Electric Breakdown in Long Discharge Tubes at Low Pressure … · 2020. 10. 20. · incandescent lamp: the Moore lamp (D.F. Moore). It was a discharge tube filled with carbon dioxide,

ISSN 1063-780X, Plasma Physics Reports, 2020, Vol. 46, No. 10, pp. 1015–1044. © The Author(s), 2020. This article is an open access publication.Russian Text © The Author(s), 2020, published in Fizika Plazmy, 2020, Vol. 46, No. 10, pp. 928–960.

LOW-TEMPERATUREPLASMA

Electric Breakdown in Long Discharge Tubes at Low Pressure (Review)

Yu. Z. Ionikh*St. Petersburg State University, St. Petersburg, 199034 Russia

*e-mail: [email protected] March 19, 2020; revised April 9, 2020; accepted April 10, 2020

Abstract—The review is devoted to studies of the processes and mechanisms of ignition of a glow discharge intubes whose length significantly exceeds their diameter (long discharge tubes) at low pressures (~10 Torr andlower) and moderate voltage rise rates (~1 kV/μs and lower). The electric field in such tubes before a break-down is substantially nonuniform. Therefore, a breakdown occurs after an ionization wave (or waves) passesthrough the discharge gap at a speed of ~105–107 cm/s. This makes the characteristics of the breakdown inlong tubes significantly different from the breakdown between large and closely spaced electrodes, where theelectric field is uniform before the breakdown and where the Townsend or, under strong overvoltage, streamermechanism is realized. On the other hand, the nature of these processes is very different from those occurringin nanosecond discharges, which arise at voltages with a steepness of ~1 kV/ns and higher and are associatedwith high-speed (~109 cm/s) ionization waves. The review is based on the materials of experimental and com-putational works published from 1938 to 2020. Breakdown processes, optical and electrical characteristics ofthe discharge gap during breakdown, and the influence of the external circuit parameters and external actions(shielding and illumination by external sources of visible radiation) are analyzed.

DOI: 10.1134/S1063780X20100049

CONTENTS 1. INTRODUCTION1. Сylindrical discharge tubes with a length much

greater than the diameter (“long” discharge tubes)began to be used in the 1850s in the experiments ofJ. Plücker and H. Geissler at the University of Bonn[1]. Using a mercury pump created by Geissler, a stablereproducible low-pressure discharge in the tube wasobtained, which was later called glow discharge. Theterm “Geissler” is used now for discharge tubes with acapillary insert (Fig. 1). Until recently, they were usedas standard spectral sources. Plücker, experimentingwith the created tubes, discovered cathode rays. In thesubsequent works of J. Hittorf and W. Crookes, butunder vacuum, the existence of the electron was proved(J.J. Thomson). For several decades, the glow-dis-charge plasma in a long tube, steady-state or decaying,has been widely used as a medium for studying elemen-tary collision processes and transport characteristics ofatoms and molecules with thermal energies [2]. Thiswas facilitated by the presence in such a discharge of aregion of a longitudinally uniform plasma: a positivecolumn. For plasma physics, such studies providedinformation on the averaged energy and transportcharacteristics of electrons, on instabilities (contrac-tion, stratification), etc. [3].

The practical application of long discharge tubesbegan with their use in outdoor advertising at thebeginning of the 20th century (“neon signs”), which

1. Introduction2. Ionization waves2.1. Fast waves2.2. Pre-breakdown (slow) waves

3. Study of breakdown in long tubes under low pressure3.1. Early works (until 1960)3.2. Works of the 1960–1980s3.3. Works of the 1990s and later

4. Manifestation of the wave nature of the breakdown upon discharge ignition in long tubes4.1. Electrical signals in the discharge circuit4.2. The effect of shielding on the breakdown4.3. Breakdown voltage4.4. “Memory effect” of the discharge gap4.5. Initiation of breakdown by visible radiation4.6. Breakdown in a tube with an ungrounded electrode4.7. Radiation spectrum of the ionization wave4.8. The discharge after the passage of the ionization wave

5. ConclusionsReferences

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Fig. 1. Geissler tube.

reached its peak by the 1960s. At the beginning of thecentury, the first gas-discharge light source appeared,competing in a number of characteristics with theincandescent lamp: the Moore lamp (D.F. Moore). Itwas a discharge tube filled with carbon dioxide, whoseradiation spectrum is close to that of natural light.Then began the development of a technology for theproduction of mercury f luorescent lamps, which grad-ually displaced incandescent lamps. The pinnacle oftheir evolution was compact energy-saving lamps witha long discharge tube coiled into a spiral, an electronicpower supply circuit, and a standard lamp base. Cur-rently, they are inferior in efficiency to LED lightsources, but surpass them in spectral characteristics.A glow-discharge plasma in a long tube served as theactive medium for the first continuous laser (He–Nemixture) [4]. This marked the beginning of the cre-ation of an extensive class of gas-discharge lasers usingvarious gases and their mixtures, as well as metalvapors. Although, at present, the field of practicalapplication of many of them has narrowed due to thedevelopment of solid-state lasers, they neverthelesscontinue to be used in metrology, material processing,medicine, etc.

In a long tube, on applying a pulse of large ampli-tude and steepness, a so-called fast ionization wavearises: a potential gradient moving at a speed almostreaching the speed of light. Numerous scientific andtechnical applications of this phenomenon showpromises in chemical technologies, for pumping lasermedia, and for generating high-energy electrons.

2. In many scientific and practical applications, apulsed or pulse-periodic form of discharge is used.This raises the question of the processes of dischargeignition, i.e., electrical breakdown of the dischargegap. Breakdown phenomena were considered both inthe earliest works devoted to discharge [5] and in laterclassical monographs [6, 7] and others, up to the mod-ern ones [3]. A number of monographs are speciallydevoted to breakdown phenomena [8–10].

Breakdown processes depend on the configurationof the electric field, which, in turn, is determined bythe geometry of the gap. The geometry best studiedboth experimentally and theoretically is the case of f latlarge-area electrodes, i.e., a uniform field. Here, twotypes of breakdown are possible, depending on theproduct of the gas pressure p by the distance d betweenthe electrodes. When this product is small (pd <200 Torr cm [3]), the avalanche mechanism proposedby Townsend is applicable. In this case, the electronsmoving (drifting) from the cathode to the anode andionizing the gas produce a series of electron ava-

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lanches, which create a plasma that fills the dischargegap and transfers the gas into a conducting state. Theinitial electrons are created at the cathode as a result ofion–electron emission, photoelectric effect, and otherprocesses. This mechanism can be extended to the caseof a not completely uniform field, e.g., the fieldbetween two coaxial cylinders [8]. At greater values ofpd and at sufficiently high gap voltages, the streamermechanism is realized. Under these conditions, ava-lanches can form that contain a sufficient (~108–109)number of electrons, the space charge of which distortsthe external field, creating regions of high field strengthat the ends of the avalanche. In these regions, second-ary avalanches are generated due to photoionization byradiation from an avalanche or ionization by fast elec-trons. This results in the formation of a plasma chan-nel: a streamer, which rapidly (with a speed muchhigher than the electron drift velocity) grows towardthe cathode or anode. The value of pd at which thetransition from the Townsend to streamer breakdownoccurs depends on the gap voltage. At voltages notmuch higher than the breakdown voltage, this bound-ary can be moved up to pd > 2000 cm Torr [10]. Withan increase in the interelectrode distance, when theexternal field becomes essentially nonuniform, thestreamer mechanism can be outperformed by the morefavorable (in terms of minimizing the breakdown volt-age) leader mechanism. A leader is a conductive chan-nel that grows from the high-voltage electrode to thegrounded along the trail left by streamers. The channelis very hot and can cover huge distances (lightning).

Based on the value of pd, a breakdown in a longtube at low pressure would have to follow theTownsend or, under strong overvoltage, streamermechanism. However, the external field in this case issubstantially nonuniform: its strength is maximal atthe high-voltage electrode (HVE) and drops to zero atthe low-voltage (usually grounded) electrode. Conse-quently, electron avalanches cannot start from thecathode with a positive polarity of the applied voltageand cannot reach the anode with a negative one.Therefore, the avalanche breakdown mechanism isimpossible here. This was first pointed out by Seeligerand Bock in 1938 [11]. Following this, in experimentalwork [12], it was shown that the initial stage of break-down in a long tube is the passage through it of a local-ized glow region. In later studies, it was found that thisis a region of a high potential gradient, or an ionizationwave (IW), which provides the initial conductivity inthe gap and the subsequent development of a glow-discharge plasma. Thus, in long tubes under reducedpressure, a special breakdown mechanism associatedwith the passage of a pre-breakdown ionization wave isrealized. Depending on the conditions, its velocity is105–107 cm/s, if the voltage rise rate lies in the rangetypical of the conditions for the ignition of a glow dis-charge (~1 kV/μs and smaller). If the potential of HVEincreases much faster (with a steepness of ~1 kV/ns or

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ELECTRIC BREAKDOWN IN LONG DISCHARGE TUBES 1017

higher), then the velocity of the IW can exceed~109 cm/s. These are the already mentioned fast IWs.

