Feature: > "Fundamental Principles of Electrical Discharges"
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4/23/08 – Withdrawal of our P-o-C Webpages: As I prepare to conduct the final series of firing trials with our prototype EDF Generator experimental assembly, Archer Energy Systems, Inc. and I regret to announce that publication of both our proof-of-concept webpages is hereby withrawn due to serious and strategic intellectual property concerns. Although the large and complex 2nd PoC Experiment page (./pro_concept2.html) in particular draws several hundred visitors per week, to my great disappointment it seems to generate no intelligent feedback whatsoever . . .
I have kept building and updating that page for quite some time now, making a quality and much-too comprehensive presentation of our significant R&D achievements, in the mistaken and perhaps naïve hope that it would stimulate some serious academic and investor interest – largely in vain . . . As a matter of fact, in the five weeks since I first posted the closing section of the 2nd PoC page's technical disclosure, I've received not a single e-mail or phone call about it from any unaffiliated party!
I've found that the very great number of people who would ordinarily be expected to love "StarDrive Engineering" and the EDF Generator technology for some reason do not, and just don't have much to say about it at all; at least those who repudiate it seem to do likewise, but only because it represents impeccable work and they haven't the ability to even begin refuting it . . .
Fortunately, I believe we have arrangements in place to demonstrate the p-o-c assembly for qualified and unbiased academic visitors of stature in the coming weeks, who will be able to verify our simple and unambiguous test results – should they be as we expect or otherwise. Once we have those results analyzed, and written up in a way that satisfies counsel and does not create IP security issues, we will republish both PoC Experiment webpages with as little editorial revision as possible.
In the meantime, those of you (if you're out there . . .) who regret not having a chance (or taking the time) to download or print any of this unique technical material may contact me about it and we will handle any subsequent requests for that information on a case-by-case basis. [A standard non-disclosure/non-competition agreement will almost certainly be required.]
Sincerely,
Mark R. Tomion
Pres.
Archer Energy Systems, Inc.
Fundamental Principles: top of page
[The material in this section is adapted from "Electrical Discharges": www.du.edu/~jcalvert/phys/dischg.htm]
A typical laboratory discharge is depicted at right, taking place in a glass tube with nickel or tungsten electrodes. The voltage source Eb is connected in series with a current-limiting resistance Rb, so that the voltage between anode and cathode is ΔV = Eb – IRb. This relation is expressed by the load lines in the diagram, for values of Rb equal to R1 > R2 > R3. The irregular curve is the V-I characteristics graph, distorted a bit to show the various regions conveniently. Point A is a "stable point of operation" for Rb = R1 : suppose that the line current I is slightly reduced, by either increasing Rb or reducing source voltage Eb. Then, ΔV becomes greater, according to the load line formula, since the resistor voltage drop (= IRb) between the anode and dc source (battery) is reduced. The now-higher remaining source voltage that gets applied to the discharge's electrodes acts to increase the line current, tending to restore it to its value before the change. If the line current is slightly increased, ΔV is reduced while the ballast resistor voltage drop increases, again tending to bring operating Point A back to the original current level. This will always be the case when the slope of the discharge's V-I curve is greater at the operating point than that of the load line, in this portion of the graph. At point A, the current is no more than a microamp; the discharge is dark and not self-sustaining, and is said to be taking place in the "Townsend region". [A Townsend discharge could be seen as decreasingly current-regulating as its source line voltage rises toward that operating point where the slope of its V-I curve equals the slope of the load line, and increasingly voltage-regulating beyond that point.]
Now consider Rb as being reduced steadily from R1 to R2. The operating Point A moves up the curve until the sparking or "firing" potential (Vf) is reached at Point A1. Immediately upon firing, the voltage between the electrodes drops to about 75 to 78% of its original value (generally, depending on voltage and inert gas parameters) at Point A2. Between the Points A2 and B are stable points of operation for R1 < Rb < R2. This is the "normal glow" region in which the voltage regulating action exhibited by a gas discharge – within a characteristic operating range – is clearly apparent, and its expressed voltage drop ΔV will remain constant across a broad range of values for Eb and Rb. The discharge is now self-sustaining, and can only be extinguished by reducing Eb nearly or completely to zero volts; but cathode heating is not yet sufficient to cause or allow transition to an arc discharge operating condition. [To recap, the voltage drop across a normal glow discharge remains essentially constant as its line current changes, throughout the normal-glow region.]
But, if Rb is further decreased toward R3 (or Eb is increased accordingly), the voltage across the discharge increases until Point B' is reached. Between Points B and B' is the "abnormal glow" region wherein voltage regulating action is no longer strictly expressed, and ΔV will no longer stay constant with significant decreases in Rb or increases in Eb. It could be said that an abnormal glow discharge is decreasingly voltage-regulating as its source line voltage rises until the operating point where the slope of its V-I curve equals the slope of the load line, and increasingly current-regulating beyond that point (as its expressed voltage drop increases progressively to the characteristics curve's peak post-strike value).
