electrical discharges - how the spark, glow and arc work

Electrical Discharges

How the spark, glow and arc work

Contents

Introduction: fundamental processesi.The Voltage-Current Characteristicsii.The Spark: Breakdown: electron avalanche, Townsend discharge, Paschen's Law, Geiger-Müllertube

iii.

The Glow Discharge: cathode phenomena, positive column, laser pumping, similitude, sputteringiv.The Arc Discharge: cathode phenomena, low- and high-pressure plasma, negative resistance,carbon arc in air

v.

Applications of Arcs: welding, lamps, rectifiers, switching, protection, fuses.vi.Referencesvii.

Introduction

An electrical discharge results from the creation of a conducting path between two points of different electricalpotential in the medium in which the points are immersed. If the supply of electrical charge is continuous, thedischarge is permanent, but otherwise it is temporary, and serves to equalize the potentials. Usually, the medium is agas, often the atmosphere, and the potential difference is a large one, from a few hundred volts to millions of volts.If the two points are separated by a vacuum, there can be no discharge. The transfer of matter between the twopoints is necessary, since only matter can carry electric charge. This matter is usually electrons, each carrying a

charge of 4.803 x 10-10 esu. Electrons are very light, 9.109 x 10-28 g, and so can be moved with little effort.However, ions can also carry charge, although they are more than 1836 times heavier, and sometimes are importantcarriers. Where both electrons and ions are available, however, the electrons carry the majority of the current. Ionscan be positively or negatively charged, usually positively, and carry small multiples of the electronic charge.

Electrical discharges have been studied since the middle of the 19th century, when vacuum pumps and sources ofcurrent electricity became available. These laboratory discharges in partially-evacuated tubes are very familiar, butthere are also electrical discharges in nature, lightning being the primary example. There are also the auroraborealis and australis, St. Elmo's Fire, sparks from walking on a rug in dry weather and rubbing cats, cracklingsounds when clothes fresh from the dryer are separated, and similar phenomena, many resulting from the highpotentials of static electricity. Technology offers a wealth of examples, such as arc welding, the corona discharge onhigh-tension lines, fluorescent lamps, including their automatic starters, neon advertising signs, neon and argonglow lamps, mercury and sodium lamps, mercury-arc lamps for illumination and UV, carbon arc lights, vacuumtubes, including gas-filled rectifiers, Nixie numerical indicators and similar devices. Some of these are historical,but all are interesting and often fascinating to watch.

A good reason for this article is also that information on electrical discharges is not easy to find in current literature,in spite of their importance in many fields of physics, astrophysics, atmospheric electricity and engineering. TheMcGraw-Hill Encyclopedia of Physics has no entry for "electrical discharge" or "electric arc," for example. Theclosest one can come are articles on plasma physics, which do not do the job. Plasma physics, as it is generallypresented, is a rather limited field mainly concerned with the luckless search for thermonuclear power. Every daywe see many examples of discharges--street lights, neon signs, fluorescent lamps--so how they work must bevaluable knowledge.

The two termini of a discharge are at different potentials. The higher, or positive, potential is at the anode, while thelower, or negative, potential is at the cathode. These electrodes are often conductors, but need not be. In athunderstorm, a cloud electrode may simply be a region of excess charge distributed over a volume. These nameswere given by Michael Faraday, with the help of the classical scholar William Whewell, when he began to studyelectrochemistry and electrical discharges in the 1830's. The word "anode" is from the Greek "aná-hodos" or "wayin," while "cathode" is from "katá-hodos," or "way out." Electrode is a later creation for "electro-hodos" or "electric

Electrical Discharges http://mysite.du.edu/~jcalvert/phys/dischg.htm

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way," and is noncommttal as to the positive direction of the current. The conventional current is in the direction ofpositive charge, so electrons actually leave at the "way in" and enter at the "way out."

Unless otherwise stated, we shall assume that the medium is a gas predominantly composed of neutral molecules(we won't distinguish between molecules and atoms), which we usually treat as ideal. Then, the pressure p of thegas is simply related to its number density n by p = nkT, where T is the absolute temperature, and k is Boltzmann's

Constant, 1.38 x 10-16 erg/K. If T is in K, and n is in cm-3, then p is in dyne/cm2. In technical work, gas pressure is

measured in mmHg, and 760 mmHg is atmospheric pressure, 1.0123 x 106 dyne/cm3, from which the conversion

can be derived. At one atmosphere and 273K, the number density in a gas is 3.22 x 1018 cm-3, which is the same forall gases (Avogadro's Law). The gas is normally electrically neutral, and contains neither ions nor electrons, and sois a nonconductor. In daily life, we rely on the air to be an insulator in our dealings with electricity.

The electrons, ions and neutral molecules are in incessant thermal motion, because their collisions are perfectly

elastic. In equilibrium, the velocities are distributed according to the Maxwell distribution, f(v) = (m/2πkT)3

/2exp(-mv2/2kT)4πv2, which integrates to unity with respect to dv. The electron temperature Te is usually very

different from the ion and neutral temperature Tn at low pressures, because the electrons receive more energy from

the electric fields in a discharge, and can exchange kinetic energy with the neutrals only with great difficulty, sothey represent a reservoir of kinetic energy that is in very weak contact with the neutrals. The much greater mass ofthe ions and neutrals also means that they move at much lower velocities. Speeds given to the electrons by electricfields are often very much greater than thermal speeds, especially near the cathode, where the electric field is veryhigh. These electrons, naturally, do not have a Maxwellian distribution until they have lost most of their energy ininelastic collisions and ionization. The rms velocity √(3kT/m) is the velocity of a particle with the average energy.Approximately 60% of the particles have less energy, 40% more. The average kinetic energy of a particle attemperature T is (3/2)kT.

If V is the difference in potential between the anode and cathode, and d is the distance between them, then theaverage potential gradient, or electric field, is V/d. Again, in technical work, V is measured in practical volts, thefamiliar ones in which a flashlight battery supplies 1.5 V. The Gaussian unit is the esu, about 300 V, which appearsin theoretical arguments. Therefore, the field E will be in V/cm, or in statvolt/cm, and the conversion between themis easy. This average field will drive a positive ion in its direction, an electron in the opposite direction.

For a discharge to occur, there must usually be a source of electrons at the cathode, and the nature of this sourcecontrols the form of the discharge. Cosmic rays and natural radioactivity continually produce a small number ofelectrons and ions in all gases at the surface of the earth, and this gives air a small conductivity. The electrons willmigrate to the anode, the ions to the cathode, and a small current will flow. This current has no visible effects, andcan be detected and measured only with difficulty, but is always present. Any charged body attracts charges of theopposite sign that sooner or later will neutralize its charge, though the usual reason for the loss of charge isconduction over the surface of the supports of the body, which is normally far greater than the small space currentfrom the ions and electrons normally present in the air.

More copious sources of electrons are necessary for a good discharge. One source is the photoelectric effect, whenlight of sufficiently short wavelength falls on a metal or semiconductor and liberates a photoelectron. Photons canalso be absorbed by a molecule, which gives up an electron and becomes a positive ion. The photon energy hν mustbe greater than the energy required to free the electron, the work function. Thermionic emission, the emission ofelectrons by a heated body, can supply heavy currents. The body must be heated to incandescence, and for efficientemission, its work function must be low. Tungsten has a work function of 4 eV, and has long been used as anelectron emitter, since it also has a high melting point. Alkali metals have a small work function, but cannot be usedby themselves because of their low melting points. Electrons striking a metal surface can knock loose secondaryelectrons readily, but this is of little use for discharges, since the electrons impact the anode, and secondaryelectrons would simply fall back into the anode, not add to the discharge current. However, positive ions can alsocreate secondary electrons. Although this is not an efficient process, it produces electrons at the right place and cansupport a discharge.

Electrons already in the discharge, such as the random electrons produced by cosmic rays and radioactivity, can addto their number by ionizing gas molecules by collision. Each ionizing collision produces a new electron, and apositive ion that moves the other way, an ion pair. An electron cannot do this unless it has acquired sufficientkinetic energy by being accelerated in an electric field. There are two ways this can be done. If the electron makesno collisions, even a small electric field will allow it to accumulate energy in a long-enough run. In this case, KE =


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mv2/2 = eEx, where E is the field and x is the distance travelled. Electron energies are often quoted in electron-volts, abbreviated eV, and such that the energy U in eV is given by eU = eEx, so that U is just the potential drop inthe distance x. On the other hand, if the probability of collision of the electron in a distance dx is dx/L

e, where L

e is

called the electron mean free path, and Le is much smaller than the distance x, then the speed of the electron is

given by v = KE, where K is the electron mobility, in cm/s per V/cm, for example. Then, the only way for theelectron to accelerate is to find a larger field E.