It should be noted that the above classification ofbreakdown mechanisms is simplified and correspondsto “pure,” limiting situations. In reality, intermediateconditions are possible, when intermediate mecha-nisms or their combinations are realized. In particular,a streamer breakdown can begin with an avalanchestage [13], ionization waves can be observed in the latephase of the Townsend breakdown [10], streamers canacquire the properties of an ionization wave [3], etc. Inparticular, if the pressure is reduced at a high voltagerise rate, streamers can gradually transform into fastIWs [14].

In view of the key role played by ionization waves ina breakdown in long tubes, this review begins with abrief description of the discovery and study of thesewaves.

2. IONIZATION WAVESAs noted above, ionization waves are divided into

fast and slow [15]. In accordance with this classifica-tion, this section is divided into two parts. The break-down processes discussed in this work are preceded bythe propagation of slow waves. However, historically,the first to be detected and then intensively studiedwere fast IWs (FIWs), which arise in the case of verysteep voltage wavefronts. The understanding that thebreakdown under typical conditions for glow-dis-charge ignition is also accompanied by the passage ofan IW came much later, as well as their study. There-fore, Section 2 begins with a review of the FIWs.

2.1. Fast WavesThe phenomenon, which was later called the ion-

ization wave (IW), was discovered by J.J. Thomson in1893 [16]. Thomson studied breakdown in a long (verylong: of length 15 m, the diameter being of 5 mm) glasstube in air at a pressure of 0.5 Torr. The electrodes ofthe tube were connected to the terminals of an induc-tion coil. It turned out that, under the action of a highvoltage, the discharge glow initially does not occur inthe entire tube, but only near the high-voltage anode,and then moves to the cathode with a finite velocity.This velocity was measured using a rotating mirror,which reflected radiation from two different points ofthe discharge and sent it to a measuring telescope. Theresulting value exceeded half the speed of light. Almost40 years later, in 1930, Beams [17] continued thesestudies. He studied breakdown in a tube 4.9 m longand 5 mm in diameter, filled with air or hydrogen at apressure of 0.05–0.4 Torr. To obtain a high-voltage(positive or negative) pulse of 20–40 kV, a condenseddischarge was used. Under the action of a pulse, at thehigh-voltage electrode, a glow appeared, the front ofwhich first had a conical shape, then, while movingalong the tube, became flat and moved with an approx-

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imately constant velocity. The article gives the values of(4–5) × 109 cm/s and asserts that the velocity increaseswith the voltage and does not depend on its polarity. Atthe moment when the glow front reaches the oppositeelectrode, a breakdown occurs and a current appears inthe discharge circuit. In some cases, after the glowreached the low-voltage electrode, its motion in theopposite direction was observed. The author discussesthe possible nature of the observed phenomenon, butdoes not come to any specific conclusion.

The next, very important step was taken in theworks of Snoddy, Beams and Dietrich (1936–1937)[18, 19]. They were first to study the electrical charac-teristics of the process in a discharge tube duringbreakdown with a cathode-ray oscillograph. Itsdeflecting plates were fed with the potentials of twoexternal ring electrodes. Tubes with a length of 15 mand an inner diameter of 1.7–18 mm were filled withair, hydrogen, or carbon dioxide at a pressure of≈0.02–0.2 Torr. The pulse amplitude was 74–171 kV.In [19], optical studies were also carried out. Oscillo-graphic measurements showed that the potential wave-front moves during the breakdown from the high-volt-age to grounded electrode, and its velocity coincideswith the velocity of the glow front. The range of mea-sured velocities is from 5 × 108 to ≈1010 cm/s, depend-ing on conditions. During its motion, the wavefrontcan slow down or accelerate. The preliminary ioniza-tion of the gas increases the velocity several-fold. Thewavefront has a finite extent; the electric field strengthaveraged over this gap reaches ≈2000 V/cm. Thepotential wave carries a current whose density reaches4000 A/cm2. In most conditions, a return wave, mov-ing in the opposite direction with a velocity of ≈1 × 1010cm/s is detected. When the low-voltage electrode isdisconnected from the ground, the return wave disap-pears, but nothing changes for the primary wave. In theauthors’ opinion, the wave moves due to the ionizationat the wavefront, which requires the presence of elec-trons preceding it. In the case of a positive wave (with apositive voltage pulse), these electrons can appear as aresult of photoionization by radiation from the wave-front or be emitted from the tube wall. A negative wavedelivers electrons from the wavefront. These state-ments are fully consistent with modern concepts. Incontinuation of these works, Mitchell and Snoddy [20]found that, when the pulse voltage decreases, the wave-front begins to attenuate: its velocity, the current that itcarries, and the brightness of the glow decrease. In thiswork, the discharge tube was placed in a groundedelectrostatic shield; such a shield was then used in moststudies of the IWs. Among the works of this condition-ally early stage, it is also worth mentioning the papers[21, 22], in which an IW propagated through a glow-discharge plasma.

Further development of experimental equipment,and above all, diagnostic capabilities, made it possibleto achieve significant progress in these studies. Inten-

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sive works in this direction were performed in Moscow(at the Joint Institute for High Temperatures and theMoscow Institute of Physics and Technology(MIPT)), in Arzamas, and Tomsk. Their results aresummarized in reviews [15, 23–26]. Currently, thesestudies are ongoing in France at École Polytechnique(S. Starikovskaya) and in the USA in Columbus(I. Adamovich) and Princeton (A. Starikovskii). InRussia, work in this direction continues at the MIPT(N. Aleksandrov) and in Makhachkala (N. Ashurbe-kov). These studies are stimulated by the prospects ofthe practical use of ionization waves in a variety ofplasma-chemical technologies, laser physics, for thegeneration of high-energy electrons, etc. In parallel,theoretical and computational methods for simulatingIWs have been developed and improved, which is alsoreflected in reviews [15, 23–26] and monographs [27,28]. It should be noted that the existing models, as arule, consider the stage of already formed ionizationwaves rather than their formation [15]. In addition, itis difficult to describe the mechanism of the appear-ance of electrons preceding the front of a positivewave; therefore, it mostly common to consider thewave moving in a preionized gas [24].

As already noted, the waves of the type under con-sideration, having a velocity of ~109 cm/s, are usuallycalled “fast ionization waves” (FIWs). (In [28], an IWis defined as fast if no appreciable displacement of ionsoccurs during the characteristic time of its motion.)FIWs arise under a high overvoltage, i.e., when thepotential U of the high-voltage electrode is muchhigher than the minimum value required for break-down. In this case, the voltage rise rate dU/dt shouldalso be sufficiently large. This condition is on its ownnecessary for the arising of FIWs. In this case, the ini-tial electric perturbation in a time shorter than the dif-fusion time creates a large gradient of potential andspace charge [23, 29]. On the other hand, a fast voltagegrowth allows it to rise to a high level before a break-down occurs. At such voltages, high-energy (runaway)electrons are generated at the wavefront, which play asignificant role in the formation of the wavefront atlow pressures [24]. Most commonly, a voltage U ~ 10–100 kV is used, which can be at least an order of mag-nitude higher than the breakdown potential. In thiscase, dU/dt ~ 1–10 kV/ns and the width of the leadingedge of the pulse is τf ≈ 2–5 ns [14, 30]. The pulseduration is usually τр ≈ 20–50 ns, and the repetitionfrequency is f ≈ 10–40 Hz. The current carried bythe wave has a typical value of ~1 kA.

2.2. Pre-breakdown (Slow) Ionization Waves

The parameters of a pulse generating a FIW, givenin Section 2.1—the amplitude, rise rate, and wavefrontduration—are very different from the values usual forthe ignition of a low-pressure glow discharge in tubes~0.1–1 m long. In this case, the characteristic values

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of the voltage pulse amplitude are U0 ~ 1 kV, i.e., oneto two orders of magnitude smaller than those used inthe excitation of FIWs. At such voltages, the condi-tions for generating runaway electrons [24, 31], whichplay a significant role in the formation of FIWs, arenot satisfied. In order to maintain the normal mode ofglow discharge, it is necessary to include in the circuita ballast resistor with Rb ~ 1 kΩ or higher. Such resis-tance leads to a delay of the voltage pulse wavefront byτf ≈ RbC ~ 1 μs (C is the stray capacitance of the circuitelements). This corresponds to dU/dt ~ 1 kV/μs. Con-sequently, the steepness of the leading edge of thepulse differs from that typical for FIW excitation bythree to four orders of magnitude. Moreover, pre-breakdown waves can be excited at dU/dt that are sev-eral orders of magnitude lower. An example is given inFig. 2, where the results of study of a breakdown in adischarge tube 80 cm long and 1.5 cm in diameter inneon at a pressure of 0.6 Torr are presented. Thebreakdown is carried out by a pulse with a linearlygrowing wavefront AB with dU/dt = 4.7 V/ms. At themoment of breakdown, at point B, a voltage drop atthe anode occurred. Section CD corresponds to asteady-state glow discharge, and, at point D, the pulsewas interrupted. In the lower part of the figure, theoptical signals recorded by two photomultipliers fromtwo points of the tube at a distance of 40 cm from eachother are shown. The presence of maxima proves thepassage of the IW from the high-voltage anode to thegrounded cathode. At the same time, the pulse param-eters initiating this wave are very different from thosetypical of FIW generation. This is especially true forthe voltage growth rate and the leading edge duration,which is almost 0.4 s.

