Correa: Pulsed Abnormal Glow Discharge (PAGD), a study primer

Paulo and Alexandra Correa, Labofex / Aetherometry, Ontario, Canada, 1992-2002. Patents US 5,416,391 (1995), US 5,449,989 (1995), US 5,502,354 (1996).

Source tags used throughout: [read] = taken from the Correa documents in the project folder; [web] = an Internet source, URL given; [memory] = recalled from training, with confidence high/medium/low; [calc] = arithmetic done for this primer, reproduced by example.py in this folder. Final verdicts come from arbiter.md.

Source gap. The folder holds three files: the rexresearch.com printout "Paul & Alexandra Correa _ Pulsed Abnormal Glow Discharges (PAGD).pdf" (44 pages, text layer) and scans of US 5,449,989 and US 5,502,354. The scans were first read only through the copies inside the printout; they have since been OCR'd, and the circuit drawings (FIGS. 8-11) and Table 7 of US 5,449,989 were read as page images in a deep read requested by quality engineering (QE) [read: deep/Eng-Conv-Sys-US5449989-60b35a.md]. A second deep read covered Tables 5, 6 and 8; a second QE round then deep-read the high-vacuum tube examples and vacuum processing of US 5,502,354 (pp.29-35), the per-pulse energy Tables 12-16 with the worked example (pp.36-43), and the motor examples of US 5,416,391 (pp.11-13) [read: deep/Paul-Alexandra-Correa-Pulsed-Abnormal-Glow-Discharges-PAGD-8687ea.md]. US 5,416,391 exists only inside the printout, and its motor figures (FIGS. 7-13, which hold the rpm, torque and power data) are not in it. Not obtained: the original lab records, the Labofex report S3-001 in full, the 1996 Denver symposium paper, any documentation of the "Aether Motor", and any independent test report. Every number below is the inventors' own. No reviewer found an independent replication or a neutral null test. The 2007 third-party PDF at rohnermachine.com has now been read: it is a reprint of Mike Carrell's Infinite Energy articles that relays data and oscillograms supplied by Dr. Correa, not a test or a replication [web: http://www.rohnermachine.com/Files/CPAGD.pdf; arbiter Round 2]. The arbiter's web search was incomplete (search tool unavailable), so "none found" means "not found by three reviewers plus the arbiter's limited checks", not "none exists".

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1. The idea in one paragraph

Take a large glass tube with two big aluminium plates a few centimetres apart, pump most of the air out, and feed it from a high-voltage battery bank through a resistor. Instead of glowing steadily, the tube flashes on and off by itself, many times a second. The Correas studied this self-pulsing regime, which they named the "pulsed abnormal glow discharge" (PAGD), and built a circuit that takes the pulses out through rectifiers and uses them to charge a second battery bank. They reported that the second bank gained two to five times more energy than the first bank lost, that each pulse threw off metal ions with enormous energy and pushed back on the cathode with an unusually strong force, and that the surplus energy came from the vacuum itself (the "aether" or zero-point energy). The self-pulsing is real and well understood. The energy surplus is a set of battery measurements made by the inventors alone, with no repeat by a neutral lab found. Rechecked against the inventors' own circuit diagram, the headline table counts as "input" only the power heating a resistor, not the power the battery actually delivers; counted properly, most runs show no gain at all.

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2. What you need to know first

Electric power and energy in circuits. The power a source delivers is P = V I (watts = volts x amperes), where V is the voltage across its terminals and I the current through it. Energy is power times time, E = P t (joules; 1 watt-hour, Wh, = 3600 J). When the current and voltage change rapidly, as in pulses, the true average power is the time average of the product, P_avg = (1/T) integral of v(t) i(t) dt, which is generally not the product of separately averaged voltage and current. Kirchhoff's laws guarantee that the power a battery delivers is its terminal voltage times its current, regardless of how that voltage is then shared among the resistors and tubes downstream. Read: Griffiths, Introduction to Electrodynamics (sections on Ohm's law and electromotive force); any circuits text such as Horowitz and Hill, The Art of Electronics.

Capacitors and RC charging. A capacitor C charged to voltage V stores E = (1/2) C V^2. Charged through a resistor R from a supply V_s, its voltage rises as V(t) = V_s (1 - e^(-t/RC)); RC is the time constant. Read: Griffiths (capacitors chapter); Horowitz and Hill (chapter 1).

