caveat: whether the 2010 code used the right formula is still not shown. The caveat in claims.md that the printed law has "no threshold" is correct for the printed text and moot if the code used 449.3.
3. External resistance. Step 1 says R_ext is unstated. True for the ESA paper; the thesis gives 100 kOhm and a gap capacitance of 0.055 pF [web: Investigator note]. The ESA paper's algebraic circuit (V = Vc - I Rext, no capacitance) may differ from the thesis's ODE circuit. Which one produced the 2010 results is unknown.
4. Trichel reference. Step 1 notes a title error. More precisely: Phys. Rev. 55, 382 is the 1939 POSITIVE-corona paper; the pulse paper is Phys. Rev. 54, 1078 (15 Dec 1938) [web: https://link.aps.org/doi/10.1103/PhysRev.54.1078, via Investigator]. The ESA paper cites the wrong paper with the wrong year for the negative pulses.
5. "Trichel reported pulses in oxygen." The ESA introduction says so [read: p.1]. The abstract of Trichel's paper speaks of negative point-to-plane corona in air [web: APS abstract, via Investigator]. Minor, but the ESA paper's attributions to Trichel are not reliable.
6. Claim 1 as "established". Step 1 records "only in electronegative gases" as background. A 2017 experimental paper disputes it (Zhang et al., Sci. Rep. 7:10135 [web: https://www.nature.com/articles/s41598-017-10118-2]; abstract quoted by Investigator: pulses are "a common phenomenon that can occur in various gases rather than only in electronegative gases"). I could not load the full text (reCAPTCHA / redirect on two fetches), so which gases were tested is not verified by me.
7. Rise-time/width. Step 1 correctly notes none is reported. Add: the thesis gives simulated pulse durations of 0.19-0.30 us (Table 8.3) [web: Investigator], versus "tens of ns" in the literature the paper cites [read: p.1]. So the mismatch the paper never examined is about a factor 10.

A new finding: the "experimental" column fits Lama and Gallo's law with the wrong onset

Lama and Gallo's law, as quoted in the thesis: f = 1/T = K1 V (V - V0)/(r d^2), K1 ~ 27 kHz mm^3 kV^-2, V0 = 2.3 kV in magnitude [read: thesis Ch. 8.2]. With r = 0.1 mm, d = 10 mm (the simulated geometry) [calc]:

• The thesis column reproduces the law with Gallo's own V0 = 2.3 kV (my arithmetic matches 11.3 / 8.1 / 6.1 / 4.8).
• The ESA column is the same law with V0 = 4.7 kV, uniformly about 5% lower (ratio 0.95 at all four voltages; a linear fit of the ESA values gives V0 = 4.71 kV and K1 = 28.5) [calc]. 4.7 kV is the model's computed onset for the simulated geometry [read: p.7], not Gallo's measured onset.
• Therefore the ESA "experimental" numbers are most likely not measured data and not a use of Gallo's own V0. This is an inference from numerical coincidence at four points with a two-parameter law; I did not see the authors say how the column was made, and Gallo (acknowledged in the paper) may have supplied different numbers. It should be put to the authors.
• Consequence: against Gallo's own law, the simulation is within 1% at 7 kV (11.33 vs 11.26) and 35-45% short at 9 and 11 kV. The "approximately 50% underestimate at all voltages" is an artefact of the reference chosen. The simulated periods follow a law with V0 = 4.64 kV and K1 about 62 [calc, linear fit of the four values], so the model does not reproduce Gallo's scaling (different onset and twice the coefficient). It reproduces only the monotonic "higher voltage, higher frequency" trend, which any space-charge model gives.
• The thesis also says the model errs in both directions (overestimate in Ch. 8.2 first paragraph, underestimate a page later, and again "overestimates" in Ch. 8.7 [read: thesis]). Gallo's observed onset of 2.3 kV, "comparatively independent of tip radius", is called "unexpected and unexplained" by those authors; the model's 4.7 kV from Peek's formula is double.

Claims

Claim 1. Negative point-plane corona in air gives regular Trichel pulses, only in electronegative gases, in a limited voltage range

a. Mathematics: nothing to check; observational claim. b. Experiment: the existence of regular pulses in air is well documented by Trichel's oscillograms (reproduced by Loeb 1939, Figs. 243, 247, 248 [web: archive.org copy, via Investigator]), Loeb-Kip-Hudson 1941, Lama-Gallo 1974 [read: p.14-15 refs], Dordizadeh et al. 2017 (rise, fall and width independent of tip radius, voltage and gap; "good agreement with Lama's and Gallo's work" [web: https://www.sciencedirect.com/science/article/abs/pii/S0304388616301735]). The "only in electronegative gases" half is contested by Zhang et al. 2017 (above). Trichel's reported circuit-independence (APS abstract) is contradicted by the same group's own simulations (period depends on R_ext, thesis Ch. 7) [web: Investigator]; this is a real discrepancy between a 1938 observation and the 2010-2011 model, not examined by the authors. c. Tests: many independent experimental groups over 85 years. Replicated. d. If false: not applicable to the pulses; the "electronegative only" half, if Zhang is right, would remove the attachment-based mechanism's exclusivity.