Not only in terms of excitation, but also in theirproperties, such waves are very different from FIWs.For example, the FIW velocity increases with increas-ing dU/dt [32–34]. In what follows, we will see that,for slow IWs, this is not so. Next, the FIW velocityincreases with increasing initial electron density [24,32]. It will be shown below that the electrons remain-ing after the previous pulse, on the contrary, can inter-fere with the generation of the pre-breakdown waveand even block it. It should also be noted that the cur-rent carried by a pre-breakdown IW has an order ofmagnitude of 1–10 mA, i.e., 5–6 orders of magnitudesmaller than that in a FIW.

A characteristic feature of slow IWs is a large roleplayed in their propagation by the walls of the dis-charge tube, in particular, the wall charging process.The models describing these waves [35, 36] pay seri-ous attention to the interaction of the plasma with theboundary. At the same time, dielectric walls of thetube do not play a key role in the propagation of FIWs,although can affect them [24]. In particular, an IW canpropagate even in the absence of walls [37, 38]. Slowwaves can differ from FIWs visually. At a speed of109 cm/s, during the lifetime of the excited atoms

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ELECTRIC BREAKDOWN IN LONG DISCHARGE TUBES 1019

Fig. 2. (a) Time dependence of the anode voltage and(b) emission of an IW. Neon, pressure of 0.6 Torr.

�3 �2 �1 0 1 2 30

1

2

0.6 0.7 0.8 0.9 1.00

0.5

1.0

1.5

DC

B

U, k

V

t, s

t, �s

A

(a)

PMT

sign

al

(b)

Fig. 3. Electric field lines in a U-shaped tube before break-down [11].

(~10–7 s), a wave travels a distance of ~1 m and, there-fore, leaves a trace in the form of a luminous volume(Beams [17] describes it as a cylinder the base of whichlies on the HVE). At a speed of 107 cm/s, this distanceis ~1 cm and the wavefront is detected as a movingpeak of the glow (see Fig. 2).

In conclusion, let us briefly dwell on the terminol-ogy. In an article [29], Loeb introduced the concept ofionizing waves of potential gradient (before that, theywere called potential waves). In subsequent works, theterm was reduced to ionizing waves, which fullyreflected their physical nature. It remained in thisform until the mid-1980s, when the term “ionizationwaves” appeared in the titles of articles. This replace-ment is hardly appropriate, because the scope of thesecond term is much wider. For example, moving stri-ations are also called ionization waves. Nevertheless,this term gradually became prevailing and it is cur-rently used in the literature. Although sometimes, it isimpossible to determine what is meant without refer-ring to the context. For example, some articles devotedto ionization waves refer to paper [39], probablybecause its title contains the words “ionization waves.”In fact, it describes the study of moving striations.

3. STUDIES OF BREAKDOWNIN LONG TUBES AT LOW PRESSURE

For better understanding, this section is dividedinto three parts, describing three time periods: (1) untilabout 1960, (2) 1960–1980s, and (3) 1990s and later.This division reflects to some extent the evolution ofresearch. The first period is the recognition of theproblem and the search for the appropriate model; the

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second is the refinement of the model and the accumu-lation of experimental data; and the third is researchusing modern equipment and computing capabilities.

3.1. Early Works (until 1960)

The first empirical regularities of breakdown inlong tubes were described in 1938 in the book [40]. Ayear before, in [41], the first theoretical model of sucha breakdown, based on the assumption of the unifor-mity of the electric field in the gap, was proposed.However, in 1938, Seeliger and Bock [11] objectedreasonably that, at the time of breakdown, there is nouniform field in a long tube. They escalate the prob-lem, taking a U-shaped tube (Fig. 3), in which thefield is concentrated between the electrodes and isabsent in the rest of the tube. Therefore, the dischargecan be ignited only after the processes forming thelongitudinal field and, in their opinion, the ignitionprocess must propagate in the form of a wave. The fol-lowing year, in 1939, Bartholomeyczeyk [12] con-ducted a thorough study of the ignition of a dischargein tubes about 50 cm long and 2–3 cm in diameter.Helium was mainly studied. One of the electrodes(high voltage) was internal, and the second was in theform of outer ring. Under these conditions, a steady-state discharge was not ignited, but a breakdownoccurred. Optical studies of the radiation from the gasin the tube revealed the following picture. Initially,near the HVE, a glowing region resembling a coronadischarge appears. Then this region is pushed out andmoves in the form of a cloud along the tube until itreaches the opposite electrode. At this moment, abreakdown occurs. The author believes that the cloudduring its motion charges the tube wall and therebycreates a guiding longitudinal field.

Regarding the works [11] and [12], one interestingcircumstance should be noted. Both of them were

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Fig. 4. Oscillograms of current through plates [48]. Р1 aredischarge pulses and Р2 are pulses of recharging the tube–plates capacitance; the distance from the HVE is (1) 5,(2) 15, and (3) 25 cm; U is the HVE potential fed to theplates through the voltage divider.

1

2

3

U

P1

P2

completed later than the work of Beams et al. [17–19],and even more so after J.J. Thomson [16]. However, in[11, 12], there is not a single mention of these studies.It is unlikely that the authors did not know aboutthem. It can be assumed that they considered the con-ditions for FIW generation to be too far from the usualconditions for discharge ignition.

Then the research on ignition of a discharge in longtubes was developed mainly in the USSR. The mainintrigue was the mechanism for creating a guiding lon-gitudinal field. Three versions were considered. In[42–44], it was suggested that such a mechanism is anelectron beam. According to the authors, in the initialstage of breakdown, electrons can have a large directedvelocity and be focused into a beam by the field cre-ated by the space and surface charges. In [42, 44], toconfirm the existence of such a beam, a magneticarmoured lens was put on a discharge tube at differentdistances from the cathode and the breakdown voltageUb was measured depending on this distance. Neon ata pressure of 0.1–0.6 Torr was studied. In [43], for thesame purpose, an electrostatic immersion lens wasused. The voltage Ub turned out to be periodicallydependent on the position of the lens [42, 44] or on theoptical power of the lens [43], which was interpretedby the authors as evidence of the presence of an elec-tron beam focused by the magnetic field. The inter-pretation of the results of these studies seems doubtful.The formation of an electron beam under the condi-tions of these experiments is extremely unlikely, atleast at a noticeable distance from the cathode. Theauthors refer to [45], where the presence of such abeam was indicated by X-ray radiation from the anodeof the tube. However, it should be noted that the mea-surements in [45] were performed at a pressure below1 mTorr (i.e., almost in vacuum) and at a high anodevoltage of about 100 kV.

Another version of the mechanism for creating aguiding longitudinal field was proposed in [46].Breakdown in standard f luorescent lamps of variouslengths was studied. One of the electrodes was free,and the second was fed with alternating voltage of theindustrial frequency and variable amplitude. At a cer-tain value of this amplitude, a glow appeared near thiselectrode. With a further increase in the amplitude,the glow region first increased and then instantly filledthe entire tube. The authors called this state “single-electrode discharge.” In their opinion, this dischargeis the first stage of breakdown. It causes ionization andthe initial conduction of the gas in the tube. At thesame time, it leaves a surface charge on the tube wall.It is this charge that creates the guiding field. In a laterarticle [47], the authors complicated the scheme bycombining the concept of a single-electrode dischargewith the idea of the dominance of the directionalmotion of electrons in it over the chaotic one.

The third breakdown mechanism, confirmed bylater studies, was proposed by Nedospasov and Novik

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[48] in 1960. They studied the ignition of a dischargein argon at a pressure of 0.5–10 Torr in tubes of variouslengths and diameters. As in [12, 46], one of the elec-trodes was connected to a voltage source and the otherwas free. In fact, the role of the second electrode wasplayed by the outer plates placed along the tube at dif-ferent points. The current through the plates was mea-sured by an oscilloscope. The integral radiation fromtwo points of the tube was detected by two photomul-tipliers. The HVE was fed either by a sinusoidal or rec-tified half-wave voltage of variable frequency andamplitude (Fig. 4, U curves). The voltage growth ratewas 105–106 V/s. The following picture was observed.At a certain voltage, near the HVE, a weak glow aroseand current pulses in the circuit of the nearest platewere recorded (Fig. 4, P1). With a further increase involtage, the glow and current pulses appeared at anever greater distance, the pulses on the farther platesbeing regularly shifted in time, which evidenced afinite propagation velocity of the process. At a suffi-ciently high voltage, the process extended to the entiretube. Similar results were obtained for neon. Fromthese oscillograms and from optical measurements,the velocity of the discharge front was found; depend-ing on the conditions, it was ≈(0.5–5) × 105 cm/s.

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Fig. 5. Oscillograms of the cathode current and anodevoltage during breakdown in a He–Ne mixture (p =4 Torr) [51]. Scale: 1 division = 25 μs.

t1

Ua

ic

t2

It should be emphasized that the novelty of thiswork in the understanding of the breakdown mecha-nism is the existence of a primary breakdown betweenthe HVE and the wall. It also proposed a computa-tional model in which the development of the dis-charge is described by a one-dimensional equation ofRC line with distributed parameters.