While B' is stable for small current fluctuations, cathode heating may be sufficient to increase the electron supply by thermionic emission and lower the discharge voltage. This change is cooperative, and the discharge characteristic can quickly move to point C, where ΔV is lower and I is far greater. This is the "glow-arc transition" region, in which true negative resistance is expressed (in that the discharge's voltage drop decreases with increasing current); and yet operating point C is stable as well. However, if Rb is reduced further still, an arc discharge would result wherein the current can increase without bound until the weakest conductor in the current path melts.
We can analyze the initial breakdown of the discharge that produces the striking or 'firing' spark by assuming that every electron emitted from the cathode creates an avalanche, and that the positive ions from this avalanche return to the cathode and liberate new electrons to join the discharge. If no electrons are emitted from the cathode, at a distance x they have multiplied to n and the electrons added to the avalanche in a distance dx will be dn = αndx, proportional both to the net number of electrons and to the distance dx. The factor α is the probability of releasing a new electron per unit length, and is generally a function of a constant electric field E (for plane-parallel electrodes, and in the absence of space-charge effects); and if α is therefore also constant, by integration we find that n = noeαx, which is the equation for exponential growth (wherein e is the base of natural logarithms, 'equal' to 2.71828...).
The number of electrons that arrive at the anode will be n = noeαd, where d is the distance from the cathode to the anode. The number of positive ions produced in the avalanche will be n - no, and we will assume that all return to the cathode where they release γ(n - no) new electrons, the factor γ expressing the efficiency of those ions in liberating additional electrons. The net number of electrons leaving the cathode will therefore be equal to no + γ(n - no), and the number eventually reaching the anode will be: n = [n+ γ(n - no)]eαd. Solving for n, and provided eαd is much greater than 1, we will find that n = noeαd/(1 - γ(eαd - 1)]. Moreover, if eαd increases to 1/γ, the denominator vanishes and the number of electrons reaching the anode increases without limit.
This is variously called the "sparking" or breakdown point, which will occur at a particular striking or firing voltage between the electrodes. The dependence of factor α on the applied electric field E is described by a complex empirical formula wherein α/p will be constant as the pressure changes, and two constants A and B express gas-dependent discharge characteristics. We can then obtain a rough estimate of the breakdown potential by finding a value of E for which eαd = 1/γ; whereby Vf is equal to Bpd/ln[Apd/ln(1/γ)], or to C1(pd)/ln[C2(pd)] in terms of new gas constants that can be empirically tabulated. The important thing about these mathematical relations is that the breakdown potential is a function of the product 'pd' (or pressure times gap distance) only, an axiom that is now called Paschen's Law. Moreover, by setting the derivative of Vf equal to zero with respect to 'pd', we find that breakdown potential has a minimum value when C2(pd) = 1, or pd = e ln(1/γ)/A.
The firing voltage as a function of pd for air is shown in the empirically-derived graph at right, and indicates a minimum of 327 V at pd = 5.67 Torr-mm. From the ionization constants for air, we find 266 V by the given equation – or within 20% of agreement with the value determined experimentally. With pd = 2000 Torr-mm the striking voltage is 10kV, and at 4500 Torr-mm it is 20kV. These figures are for plane-parallel electrodes, so they give the firing voltages for the corresponding values of field strength (since E = V/d). It can also be seen, of course, that the firing voltage decreases with increases in gas pressure for all values of pd below that at which the minimum strike voltage will result.
The minimum value of the firing potential has a strange consequence: For devices intended to be operated at values of 'pd' to the left of the minimum (in the negative-slope region), if the discharge has a choice of two paths of different lengths it will choose the longer path because it breaks down at a lower voltage (to the right of the minimum, if possible). In such a case, bringing the electrodes closer together can actually increase the breakdown voltage. Breakdown can and will occur: (i) as the voltage is raised; (ii) as the cathode-to-anode distance is increased; or (iii) as the gas pressure's reduced (for pd to the right of the minimum). Space charges can cause the voltage distribution to change, and increased space charge fields have the same effect as an increase in the overall voltage.
It has been assumed and shown herein that the mechanism of breakdown comprises electron avalanches and positive-ion production of electrons at the cathode. The excited positive ions can also emit radiation that ejects photoelectrons from the cathode with the same effect, and cathode heating due to high levels of ion bombardment can liberate even more discharge electrons through thermionic emission. Thus, a complex cooperative amplification of the electron current can occur which perhaps greatly exceeds that expected or desired, without adequately precise control of a gas discharge's primary operating parameters (i.e., the voltage, pressure, and electrode gap).
Even so, it's important to point out that many other factors have an effect on the breakdown of a discharge gap, besides the described cathode photoelectric and thermal emission effects, including dust, moisture, non-uniformity of gap, and even choice of electrode material. It is also interesting to note that Paschen's Law [essentially ΔVstrike = ƒ(pd)] should perhaps be restated such that ΔVstrike = ƒ(Nd), where N is the actual molecular gas density – taking into account gas temperature as well as pressure according to the ideal gas equation [wherein N = pV/kT ; k is Boltzmann's constant and V in this case is the gas volume]. Ultimately, intensive theoretical analysis may be helpful in providing a good model for electrode gap breakdown mechanisms, but will not necessarily provide a precise value for the breakdown voltage in any particular situation . . . top of this section top of page
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