The mean free path L is inversely proportional to the pressure, so pressure has a great effect on how an electrongains energy. The molecules of the gas also have a mean free path, but since molecules are larger, their mean freepath L is shorter than L

e. As an estimate, we can take L

e = 5.64L. In Ne, the mean free path at 760 mmHg and

273K is 1.93 x 10-5 cm, while in air it is 9.6 x 10-6 cm. By "air" we mean the usual mixture of nitrogen and oxygen,and the values are an average.

The energy required to ionize neon, called the ionization energy, in the reaction Ne → Ne+ + e-, is 21.559 eV, andto knock two electrons off requires 41.07 eV. To raise a Ne atom to its first excited state requires 16.58 eV, which iscalled the resonance energy. This gives an idea of the energy required to produce an ion pair. Since most collisionsdo not result in ionization, and there are many ways to fritter energy away uselessly, the average energy per ion pairproduced is greater than the ionization potential, rather closer to twice this value. To give an electron sufficient

energy to ionize Ne at one atmosphere, the field strength would have to be E = 21.559/(5.64)(1.93 x 10-5), or about200,000 V/cm, an extremely high field that would have some untoward effects. At 1 mmHg, the field would have tobe 260 V/cm, a more tractable value.

The energy required to excite a molecule or atom to its first excited state above the ground state is called theresonance energy, and is, of course, less than the ionization energy. The inert gases, which have a closed shell ofelectrons in the ground state, have very large resonance energies. For He, it is 19.81V, and for Ne, 16.62 eV. Theselevels are also metastable, which means that a transition to the ground state by radiation is difficult, and they mayretain their excitation energy for an extended period, perhaps until they collide with a wall, or experience anothercollision with an electron or atom. This makes cumulative ionization possible, where an atom can be ionized bymultiple collisions in which the electrons have insufficient energy to ionize in a single collision. The energy of ametastable can be transferred to a different atom or molecule by a collision of the second kind. Alkali metals, with asingle s electron outside a closed shell, have very low resonance potentials. For sodium, V

i = 5.138V and V

r =

2.102V. For caesium, the figures are 3.893V and 1.39V, respectively. Mercury, often used in discharges, has Vi =

10.43V and Vr = 4.67V, and the lowest excited states, 3P's are metastable to the 1S ground state (but still give a

strong ultraviolet line). The spectroscopic notation is included for those who will appreciate it. The fundamentals ofatomic structure and spectra are important in understanding discharges.

The emission of light is one of the principal characteristics of discharges. Light of a definite frequency is emittedwhen an excited atom falls to a lower energy level. If there is an electric dipole transition moment, then the

transition is called allowed, and occurs in about 10-8 s if nothing intervenes. The collision frequency is about 1011

per second at atmospheric pressure, so usually the excitation energy is lost in a collision before it can be radiated.At 1 mmHg, however, the collision frequency is comparable to the radiation lifetime, and radiation is a possibility.Radiation is always a competetion between de-excitation processes. If the dipole transition moment is forced to bezero by symmetry considerations, then radiation may occur by other means, such as magnetic dipole or quadrupoleradiation, but the radiative lifetime for these is much longer, so they are not seen even at 1 mmHg pressure. Theseare forbidden transitions. They are not really forbidden, just improbable. At higher pressures, excited atoms arecontinually affected by collisions, which broaden the lines emitted. At still higher pressures, the atom states aresmeared out, and the radiation begins to assume the characteristics of black-body thermal radiation.

Mercury has strong lines at 253.65 nm, 404.66 nm, 407.78 nm, 435.84 nm, 546.1 nm, 576.96 nm and 579.06 nm(and many others not as strong). The first is the resonance line in the ultraviolet that strongly excites fluorescence,and the next two are at the short-wavelength limit of human vision. The cyan line at 436 nm, the green line at 546nm, and the yellow doublet at 577 and 579 nm can easily be seen in the spectrum of a fluorescent tube, and shouldbe familiar to all. They can be separated by filters for use in optics experiments, and this was commonly donebefore the He-Ne laser appeared around 1971. The 254 nm, 408 nm and 577 nm lines are all "forbidden" by theusual selection rules, but happen to be very strong in Hg, where singlet-triplet combinations among lower levels arenot very forbidden.


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If an electron frees another by an ionizing collision, then these two can both free additional electrons, and so on.This creates an electron avalanche, which may send a burst of electrons toward the anode, leaving in their wake acloud of slow positive ions that will make their way to the cathode. The net result is to multiply the originalelectron current, an effect used in gas phototubes to increase the photocurrent for a given amount of light. This doesnot start a sustained discharge, but merely increases the current that otherwise would be available. This type ofdischarge produces little light, so it is called a dark or Townsend discharge, after the man who studied them in detailfirst.

That cloud of positive ions will sooner or later collide with the cathode. It is rather unlikely for a positive ion tosnatch an electron from the few that are available while it is moving through the gas. Recombination is a verydifficult process, since only one particle is the outcome, rather than the three particles that come out of anionization, so it is hard to conserve both momentum and energy. Therefore, most of the positive ions created in anelectron avalanche reach a surface eventually, and they are driven to the cathode by the electric field. When theyarrive, they recombine at the surface, and in some cases eject an electron. For Ne on an Fe cathode, one out ofabout every 45 ions produces an electron. However, if the electron avalanche produces more than 45 electrons, thenthere will be sufficient positive ions to replace the electron that originally left the cathode (or came in fromelsewhere). Now the discharge produces its own electrons, without relying on cosmic rays or natural radioactivity,and becomes self-maintained. This is a significant event in the life of a discharge, and usually means that thedischarge becomes evident through light or noise. The potential between anode and cathode at which this occurs iscalled the sparking potential V

s. Now the whole path between anode and cathode becomes conducting because of

the electrons and ions distributed along it.

Unless something limits the current, such as the disappearance of the potential difference, it increases rapidly andwithout bounds. The ion bombardment heats up the cathode surface, which becomes incandescent, and begins toemit electrons thermionically, without reference to the number of ions coming in or the efficiency of the electronavalanche. Any spot that becomes hotter than its neighbor, tends to become even hotter as the extra thermionicelectrons attract the positive ions to the spot. This, the final state of the discharge, is called an arc. The name camefrom the way the path of the discharge, when arranged to be horizontal, rose in a flaming arch, or arc. It requiresvery little potential difference to support the arc, mainly just enough to keep the path of the discharge supplied withions to replace those lost in various ways. A lightning stroke is an example of such a discharge, but with anode andcathode that are quite different from those in a carbon arc light. In the carbon arc light, the discharge is started bydrawing the carbons apart, which produces an arc at once, since the discharge does not have the difficult task ofestablishing a conducting path over a great distance, as in lightning. An arc is also produced whenever an electriccircuit is interrupted, and must be extinguished before it does any damage.

The nature of a discharge depends, as we have seen, on the method for supplying electrons at the cathode, and onhow the discharge is confined. The lightning stroke, and the carbon arc, are both unconfined arcs. The lightningstroke draws its electrons from the cloud, its cathode, and transmits them to the earth, its anode. The carbon arcobtains its electrons from the cathode spot on the negative carbon, which it heats to incandescence. Both areself-confined, the surface of the conducting channel arranging itself so that the net outward current is zero. Adischarge between metal electrodes in a glass tube that gets its electrons from positive-ion bombardment of thecathode, and is confined by the glass walls, is called a glow discharge. Glow discharges are useful and convenientto study, so their properties are very familiar, if not those of the majority of discharges. A discharge may exist in thevicinity of a sharp point, or other place with a small radius of curvature where the electric field is increasedsignificantly from its average value. A negative potential on the point makes it a cathode, while the anode is anindefinite volume in the surrounding gas. A positive potential makes it an anode, and attracts electrons from anindefinite surrounding volume, which becomes the cathode. These two discharges look quite different with constantpotentials, but with alternating current the opposites succeed one another and make an average impression. If thedischarge occurs at about atmospheric pressure, it is called corona.

In any discharge, multiple processes compete at the electrodes and in the gas, so explanations and theories canbecome subjects of dispute. A theory usually takes into account only the principal process operating under theconditions of the problem, and this is often quite satisfactory. Sometimes different assumptions and mechanismscan lead to the same outcome, which further complicates things. The reader should keep in mind that completeexplanations are probably impossible in many cases, and we must be satisfied with qualitative or semi-quantitativeresults. Also, the variety of phenomena in discharges is very rich and depends on many factors, such as purity andsurface preparation, that are difficult to quantify. The whole variety cannot be mentioned here, only what is typicalunder reasonable assumptions. There is great scope for thought and reasoning in this field, which makes itfascinating, along with the beauty of the phenomena.