3.2. Works of the 1960–1980s

More recent studies have not changed much inunderstanding the breakdown processes in long tubes.The dependences of the quantitative characteristics ofthe process on the type of gas and experimental condi-tions were mainly studied. In almost all works, thevelocity of the pre-breakdown IW, , was measured.The wave is easily detected by radiation from its front.In [49], breakdown was studied in different gases (Н2,Не, Ar, and О2) in a wide range of pressure p = 10–2–100 Torr and in tubes of various diameters and lengths.The dependence turned out to be nonmono-tonic, with a maximum in the region of p ~ 1 Torr.This is similar to FIWs, for which this function is non-monotonic too [23–25]. On the other hand, a signifi-cant difference from FIWs is that the IW velocityproved to be independent of the voltage rise rate in therange 107–1011 V/s, which is completely unusual forFIWs [32–34].

In [50, 51], breakdown processes were studied in ahelium–neon laser mixture at p = 4 Torr in a sitall cellwith a diameter of 3.5 mm and a glass tube with adiameter of 6 mm. The voltage at the high-voltageanode, the cathode current, and radiation from differ-ent points along the discharge gap were recorded. Abreakdown began with a small drop of the anode volt-

vw

v ( )w p

PLASMA PHYSICS REPORTS Vol. 46 No. 10 2020

age Ua (Fig. 5) and, simultaneously, with short spikesof the cathode current ic and radiation intensity fromthe anode region (at a certain time t1). After some time(at t2), the same surges of ic and Ua occurred, but of amuch larger amplitude. The voltage dropped almost tozero, and the current reached a maximum. Then theyvaried nonmonotonically and eventually reached thelevel of a steady-state discharge. In the intervalbetween t1 and t2, the glowing region, i.e., IW, movedfrom the anode to the cathode. The velocity of thewave was almost constant and, depending on theparameters of the electric circuit, was from ~105 to~106 cm/s in the cell and higher than 4 × 107 cm/s inthe tube. The shielding of the tube reduced this valueby more than an order of magnitude. In [51], theauthors propose the following qualitative picture.When moving from the anode, the IW carries in frontof it an electric field, in which the electrons producesubsequent ionization and excitation. Electrons pre-ceding the wavefront are born as a result of photopro-cesses (photoemission from the tube walls). Behindthe leading part of the IW, a conducting plasma col-umn is formed, through which an electron currentflows to the anode and the ions charge the distributedplasma–ground (or plasma–screen) capacitance. Thecurrent lines close through the bias current. In accor-dance with this picture, an approximate semi-empiri-cal model is proposed, which, using adjustable param-eters, gives correct dependences of the IW velocity onthe applied voltage.

The work [52] is the only one in which IWs wereregistered using Langmuir probes. Two probes with adiameter of 25 μm and a length of 3 mm were locatedon the tube axis at a distance l = 2 cm from each other.

1022 IONIKH

The diameter of the tube is 4 cm, and the studied gasesare helium and argon at various pressures and pulseamplitudes. During the passage of an IW, the potentialof each probe underwent a jump of ~1 μs duration.The jumps were shifted relative to each other by thetime the wave travels the distance l. Hence, the veloc-ity of wave could be found. The range of valuesobtained was ≈ (1–20) × 106 cm/s. For both gases,the dependence of the IW velocity on pressure wasnonmonotonic, with a maximum at p ≈ 2–3 Torr forHe and ≈0.7 Torr for Ar; the velocity in helium was 2–4 times lower than in argon. The dependence of onthe pulse amplitude is approximately linear for heliumand essentially non-linear with a power-law shape forargon. The paper proposes an approximate semi-empirical model for calculating the IW velocity. Forthis, the authors use the plasma parameters obtainedby processing the probe characteristics, but without ananalysis of how applicable the probe theory is for theobject under study. The possible influence of theprobes and elements of the probe circuit on the IWcharacteristics is also not discussed. In the subsequentworks [53, 54], the same authors used the probemethod to measure the time dependence of the elec-tron density ne at the initial phase of the discharge inargon at a pressure of 0.3–0.75 Torr in the same tube.The values obtained reach a steady-state level for 50–70 μs. In this case, measurements begin 5 or 10 μs afterthe voltage is applied. If we use the authors' data forthe IW velocity from [52], it turns out that, by thismoment, the wave has passed the entire discharge gap.Thus, the data obtained illustrate the ionization mul-tiplication of electrons left by the wave. In both papers,a theoretical model is also proposed.

3.3. Works of the 1990s and Later

Since the end of the 1980s, the study of breakdownin long tubes sharply intensified. This was directlyrelated to the start of production and the widespreadintroduction of compact f luorescent lamps (CFLs),convenient and economical. Most likely, if LEDlamps have not appeared, they would completely dis-place incandescent lamps and become the numberone light source. Specifically, the interest in studyingthe discharge ignition processes in CFLs was con-nected with the optimization of the operating modesof the lamp itself and the pulsed electronic power cir-cuit. The former, linear lamps were fed with a mainscurrent through a ballast device (usually a choke).Research was conducted in the universities of Eind-hoven (Holland) and Augsburg (Germany) and in thelaboratories of the leading CFL manufacturers: Phil-lips and OSRAM. The main results are presented in[35, 36, 55–60], of which [56, 57, 59] are purelyexperimental, [35, 36, 58] are computational, and theresults of both experiments and modeling are pre-sented in [55, 60]. The gases under study were the

vw

vw

vw

P

components of the mixtures used in the lamps: argon[35, 56, 57, 60] or argon with mercury vapor [36, 55,58, 59]; in [59], there were also neon or krypton addi-tives. The total pressure in all cases was about 3 Torr.The discharge tubes had an internal diameter of10 mm, the same as of standard CFLs; in [55] a tubewith an outer diameter of 32 mm was used. The cath-ode or both electrodes of the tube were incandescent.High-voltage pulses are rectangular, with an ampli-tude U0 ~ 1 kV or smaller and a leading edge durationof ~1 μs (correspondingly, dU/dt ~ 1 kV/μs). In [35,36, 56, 57], the polarity of the pulses was negative; inother works, pulses of both polarities were studied.The pulse duration in [55] was 10 ms and, in the rest ofthe papers, ~100 μs; the repetition period was 200 ms(400 ms in [55] and 10 s in [59]). With the exception ofthe latter, in other works, in the intervals between themain pulses, short resetting pulses with an amplitudeobviously exceeding the breakdown voltage wereapplied to the electrodes. Their purpose was to neu-tralize the surface charge that could remain on the wallif the IW of the previous pulse has not reached thegrounded electrode and breakdown has not occurred.In [60], in addition, immediately before the mainpulse of positive polarity, a short negative pulse ofsmall amplitude was applied to the anode. It did notlead to a breakdown, but preionized the gas in theanode region and thereby eliminated the statisticaldelay of the breakdown. With the exception of [59],the discharge tube was surrounded with an electro-static shield: a grounded metal pipe with a diameter ofabout 5 cm (3.5 cm in [55]). The purpose of the shieldwas to eliminate electrical interactions between thedischarge and the remaining elements of the equip-ment, and, in the modeling, impose the boundaryconditions for the IW. In addition, the shield made itpossible to maintain a constant temperature andhumidity inside it. As a rule, two ionization waves wereobserved: the first (forward) and return. However, theauthors of [59] report about only one wave and theauthors of [55] about three.

Breakdown IWs were diagnosed by two methods:optical [56, 59, 60] and electrical: using a capacitiveprobe [55, 57, 60]. In the first case, an IW was diag-nosed by the radiation from its wavefront, and, in thesecond case, by the potential of the wall on which thewave left a charge. In [59], the radiation of the wavewas recorded using 8 photomultipliers placed along itspath, and, in [56, 60], using an intensified CCD cam-era. The capacitive probe in [55] was an outer ringmounted in an electrostatic screen and connected to itthrough a low ohmic measuring resistor. Such ascheme minimized the disturbance introduced by theprobe, but had a low spatial resolution due to the gapbetween the probe and the tube. In [57, 60], such a gapwas absent and the perturbation introduced in thiscase was minimized by the special design of the loadresistor and the use of an electronic feedback circuit.

LASMA PHYSICS REPORTS Vol. 46 No. 10 2020

ELECTRIC BREAKDOWN IN LONG DISCHARGE TUBES 1023

Fig. 6. IW velocity vs. pulse amplitude for the (1) positiveand (2) negative polarity (according to [60]). Argon, p =3 Torr.

2

1

10

vw, 106 сm/s

8

6

4

2

0400 500 600 700 800

|U0|, V

Both methods made it possible to measure the IWvelocity [55, 56, 59, 60]. The range of values obtainedis ~ 105–107 cm/s. In all cases, the velocityincreased with increasing pulse amplitude U0. In [55],

it varies as , where q ≈ 6 for positive polarity andq ≈ 1.5 for negative polarity, as a result of which, forU0 < 500 V, the negative wave is faster than the positivewave and, for U0 > 500 V, vice versa. In [60], thedependence is close to linear and, for a positivewave, it is also steeper than that for a negative one;therefore, these lines intersect at U0 ≈ 550 V (Fig. 6).In [59], for U0 = 800–1100 V, the positive wave is fasterthan the negative wave. As the wave moves, its velocitydecreases: the lower U0, the faster the decrease. At asufficiently low U0, it may occur that the wave does notreach the grounded electrode and disappears at anintermediate point [56, 60]. In this case, a breakdownof the entire tube and a discharge ignition do notoccur. Here, a “memory effect” arises [60], whichaffects the breakdown processes; in particular, thenext breakdown may not occur at all. The authorsrelate this effect to the surface charge left by the wave.To neutralize this charge, in the interval between themain pulses, additional short pulses with an amplitudelarge enough to ignite a discharge, which will removethe wall charge, were supplied to the electrodes. Basedon these observations, the following statement is for-mulated: a necessary condition for a complete break-down of the tube and a discharge ignition is that thepulse be long enough so that the IW can pass the entiregap during the pulse.