Gas discharges and Paschen's law. A gas at low pressure is an insulator until enough voltage is applied. Then a stray electron is accelerated, ionises a gas molecule, the new electrons ionise more (an "avalanche"), and positive ions hitting the cathode knock out further electrons. When each avalanche regenerates at least one starting electron, the gap breaks down. The breakdown voltage depends on the product of pressure p and gap d (Paschen's law, section 3). Above breakdown, a discharge passes through several regimes as current rises: dark (Townsend) discharge, normal glow, abnormal glow (glow covers the whole cathode, voltage rises with current), then arc (low voltage, high current, concentrated hot spots). Read: Yu. P. Raizer, Gas Discharge Physics (Springer, 1991); M. A. Lieberman and A. J. Lichtenberg, Principles of Plasma Discharges and Materials Processing (Wiley, 2nd ed. 2005). [memory, high: these books exist and cover these topics]

Relaxation oscillators. A device that conducts only above one voltage and stops below a lower one, put across a capacitor charged through a resistor, flashes on and off by itself. The classic example is the neon-lamp flasher. This is the key to claim 1. Covered in most electronics texts and in Raizer. [memory, high]

Field emission and the Fowler-Nordheim law. Electrons can leave a cold metal if the electric field at its surface is so strong (around 10^9 V/m) that they quantum-mechanically tunnel through the surface barrier. Fowler and Nordheim (1928) derived the current. Real surfaces have microscopic whiskers and adsorbed layers that multiply the local field by a factor beta, often tens to hundreds. Read: any modern-physics text on tunnelling (e.g. Griffiths, Introduction to Quantum Mechanics, on the WKB approximation), then the Fowler-Nordheim original, Proc. R. Soc. A 119, 173 (1928). [memory, high]

Momentum and force. A body that throws out mass m at speed v per time t feels a recoil force F = m v / t (Newton's second law in momentum form; this is how a rocket works). In centimetre-gram-second (CGS) units, force is in dynes: 1 dyn = 1 g cm/s^2 = 10^-5 N. Read: any classical mechanics text (Kleppner and Kolenkow, An Introduction to Mechanics, momentum chapter).

Ions and electron-volts. An ion of charge z e (e = 1.602 x 10^-19 C, z = number of electrons removed) falling through a potential difference V gains kinetic energy z e V. One electron-volt (eV) is 1.602 x 10^-19 J. A singly charged ion crossing 560 V gains 560 eV, no more.

Average versus rms current. For a current i(t) that varies in time, the average (mean) is I_avg = (1/T) integral of i dt, and the root-mean-square (rms) value is I_rms = sqrt[ (1/T) integral of i^2 dt ]. For steady DC they are equal; for short tall pulses the rms is much larger. Example: a current that is 10 A for 1% of the time and zero otherwise has I_avg = 0.1 A but I_rms = sqrt(0.01 x 100) = 1 A. Energy delivered by a battery at fixed voltage V is V x I_avg x t, so a meter set to rms on a pulsed current overstates it. The Correas read their currents on "rms multimeters" without saying which mode [read: deep read of US 5,449,989, p.16]. Read: Horowitz and Hill, chapter 1.

Batteries as meters. Lead-acid batteries are poor energy meters. Their open-circuit voltage drifts for minutes to hours after charging or discharging ("relaxation"), and the capacity you get out depends on discharge rate, temperature and history. Right after charging, "surface charge" shows an elevated voltage; for a voltage-based reading of state of charge a battery should rest open-circuit for at least four hours, and lead-acid makers recommend 24 hours [web: https://batteryuniversity.com/article/bu-903-how-to-measure-state-of-charge]. The Correas allowed a minimum of 15 minutes [read: deep read 1, pp.17-19]. Whether the effect is large enough to produce their apparent gains is not established [memory, unverified]. This matters because the Correas measured their energy surplus with batteries. Read: D. Linden and T. Reddy (eds.), Handbook of Batteries (McGraw-Hill), lead-acid chapter.

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3. The textbook view

3.1 Gas breakdown: Paschen's law

For a uniform gap d (cm) in gas at pressure p (Torr), the breakdown voltage is

V_b = B p d / [ ln(A p d) - ln( ln(1 + 1/gamma) ) ]

• V_b: breakdown voltage (V).
• A, B: constants of the gas; for air A = 15 cm^-1 Torr^-1, B = 365 V cm^-1 Torr^-1 [web: https://en.wikipedia.org/wiki/Paschen's_law].
• gamma: secondary emission coefficient, the number of electrons knocked out of the cathode per arriving ion (about 0.01 is typical for metals in air; it is a rough number).

For the Correas' typical tube (air at 0.8 Torr, 3 cm gap, pd = 2.4 Torr cm): ln(36) = 3.58, ln(ln 101) = 1.53, so V_b = 876 / 2.05 = 426 V [calc]. The tubes are reported to fire at about 500-560 V [read]. Given that the constants are approximate and the electrodes are not ideal parallel plates, this is the same ballpark: ordinary gas breakdown explains the firing voltage of the gas-filled tubes (0.09-1.5 Torr), which are the tubes used in all the energy-conversion runs.