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The Voltage-Current Characteristics

Let's now consider a typical laboratory discharge, taking place in aglass tube with metallic electrodes. The nature of the electrodes haslittle effect on the characteristics of the discharge. Commonly-usedmaterials are carbon, platinum, iron, nickel or tungsten. The voltagesource E is connected in series with a current-limiting resistance R,so that the voltage between anode and cathode is V = E - IR. Thisrelation is expressed by the load lines in the diagram, for values ofR equal to R

3 > R

2 > R

1. The irregular curve is the V-I

characteristic of this device, distorted to show the various regionsconveniently. Point A is a stable point of operation for R = R

1. This

can be seen as follows: suppose the current I to be slightly reducedfor some reason. Then V becomes greater, according to the loadline, while the voltage between anode and cathode becomessmaller. The difference in voltage acts to increase the current,restoring it to the value before the disturbance. If the current isslightly increased, we find a voltage deficit, which reduces thecurrent, again bringing the operating point back to the originalplace. This will always happen if the V-I curve is more steeplyinclined than the load line. At point A, the current is no more than amicroampere, the discharge is dark, and is not self-sustained. We are in the Townsend region.

Now imagine R reduced steadily from R1 to R

2. Point A moves up the curve until the sparking potential is reached.

Now the voltage is sharply reduced, and the operating point is B, which is stable. The discharge is nowself-sustaining as a glow discharge, and cathode heating is not sufficient to cause transition to an arc. If R is furtherdecreased, towards R

3, the voltage across the discharge increases until point B' is reached. Although B' is stable

with respect to small fluctuations, cathode heating may be enough to increase the electron supply and lower thedischarge voltage. This change is cooperative, and the discharge quickly moves to point C, where V is lower and Iis greater. This is the arc, and operating point C is stable. However, if R is further reduced, the current will increasewithout bound until something melts. The regions where the discharge type changes are shown cross-hatched, toshow that the actual values may not be clearly defined. This characteristic tells a lot about the circuit behavior ofdischarges, but it does not say much about the dynamic relations, only about the stable operating points. We shalldiscuss each of the principal discharge species below.

The Spark: Breakdown

Let's begin by analyzing the initial breakdown of the discharge, that produces the spark. We assume that everyelectron emitted from the cathode creates an avalanche, and that the positive ions from this avalanche return to thecathode and liberate new electrons to join the discharge. Suppose n

o electrons start at the cathode, and at a distance

x they have multiplied to n. The electrons added to the avalanche in a distance dx will be dn = αndx, proportionalboth to the number of electrons, and to the distance dx. The factor α is the probability of creating a new electron perunit length (or, the average number of electrons created per cm of path), and is called the first Townsend coefficient.If α is constant, we can integrate the relation to find that ln n = αx + C, and determine that C = ln n

o, so that ln

(n/no) = αx or n = n

oeαx, the equation for exponential growth.

The number of electrons that arrive at the anode will be n = noeαd, where d is the distance from the cathode to the

anode. In general, α will be a function of the electric field E, but here we assume E is constant, so our equationholds exactly only for plane-parallel electrodes and in the absence of space-charge effects. Nevertheless, it will giveus order-of-magnitude results. The number of positive ions produced in the avalanche will be n - n

o. We assume

that all return to the cathode, where they release γ(n - no) new electrons. The factor γ expresses the efficiency of the

ions in liberating electrons. This means that the net number of electrons leaving the cathode will be no + γ(n - n

o),

and the number eventually reaching the anode will be n = [no + γ(n - n

o)]eαd. If we solve for n, we find that n =


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noeαd/[1 - γ(eαd - 1]. If eαd is much greater than 1, we have simply n = n

oeαd/(1 - γeαd).

If eαd increases to 1/γ, the denominator vanishes, and the number of electrons reaching the anode increases withoutlimit. This is the sparking or breakdown point. The dependence of α on the electric field E is described by the

empirical formula α/p = Ae-Bp/E, where A and B are constants, p is the pressure, and E the electric field. Thepressure comes in because the important thing is the energy gained in a mean free path, EL, and L is inverselyproportional to pressure. Therefore, if the pressure changes, Bp/E will remain constant. α itself depends oncollisions, and will be proportional to the pressure for the same reason. Therefore, α/p will be constant, as will Ap,as the pressure changes. Hence, the constants A and B need be determined for only one pressure. The dimensions of

A and B are (cm-mmHg)-1 and V/cm-mmHg, respectively. For air, A = 14.6 and B = 365, and for helium A = 2.8and B = 34. These figures hold only over certain ranges of electric field, of course. The factor γ for air on a nickelcathode is 0.036, for neon 0.023, which are typical figures.

We can now estimate the sparking potential by finding the value of E for which eαd = 1/γ. The condition is ln(1/γ) =αd = Apde-Bpd/V

s, which we solve for V

s. This gives V

s = Bpd/ln[Apd/ln(1/γ)], or C

1(pd)/ln[C

2(pd)] in terms of

new constants that can be tabulated. The striking thing about this relation is that the sparking potential is a functionof the product pd only. This is called Paschen's Law. Moreover, by setting the derivative of V

s with respect to pd

equal to zero, we find that the sparking potential has a minimum when C2pd = 1, or pd = e ln(1/γ)/A.

The sparking voltage as a function of pd for air is shown in thegraph at the right, showing a minimum at 327 V at pd = 5.67mmHg-mm. From the ionization constants for air, we find 266 Vusing the above equation, which is not bad agreement. At pd = 2000mmHg-mm the sparking voltage is 10kV, and at 4500 mmHg-mm itis 20kV. The figures are for plane-parallel electrodes, so they givethe sparking voltages for the corresponding values of field strength.

We have assumed the mechanism of breakdown to be electronavalanches and positive-ion production of electrons at the cathode.The excited positive ions could also emit radiation that would ejectphotoelectrons from the cathode with the same effect. Therefore, thefact that we have cooperative amplification of the electron currentdoes not unambiguously determine the mechanism. This occurs often in the study of electrical discharges, and oftenmechanisms are obscure while their effects are well-known.

The minimum of the sparking potential has a strange consequence. For values of pd tothe left of the minimum, 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 ofthe minimum), as shown in the figure. In this case, bringing the electrodes closertogether can actually increase the breakdown voltage.

At low pressures, breakdown occurs with a silent spark of fine filamentary form. Athigh pressures, the spark is bright and noisy. Breakdown can occur as the voltage is raised, or the cathode-anodedistance is increased or the pressure reduced (for pd to the right of the minimum). Space charges can cause thevoltage distribution to change, and increased fields have the same effect as an increase in the overall voltage.Lightning shows progressive breakdown over a long path by this mechanism. A simple increase in primaryionization that raises n

o will not cause breakdown by itself. Sparks have chemical effects, creating ozone and

nitrogen oxides in air because of the ionization and excitation, and initiating chemical reactions.

The Geiger-Müller counter tube is an interesting example of breakdowncharacteristics. It consists of a cylindrical metal cathode with a fine wire anode onthe axis, as shown in the diagram. The thin window for entry of β particles(electrons) is not shown, if the counter is designed for this purpose. The counteralso detects γ rays, that eject photoelectrons from the cathode, undergo Comptonscattering, or create electron-positron pairs. The GM counter is not a sophisticatedinstrument, but has the great advantage of giving a large pulse that can even beheard directly through earphones without amplification. It is filled with Argon and a little ethyl alcohol vapor.


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The creation of a free electron in the volume of the counter or at the cathode initiates an avalanche discharge thatgenerally involves the whole length of the tube. The electrons are collected by the anode wire causing the leadingedge of the pulse, and then the ions move more slowly to the cathode, making the pulse tail. The ions are swept outin about 100 µs, during which the tube is insensitive. The maximum counting rate is about 5000 counts/s, and theloss of counts because of the dead time is called the coincidence loss.

If the counting rate with a certain source is measured as a functionof the voltage applied to the tube, a characteristic like the one inthe figure is found. Counting begins at the starting potential, whenthe electric field is first strong enough to support an avalanche. Thecounting rate increases until the Geiger threshold, and remainsnearly constant across the Geiger plateau. It is the existence of thisplateau that allows the instrument to be calibrated. All thedischarges in this region are of similar strength. If the ionsliberated a sufficient number of electrons at the cathode, thedischarge would become self-sustaining, rendering the tubeinoperative. To prevent this, a quenching gas, often ethyl alcohol,but also a halogen such a chlorine or bromine, that sucks up

electrons is added. The GM counter is between a Townsend discharge on one hand in which the current depends onthe ionization, and breakdown, where the discharge is self-maintained. At a sufficiently high applied voltage,however, a glow discharge cannot be avoided.