The main purpose of using a capacitive probe wasto obtain information about the electrical characteris-tics of the IW. In [55], the bias current to the probe wasmeasured. The integration of the current over timegave a charge, and, by dividing the charge by thecapacity of the tube–screen system, the potential ofthe wall was obtained. Measurements showed thatboth quantities, after the start of the pulse, reachsteady-state values at a distance from the HVE on theorder of the tube diameter, and the potential reachesthe amplitude value of the pulse voltage. After reach-ing the grounded electrode, they decrease (in absolutevalue), which the authors relate to the return wavemoving toward the HVE and partially discharging thewall. At the time of its arrival at the HVE, the thirdwave is generated, propagating in the original direc-tion. In [60], the probe touched the tube surface and,thanks to the corresponding electronic circuit, made itpossible to directly measure the wall potential. Differ-entiation with respect to the axial coordinate gave thelongitudinal electric field strength E. The curves pre-sented in [60] give the time dependence of E. Thecurves exhibit oscillations, the cause of which is notdiscussed. In a negative wave, E = 100–115 V/cm forthe range U0 = 400–800 V. For a positive wave, E =150–200 V/cm for U0 = 500–700 V, except for the

vw

0qU

v 0( )w U

PLASMA PHYSICS REPORTS Vol. 46 No. 10 2020

moment when the wave arrives at the cathode at U0 =500 V; at this point, E = 283 V/cm. Data on the biascurrent and wall charge were also obtained.

In [59] and [60], it was found that the breakdownpotential of Ub depends on the pulse polarity, but thespecific data of these studies differ significantly. In[59] (Ar–Ne and Ar–Kr mixtures), Ub is higher fornegative polarity. Moreover, it is said that, in this case,it is almost never possible to realize a breakdown. In[60] (Ar), the situation is opposite: for positive andnegative voltages, Ub = +455 and –300 V, respectively.

As mentioned above, in a number of studies, modelcalculations of various stages of breakdown are carriedout. The calculations performed in [55] are basedentirely on the Nedospasov and Novik model [48].The discharge gap is simulated by a set of 125 series-connected RC circuits, where R describes the resis-tance of the plasma column section, and C describesits capacity relative to the ground. The difference fromthe model [48] consists only in the fact that R isassumed to be time-dependent. Volume ionizationprocesses are described by a very primitive semi-empirical model. Nevertheless, it implies the very factof the feasibility of a self-sustaining motion of theplasma boundary, i.e., the wavefront. However, itshould be emphasized that only a negative wave is con-sidered and it is assumed that charged particles are ini-tially present in the gas. In [35] (breakdown in argon),the reactions in the volume are considered more cor-rectly. The hydrodynamic approximation is used, con-tinuity equations for charged particles are written withallowance for various ionization processes, includingthose involving excited atoms, Poisson equation tak-ing into account the presence of electrodes and adielectric wall, and processes at the plasma–wallinterface. The rate constants of the processes are con-sidered as a function of the mean energy, which is

1024 IONIKH

related to the parameter E/p using the calculated elec-tron energy distribution function. The result of thecalculations is a set of axial dependences of electricalparameters (surface charge, field strength, potential,electron density, and mean electron energy), thevelocity of the ionization wavefront at different times,as well as the dependence of the calculated quantitieson the parameters: pulse amplitude, pressure, tubediameter, etc. Only a negative wave is considered, andthe presence of a heated cathode, emitting initial elec-trons, is assumed. The results qualitatively agree withthe experimental picture of the IW motion. In [36],similar calculations were performed for a mixture con-taining argon with mercury vapor. It turned out thatthe Penning ionization reaction of mercury atoms cansignificantly increase the electron density and affectthe velocity of the wave, especially the return one. In[58], a similar approach is used for the case of period-ically repeated pulses of alternating polarity of a ratherhigh frequency, up to 120 kHz, i.e., for the region typ-ical of CFL power supply. Symmetrical trapezoidalpulses are considered. In this case, the IWs propagatealternately in opposite directions, and the picture iscomplicated by the fact that the positive and negativewaves have different velocities. The process of estab-lishing the lamp parameters and their dependence onthe repetition rate and pulse amplitude is theoreticallystudied. When analyzing the ionization in the wave,the authors neglect stepwise processes, which, at ahigh pulse repetition rate, may be incorrect.

A different approach to modeling the IW motion isproposed in [60]. The wavefront is approximated by arectangular region F with a high electric field strength.In front of it, the field is zero, and after it (in theplasma wake), finite but small. Inside F, avalanche(Townsend) ionization occurs. Electrons disappear onthe tube wall as a result of free diffusion. In the case ofa negative wave, the ionization rate is equal to the elec-tron loss rate. The motion of the IW is possible due tothe electron drift f low directed from the front to theanode. The electron density in the conducting wake ofthe wave is maintained due to the arrival of electronsfrom the cathode. The equality of the ionization anddiffusion rates determines the field strength at thewavefront, and the velocity of the wave is determinedby the rate of charging the tube capacitance relative tothe ground (as in [48]). In the case of a positive wave,seed electrons cannot be caused by the electron driftfrom the wavefront. Analyzing their possible sources,the authors stop on photoelectron emission from thetube walls under the action of UV resonant radiationof the wave. Since the quantum yield of the photoelec-tric effect is most likely small, a high rate of excitationof resonant levels is needed; this requires a higher elec-tric field strength at the wavefront than in the case of anegative wave, which is consistent with reality. Itshould be noted that, evaluating the electron photo-emission efficiency, the authors neglect the reabsorp-tion of photons. Nevertheless, the model using fitting

P

parameters gives correct values of the IW velocity andits time dependence.

In the relatively recent experimental works [61, 62],the stages after the passage of the ionization wave—theignition of a glow discharge with the subsequent tran-sition to the arc mode—were investigated. A U-shapedfluorescent lamp 1 m long and 17 mm in diameter wasstudied. At a distance of 1 cm from the lamp, there wasa grounded metal plate, the presence of which facili-tated ignition. The lamp was powered by a sinusoidalvoltage with a frequency of 25 kHz and an effectivevoltage of 400–600 V. The so-called cold start wasstudied, when the cathode of the lamp is not heated byan external current as in the traditional scheme. Thismode is more economic and eliminates the pause nec-essary for heating the cathode. The time course of thevoltage and discharge current after turning on the volt-age was recorded. From the oscillograms obtained,one can trace the entire evolution of the dischargeignition: the IW propagation interval, ignition of anormal glow discharge, its transition to the anomalousmode accompanied by heating the cathode by the dis-charge current, and, as a result, the ignition of an arc.The dependences of the energy deposition to the dis-charge and the lifetime of the discharge in glow formon the supply voltage are obtained.

4. MANIFESTATION OF THE WAVE NATURE OF BREAKDOWN DURING DISCHARGE

IGNITION IN LONG TUBES

The fact that the initial stage of breakdown in longtubes is the passage of an ionization wave through thedischarge gap leads to a number of features differing itfrom the “waveless” Townsend breakdown. One ofthem has already been mentioned: this is the depen-dence of the breakdown potential on the polarity ofthe applied voltage [55, 59, 60], in other words, onwhich of the electrodes—the cathode or the anode—isgrounded or at least is at a low potential relative to theground.

The need for grounding is caused by the specifics ofbreakdown in long tubes: the presence of primarybreakdown on the wall as the initial stage of dischargeignition. This circumstance is illustrated by Fig. 7. Init, r1 and r2 are the limiting (ballast) resistors (one ofthem is usually absent, i.e., its resistance equal to zero)and R1 and R2 are the resistances of the insulation(leakage) of the terminals of the power source. Usu-ally, R1 ~ R2 ≫ r1, r2. Let the potential of the groundand the surrounding space be zero. Before the voltageis turned on, the potentials of both electrodes and thetube wall are also zero. Suppose that none of the elec-trodes is grounded. Then, after turning on the voltageU, but before the current appears, the potentials of theelectrodes will be [+R1/(R1 + R2)]U and [–R2/(R1 +R2)]U, while the potential of the wall is still zero. Dueto the uncertainty and instability of the resistances

LASMA PHYSICS REPORTS Vol. 46 No. 10 2020

ELECTRIC BREAKDOWN IN LONG DISCHARGE TUBES 1025

Fig. 7. Schematics of connecting a discharge tube at a pos-itive pulse polarity.

A C

r2

t

r1

U

R1 R2

+ –

Fig. 8. Breakdown in an Ar–Hg mixture (p = 3 Torr andрHg = 1 mTorr). Oscillograms of the anode voltage, theanode (ia) and cathode (ic) currents, and the integral emis-sion intensity near the anode (Фа) and cathode (Фс) [63].