Where Paschen's law stops. The Paschen curve has a minimum (for air near pd of about 0.5-1 Torr cm [memory, high]). To the left of it, there are too few gas molecules in the gap for an avalanche to build, and the breakdown voltage climbs steeply; at pd far below the minimum, gas breakdown at a few hundred volts cannot happen [memory, high]. Some Correa tubes were sealed at 1 x 10^-6 Torr with a 5 cm gap, so pd = 5 x 10^-6 Torr cm, about 100,000 times below the minimum [read: printout, US 5,502,354 Example 1; calc]. For such tubes the relevant mainstream physics is vacuum breakdown: field emission from enhanced spots heats microscopic points and releases metal vapour and adsorbed gas, which then supports a discharge; loose microparticles can trigger it too [memory, medium]. Paschen's law says nothing about these tubes, so the rebuttal in section 4 is limited to the gas-filled ones.

3.2 Self-pulsing: the relaxation oscillator

Put a capacitor C (including the tube's own capacitance and any capacitor in parallel) across the tube and feed both from supply V_s through resistance R. The capacitor charges toward V_s. When it reaches the breakdown voltage V_b, the tube fires and dumps the capacitor's charge until the voltage falls to the extinction voltage V_ext, below which the discharge cannot sustain itself. Then it goes out and the cycle repeats. If firing and discharge are fast, the period is the recharge time

T = R C ln[ (V_s - V_ext) / (V_s - V_b) ]

• T: time between pulses (s); R: series resistance (ohms); C: capacitance (F).

Oscillation needs R large enough that the steady current V_s / R cannot keep the discharge lit; otherwise it settles into a steady glow or arc. That is exactly the Correas' recipe: DC source, "enough impedance to avoid a sustained arc", and a capacitor in parallel [read]. They also report that pulse rate changes with the parallel capacitance and the series resistance [read], as the formula predicts.

3.3 Field emission: Fowler-Nordheim

The current density of electrons tunnelling out of a metal is

J = (a F^2 / phi) exp( -b phi^(3/2) / F ), F = beta E

• J: emitted current density (A/m^2).
• F: the local electric field at the emitting spot (V/m).
• E: the average (macroscopic) field, e.g. voltage divided by gap.
• beta: field-enhancement factor (dimensionless) from whiskers, grain edges, oxide and dust.
• phi: work function of the metal (eV), about 4.1 eV for aluminium [memory, high].
• a ≈ 1.54 x 10^-6 A eV V^-2 and b ≈ 6.83 x 10^9 eV^(-3/2) V/m are combinations of fundamental constants [memory, high].

The exponential means emission switches on sharply once F approaches about 10^9 V/m. What matters is F at the emitting spot, not the average E.

3.4 Vacuum-arc cathode spots and recoil forces

In an arc, current concentrates in tiny cathode spots that explosively vaporise metal. Measured cathode-spot ions have directed kinetic energies of about 19-150 eV and speeds of order 10^4 m/s, with several charge states [web: https://www.osti.gov/servlets/purl/810482, A. Anders review]. The jet of plasma leaving the cathode pushes back on it. Tanberg (1930) measured this recoil and the ion speeds [read: cited in the printout]; the standard explanation is momentum carried by the plasma jet, F = (mass flow) x (speed) [memory, medium].

3.5 Magnetic force between moving charges

Introductory E&M (Griffiths) gives the Lorentz force on charge q moving with velocity v: F = q(E + v x B). For the magnetic field made by a second slow-moving charge q' with velocity v' at displacement r from it (the point-charge Biot-Savart law), the force on q is, in SI units,

F = (mu0 / 4 pi) (q q' / r^3) v x (v' x r) = (mu0 / 4 pi) (q q' / r^3) [ (v . r) v' - (v . v') r ]

• mu0 / 4 pi = 10^-7 N/A^2 (the magnetic constant over 4 pi); r points from q' to q; the dot is the scalar product, x the cross product.

This force between two isolated moving charges is not always equal and opposite to the force on the other one; standard electrodynamics restores momentum conservation by counting momentum stored in the electromagnetic field [memory, high]. That gap is where alternative force laws (Ampère's, Weber's, Aspden's) have historically tried to enter.

3.6 Energy conservation and the "zero-point"

In any closed circuit, energy delivered to loads plus losses equals energy taken from sources. The quantum vacuum's "zero-point energy" is the energy of the lowest possible state; you cannot extract energy by going lower than the lowest state. The Casimir effect is a static force between plates set by boundaries, not a continuous power source [memory, high; no verdict depends on this].