The Glow Discharge

If we reduce the gas pressure to between 1 mmHg and 1cmHg, we get a glow discharge that looks like the one inthe diagram, a typical low-pressure glow discharge. If westarted with the pressure at atmospheric, we would find itimpossible to start a discharge with, say E = 300 V. As wepumped the tube down, at some point a discharge wouldstart, filling the tube with pink light, if the gas was air, butthe current would be low and the light not intense. Withfurther evacuation, the current would increase as thevoltage across the tube decreased, and we would see adark region coming out of the cathode. Continuing, thedark region would increase in width, and the cathodewould seem to be covered with a soft bluish light. Thelight of the pink column may begin to fluctuate in movingwaves. At the pressure mentioned above, the voltageacross the tube would be least and the current greatest,and this is the discharge state shown in the diagram.

At lower pressures, the dark region would expandproportionally to the reciprocal of the pressure, the glowaround the cathode would also expand, and perhaps a darkregion between it and the cathode would become evident. The pink column of light would grow steadily shorter,and eventually be swallowed up by the dark zone. Now the glass of the tube might begin to fluoresce green wherefast electrons struck, and the voltage across the discharge would rise as the current fell. The electron mean free pathis now comparable to the dimensions of the tube. Finally, the glow at the cathode would flicker and go out, and thedischarge would cease, as the electrons could find no molecules to ionize as they traversed the tube from end toend.

The names of the various regions are shown on the diagram. There are two principal parts of the discharge. At theleft, the region between the cathode and the Faraday dark space (D.S.) is the engine that drives the discharge,creating the necessary electrons. If we lengthen the tube, this region does not alter, but remains the same. At theright, the region between the Faraday dark space and the anode serves to connect the electron engine with the anodewith a conducting path. It is almost electrically neutral, a plasma confined between the walls, the anode, and theFaraday dark space. It is surrounded on all sides by what is essentially a plasma sheath that cuts off current to the


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walls (which assume a negative potential relative to the plasma), allows just the right amount of electron current togo to the anode, and to come from the Faraday dark space.

The cathode is bombarded by positive ions coming mainly from the negative glow region, where they are createdby collisions with fast electrons. These ions recombine at the cathode, then fall to the ground state with theemission of light. This light constitutes the cathode glow, which is separated from the cathode by a very narrowdark interval, the Aston dark space. The "dark" regions are not really dark, just less luminous than the brightregions. The cathode dark space has the strongest electric field in the discharge, which increases proportionally tothe distance from the cathode. This region is filled with a positive space charge of ions moving in the otherdirection. When the electrons acquire sufficient energy to ionize, they begin to do so as they enter the negativeglow, the brightest part of the discharge. In the width of the negative glow, all the positive ions that the dischargeneeds are continually being created, and then they are accelerated towards the cathode. Even the ions may beexcited by the fast electrons, and both the neutral and ionized molecules contribute to the light. The electrons areexhausted by this effort, and drift out into the Faraday dark space at low velocity. There are now much fewer ionsaround, so the electrons can be accelerated in the gentle field. As they speed up, their number density goes down.Except close to the cathode, the electrons carry practically all of the discharge current. When they have sufficientenergy to excite the molecules of the gas, the emitted light becomes evident. This light is produced with minimalexcitation, and consists only of light emitted by neutral atoms which have been excited above their resonanceenergy, which explains its different character from the light emitted by the negative glow.

From here to the vicinity of the anode, the potential gradient must only be sufficient to allow the most energeticelectrons to form ions to replace those that diffuse to the walls. The electrons carry most of the discharge current inthis region, the ions mainly just ensuring electrical neutrality. As the anode is approached, adjustments must bemade to suit the anode current. The random electron current may be larger than required, so the electrons must beslowed down by an extra electron density near the anode, or, alternatively, a positive ion sheath may be required todraw extra current out of the plasma. This is the case shown in the figure. The extra ions required are made in theanode glow, while little excitation occurs near the anode, making a dark space. What happens at the anode isvariable, and depends on the details of the individual discharge.

The diagram is slightly different than the one that appears in many references, which seems to be copied from anoriginal by Loeb. The common diagram has, I believe, some inaccuracies, the most important of which is thepositive ion density in front of the cathode, which cannot fall to zero, as Loeb seems to indicate, but must remainfinite.

We should now discuss the important property of similitude in gas discharges. This rests essentially on the fact that

the mean free path is given by L = 1/nπd2, where n is the particle density and πd2 is an effective cross section forcollision. The diameter of an equivalent sphere is d. This expression may be multiplied by a constant near unity toaccount for a difference in speed of the colliding particles, or the distribution of molecular relative velocities, butthe essential thing is the proportionality to 1/n, which holds very well for the dilute gases important in discharges.The number density, in turn, is given by n = p/kT in terms of the pressure and temperature.

We have already seen this in Paschen's Law. The product pd= pL(d/L), in which pL is a constant, and the ratio d/Ldetermines the nature of the discharge, so the same thingshappen for the same values of pd. The diagram at the rightshows two discharge tubes of similar shape, in which thelinear dimensions are in the ratio a. The potential differenceacross the tubes is the same. If the pressures scale in theinverse ratio a, then the number of mean free paths in anysimilar distances is the same, and pd is a constant for similarbehavior. Since the potential difference is constant, theelectric fields E = -dV/dx also scale with the pressures, so that the ratio E/p is constant. The ratio α/p is a functionof E/p only, so it is constant. From the expression for the currents in the Townsend region, we find that the currentdensities are constant if the initial current densities at the cathodes are the same. Note that the ratios of chargedparticle densities are not the same as the ratio of neutral molecule densities. Neutral molecule densities are

determined by p = nkT, but charged particle densities are determined by Poisson's equation d2V/dx2 = -4πn±. Ratesof change of particle densities are also in a different ratio. Not everything scales properly, but in most casessimilitude is a very good approximation. This shows, incidentally, that tests at reduced voltage cannot be made onmodels, since the discharges will not be comparable if the voltages are different.


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Most of the voltage between anode and cathode is represented by the cathode fall Vc near the cathode. Aston found

experimentally that the electric field is greatest at the cathode, and falls linearly to zero at the end of the cathode fall

in the negative glow. This linear decrease means that the potential rises parabolically: V(x) = (2Vc/d2)x(x - 2d).

This means that there is a constant positive space charge in the region of amount Vc/2πd2, and the field at the

cathode is Eo = 2V

c/d. If K is the mobility of the positive ions, then the positive ion current can be found. The

electron current is γ times this, so the total current density at the cathode is jo = V

c2K(1 + γ)/πd3.

The electrons are accelerated by the strong field near the cathode to a rather high energy. They are then movingmuch faster than their mobility in the electric field, but are not slowed down much by elastic collisions with neutralatoms, and continue to ionize with increasing efficiency as they slow, doing the most work in the negative glow.The appearance of the spectrum of ionized atoms as well as neutral shows that the electrons still have high speedsin this area, though they are moving in random directions. The width of the negative glow is approximately equal tothe "range" of the electrons at the prevailing pressure. This range is not exactly the same as the concept of the samename in the stopping of radioactive beta rays.

It may be naively believed that the electrons are accelerated in the cathode drop as if in a vacuum, and then startionizing when they reach sufficient energy, but this is not a valid picture, and leads to confusion when trying tounderstand the discharge. The mean free path is still short even at 1 mmHg, and neutral molecules far outnumber

electrons and ions. While the neutral density is about 4 x 1015 cm-3 at 1 mmHg, the electron and ion densities do

not exceed 1010, and are usually no greater than 108. Only one in ten million molecules is ionized, and the motionof electrons and ions is governed by mobility rather than by free acceleration. The electron mean free path in neonat 1 mmHg is about 0.5 mm, which does give the electrons considerable freedom to roam. It is no wonder that thecathode phenomena hug the cathode tightly at higher pressures, and expand as the electron range increases. A veryhigh electric field at the surface of the cathode is a feature of all discharges, and here is where the electrons get theirinitial energy.

Only a few of the necessary positive ions are created in the cathode dark space, where most of the potential risetakes place. Most appear in the negative glow where ionization is most effective, then drift towards the cathode.The range of a fast charged particle is familiar from radioactivity. It is the projected distance in the generaldirection of motion, not the actual path length, especially for electrons, and is the distance to the point where theparticles have insufficient energy for further ionization. The range of electrons of U eV energy in a gas of molecular

weight M is about R = 1.4 x 10-7 (TU2/pM) cm, where p is in mmHg, and T is in K. The negative glow grades intothe Faraday dark space as the electrons become relatively slow and unable to ionize. Now they simply have to maketheir way to the anode somehow without using up much voltage.

The distribution of light intensity in the cathode dark space and the negative glow is a good subject forcontemplation. The light does not come from the positive ions (unless they have been further excited, which doeshappen), but from ions that have recombined. The entire region between the cathode and the Faraday dark space isfull of positive ions, but recombination is more likely where the electrons are moving slowly, and this meanselectrons that have already ionized and are now drifting about, and slower ions that have not yet been acceleratedby the field. Electrons in the dark space are still moving too rapidly for this, so there is little light there.