0 2 15 200

0.5

1.0

1.5

2.0

0 2 15 200

0.5

1.0

0

20

40

60

80t2t1

ia

ic

Ua

t0

Ua,

kV

i, m

A

�, a

rb. u

nits

�a �с

t, �s

R1 and R2, the potential of the electrodes relative to thewall will also be undefined, which will lead to unpre-dictability and irreproducibility of the primary break-down. This will not happen if one of the electrodes ofthe tube is grounded, directly or through a low resis-tance. The polarity of the ungrounded electrode deter-mines the direction of propagation and the propertiesof the IW and, ultimately, the breakdown characteris-tics. This is obviously not the case of the Townsendbreakdown, in which, if the discharge gap is symmet-rical, only the potential difference between the elec-trodes is important, and the polarity of the groundedelectrode, as well as the presence of grounding, do notplay a role.

In addition to the dependence of the breakdownpotential on the sign of voltage, there are other specific-ities of the breakdown processes in long tubes, causedby its wave mechanism. They are considered below.

4.1. Electrical Signals in the Discharge Circuit

The time dependence of the electrical characteris-tics of the discharge (currents and voltages) can carryuseful information about the breakdown process.Despite this, such studies are few. In [51], oscillo-grams of the voltage at the high-voltage anode and ofthe current through the cathode during breakdown ina tube filled with a He–Ne mixture are shown (Fig. 5),and, in [55], the time course of the current through thehigh voltage cathode for the Ar–Hg mixture isdemonstrated. More detailed and illustrative resultswere obtained in [63, 64]. Figure 8 shows oscillogramsrecorded in the study of breakdown in a tube 80 cmlong and 23 mm in the inner diameter in argon withmercury admixture at a total pressure of 3 Torr and aHg vapor pressure of 1 mTorr with a grounded cathodeand a ballast resistance of 20 kΩ. At the time t0, a pulsewith an amplitude U0 = 2 kV is fed to the anode. At thesame time, a surge in the anode current, caused bycharging the tube–ground capacitance, is seen. At thepoint t1, the anode current sharply increases: a primarybreakdown occurs. Simultaneously, the anode voltage

PLASMA PHYSICS REPORTS Vol. 46 No. 10 2020

abruptly decreases by the value of the drop in the bal-last resistance. For 2.5 μs, a current f lows through theanode; since, in this case, the cathode current is zero,the anode current charges the wall, and its circuit isclosed through the plasma–ground capacitance, i.e.,through the bias current. At the time t2, a cathode cur-rent appears and the breakdown is completed. Theanode and cathode currents increase, approach eachother, and reach a steady-state level. In the intervalfrom t1 and t2, the luminescence peak moves from theanode to the cathode; i.e., the IW generated at theanode at the time of primary breakdown moves andarrives at the cathode at the moment of completebreakdown. The time interval from t0 to t1 is the timedelay of the primary breakdown. From pulse to pulse,it changes randomly, as is also observed during thebreakdown of short gaps [8].

Similar curves for a pulse of negative polarity areshown in Fig. 9. The most noticeable difference fromthe previous picture is the absence of a peak in the sig-nal of the current in the low-voltage electrode (in thegiven case, anode) at the time of complete breakdown.

The data presented in these figures were obtainedin a tube with a cold (non-incandescent) high-voltageelectrode. With a positive pulse polarity, the low-volt-age cathode was incandescent, but this did not affectthe shape of the curves. Incandescence of the cathodeprevented its sputtering and destruction due to ionbombardment. Figure 10 demonstrates the effect ofthe heating of the high-voltage cathode. In this case,the primary breakdown occurs at the leading edge ofthe pulse, i.e., there is no delay of breakdown. This isquite expectable, since the time delay (more precisely,

1026 IONIKH

Fig. 9. Breakdown in an Ar–Hg mixture by a pulse of neg-ative polarity. Oscillograms of cathode voltage and thecathode (ic) and anode (ia) currents [64]. The conditionsare the same as in Fig. 8.

�Uc,

kV

2 10 15 200

0.5

1.0

1.5

2.0

t2t1

iaic

Uc

t0

0

10

20

30

40

50

t, �s

i, m

АFig. 10. Breakdown in an Ar–Hg mixture by a pulse ofnegative polarity with cathode heating. Oscillograms ofcathode voltage, cathode (ic) and anode (ia) currents, andemission intensity near the anode (Фа) and cathode (Фс)[64]. The conditions are the same as in Fig. 8.

0 10 20 30 400

0.5

1.0

1.5

2.0

0 10 20 30 400

1

0

20

40

60

80

100

ia

t2t1

Uc

ic

t0

t, �s

�Uc,

kV�

, arb

. uni

ts

�a�c

i, m

A

its statistical component: under the given conditions,the main one [65, 66]) is determined by the frequencyof appearance of the electrons initiating the break-down. When the cathode is heated, this frequencybecomes very large. The delay of the leading edge ofthe voltage pulse in Fig. 10 is caused by the capacity ofthe heating circuits.

4.2. The Effect of Shielding of the Tubeon the Breakdown

As noted above, in many studies of breakdown, thedischarge tube was surrounded with a conductivegrounded shield. The purpose of the shield was toeliminate the electrical effect of other elements of theequipment on the discharge. Although this effect isindeed eliminated, it is replaced with an effect of theshield. To determine the degree of this effect, experi-ments with conducting shields were carried out in[63–65]. The shields had the form of cylinders of var-ious diameters: from 3 to 67 cm and a length equal tothat of the discharge tube (80 cm). Their ends wereopen; therefore, the shielding of the tube was not com-plete. The shields were grounded either directly or, forthe purpose of measuring the current in the shield–ground circuit, through a low measuring resistance. Itcan be seen in Fig. 11 that even incomplete shieldingsignificantly affects the breakdown. The presence ofthe shield dramatically enhances the dip of the anodevoltage during the initial breakdown and increases theanode current during the propagation of the ionizationwave. The spike of the cathode current, on the con-trary, decreases, and can even disappear completely(Fig. 12). The smaller the diameter of the shield, thestronger these effects. For a shield of maximum diam-eter (67 cm), they are almost invisible.

Obviously, the effect of the shield is due to anincrease in the capacitance CS between the tube and

P

the ground. Through this capacitance, the bias currentflows during the initial breakdown and the motion ofthe ionization wave. The presence of a shield increasesthis capacitance and decreases its impedance, whichleads to an increase in the anode current and a voltagejump at the time of the initial breakdown. At the finalstage of breakdown, this capacitance, being charged,counteracts the completion of the breakdown: itreduces the jump of the cathode current or smooths it.Figure 12 also shows the waveform of the current is inthe shield–ground section. In fact, in this way, the biascurrent going to ground is recorded. In the intervalfrom the initial breakdown to the appearance of thecathode current, the shield current is equal to theanode current. After the appearance of the cathodecurrent, as expected, is = ia – ic.

Figure 13 illustrates the effect of shielding on themean velocity of the ionization wave. This effectdepends on the size of the shield. With a sufficientlylarge diameter ds, the effect disappears. With smallerds, the dependence is nonmonotonic. In [63],the following qualitative explanation was given. On theone hand, a decrease in ds, i.e., an increase in thecapacitance CS, leads to an increase in the energydeposited in the primary discharge, which can lead toan increase in the initial velocity of the wave. On theother hand, the wave during its motion must chargethis capacitance; therefore, an increase in CS mustslow down the wave.

Thus, the shielding of the tube, excluding the elec-trostatic interaction of the discharge with external

v ( )av sd

LASMA PHYSICS REPORTS Vol. 46 No. 10 2020

ELECTRIC BREAKDOWN IN LONG DISCHARGE TUBES 1027

Fig. 11. Time dependences of the anode voltage duringbreakdown in an Ar–Hg mixture in a tube (1) without ashield and with a shield with a diameter of (2) 67, (3) 25,(4) 5, and (5) 3.3 cm [65]. The conditions are the same asin Fig. 8. © IOP Publishing. Reproduced with permission.All rights reserved.

0 0.5 1.0 1.5 2.0

0

0.5

1.0

1.5

2.0

2.5

5

432

1

t, �s

Ua, kV

Fig. 12. Time dependences of the anode voltage and theanode (ia), cathode (ic), and the shield (is) currents. Thediameter of the shield is 3.3 cm. Ar–Hg mixture [63]. Theconditions are the same as in Fig. 8.

10 12 14 16

�1

0

1

2

3

�40

�20

0

20

40

60

80

Ua

is

ia

ic

18

Ua,

kV

i, m

A

t, �s

Fig. 13. Length-averaged IW velocity vs. the diameter ofthe shield at different voltage pulse amplitudes; horizontallines: represent measurements without a shield. Ar–Hgmixture, positive pulse [63]. The conditions are the sameas in Fig. 8.

10 100ds, сm

100

101

10�1303

2.5 kV2.0 kV

1.5 kV

1.0 kV

vw, 106 сm/s

devices, leads to a much stronger interaction with theshield. The shields described here did not provide fullshielding; it is clear that, otherwise, its effect is evenstronger. This means that the results of studying abreakdown in a shielded tube depend not only on thecharacteristics of the discharge gap, the type of gas,etc., but also on the geometry of the shield. In partic-ular, these results may not be applicable for anunshielded tube. By the way, it is precisely such tubesthat are used in compact f luorescent lamps.