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4. Where the Correas depart

The exact point of departure is not a new equation. It is bookkeeping: which voltage multiplies the input current, which current normalises the force, and which energy is shared among the ions. At each point the Correas chose the convention that makes the effect large, and the text does not justify the choice. The one place where real physics may be unexplained is the high-vacuum tubes, and there the problem is that the key quantity (the pressure, and what gas is present) was measured only on the pump side at seal-off, never inside a tube that had been running.

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5. Worked example: does the energy add up for one pulse?

This follows the inventors' own "typical PAGD" paragraph [read, printout p. 39, section "Anomalous Reaction Forces in the PAGD Regime"]. All steps are reproduced by example.py.

Given [read]: mean net pulse energy E = 86.4 J (the text calls it "net": output reactor energy minus input reactor energy, so it already assumes a surplus); cathode metal ejected per pulse V = 3.1 x 10^-8 cm^3; density used rho = 1.86 g/cm^3; pulse lasts 40-50 ms; reactor pulse voltages 100-500 V; drive-pack voltage about 549-565 V (Table 7).

Step 1. Mass ejected. m = rho V = 1.86 x 3.1 x 10^-8 = 5.77 x 10^-8 g. (Text: 5.8 x 10^-8 g.)

Step 2. Number of ions. One Al atom weighs 26.98 u = 26.98 x 1.661 x 10^-24 g = 4.48 x 10^-23 g. N = 5.77 x 10^-8 / 4.48 x 10^-23 = 1.29 x 10^15 ions. (Text: 1.3 x 10^15.)

Step 3. Their ion energy. Share the whole 86.4 J among N ions: 86.4 / 1.29 x 10^15 = 6.71 x 10^-14 J = 4.19 x 10^5 eV. (Text: 4.8 x 10^5 eV. The printed figure corresponds to about 100 J, not 86.4 J [deep read 4]; the mismatch is a slip and does not change the conclusion.) Note what has happened: the ion energy is the claimed pulse energy divided by the ion count. Nobody measured it. The 86.4 J is also not an ion energy in the first place: it is a net electrical figure (output minus input), and it cannot be traced to any row of the authors' own Table 14 [deep read 4].

Step 4. Their ion speed. v = sqrt(2 KE / m_atom) = sqrt(2 x 6.71 x 10^-14 J / 4.48 x 10^-26 kg) = 1.73 x 10^6 m/s = 1.7 x 10^8 cm/s. This matches the text's 1.7 x 10^8 cm/s, confirming Step 3 is their method.

Step 5. What the electric field can supply. The only thing in the tube that accelerates ions is the voltage, at most about 560 V. Each ion can gain z e V:

Even the impossible upper bound falls 58 times short of 86.4 J.

Step 6. What it costs to vaporise the metal. Heat aluminium from 300 K to its boiling point 2743 K (molar heat capacity 24.2 J/(mol K)), melt it (10.71 kJ/mol), vaporise it (284 kJ/mol) [web: https://en.wikipedia.org/wiki/Aluminium]: 24.2 x 2443 + 10,710 + 284,000 = 354 kJ/mol = 13.1 kJ/g. For 5.77 x 10^-8 g that is 7.6 x 10^-4 J, about 100,000 times less than 86.4 J. So the energy in the ejected metal cannot be the 86.4 J either.

Step 7. Density check. Aluminium's density is 2.70 g/cm^3 [web: https://en.wikipedia.org/wiki/Aluminium], not 1.86. (The plates were partly "Alzak", an anodised finish; whether 1.86 refers to that is unknown.) With 2.70: m = 8.4 x 10^-8 g, N = 1.9 x 10^15, E/N = 2.9 x 10^5 eV. Same order; nothing changes.

Step 8. Compare with measurement. Measured cathode-spot ions move at about 10^4 m/s [web: OSTI 810482]. The claimed 1.73 x 10^6 m/s is 170 times faster.