Verdict: Established for pulses in air. The "only in electronegative gases" part: Tested, not supported by at least one experimental group (single paper; the strength of that test is not verified by me), so state it as disputed.

Claim 2. Mechanism: positive ions absorbed by the needle switch off ionization; slow negative-ion drift sets the period

a. Mathematics: the order of magnitude is checkable [calc]. Positive ion speed at 2e7 V/m with mobility 2e-4: 4000 m/s, crossing a 30 um ionization layer in about 8 ns, consistent with the paper's "few nanoseconds" [read: p.9]. Negative ion speed in the 7 kV gap with mean field about V/d = 7e5 V/m: 140 m/s, 1 cm in 70 us; closer to the tip fields of 1e6 to 1e7 V/m give 200-2000 m/s, so clearing 1 mm takes roughly 0.5-5 us. This is the right order for 3-20 us periods. The mechanism is arithmetically plausible. Whether it is the right mechanism is a different matter. b. Experiment: the picture "space-charge formation and subsequent clearing" is Trichel's own, from his 1938 abstract [web: APS]. Supporting: period depends on current and tip radius, as Trichel found. Against or complicating: (i) Zhang et al. 2017 argue positive ions predominate and negative ions are "not necessary even if they affect greatly the pulsing process" and that simulated waveforms often fail to match measured ones [web: Investigator quote]. (ii) Gallo's unpublished microscope observation of an "extremely narrow bright ionization channel" 0.12-2 um wide at the negative tip, which "is not described by present theory or simulations" and which drives the irregular pulses at sharp tips [web: thesis Ch. 8.3, via Investigator]. That is an observation from an interested party's collaborator, reported second-hand, with no independent publication found. It is evidence, not hearsay, and it is outside the model (the model has a smooth 100 um tip). (iii) Trichel's circuit-independence versus the model's R_ext dependence. c. Tests: the mechanism has been tested only through models; the models have never agreed with experiment to better than a factor of order 1.5-2 on timing in this paper, and rely on rate coefficients from an unpublished 1997 contract report for ABB, an interested commercial party, not available online [read: p.15; web: Investigator]. No controlled experiment that removes negative ions while holding everything else fixed is on record in this folder. d. If wrong: a positive-ion-cloud-rebuild mechanism (Zhang) would replace the negative-ion-clearing mechanism. Little in fundamental physics changes; it is plasma and discharge physics.

Verdict: Plausible, untested as to the specific mechanism (negative-ion drift sets the period); the existence of space-charge-controlled pulsing is Established. Note the competing mechanism has a published experimental basis; neither has been decided by a clean test.

Claim 3. The 2D FEM-FCT three-species model reproduces regular pulses, a post-pulse and a large delayed first pulse; first successful 2D FEM-FCT simulation

a. Mathematics: Step 1 found the printed equations (6) and (7) have ionization and attachment sources proportional to N_p and N_n instead of N_e. I agree it looks like a typographical error; the thesis was not checked for the corrected form. Units: N appears to be charge density (figures in C/m^3) but eq (5)'s recombination term and eq (1) do not carry a consistent factor of e, so the equations are not simultaneously consistent as printed. Electron diffusion uses the gas-temperature Einstein relation (D about 1.3e-3 m^2/s), which for electrons at hundreds of Td [memory, medium] is much too low; the constant electron mobility 0.05 m^2/Vs gives drift speeds of 5e5 m/s at 1e7 V/m, above typical measured values in air near 2e5 m/s [memory, medium; not web-checked]. The "air" model uses an oxygen rate set with N = all-molecule density labelled O2 (the thesis repeats this) [read]. Convergence tolerance 0.01 in the text, 0.05 in the flowchart [read: p.6]. No mesh or time-step convergence study; ionization layer about 25 um resolved with 5 um mesh [read]. Internally the model converges to periodic pulses, which is a numerical result, not evidence of correctness. b. Experiment: the post-pulse is not claimed to be observed; the paper cites no measurement of a 12-20 times larger first pulse. The ESA paper compares only period, not amplitude, charge per pulse, rise time or width. Simulated steady amplitude (about 1.8-2 mA) and duration (0.2-0.3 us per the thesis) are far from the "tens of ns" widths the paper quotes. In the thesis, charge per pulse (about 115 pC at 100 um) is compared with another group's data and disagrees (thesis: Qi/Q > 0.5 against < 0.5) [web: Investigator]. The 25-37 mA first pulse versus 2 mA steady is a start-up transient from the initial seed charge (magnitude not given) and may or may not occur in real needles; I found no source that has measured it. c. Tested: by its own authors. Later: the thesis adds a fitted "effective tip radius" of 10 um, giving 2.3 vs 2.0 us (15% high), which is tuning to one point [web: Investigator]. A 2023 successor tests alternative rate-coefficient sets and claims validation against experiment [web: https://iopscience.iop.org/article/10.1088/1361-6463/acdd0f/meta; abstract only]. No independent group's replication of this model is in the record I examined. The priority claim ("first time FEM-FCT ... 2D ... different voltages") is the authors' own and I did not verify it; it is a statement of method novelty, not physics. d. If false: nothing in physics changes; the model is a computational tool.