Analysis shows that the cathode fall where the current density required is not too high is V = (3B/A)ln(1 + 1/γ), the

current density is j = 5.92 x 10-8(AB2)(Kp)(1 + γ)p2/ln(1 + 1/γ), in µA/cm2 and where the various constants havetheir usual units, and the width of the cathode dark space is d = 3.76 ln(1 + 1/&gamma:)/Ap cm. These equations

can be used to find empirical values for the constants A and B. For neon, K = 7.52 x 103 cm/s/V/cm at 1 mmHg,

and γ = 0.022 on an iron cathode. Experiment gives d = 0.72 cm at 1 mmHg, j = 6 µA/cm2, and V = 150V. Fromthese data, A = 20 and B = 261, which is not unreasonable. Note that V is independent of the pressure, d variesinversely with the pressure, and j is proportional to the square of the pressure. This applies, of course, in the rangeof pressures where the approximate analysis is valid.

The current through a glow discharge is controlled by the external circuit. If a current i is demanded, then a cathodearea A = i/j is necessary under the conditions of our analysis. If this cathode area is not available, then the cathodefall must increase to provide a greater current density. This region is called the abnormal glow. The increasedcathode fall generates faster electrons and faster ions, so the negative glow expands and brightens, and the fast ionsbombard the cathode. In a glow lamp, it is easy to see the negative glow spread as the current through the lamp is


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increased.

Fast ion bombardment causes sputtering of the cathode material. The rate of sputtering is proportional to (Vc - V),

where V is the normal cathode fall, and Vc the established cathode fall. 850V would not be an unusual figure,

where V = 200V, say. The exact mechanism of sputtering is in doubt, but it seems that cathode material is ejected tothe cathode surface, and then evaporated by the local heating. The rate of deposition obeys the inverse-square law.The films produced are quite coherent and uniform. Silver sputters relatively easily, aluminum with difficulty.Where cathode surfaces are specially prepared, perhaps with low-work function substances as in thermioniccathodes, sputtering can destroy them quickly, even at relatively low overvoltages. There seems to be littlesputtering at the normal cathode fall. The electrodes of glow lamps are treated with low-work-function materials, sothey are injured by overcurrent, and their striking voltages may rise.

In the Faraday dark space, the electric field is again controlled by space charge and the mean free path, this time of

the electrons, which carry nearly all of the current. The kinetic energy gained in a mean free path L is mv2/2 = EeL,

so we can find the velocity and hence the current density, j = ne(2EeL/m)1/2. Then Poisson's equation is dE/dx =

4πne = 4πj(2EeL/m)-1/2. Integrating this equation, we find that E = (6πj)3/2(2eL/m)-1/3x2/3. Hence, the electric fieldrises as we move through the Faraday dark space. When it reaches a value sufficient to give the electron a kineticenergy equal to the resonance energy V

r, then the electrons can excite the neutral molecules and light emission

begins. This happens in a distance x at which EL = Vr, which is proportional to 1/Lj, or inversely proportional to p.

If the pressure is sufficiently low, then the electrons move almost as in a vacuum, and the normal Childs 3/2-powerlaw applies. Then the distance x is proportional to 1/√j, again inversely proportional to pressure. Like the cathodefall and the negative glow, the Faraday dark space also expands inversely as the pressure. Therefore, the wholecathode region expands or contracts without any change in relative dimensions as the pressure changes.

When the average electron has sufficient energy to excite a neutral molecule to its resonance level, the occasionaloverzealous electron can ionize a molecule to create a positive ion to replace one that is lost by diffusion to thewall, where it recombines. This is a delicate balance that keeps electron and ion densities equal in the positivecolumn or plasma. The smaller the diameter of the tube, the greater is the diffusion, and the greater the longitudinalpotential gradient required to keep the electrons up to working speed. The random current density is the currentcrossing unit area in one direction in the plasma, j = nec/4, where c is the average thermal velocity of the chargecarrier, √(8kT/πM). This presumes a Maxwellian distribution, which is not a bad assumption. However, the electrontemperature may be 10,000K or more while the neutral and ion temperatures are not much above 300K. Thisdifference is due to the extreme difficulty of transferring kinetic energy between the light electrons and the heavymolecules, especially when the electrons are being driven by a longitudinal field. This means that the randomelectron current to the wall is much greater than the random ion current. So that the net current to thenonconducting wall is zero, the wall must collect electrons to form a repelling field. This layer of excess charge iscalled a plasma sheath, and is a common phenomenon, well seen in glow discharges.

For a neon glow discharge carrying 25 mA, the voltage gradient in the positive column for a tube radius R = 2 cm is1.45 V/cm. For R = 1 cm, it is 3.0 V/cm, and for R = 0.75 cm it is 4.3 V/cm. For helium, the drop in a tube of 1.5cm radius is 5.0 V/cm. A neon display lamp uses the positive column for its light. The tube diameter may be 0.6"diameter and its length 60 ft. The total drop in the positive column is 130 V/ft x 60 ft = 7.8kV, and the electrodedrops amount to 230-300V. The illumination is about 36 lumen/ft, and the efficiency 24 lm/W. On open circuit, thetransformer supplies 15kV. However, it is made with large leakage reactance that lowers the voltage depending onthe current drawn to stabilize the discharge at something less than 10kV across the tube. The pressure in the tube islarger than the value giving minimum voltage to suppress sputtering of the cathode, which darkens the walls of thetubes and limits the life of the tube. Neon gives red-orange, helium yellow, nitrogen pink. Mercury can be added forfurther colors, and colored glass can be used, to make blue and green displays. These glow discharges are still afrequent sight.

Corona is the name given to glow discharges at high pressure near points of high fields, usually caused by a smallradius of curvature. Points are an obvious place for corona, and this is their intention in lightning rods. High tensionconductors are another good place, but here it is very undesirable. It is commonly stated that the breakdown fieldfor air is 30kV/cm, but the phenomenon is far too complex for such a simple criterion. Nevertheless, this value is ofuse for engineering estimates. A negative wire becomes a cathode, and the glows contract to regular regions alongthe wire, like beads, each surrounded by a brush. A positive wire becomes an anode, with a uniform anode glowspread along it. Corona loss may exceed resistive loss in the conductors. It is less if the conductors are smooth and


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of large diameter.

The glow discharge is often used for gas laser pumping, as in the familiar He-Ne laser. The object is to create apopulation inversion between the upper and lower levels of a radiative transition. The upper level for the 633 nm

laser transition is the Ne2p55s'[1/2]0 at 166658.484 cm-1 above the Ne ground state, which is nearly resonant with

the He21S0 metastable excited state of helium, and the lower state is the Ne2p53p'[3/2]

2 state at 150860.468 cm-1,

which can decay rapidly to the Ne2p53s[3/2]2 metastable state of neon via 594.5 nm radiation, keeping the lower

state empty. This is a very fortunate and ideal scheme for laser pumping. There are also infrared transitions in thesame region that can be used, at 1152 nm and 3391 nm. The upper level of the first is resonant with the metastable

He23S1 state, which also facilitates pumping.

The discharge tube is typically filled with 0.8 mmHg helium and 0.1 mmHg neon, excited by a dc discharge, an acdischarge, or radio-frequency discharge. The population inversion is in the pink positive column. The laserfrequency is picked out by an optical resonance between external mirrors, and energy is pumped into it by thepopulation inversion. The cathode and anode are usually in side tubes so the optical path is not obstructed.

A radio-frequency field from an external coil around the discharge tube can be used to create a plasma. It isnecessary for the rf electric field to be strong enough to give the excitation or ionization energy to an electron in amean free path. This is not strictly a discharge, since there is no net current flow, but it produces a weakly-ionizedplasma like that in the positive column of a glow discharge.

As the gas pressure is reduced, it becomes more and more difficult to produce a sufficient number of positive ionsto maintain the discharge. The anode-to-cathode voltage must be continually increased, and the electrons becomemore and more energetic. The electron mean free path becomes comparable to the size of the discharge, andpractically the whole space represents the Faraday dark space. This is the region of cathode rays, as the linearelectron trajectories were called before electrons were recognized, that can cast shadows, deflect in transverseelectric and magnetic fields, cause the glass to fluoresce, and produce X-rays when they are stopped suddenly bythe anode or the glass. Finally, the tube becomes nonconducting.