Step 9. The force and the "100x" figure. The momentum carried per pulse is m v = 5.77 x 10^-8 g x 1.73 x 10^8 cm/s = 10.0 g cm/s. "Tanberg's formula" F = m v / 1.39, as printed, gives units of momentum, not force. Dividing also by the pulse time gives 10.0 / 1.39 / 0.050 s = 144 dyn, which reproduces their 143.6 dyn (180 dyn at 40 ms) [calc]. But this force uses the speed from Step 4, so it inherits the circular reasoning. Graneau's figure of merit is k = F / [(mu0/4pi) i^2] with F in newtons. 143.6 dyn = 1.436 x 10^-3 N. - With i = 1.6 A (the DC input current, used in Table 15 [read]): k = 1.436 x 10^-3 / (10^-7 x 2.56) = 5,600. This is the "100 times vacuum arcs" value. - The text itself says pulse currents in the reactor are "of the order of 0.5 to >200 A", and ">150 A" at 1.2-1.7 A input [read: p.39-40]. With an assumed 150 A: k = 1.436 x 10^-3 / (10^-7 x 22,500) = 0.64 (1.09 for the 245.2 dyn reading). The anomaly vanishes. Solving for the current at which k equals the vacuum-arc value of about 100 gives i = 12.0 A (143.6 dyn) or 15.7 A (245.2 dyn) [calc, deep read 4]. So "10 to 100 times vacuum arcs" holds only if the pulse current stayed under 12-16 A, against the authors' own statements. No peak current was reported for the force runs.

Step 10. One row of the headline table. Table 7, run 1 [read]: drive pack X = 562 V, plate voltage Y = 350 V, drive current I = 0.65 A; charge pack 375 V at 1.25 A. - Charge-pack power: 375 x 1.25 = 468.8 W (table: 468.8). - Printed "drive pack total watts": 137.8 W = (562 - 350) x 0.65. It subtracts the plate voltage. - Printed efficiency: 468.8 / 137.8 = 340%.

What (X - Y) x I is. The circuit drawing (US 5,449,989, FIG. 9) shows, in words: the drive pack's positive terminal feeds a diode D1, then the ballast resistor R1, then the tube's anode; current leaves the cathode through a second diode D4 and returns to the pack. That is one series loop. The charge pack sits on a separate rectifier bridge that touches the tube only through two capacitors, C3 and C5; the authors say the aim is "DC isolation of the two battery packs" [read: deep read, page images pp.6-8 and p.18]. Kirchhoff's voltage law around the drive loop gives X = V(R1) + V(diodes) + Y, where Y is the voltage across the tube. So X - Y is the voltage across the ballast and diodes, and (X - Y) x I is the power heating the ballast. The table itself confirms this: its column "Total Resistance" equals (X - Y) / I, here 212 / 0.65 = 326 ohms, which is the size of a ballast resistor (R1 is 300 or 600 ohms elsewhere in the patent) [read; calc]. The drive pack delivers X x I, of which 138 W heats the ballast and 228 W goes into the tube. - The drive pack's actual output: 562 x 0.65 = 365.3 W. Efficiency: 468.8 / 365.3 = 128%.

Step 11. All 14 rows. example.py Part D repeats Step 10 for every row of Table 7 (values checked against the original scan). On X x I the ratios run from 57% to 146%, median 92%; 10 of 14 runs are at or below 100%, and only rows 1, 4, 10 and 13 (104-146%) stay above [calc; arbiter]. Those four are ratios of 10-second meter readings on pulsed currents, read on rms meters in an unstated mode (section 2), and they compare charging power into one battery with discharge power from another. They are not an energy balance over time. Two further facts weaken them: adding cells to the charge pack changes the pulse rate (29 to 31 cells cuts it 10-fold; more cells stop the pulsing), so the "output" battery is part of the oscillator, not a passive meter; and at about 0.5 A applied, the pulse rms current is up to 7.5 times the DC current [read: digest of US 5,449,989 pp.18, 20].

Step 12. Three energy-budget checks (example.py Part D). - Energy per gram of cathode. The authors call cathode erosion "a fuel consumption process" [read]. If 86.4 J came from 5.77 x 10^-8 g of metal, that is 1.5 x 10^9 J/g: about 50,000 times the energy of burning aluminium (about 31 kJ/g [memory, high]) and about 2% of complete uranium fission (about 8 x 10^10 J/g [memory, high]). Either the 86.4 J is wrong, or the metal is not the fuel. - Table 8's floor. The authors state the drive current is 0.2-0.6 A from a pack at 489-590 V [read], so the pack must deliver at least 0.2 x 489 = 98 W. Table 8 books average drive-pack losses of only 5.6-89 W, all below that floor [read; arbiter]. Its losses are underbooked, so its 406-3,485% gains are not an energy balance. - Table 5's impossible power. Run 6 books 1.551 kWh lost from the drive pack in 21.5 minutes, an average of 4,330 W. Through a 300-ohm ballast from 589 V the most that can flow, even with the tube a dead short, is 589^2 / 300 = 1,160 W [read; calc]. The open-voltage method behind Table 5, including its 6,750% run 5, is therefore not measuring energy. - The per-pulse tables (12-16, "3 to over 50 times"). Every "input energy per pulse" in Table 13 reproduces as V x I_DC x t_pulse, so it counts only the conduction time of the pulse, not the recharge between pulses [deep read 4]. The largest ratios (28-60x) sit at the lowest pulse rate (0.2 pulses/s), as that omission would predict. The "reactor energies" (for example 367.7, 261.5 and 71.5 J) match (1/2) C V^2 on the 17.5 mF capacitor bank at 90-205 V, and the "dynamic capacitance 0.2-80 mF" the authors attribute to the tube is back-calculated as 2E / V^2, which brackets the external bank, not the tube's own few picofarads [calc, deep read 4; inference]. The integration window and instrument bandwidth are not stated. Oscillograms that Dr. Correa later supplied to Carrell suggest the drive pack draws little current between pulses in some runs, which weakens the "omitted recharge" explanation for those runs; but they are the inventors' traces, uncalibrated in print [web: http://www.rohnermachine.com/Files/CPAGD.pdf]. The per-pulse figures are not an independent measurement of net energy.