Verdict: Plausible, untested for "reproduces regular pulses"; Not testable as stated for "first successful"; the comparison to experiment is incomplete (period only, and see claim 5). I do not call this "Internally inconsistent" because the likeliest explanation of the equation problems is a misprint, which the authors' own thesis partly confirms (449.3), though the unit and diffusion points remain open.

Claim 4. Pulse frequency rises with voltage; simulated periods 11.33 to 2.46 us follow the trend of Lama and Gallo's data (21.85 to 5.07 us)

a. Mathematics: fine. The simulated average excludes the first interval; I reproduced both averages from the listed intervals (11.33 and 3.39 us) [calc, from deep read]. At 7 kV the first interval (11.5 us) is shorter than the mean, contrary to the text's "usually longer" [read: p.7]. b. Experiment: frequency rising with voltage is consistently observed (Lama-Gallo f proportional to V(V - V0) [web: thesis Ch. 8.2]; Dordizadeh 2017). The simulation reproduces that qualitatively. The specific experimental numbers are in doubt (see "A new finding"): they appear to be Lama and Gallo's formula evaluated with V0 = 4.7 kV, not their measured onset 2.3 kV. The "Lama and Gallo data" of 21.85 us at 7 kV is therefore not a number I can trace to their paper. The Fig. 17 "experimental" line is a smooth curve, not points [read: deep read, page image p.13]. c. Tested: four voltages, one run each, no uncertainty on either side [read]. The thesis later shows standard deviations of 0.6-2.1 us on its averages [read: thesis Table 7.1]. d. If false: nothing.

Verdict: Established for the qualitative trend (frequency rises with voltage; independent experiments). Never properly tested for the quantitative match within this paper because the reference column is not demonstrably measured data.

Claim 5. Simulated periods are about half the measured ones; cause "approximations in the numerical technique"

a. Mathematics: ratios 0.52, 0.47, 0.37, 0.49 [calc, deep read]; "approximately 50%" is loose at 9 kV (0.37). Against Gallo's law with his own V0 the ratios become 1.01, 0.78, 0.55, 0.64 [calc], i.e. no uniform factor of two. b. Experiment: the shortfall is not a fixed physical fact. It depends on which "experimental" numbers are used. The thesis (same authors) finds the model overestimates relative to its Gallo values, then writes that it underestimates. The parametric study of the thesis shows that period depends on R_ext (lower R_ext gives longer period), mobility (higher mobility, shorter period) and not significantly on gamma [web: Investigator, Ch. 7]. Those are candidate causes the paper itself never tested. One caveat the authors mention: geometry in Lama-Gallo may differ from the model (tip to plane spacing) [read: thesis Ch. 8.2 last paragraph]. c. Tested: nothing in the paper. The authors say the cause is "being further investigated". d. If true as a physical discrepancy: a model-input issue (R_ext, rate coefficients, tip geometry, Gallo's channel), not new fundamental physics.

Verdict: Not testable as stated (the size and even the sign of the discrepancy depend on an undocumented reference). If the ESA experimental column is what I infer, the claim is Refuted by calculation as a statement about the data: the column is the empirical law with the model's own onset. I mark that as an inference to be confirmed with the authors.