The Arc Discharge

The arc discharge is a high-current, low-voltage discharge, in contrast with the low-current, high-voltage glowdischarge. It is characterized by a negative-resistance V-I characteristic, and high temperatures. Electrons for thedischarge are supplied by a cathode spot that is a much more efficient electron emitter than the glow dischargecathode phenomena. The current density in the cathode spot is high and constant, so it adjusts its size to suit thedischarge current. The electrons are liberated either by thermionic emission, or by high-field emission. The relativeimportance of these mechanisms has long been in dispute, but it is convenient to assume that the fixed cathode spotof refractory electrodes (such as carbon or tungsten) is thermionic, while the wandering cathode spot oflow-melting-point cathodes (such as mercury) is high-field. A typical current density for a thermionic cathode spot

is 470 A/cm2, and of a high-field spot, 4000 A/cm2.

High-field emission is essentially quantum-mechanical tunneling through the potential barrier at the surface of the

cathode. The current density is given by the Fowler-Nordheim equation J = CE2exp(-D/E), where C = [6.2 x 10-6/(φ

+ EF)](E

F/φ)1/2 A/V2, and D = 6.8 x 109φ3/2 V/m. E

F is the Fermi energy and φ is the work function, both in volts.

E is the field in V/m. For tungsten, φ = 4.52V and EF = 8.95V. The fields required are very high. A field of 2 x 107

V/cm produces emission of only 1.7 µA/cm2 in tungsten. However, the current increases quite rapidly with electric

field. With a field of 3 x 107 V/cm, the current is already 0.2 A/cm2. At atmospheric pressure, the mean free path is

about 10-5 cm in air, and if the cathode drop is 10V, the resulting electric field if the cathode drop occurs over one

mean free path is 106 V/cm. This is about a factor of 20 less than is required, so some investigators have questionedthe importance of high-field emission in arcs. However, it is at least close to the required value, and some localstrengthening of the field by the arrangment of adsorbed positive ions may make up the difference.

The Richardson-Dushman equation for thermionic emission, J = AT2exp(-b/T) is very similar in form to the

Fowler-Nordheim equation, with the absolute temperature T replacing the field strength E. A = 60.2 A/cm2, and b =


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11600φ. At the boiling point of tungsten, 5993K, J = 3.45 x 105 A/cm2, a quite ample result. Even at the melting

point, the current density is 541 A/cm2. Mercury has about the same work function as tungsten, 4.5V, but the

thermionic emission at its boiling point, 630K, is only about 10-29 A/cm2, which is wholly inadequate. Therefore,high-field emission seems to be the only alternative.

A typical low-intensity carbon arc for lighting operates at atmospheric pressure between two cylindrical carbonelectrodes separated by a few millimeters, at a voltage of 55V and a current of 30A. The cathode spot is at atemperature of about 3500K, while the crater eroded in the anode carbon is around 4200K, with a brilliance of 170

cp/mm2. Between them is a bright violet glow, and a yellow tail flame, projected towards the anode. Material isblown out by the cathode, and may deposit on the tip of the anode. The light is characteristic of a 3810Kblack-body, with strong radiation in the near UV at 380-390 nm, the cyanogen peaks due to that compound ofcarbon and nitrogen. There is also a peak near 250 nm. These ultraviolet emissions make protective glassesnecessary when observing an arc directly. The radiation is also rich in infrared, because of all the heat in thevicinity.

The carbons are continually consumed in the arc. They may be of hard carbon for durability outside, with a core ofsoft carbon for conductivity inside, that stabilizes the arc. Special core materials may give colored arcs by coloringthe tail flame. They cannot be focused accurately as the postive crater can. A core of cerium oxide and cerium

fluoride forms cerium carbide in the crater, giving up to 500 cp/mm2 in what is called a high-intensity arc light. Thetail flame is white from the incandescent cerium particles. A typical positive carbon is 16 mm in diameter, with an 8mm core, while the negative carbon is 11 mm in diameter, with a 3 mm soft carbon core.

The arc can operate either in the ambient gas, or in the vapor emitted by the cathode and anode as they arevaporized. The electrodes operate at their boiling points, which determines the maximum temperatures available.For example, a copper arc is typically green, with emission from the copper vapor in the arc. The arc consists of thecathode drop, the positive column, and the anode drop. No interesting detailed structure is seen, as in the glowdischarge. The cathode drop is a little less than the ionizing potential of the gas or vapor. For carbon, the ionizationpotential is 15.8V, but the cathode drop is 9-11V. The width of the cathode drop region is little longer than a meanfree path of an electron, so the cathode region is very thin. The anode drop occurs in a wider region, and resemblesa probe sheath, as in a glow discharge. The anode drop in the carbon arc is about 20V. Between the narrow cathodeand anode regions is the positive column with a linear voltage gradient. The voltage of a carbon arc in air is givenapproximately by V = 38.9 + 2.0x + (16.6 + 10.5x)/I, where V is in volts, I in amperes, and x is the arc length inmillimeters. This applies in the silent region where the characteristic is hyperbolic. At higher currents, the arcbecomes a hissing arc, and the voltage is roughly constant.

Thermal effects play an important role in arcs. The cathode is heated by positive ion bombardment, where the effectof the ions is purely thermal and any positive-ion induced electron emission is unimportant. There must always besufficient ions to keep the cathode hot. Often the cathode is externally heated, at least until the arc is established, tohelp starting. This is seen, for example, in fluorescent tubes. In some cases, as in rectifier gas diodes, the cathode iscontinuously heated. These cathodes are oxide-coated to stimulate copious electron emission. External heating ofthe cathode does not affect the nature of the discharge significantly. By considering the positive-ion space charge,the field at the surface of the cathode can be estimated as E = 4V/3d, where V is the cathode drop and d is the width

of the cathode fall region. If V is about 10V and d is about a mean free path, then E is 105 to 106 V/cm. Such a highfield is great encouragement for electrons to join the discharge. Also, a superheated area may form at the surface ofthe cathode from adsorbed atoms.

The positive column differs significantly between arcs operated at low pressures (say, below 10 cmHg pressure)and arcs at higher pressures, such as atmospheric. At low pressures, it is like the positive column of a glowdischarge, with a very high electron temperature (40,000K is not unusual) and a low ion and gas temperature (say,300K). Ionization in this plasma is by electron impact, and the plasma dissipates if the walls are not present. Athigh pressures, electron, ion and gas temperatures are equal and high (perhaps 6000K), and ionization is principallythermal. This is the kind of hot plasma studied in plasma physics. The longitudinal voltage gradient depends on

current as E = BI-n and on pressure as E = Cpm, where m and n are empirical exponents. For a carbon arc in air, n =

1 and m = 0.3, approximately. At 1 atm, the current density in a positive column in nitrogen is about 6 A/cm2. Thereason for the decrease in voltage with an increase in current is that the current increase causes a decrease in theresistance of the column by making more of everything available.

The degree of ionization x in a hot plasma can be estimated by the Saha equation, [x2/(1 - x2)]p = 3.16 x 10-7


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T5/4exp(-eVi/kT), where p is in atmospheres, T is in K, and V

i is in volts. If we take an ionization potential of 10V

(about that of mercury), then at 10,000K and 1 mmHg the Saha equation gives x = .033, or the plasma is about 3%ionized. At 100,000K, the degree of ionization is x = 0.997, so the plasma is almost completely ionized. Even at 1

atm, the degree of ionization is still about 41% at 105K and 0.1% at 104 K. A fairly small degree of ionizationsuffices to maintain the conductivity of a high-pressure arc plasma.

In hot plasmas, oxygen and nitrogen are generally dissociated: O2 → 2O (5.09 V) and N

2 → 2N (7.9 V), and the

reaction N2 + O

2 → 2NO. NO has the rather low ionization potential of 9.5V. The ionization potential of O

2 =

12.2V, O = 13.614V, N = 14.54V, N2 = 15.377V. Even when the electron and ion number densities and temperatures

are roughly equal, electrons still carry the preponderance of the current because of their higher mobility.

The high-pressure positive column adjusts to a finite diameter D depending on the discharge current. It will notexpand indefinitely if unconfined. This is a result of a delicate balance between heat loss and heat generation in theconducting region, and not anything similar to a "pinch" effect. If the column expands, heat loss increases andionization decreases. The current, therefore, tends to shift to the more conductive center, and raises the temperaturethere. This feedback keeps the column at a constant diameter. The positive column is a cylindrical region in theambient gas, and can move about freely, so long as it does not become too long and require more voltage than isavailable. It is accompanied by active convection that carries off its heat. The positive column can be blown aboutby air currents, and moved by magnetic forces. Its low density causes it to rise when surrounded by cooler air,which, as we have mentioned, gave the name "arc" to the phenomenon. Curiously, if the acceleration of gravity iszero (as in a space station, for example) the longitudinal voltage gradient becomes zero! The reason is that gravitydrives convection, and in the absence of convection the column does not cool, and so does not need any power, atleast to a good approximation. Note that this means that the whole arc, including the gas, is under zero gravity. Ifwe just let the electrodes fall, it is only like applying a blast of air.