Try it yourself: safety first. Every step above is a pencil-and-calculator exercise, and example.py reproduces them; you do not need to build anything. If you go further and try the cheap experiment in section 7, keep to the low-voltage gas-pressure regime the energy runs used (0.09-1.5 Torr, a few hundred volts, behind a ballast resistor). Do not build or run a sealed or diffusion-pumped high-vacuum tube. The authors report that at higher vacua (below about 10^-5 Torr in their text) and higher voltages the PAGD "gives way to the production of cathode rays and very weak x-rays" [read: US 5,502,354, scan p.23; printout p.31], and that their 25 kV tube processing produced x-rays at the plate edges detectable with a Geiger counter at 10^-6 Torr [read: US 5,502,354, scan p.20; printout p.30]. Any such work needs radiation shielding, a dosimeter and qualified supervision. Even in the gas regime, about 560 V DC from large battery banks and capacitors of tens of millifarads can kill: the 17.5 mF bank at 560 V holds about 2.7 kJ (Check yourself, question 4).

What the example teaches. Step 5 is the decisive check: whatever the mechanism, energy given to a charge by a voltage is charge times voltage. When a derived number violates that by a factor of hundreds, the derivation, not physics, is at fault. Step 10 shows how a single choice of convention turns 128% into 340%, and Kirchhoff's voltage law applied to the authors' own drawing shows which convention is right. Step 12 shows the habit to build: before believing any energy figure, check it against the largest power the circuit could possibly carry.

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6. Evidence table

No document in the folder, and nothing the reviewers found, records a refusal to test or blocked publication. The only documented obstacle is the lab running out of funds [read].

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7. What a learner should take away

Solid. - A DC-fed, ballasted, capacitor-shunted cold-cathode tube self-pulses, and its rate depends on R, C and gas pressure. The Correas' systematic measurements of this are a respectable piece of discharge engineering. - Such a tube can drive a motor as a crude DC-to-AC inverter. - Cathode recoil forces from discharges are real and were measured by Tanberg in 1930.

Wrong, and why the mistake is instructive. - Average vs local field. Comparing the gap-average field with Fowler-Nordheim ignores field enhancement and ignores that the tube is a gas discharge. Lesson: use a law only in the regime and with the variable it is written for. - Circular inference. The "0.5 MeV ions" come from assuming the energy surplus and then dividing it among the ions. A quantity derived from the claim cannot be evidence for the claim. - Energy per charge. Charges cannot gain more than z e V from a voltage V. This one-line check rules out the ion-energy figure without any experiment. - Normalisation choice. Dividing a force by the small DC current instead of the large pulse current creates a "100x" anomaly. Always ask what a figure of merit was divided by. - Power bookkeeping. Subtracting the tube voltage from the drive voltage before computing input power makes input look smaller. Kirchhoff's voltage law on the authors' own drawing shows that (X - Y) x I is the heat in the ballast resistor. A battery supplies its terminal voltage times its current, whatever happens downstream. - Check the ceiling. An energy figure that needs more power than the circuit can carry (Table 5 run 6: 4.3 kW through a ballast that allows 1.2 kW) is a measurement-method failure, whatever it seems to show. - Batteries as meters. Small apparent gains in lead-acid state of charge are within what relaxation, rate and history effects can produce. The authors themselves say the open-circuit method "in all likelihood, overestimates", that their methods disagree by up to 10-fold, and that "the energy captured by this circuit at the output, is not directly related to that utilized in triggering the pulses from the input" [read]. The output battery also sets the pulse rate, so it is part of the oscillator, not a neutral meter. Lead-acid makers recommend 24 hours' rest before a voltage-based reading; the Correas allowed 15 minutes [web: batteryuniversity.com BU-903; read]. Even Mike Carrell, a sympathetic writer, conceded that the rms meters "were probably not giving accurate readings because of the low duty cycle of the pulses" and that Table 8's losses are "differences of large numbers" [web: rohnermachine.com/Files/CPAGD.pdf]. - Energy from a capacitor is not energy from nowhere. The per-pulse "reactor energies" match the energy stored in the authors' own 17.5 mF capacitor bank, and the "input" per pulse leaves out the recharge time. Before crediting a pulse with net energy, ask where every storage element in the circuit started and ended the cycle.