4.3. Breakdown Voltage

The breakdown voltage or breakdown potential Ubis the most important characteristic of the dischargegap. In the Townsend breakdown in a uniform field,the breakdown potential is found from the Townsendcriterion and its value for a given gas is determined bythe similarity parameter pd (Paschen curves) [3, 8].For a cylindrical discharge tube of length l and radius r,it seems that another similarity parameter, r/l,appears. If we assume that the field in such a tube isstill uniform, then the only new factor will be theescape of electrons from the gap in their radial diffu-sion and the role of this process can be determined bythe parameter r/l. In the works of Lisovskiy et al. [67,68], a modified Paschen law was proposed, whichtakes into account the radial diffusion of electronsand, according to which, Ub is determined by theparameters pl and l/r. It can be seen from Fig. 14 thatl/r is indeed a similarity parameter. However, it shouldbe borne in mind that, in this example, the distancebetween the electrodes is almost equal to their diame-ter: l/2r = 1.2; i.e., this is a case of a weak nonunifor-mity of the field. On the whole, the approach of [67,

PLASMA PHYSICS REPORTS Vol. 46 No. 10 2020

68] assumes the field uniformity and, therefore, is notapplicable to long tubes, where the field is essentiallynonuniform and the wave mechanism of breakdown isrealized.

In a long tube, the process begins with a primarybreakdown between the HVE and the nearest sectionof the tube wall [48]. Therefore, the first breakdowncondition is as follows: the amplitude U0 of the pulseapplied to the HVE should be large enough for the pri-mary breakdown to occur and the pre-breakdown IWto start. Further on, it is necessary that the IW pass theentire gap and reach the low-voltage electrode. If U0 isnot high enough, it may turn out that the wave doesnot reach the grounded electrode and disappears at anintermediate point [56, 60]. In this case, the break-down of the entire tube will not occur. This is the sec-ond condition for U0. In addition, this imposes a con-

1028 IONIKH

Fig. 14. Modified Paschen curve for argon at l/r = 2.4 [67];l = (1) 1.1 and (2) 3.3 cm.

Ub, V

800

600

400

200100 101

pl, Тоrr сm

12

dition on the voltage pulse duration [60]. If, along witha breakdown, the ignition of a steady-state discharge isrequired, then U0 should be sufficient to maintain it.The first condition obviously depends on the geome-try of the region near the HVE (tube diameter, elec-trode size, etc.) and does not depend on the length ofthe discharge gap. The second condition is determinedby all these parameters, including the length. For thethird condition, cathode material, tube length anddiameter, etc. are important. These three conditionsare practically independent, and, therefore it is impos-sible to establish a general regularity such as Paschenlaw, which would connect Ub with the parameters ofthe discharge gap.

The wave, due to the “concentration” of the elec-tric field at its front, is an effective mechanism for cre-ating the initial ionization in the gap. In this, it is sim-ilar to moving striations in the positive column of adischarge, where the field is concentrated in the headof the striation, due to which the voltage drop acrossthe column is lower than if the field were uniform [3].In the same way, an IW can reduce the breakdownpotential. This is illustrated by the following experi-ment [46] (Fig. 15). Using two plates connected to theelectrodes of the tube, the field in it is made close touniform. In this case, the breakdown potential

P

Fig. 15. Schematics for studying breakdown in a fie

B T

220 V V

increases: the longer the gap, i.e., the greater the non-uniformity in the tube without plates, the larger theincrease: from 20% for l = 20 cm to 2.2 times for85 cm.

Usually, the breakdown voltage is understood asthe so-called static breakdown voltage US. This is theminimum voltage at which a self-sustained form ofdischarge is maintained [69]. The classical Townsendbreakdown condition for short gaps refers to thisquantity. If, starting from zero, the interelectrode volt-age U is continuously increased with a rate dU/dt, thenthe value of Ub at which the breakdown will occur,generally speaking, will exceed US. This is due to thedelay of the breakdown relative to the moment whenU = US, as a result of which

(1)where td is the breakdown time delay. If we measure Ubat various voltage rise rates and then extrapolate thedependence obtained to the zero of dU/dt, we obtainthe value of US [69]. The time delay of the breakdowncan be represented [8] as the sum of two quantities:statistical time delay ts and formative time tf :

(2)

The statistical delay is the time during which, in thegap, an electron appears that initiates an avalanche,the development of which leads to a breakdown (effec-tive electron [69]); therefore

(3)where z is the frequency of appearance of effectiveelectrons. The quantity ts is stochastic and can fluctu-ate in a wide range. The formative time tf is the inter-val from the moment of the appearance of such anelectron to the current jump in the discharge circuit,i.e., to the breakdown. The stochasticity of ts leads tofluctuations in the total time delay td. In turn, the scat-ter of td, according to relationship (1), leads to a scatterof the values of the breakdown voltage Ub, for which,in this case, the term “dynamic breakdown voltage” isintroduced (sometimes this term is used for the quan-tity obtained by averaging over a large number ofbreakdowns).

= + ( / ) ,b S dU U dU dt t

= + .d s ft t t

= –1,st z

LASMA PHYSICS REPORTS Vol. 46 No. 10 2020

ld close to uniform [46]; S1 and S2 are metal plates.

S1

K1 K2

S2

ELECTRIC BREAKDOWN IN LONG DISCHARGE TUBES 1029

Fig. 16. IW velocity vs. breakdown voltage in nitrogen andhelium for dU/dt = 0.5–7.0 kV/ms (N2) and 3–140 kV/ms(He). Pressure p = 1 Torr, a tube with a diameter of d =28 mm and a length of l = 40 cm [70].

1.0 1.5 2.0 2.5 3.0 3.5Ub, kV

100

101

102

He

N2

vw, 106 сm/s

It is believed that the primary breakdown in a long

tube between the HVE and the nearest section of thetube wall proceeds according to the Townsend mech-anism [60]; therefore, relationships (1) and (2) holdalso for it. Since the moment of breakdown of theentire gap is separated from the initial breakdown bythe time of passage of the ionization wave (or waves),the total time delay increases by this value:

(4)

where ts and tf refer to the primary breakdown and tw isthe time of the IW motion. As in the case of a short dis-charge gap, the scatter of ts leads, according to rela-tionship (1), to a scatter of the breakdown voltage Ub.This, in turn, causes a scatter of the pre-breakdown IWvelocity . Experiment shows that the correlationbetween Ub and is preserved. Figure 16 shows thedependences of the IW velocity on the breakdownvoltage at various values of dU/dt in nitrogen (6 valuesin the range 0.5–7.0 kV/ms) and helium (10 values inthe range 3–140 kV/ms). Points of different configu-rations correspond to different values of dU/dt, and therange for points with a given dU/dt is due to the scatterof Ub and . It can be seen that all points fit into acommon curve, regardless of dU/dt. Hence, doesnot depend explicitly on dU/dt, although it depends onUb. For fast IWs and, accordingly, high voltage riserates (dU/dt > 0.1 kV/ns), this is not so: the velocity ofthe wave increases with increasing dU/dt [32–34].

The time ts and, therefore, the scatter of td and Ubcan be suppressed using an additional source of elec-trons initiating the primary breakdown. With a nega-tive potential at the HVE, this can be thermal emissionfrom a heated cathode [55–57, 60]. The same result isobtained from irradiation of gas or the surface of thehigh-voltage cathode with UV, X-ray, or gamma radi-ation [8]. With a positive potential of the HVE, thiseffect can be achieved by illuminating the anoderegion of the tube with radiation with a wavelengthshorter than ≈500 nm [65, 66, 71, 72]. This issue willbe discussed in detail below.

As follows from (1), with an increase in dU/dt, amonotonic increase in Ub must be observed. It is thisdependence that is obtained when studying break-down in uniform fields [69, 73–75]. The computa-tional work [76] gives the same result. In the experi-ment, this increase is, however, slower than linear (1)(in particular, in [75, 77] Ub increases as (dU/dt)1/2).This can be explained by the fact that τf decreaseswith increasing voltage [69]. In a long tube, the break-down voltage as a function of dU/dt was measured in[78] for neon and Ne–Ar and Ar–Hg mixtures. Theresults of these measurements are presented in Fig. 17.These measurements were carried out under externalillumination of the tube. Due to this, f luctuations ofUb were significantly smaller. This means that, inequality (3), ts ≪ tf + tw. In the region dU/dt > 1–

= + + ,d s f wt t t t

vw

vw

vw

vw

PLASMA PHYSICS REPORTS Vol. 46 No. 10 2020

10 kV/ms, an increase in Ub with an increase in dU/dtis indeed observed, although here it is also slower thanlinear. This can again be explained by the fact that τfdecreases with increasing voltage, for long tubes aswell [65]. The value of τw also decreases with increas-ing voltage due to an increase in the IW velocity. In anycase, however, one can quite confidently assert thatthe right branch of the curves in Fig. 17 is caused by anincrease in the second term of equality (1) withincreasing wavefront steepness dU/dt. It is more diffi-cult to explain the increase in breakdown voltage witha decrease in the wavefront steepness when it is smallerthan ~1 kV/ms. For short gaps, this was not observedin the entire studied range of dU/dt, up to very smallvalues: 10–2 V/s for breakdown in nitrogen [73] and10–1 V/s in neon [75].