The potential distribution in an arc is shown at left. The widths of the cathodeand anode drops are exaggerated for clarity. In a short arc, the potential isalmost just the sum of the cathode and anode drops. Because of the largecurrent, an arc has a small longitudinal voltage gradient E

L in the positive

column, especially in a high-pressure arc. The gradient depends on theefficiency of cooling of the positive column by the ambient atmosphere, andbecomes small if cooling is slow. The current flowing through the cathode andanode drops generate large quantities of heat very close to the electrodes,which is one of the characteristics of the arc.

An arc can be started either by a transition from a glow discharge, or by separating contacts already carryingcurrent. If we increase the current in a glow discharge, we enter a region in which the width of the cathode falldecreases (the "abnormal glow"). This causes the ion energy to increase, and the cathode becomes heated. In arcswith thermionic cathodes, the transition is gradual as the thermionic emission increases with temperature and thedischarge voltage decreases. With field-emission cathodes, such as with mercury, the transition may be sudden, as acathode spot is created at some favorable spot. The mercury is initially in liquid form, either as a pool or as a drop,and must be raised to a temperature where the mercury vapor pressure will support the discharge. Starting amercury arc always requires some special action, either a separately heated cathode or an ignition electrode. Thepressure can also be increased to start an arc if a glow discharge already exists. The current rises as the square ofthe pressure, so a critical value is soon reached.

The distinction between stable and unstable V-I characteristics isshown in the diagram at the right. On the left we have the usualcase where the current increases monotonically with the voltage,so that the slope 1/R = dI/dV is positive. Suppose we are operatingat point A with a certain applied voltage, and there is a suddenincrease in the current δI (caused, say, by a spark). Now thevoltage required by the device is greater, so we have a voltagedeficit in the circuit that will cause the current to decrease. If thecurrent were suddenly less, then we would have a voltage surplus,and the current would be driven to increase. In either case, wereturn to the status quo and the circuit is stable.


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On the right, we have a characteristic like than of an arc, where the current decreases monotonically with thevoltage. The slope 1/R = dI/dV is now negative. The device is said to exhibit negative resistance R. If we have asudden current increase δI from point B, then we have more voltage available to increase the current still more, avoltage surplus. The more the current increases, the more it is driven to increase. The circuit is unstable, and someexternal means is necessary to limit the current. Any device with a negative resistance can be used as an oscillator,and an arc is no exception.

A negative-resistance oscillator using an arc is shown at the left. It should notbe confused with the spark-gap oscillating circuits used in early radio, whichwere something completely different. L and C make a tuned circuit in serieswith the arc, and R is the resistance of L. The arc is supplied from source Ethrough a large inductance L

b that blocks the oscillating current and keeps the

arc voltage constant. The arc current is regulated by resistance Rb. Kirchhoff's

voltage law around the loop including the arc, L, C and R gives Li" + (R + de/di)i' + i/C = 0. If the arc current isadjusted so that de/di = -R, then we have Li" + i/C = 0, so that the solution for i is a harmonic function of frequencyf = 1/2&pi√LC. Since de/di is a function of the current, large current excursions will be damped out and theamplitude of the oscillation will stabilize. The maximum voltage across the capacitor will be I√(L/C), where I is thearc current. I do not know of any practical use of this oscillator, but the oscillations may occur unexpectedly insome cases.

Applications of Arcs

Welding is an important application for arcs. Although oxyacetylene flames are hot enough to make fusion weldsand are very useful, arc welding is relied upon for heavy-duty welding. In carbon-arc welding, the arc is struckbetween a carbon rod and the work, and a filler rod is used if extra material is needed. Inert-gas welding uses atungsten electrode bathed in an inert gas such as helium to avoid oxidizing the work, and a filler rod. Argon is alsoused, though one source says it is not suitable. Since helium, and even argon, are quite expensive, welding withCO

2 has also been tried with success. Atomic-hydrogen welding uses a pair of tungsten electrodes between which

the arc is struck. Hydrogen is blown onto the arc, where it dissociates. The atomic hydrogen then recombines on thesurface of the work, creating the necessary high temperature. These methods are useful in special cases, but themost general type of arc welding is the metallic arc. The arc is struck between a welding rod and the work, with thewelding rod providing the filler metal.

It is necessary to exclude the oxidizing atmosphere from the molten metal in any welding, and this is done by thegases created from the coating of the welding rod. This coating also provides material that makes a slag that carriesaway impurities and is brushed off the surface when it is cool. Special alloys in the welding rods provide additionsnecessary for the quality of the weld material. The selection of the proper welding rod is an important requirementfor successful welding. The blast from the cathode when the welding rod is made negative and DC is used allowsoverhead welding, a great advantage of metallic arc welding, though it is not used except when absolutelynecessary. The arc length is short, 4 mm or less, the coating generally touching the work as the weld is made. Avoltage of 21V and currents of 40 to 240A are typical. A generator for DC welding supplies 40-60V on opencircuit, but is strongly negative compounded to limit the current to the desired level. A transformer with largeleakage flux is used for AC welding, for the same reason. When DC is used, the work is generally positive becauseof the higher temperature at the anode, but it depends on the welding rod used. Proper welds are strong and reliable,and the ease and economy of making them has led to their general use instead of riveted joints.

The Cooper-Hewitt low-pressure mercury arc lamp isshown at the right. It produced 16 lm/W of the linespectrum of mercury, including the UVA resonanceline at 257.3 nm. It was used, among other things, forexposing blueprints and blueline prints (as was thecarbon arc). It is interesting for using two anodes foroperation on AC, a mercury-pool cathode, and acapacitance igniter. The pressure of mercury inoperation was a few mmHg, controlled by the bulbtemperature. The discharge current was limited by theballast L, and the anode currents equalized by the resistances R. The AC supply was arranged as an


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autotransformer. The capacitance igniter consisted of a ring around the bulb at the level of the mercury surface.When the switch was closed (this switch was a mercury tilt switch) DC passed through L, so that opening theswitch produced a large inductive kick that was applied to the ring through the capacitance C. This apparentlycreated high-field emission at the mercury meniscus inside the bulb, which started the discharge. Residualionization was enough to restart the discharge on each voltage cycle.

Starting a discharge with a mercury-pool cathode means establishing a cathode spot on the surface of the mercury.This could be done with a small auxiliary pool that was connected to anode potential and then tilted to separate themercury from the main cathode, after which the discharge would transfer easily to the main anode. Another methodused a resistive rod that was not wet by mercury dipping into the pool, called a resistive igniter. A small auxilaryanode, called an arc-holding anode, was sometimes provided to keep the discharge going when the main anodecurrent was cut off, perhaps by some current control action. The capacitance igniter eliminated the inconvenienceof a conductive connection to the discharge, simplifying control.

The cathode spot makes a small depression in the surface that moves about rapidly, with agitation and splashing ofthe mercury. Mercury is vaporized at the cathode spot, and condenses on the cooler parts of the envelope, fromwhere it drains back into the pool. This self-renewing property of the mercury pool cathode is a great advantage.However, the mercury must not splash on an anode, where it offers the hazard of creating a secondary cathode thatmay conduct on reverse voltage, causing a backfire.

Large mercury-pool rectifiers were once used to produce large DC currents. The ignitron even allowed phasecontrol. These rectifiers have now been superseded by silicon rectifiers, which are much cheaper and moreconvenient to use, but much less dramatic.

The sodium-vapor lamp is another interesting device. It was necessary to find a glass that would not be attacked byhot sodium vapor before any such lamp was possible. The lamp uses a separately-heated oxide-coated cathode anda molybdenum anode in about 2 mmHg of neon. The discharge is first started in the neon, and the lamp allowed towarm up until the sodium metal vaporizes. This requires up to 10 minutes. Sodium melts at about 93°C, and at theworking temperature of 220°C has a vapor pressure of about 0.3 µmHg. A Dewar enclosure around the envelopekeeps the heat in. This is a small pressure, but the efficiency of radiation of the sodium resonance lines is so greatthat most of the light comes from the sodium. A short lamp, 8 cm, relies on cathode phenomena and has no positivecolumn. Its voltage drop is about 17V, and it produces 4000 lm, for an efficiency of about 22 lm/W. A longer 16 cmlamp will get its light from the positive column, and the voltage drop will be about 25V. This lamp will produce7000 lm, with an arc efficiency of 72 lm/W, and an overall efficiency of 52 lm/W, the highest known. The light,however, is monochromatic, in the range 560-610 nm, formed by the broadened sodium D lines. This orange-yellow light was once very familiar as highway illumination.