Genuinely open. - The sealed high-vacuum tubes (1-2 x 10^-6 Torr, a Penning-gauge reading on the pumping system at seal-off) and the plate-area effect. Paschen's law cannot explain them, but nobody measured the pressure or the gas (residual argon, pump-oil vapour, hydrogen) inside a tube after it had run. Measuring both inside the sealed tube (a residual-gas analyser), plus breakdown voltage against plate area with a calibrated surface-field map and edge-field controls, would settle whether anything beyond ordinary vacuum breakdown is going on. Two unexplored clues point to surface and oxide effects: a polarity asymmetry (2 A against 200 mA peak) and a factor of 9 in pulse counts between anodised (Alzak) and bare (H34) aluminium [read: pp.30-31, 34]. - The four Table 7 runs at 104-146% on X x I. Candidates: rms-mode meters on pulsed currents, comparing charging power with discharge power, and battery surface-charge effects. None has been checked. - The one 245 dyn balance reading: was it per pulse or time-averaged (a factor of about 70 apart), and at what peak current? - How a motor ran at 2800-3000 rpm on 10 pulses per second (a remark in US 5,449,989), well above the 600 rpm synchronous speed of a 2-pole motor at 10 Hz [calc]. It would need about 5 cycles per pulse; a ring-down in the motor-capacitor circuit is a plausible hypothesis, not shown. - The decisive experiment is cheap: run the circuit from a calibrated DC supply into a resistive load, log drive voltage, drive current and output current continuously, integrate true mean power at both ports with a wide-bandwidth power analyser (or calorimetry) for hours, then try closing the loop. Nobody has published it (none found). Safety: this is lethal-voltage work (about 560 V DC from large battery banks and capacitors of tens of millifarads). Keep to the gas-filled regime of the energy runs (0.09-1.5 Torr). The authors report that at higher vacua (below about 10^-5 Torr in their text) and higher voltages the tube gives "cathode rays and very weak x-rays" [read: US 5,502,354, scan p.23], and their 25 kV processing made x-rays at 10^-6 Torr [read: scan p.20]. Do not build or run a sealed high-vacuum tube without radiation shielding, a dosimeter and qualified supervision (see the safety note at the end of section 5).

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8. Check yourself

1. The Correas say the average field in their gap (about 2 x 10^4 V/m) is far too small for Fowler-Nordheim emission. Give two separate reasons why this does not show that the emission is anomalous.
2. Table 7, run 13 [read]: X = 553 V, Y = 438 V, I = 0.35 A; charge pack 381.5 V at 0.59 A. Compute the printed efficiency and the efficiency on the drive pack's terminal power. Then compute (X - Y) / I and say what physical part of the circuit that number, and the printed "drive pack watts", describe.
3. Suppose you want the 1.29 x 10^15 ions from the worked example to carry 86.4 J using only a 560 V supply and singly charged ions. What voltage would you actually need? Is this consistent with the tube's stated reactor voltages?
4. The Correas used series capacitors as large as 17.5 mF in their pulse measurements [read via reviewers]. How much energy does such a capacitor hold at 560 V? Why does that make a per-pulse "output energy" of 100-350 J, read off an oscilloscope, weak evidence of net gain?
5. A relaxation oscillator has V_s = 560 V, V_b = 500 V, V_ext = 300 V, R = 100 kOhm and C = 1 microfarad. What is the pulse period, and what happens to the pulse rate if R is doubled?

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9. Further reading

Mainstream - Yu. P. Raizer, Gas Discharge Physics, Springer, 1991: breakdown, glow and arc regimes. [memory, high] - M. A. Lieberman and A. J. Lichtenberg, Principles of Plasma Discharges and Materials Processing, 2nd ed., Wiley, 2005. [memory, high] - A. Anders, Cathodic Arcs: From Fractal Spots to Energetic Condensation, Springer, 2008 [memory, high]; and the shorter Anders review at https://www.osti.gov/servlets/purl/810482 [web] for cathode-spot ion energies. - R. H. Fowler and L. Nordheim, "Electron emission in intense electric fields", Proc. R. Soc. A 119, 173 (1928). [memory, high] - D. J. Griffiths, Introduction to Electrodynamics: Lorentz force, Biot-Savart law, field momentum. - Paschen's law summary with constants: https://en.wikipedia.org/wiki/Paschen's_law [web] - R. V. Latham (ed.), High Voltage Vacuum Insulation: Basic Concepts and Technological Practice, Academic Press, 1995: vacuum breakdown, field-emission sites, microparticles; the mainstream frame for the sealed high-vacuum tubes. [memory, medium] - D. Linden and T. Reddy (eds.), Handbook of Batteries, McGraw-Hill: lead-acid behaviour. [memory, high] - Battery University, "BU-903: How to Measure State-of-charge", https://batteryuniversity.com/article/bu-903-how-to-measure-state-of-charge [web]: surface charge and rest times for lead-acid.