How the claims were treated (rejection and suppression)

There is no rejection story here. Trichel's work was accepted at once by his supervisor Loeb, who thanks him in the 1939 book preface and reproduces his oscillograms [web: https://archive.org/stream/in.ernet.dli.2015.74804/2015.74804.Fundamental-Processes-Of-Electrical-Discharge-In-Gases_djvu.txt, via Investigator]. The absence of later Trichel work is explained: Gervais W. Trichel, a Coast Artillery and Ordnance officer, left for fire-control and rocket work (colonel; Chrysler 1947-63) [web: Prabook https://prabook.com/web/gervais_william.trichel/90642; Redmond and Smith, Project Whirlwind, archive.org]. That is a competing-explanation check I can close: career change, not suppression. One caveat: Prabook is a compiled biography, and the claim that the 1934-38 gap equals the doctorate is the Investigator's inference.

Two things do deserve flagging as "how the claim was treated": - Gallo's narrow-channel observation and the 2.3 kV radius-independent onset are described by the model's authors as unexplained and outside present theory, yet the 2010 paper does not mention them while thanking Gallo [read: p.14]. The data that a smooth-tip model cannot reproduce was not in the paper. It appears only in the 2011 thesis, and no independent publication has been found. - Rate coefficients rest on a contractor report for ABB that is not publicly available [read: p.15]. ABB has a commercial stake in corona modelling; the report is the authors' source, not an independently checked one.

Strongest honest case for the work

• Trichel pulses are real, regular, and reproduced worldwide in air.
• A first-principles drift-diffusion model with only three species, no tuning of geometry, gives periodic pulses with periods in the correct range (µs) and the correct sign of the voltage dependence. At 7 kV it lands within 1% of Gallo's own law (11.33 vs 11.26 us) [calc].
• The order-of-magnitude timescales for positive-ion absorption (about 10 ns) and negative-ion clearing (a few µs) check out by hand [calc].
• The authors' later thesis fixed the formula misprint and gave R_ext, and their later experiments agree with Lama and Gallo [web: Dordizadeh 2017].

Strongest honest case against

• Only one scalar (period) is compared, at four voltages, with no uncertainty, to a reference that cannot be traced to measurements.
• Pulse shape (rise time, width, amplitude, charge per pulse) is not compared; where the thesis does compare, widths and charge disagree.
• The onset voltage is off by about a factor of 2 relative to Gallo's measurements (4.7 vs 2.3 kV), and the model cannot reproduce the radius independence.
• Key input constants are unpublished, oxygen-based, and treated as air; some choices (gas-temperature diffusion, constant electron mobility) are not physical at these fields.
• A competing experimental paper rejects the negative-ion-clearing explanation.

Applying the same rigour to the inventor-side

The authors claim success, are the model's developers, and are interested parties for "successfully reproduced". The same standard applies to the experimentalists: Gallo's channel observation is reported with estimated, not measured, sizes (0.12-2 um channel diameter) in a table of estimates [web: Investigator, thesis Table 8.1]; it is a lead, not an established fact.

Verdict table

What would settle open points

1. Obtain Lama and Gallo 1974 (J. Appl. Phys. 45, 103) and check their tabulated periods at 7-11 kV, geometry r = 100 um, d = 1 cm, R_ext. Compare with 21.85 / 13.32 / 9.09 / 5.07 us. This decides whether the ESA reference column is data or a formula with V0 = 4.7 kV.
2. Reproduce the periods with the thesis ODE circuit (R_ext = 100 kOhm, Cd = 0.055 pF) vs the 2010 algebraic circuit, to see whether circuit treatment, not "numerical approximations", closes the gap.
3. Measure rise time and width at 100 um tip, 1 cm, -7 kV with a fast scope; compare with the model's 0.2-0.3 us. Dordizadeh 2017 appears to have data (values not extracted by me or the Investigator).
4. A direct test of mechanism: vary negative-ion mobility or sweep gas flow across the tip, and see whether the period scales as the model predicts, versus Zhang's positive-ion account.

Source-check notes

• Web checks done: Lama-Gallo reference details (search result confirming journal, volume, pages and the study design: https://www.nature.com/articles/s41598-017-10118-2 appears in the search listing along with the Dordizadeh pages); two attempts to read Zhang 2017 full text failed (reCAPTCHA on PMC, redirect on nature.com), so statements about Zhang rest on the Investigator's abstract quote. Lama-Gallo's abstract itself was not retrieved; the law and constants are from the Sattari thesis, which quotes them.
• [memory, medium, not web-checked]: electron drift velocity in air near 2e5 m/s at these fields; Einstein relation limits at high E/N. They support concerns, not verdicts.
• Everything marked [calc] I computed with numpy from numbers in the documents; the "ESA column equals the law with V0 = 4.7 kV" result is a numerical coincidence of four points and I flag it as inference.