The neon in the lamp, though it does not contribute to the light, has the important function of decreasing theelectron mean free path so that the electrons spend a lot of time in the discharge, and have a high probability ofexciting sodium atoms. The cathode fall of the lamp is about 15V, low enough that ion bombardment of the cathodeis not damaging (this happens at 25V and above). The cathode fall is set by the neon, but the resonance energy ofthe sodium is only 2.5V, allowing nearly all the sodium to be excited. The electron temperature in the positivecolumn is about 40,000K. The voltage gradient is small because the neon can be cumulatively ionized, since it hasmetastable levels and can save excitation energy between successive collisions with electrons. The number density

of sodium in cm-3, is given in terms of the temperature T in K by log n = -5573.3/T - 1.6794 log T + 28.7134.

When the walls are at 390K, this gives 5 x 1010cm3. At these temperatures, the resonance radiation has an

absorption coefficient of 143 cm-1, so it does not get far before it is absorbed and then re-radiated. Only a thin outerskin of the positive column emits the light that is seen.

High-pressure sodium lamps have now been developed, in which the high pressure produces a very hot plasma thatradiates throughout the visble, making a golden light that is more acceptable than the pure yellow of thelow-pressure lamp. They are widely used as streetlights, giving an annoyingly bright glare. It is interesting to watchthese lamps light with a spectroscope. When they first are connected, they show argon or neon lines, then the blueof a mercury discharge and its typical yellow, green and red lines. The sodium D lines soon appear, and theyincrease in brightness, and then in width. Finally, when the lamp is at operating temperature, there are two blacklines against the continuous background, as the sodium vapor absorbs these frequencies, that by contrast look dark.This is similar to the production of the Fraunhofer dark lines in the solar spectrum by line absorption of thephotospheric continuum in the chromosphere.


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The high-pressure mercury arc lamp was developed earlier than thehigh-pressure sodium lamp, since the problems with its construction were notas challenging. It is filled with argon to a few mmHg, and contains a smallmercury drop, perhaps 200 mg in weight, that will supply the operatingpressure in a tube 15 cm long and 3 cm in diameter. The operating walltemperature is about 350°C. A glow discharge at the starting electrode close toone main electrode provides sufficient ionization for a glow discharge to beginbetween the main electrodes, which raises the wall temperature. When themercury is vaporized, the arc strikes, and the oxide-coated cathodes are heatedby ion bombardment. The lamp is supplied through a transformer with leakageflux, so that it behaves as a ballast as well. The inductive current is balancedby a capacitive current to correct the power factor, if this is a problem. These lamps produce a whitish-blue lightfrom the broadened spectral lines of mercury, which at the highest pressures becomes practically a continuum.

The fluorescent lamp is a very familiar device, that provides us with examples of a low-pressure mercury arc, andan argon glow discharge as well. The tube, which is from 5/8" to 1.5" in diameter, and 9" to 48" long, has an oxide-coated cathode with heater at each end. The 253.7 nm mercury resonance line is ideal for exciting phosphors suchas manganese-activated zinc silicate. This phosphor has an excitation peak at 253 nm, and re-emits the radiation inthe region 460-600 nm in the middle of the visible spectrum. There are many phosphors to choose from, andcombinations of them are used to secure desirable spectral characteristics. They operate at rather low currents, 0.15to 0.42 A, and at voltages from 45V for a 9" tube to 108V for a 48" tube. A ballast inductor is used to limit thecurrent. A resistor would work as well to limit the current, but the inductor dissipates less heat, though at theexpense of a poor power factor. The inductor, however, plays an important role in starting the discharge.

Since the tube contains a drop of mercury that must be vaporized before the dicharge can start, the cathode heatersare connected in series across the line to warm up the mercury and provide some ionization. When the startingswitch is opened, the inductor gives a high-voltage kick that initiates the arc, though it may be a while before thetube comes up to operating temperature. Fluorescent lamps are very efficient, a green phosphor giving as much as70 lm/W, though normal lamps are less efficient. There is little infrared in the radiation produced. The visiblemercury lines shine through the phosphors, and can be seen in a spectroscope. The light is not very pleasant, butgives good illumination of large areas.

The "glow switch," an automatic starter, was invented by R. F. Hays in 1940. It has a U-shaped bimetallic strip thatcloses the circuit through the lamp heaters when it is hot, but the contacts are normally open. There is anotherelectrode in the envelope so that a glow discharge can occur when voltage is applied. The normal supply voltage isenough to start the discharge, which is in the abnormal glow region to supply a good amount of heat to one end ofthe bimetallic strip. The strip closes the contacts and shorts out the glow discharge, and the tube heaters areenergized. It is arranged that the bimetallic strip continues to heat a short time after the discharge ceases, so thecircuit does not reopen immediately. When the bimetallic strip cools the contacts open, causing the inductive kickthat starts the main discharge, as well as the glow discharge in the starter. However, the voltage across the maindischarge is insufficient to maintain the glow discharge, so the glow discharge goes out before it can heat thebimetallic strip again. If the main lamp does not light, the cycle repeats until it does. These starters are practicallyuniversally used, and may be included as part of the lamp.

Arcs are also involved in power switching. The ordinary AC houshold supply is one of the easiest circuits toswitch. A DC supply, even of the same voltage, is much more difficult to interrupt. A switch that can handle 10AAC will do well to handle 1A DC at the same voltage. High-voltage transmission circuits are very difficult toswitch, even with AC, and a large amount of technology has been developed to meet the problems. When a circuitcarrying current is interrupted, an arc always forms at the switch contacts, and the arc must be lengthened until thevoltage will not support it. Inductance in the circuit always makes switching more difficult. Care must be taken notto end the current abruptly and cause an excessive inductive kick, while the inductance extends the persistence ofcurrent flow. Alternating current has the great advantage that the current is zero twice in every cycle, and advantagecan be taken of this to break the circuit. DC of several thousand volts is very difficult to interrupt, since the voltagecan support a long arc that must be extinguished in creative ways. Opening a simple knife switch would only resultin a continuous arc in this case.

The arc can extend itself by climbing arc horns driven by its buoyancy and convection of the air around it, or thecurrent can be used to create a magnetic field with the same effect, called a magnetic blowout. The arc can bedriven into an arc chute that lengthens its path, by a blast of air. In the most difficult cases, the contacts open in an


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oil bath. This creates a cloud of vapor under high pressure that may be used to blow out the arc, and occasionally anasty explosion. A great deal of ingenuity has gone into high-voltage switchgear to make economical hightransmission voltages practical. However, one supposes a high-voltage DC transmission line cannot be switched atall, and its supply must be removed instead, or it simply must be shorted.

Lightning offers further problems. Here, the voltages can rise to several million volts in a few microseconds, withcurrents of thousands of amperes. Lightning protection must allow a discharge that bypasses equipment that wouldbe damaged by the stroke. Here we are talking about actual lightning strikes, not just disturbances due to nearbylightning that affect telephone wires and such. The protection that routes a stroke around an insulator may leaveionization that facilitates an arc over the insulator from the normal line voltage, damaging the insulator, soprotection equipment must work quickly to de-energize the line when a lightning stroke is detected. When yourlights flicker briefly, the usual reason is that a lightning strike has caused the protective circuits to disconnect andreconnect the line automatically. This is just a sample of the many problems that occur in this field.

Even voltages as low as 1.5V can cause a "spark" when contacts open. This is not a true spark, but the effect ofhigh temperatures produced at the last point on the contacts to open, when the current is confined to a small area.This is not a switching hazard, but does degrade the contacts. A capacitor can be used to keep the voltage acrossopening contacts small, but a resistor is necessary in series with it. Otherwise, when the circuit is closed, thevoltage across the charged capacitor would be discharged through the low resistance of the contacts, which couldweld them together. This combination is called a snubber, and it makes low-voltage DC switching a little better.

Fuses are an excellent overcurrent protection. They consist of a wire or equivalent that melts at a current that isgreater than the working current by some small factor, say 1.5. When the wire melts, an arc is formed that thenmust be extinguished, often by being enclosed in some material that vaporizes and blows out the arc, or absorbs the

energy of the arc. The current that melts a wire can be estimated by Preece's formula, I = Ad3/2, where I is inampere and d is in inches. For copper, A = 10,224, for aluminum, A = 7585, for lead A = 1379, and for GermanSilver, A = 5230. A #30 copper wire fuses at a current of about 10A.

References

More complete bibilographies will be found in the references.

J. D. Cobine, Gaseous Conductors (New York: Dover, 1958).

J. Millman and S. Seely, Electronics (New York: McGraw-Hill, 1951). Chapters 9, 10 and 11.

G. Herzberg, Atomic Spectra and Atomic Structure (New York: Dover, 1944).

Return to Physics Index

Composed by J. B. CalvertCreated 3 November 2002Last revised 29 July 2009


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electrical discharges - how the spark, glow and arc work

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