The Correas' own work - US 5,416,391, "Electromechanical transduction of plasma pulses" (1995). [read, in the printout] - US 5,449,989, "Energy conversion system" (1995). [read, page images and printout] - US 5,502,354, "Direct current energized pulse generator utilizing autogenous cyclical pulsed abnormal glow discharges" (1996). [read, page images and printout] - rexresearch.com compilation "Pulsed Abnormal Glow Discharges (PAGD)", including the press release and "Power From Autoelectronic Emissions" (in the project folder). [read] - Correa publication list: https://www.aetherometry.com/correa_publications.php [web, via mathematician review] - M. Carrell, "The Correa Invention: An Overview and an Investigation in Progress" and "The Correa PAGD Reactor: Errata and Supplement" (Infinite Energy), reprinted as http://www.rohnermachine.com/Files/CPAGD.pdf (2007) [web]: a sympathetic explanation relaying Correa-supplied data, not an independent test. - Background on Aspden's force law: H. Aspden, "The law of electrodynamics", J. Franklin Inst. 287, 197 (1969) [read: cited in the printout; not checked].

Earlier work and people the Correas cite [read: digests of the printout, mainly PAGD.01-02 (pp.2-4); not checked further]: Ernesto Manuel's 1969 patent on pulsed abnormal glow discharges (US 3,471,316); A. Chernetskii's 1989 discharge "reactor" (reported by Novosti); Tanberg's 1930 cathode-recoil measurements; Kimblin and Plyutto on vacuum-arc ion flows; Compton's finding that the vapour jet carries under 2% of the arc's energy; patents by G. Spence; claims by W. Reich and T. H. Moray. The second laboratory involved was ABRI (Aurora Biophysics Research Institute). The printout also carries endorsements by W. Tiller, M. Carrell and U. Soudak; these are testimonials, not tests.

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Answers

1. (a) Fowler-Nordheim depends on the local field at the emitting spot, F = beta E; microscopic whiskers and adsorbed layers raise it by large factors, so a small average field says little about the local one. (b) The gas-filled tubes used in the energy runs operate at 0.09-1.5 Torr, where gas (Townsend) breakdown sets the firing voltage; Paschen's law gives about 426 V for 0.8 Torr x 3 cm air against the observed 500-560 V. Field emission is not needed. This second reason does not cover the tubes sealed at 1-2 x 10^-6 Torr, far left of the Paschen minimum; for those, reason (a) and ordinary vacuum breakdown are the mainstream candidates, and the question was never properly tested.
2. Printed: (553 - 438) x 0.35 = 40.25 W input; 381.5 x 0.59 = 225.1 W output; 225.1 / 40.25 = 559%, printed as 563% (they rounded the input to 40 W). Terminal: 553 x 0.35 = 193.6 W, so 225.1 / 193.6 = 116%. (X - Y) / I = 115 / 0.35 = 329 ohms, the resistance of the ballast resistor plus the input diodes, which are in series with the tube (FIG. 9). So the printed "drive pack watts" is the heat in the ballast, not what the battery delivers.
3. E = N e V gives V = 86.4 / (1.29 x 10^15 x 1.602 x 10^-19) = 4.2 x 10^5 V, about 420 kV. The text says reactor voltages are 100-500 V and cannot exceed breakdown, so the ion energy contradicts the authors' own description.
4. E = (1/2)(0.0175 F)(560 V)^2 = 2,744 J, about 2.7 kJ. A few hundred joules flowing into and back out of such a capacitor each cycle is circulating energy, not net energy; integrating v x i over part of a cycle can show large "output" with zero net transfer. Only a full-cycle, both-ports measurement of true mean power settles it.
5. T = R C ln[(V_s - V_ext)/(V_s - V_b)] = 10^5 x 10^-6 x ln(260/60) = 0.1 x 1.466 = 0.147 s, about 6.8 pulses per second. Doubling R doubles T, halving the rate (to about 3.4 per second).