In [78], the following explanation of the observedregularities was proposed. Under standard conditionsof the discharge ignition, before the voltage is appliedto the HVE, the entire tube together with the elec-trodes is at zero potential relative to the ground. Whena voltage U is applied to the HVE, all this voltage isapplied between the electrode and the wall and thepossibility of primary breakdown is determined by thevalue of U (in particular, a necessary condition for abreakdown is U > US). Suppose that some time beforethe voltage U is turned on, a potential u0 is applied tothe HVE. If u0 < US, this potential will not produce abreakdown, but, due to a finite conductivity of theglass surface and the presence of adsorbed electrons onit, it can increase the wall potential near the HVE,possibly up to u0. Then, when a voltage U is applied tothe HVE, the potential difference between the elec-trode and the wall will be smaller than U and, now, thenecessary condition for a breakdown will be the

1030 IONIKH

Fig. 17. Breakdown potential vs. anode voltage rise rate in(1, 4) Ne, (2) Ne–Ar 3:1 mixture, and (3) Ar–Hg (pHg =1 mTorr) mixture; p = (1–3) 3 and (4) 0.6 Torr; l = 80 cmand d = (1, 2, 4) 15 and (3) 23 mm [78].

10�4 10�3 10�� 10�� 10� 10� 10�dU/dt, kV/ms

0

1

2

3

4

5Ub, kV

4

3

2

1

Fig. 18. Breakdown voltage vs. constant bias potential in(1) Ne at p = 0.6 Torr, (2) Ne–Ar (3 : 1) mixture at 3 Torr,and (3) Ar at 1 Torr; dU/dt = (1, 2) 1 and (3) 0.05 kV/ms;d = (1, 2) 15 and (3) 28 mm; straight lines: calculation byformula (5) [78].

0 0.1 0.2 0.3 0.4 0.5u0, kV

0

0.4

0.8

1.2

1.6

Ub, kV

3

21

inequality U – u0 > US. Thus, the breakdown voltagewill increase by u0 (or, possibly, by a smaller value ifthe wall potential does not reach u0). To verify thisassumption, an experiment was conducted in whichpulses with a linearly growing wavefront were superim-posed on a constant voltage u0 and the breakdownvoltage was measured for various u0. The results arerepresented by dots in Fig. 18. The straight lines in thisgraph depict the functions

(5)

where is the value of Ub at u0 = 0. It can be seenthat, in all cases, the breakdown voltage increases byan amount close to u0.

Returning to the results presented in Fig. 17, itshould be noted that, for the region of dU/dt to the leftof the minimum, the time interval from the beginningof the voltage growth to the breakdown is from ~10 msto almost 100 s. It may be assumed that (i) during thistime, the wall potential in the anode region also grows,although slower than the potential of the anode itselfand (ii) the lower the voltage rise rate, the smaller thelag of the wall potential from the anode potential. Abreakdown will occur when the potential differencebetween them exceeds US (the contribution of the sec-ond term in equality (1) for small dU/dt is insignifi-cant). As a result, with a decrease in dU/dt, the break-down voltage increases. In this case, the actual valueof the static breakdown voltage is higher than thenominal value of US corresponding to the absence ofcharge on the wall. Thus, in contrast to the rightbranch of the curves in Fig. 17, the left branch can bequalitatively explained by the increase in the first termof equality (1) with a decrease in the wavefrontsteepness.

= +0 0,bb UU u0bU

P

4.4. The Memory Effect of the Discharge Gap

It was said above that the delay of a breakdown canbe reduced if there is an additional electron source,e.g., thermionic emission from the high-voltage cath-ode. The presence of charged or excited particlesremaining in the gap after the previous discharge pulsecan lead to a similar result. This, in turn, can affect thetemporal and other characteristics of the discharge.This kind of “memory effect,” apparently discoveredfor the first time in [79], manifests itself in various sit-uations: during the decay of an arc-discharge plasma[80], the propagation of streamers [81], the motion ofan IW in a plasma jet [82], and in nanosecond [83] andbarrier [84] discharges. Upon excitation of fast ioniza-tion waves, the electrons remaining after the break-down are the seeds for the generation of the next wave[22]. In a low-pressure glow discharge, this phenome-non was studied by researchers from Serbia in a largeseries of works, in particular [69, 73–75, 77, 85], inwhich the time delay (td) of the development of a dis-charge pulse relative to the time at which the voltageapplied to the electrodes, depending on intervalbetween pulses, was measured. The Townsend break-down in a uniform field with an electrode spacing of~0.1–10 mm in nitrogen and noble gases at a pressureof ~1–10 Torr was studied. For small intervals betweenpulses, τ ~ 0.1 s and shorter, td was ~100 μs. With anincrease in τ, it increases, and this increase continuedup to τ ~ 103–104 s, where td reached ~10–100 s. Thus,the “memory” of the previous discharge could be pre-served for dozens of minutes. Since such a long life-time of free electrons in a gas is excluded, it should beassumed that electrons appear in the post-dischargephase due to reactions involving long-lived particles.The authors suggest two such reactions, both occur-ring on the electrode surfaces: ion-electron emission

LASMA PHYSICS REPORTS Vol. 46 No. 10 2020

ELECTRIC BREAKDOWN IN LONG DISCHARGE TUBES 1031

Fig. 19. Time dependences of the anode voltage duringbreakdown by two pulses with a variable interval betweenthem. Nitrogen, 1 Torr [86].

5 10 15 20t, ms

0

0.5

1.0

1.5

2.0

U, kV

2nd pulse

1st pulse

and recombination of nitrogen atoms, accompaniedby the ejection of an electron from the metal (it isassumed that nitrogen is always present in the gas as animpurity).

Obviously, at a finite rise rate of the interelectrodevoltage, a decrease in the breakdown delay must leadto a decrease in the breakdown potential, according torelationship (1). This effect during breakdown in longtubes was studied in [86] (nitrogen), [87, 88] (argon),and [89] (argon with an admixture of nitrogen). Fig-ure 19 shows the voltage waveforms at the high-voltageanode during breakdown in nitrogen in a tube 40 cmlong and 28 mm in diameter. The pulse front is linear,and dU/dt = 5.1 kV/ms. The voltage pulses weregrouped in pairs with a repetition period of 220 ms anda variable interval between pulses inside a couple τ =0.5–64 ms. Breakdown occurs at the point of maxi-mum U. It can be seen from the figure that the break-down voltage in the second pulse of the pair changeswith τ and, for the most part, it is lower than in thefirst. Figure 20 presents the results of similar measure-ments in argon. The repetition period of pairs is 2 s.The dots represent the result of averaging over50 pulses. It can be seen that, at τ ≈ 500 ms andsmaller, the value of Ub for the second pulse is signifi-cantly smaller than the average value for the first pulseand is close to its minimum value (the region τ < 20 mswill be considered separately). This, obviously, indi-cates a sharp decrease in the breakdown delay time, upto the complete suppression of the statistical compo-nent ts. The latter can also inferred from the disappear-ance of the scatter of Ub in the region τ < 300 ms. In[86, 88], estimates are given that imply that theobserved effect in nitrogen can be explained by theprocesses on the electrode surface and the tube wall,suggested in [69]: ion–electron emission and hetero-geneous recombination of N atoms accompanied byelectron emission; in argon, they can be explained bythe presence of electrons remaining in the anoderegion after the previous pulse.

It seems obvious that the previous pulse can reducethe breakdown voltage if it ever can affect it. In reality,it follows from Fig. 19 that, for some intervals betweenpulses (2–3 ms), the breakdown voltage in the secondpulse is higher than in the first. We can say that thereis an anomalous memory effect. Figure 21 shows whatconsequences it can have. The oscillograms of voltageand discharge current in nitrogen during breakdownby a periodic sequence of pulses are shown for aninterval of 1.7 ms, for which the memory effect isanomalous. The amplitude of the voltage pulse U0 issufficient for the breakdown in the first pulse, but notsufficient for the breakdown in the second. The next(third) pulse is already outside the anomaly zone, anda breakdown is again possible. As a result, a break-down occurs after one pulse. Such a picture isobserved only in a certain range of the pulse frequency.If, without changing U0, the frequency is decreased or

PLASMA PHYSICS REPORTS Vol. 46 No. 10 2020

increased, then the second pulse can also leave theanomaly region and the missed pulses appear.

The manifestation of the anomalous memoryeffect can also be seen in Fig. 20. In the interval τ ≈ 2–20 ms, a breakdown in the second pulse occurs at avoltage higher than the minimum value for the firstpulse. This effect is more clearly seen in Fig. 22. Thedifference from Fig. 20 here is that the repetitionperiod of the pulse pairs is reduced to 200 ms. Now thefirst pulse of the pair falls within the range of the ordi-nary memory effect with respect to the second pulse ofthe previous pair and is found in the horizontal sectionof the lower curve of Fig. 20. For the second pulse inthe interval τ = 1–20 ms, an anomalous effect isobserved.

Another anomaly of the effect is that, in the rangeof its existence and at even smaller τ, no ionizationwave before the second pulse is detected. Under theconditions of Fig. 19 (nitrogen), an IW appears start-ing only with τ ≈ 2–3 ms, and, under the conditions ofFigs. 20 and 22 (argon), starting with τ ≈ 10–15 ms.

In [86–88], the following explanation of the causesof the anomalous memory effect is suggested. Whenthe duration of the interval between pulses is small, thebreakdown in the second pulse occurs under condi-tions of a high bulk and surface concentration ofcharged particles remaining after the previous dis-charge. As a result, the potential of the wall in thenear-electrode region is close to the potential of theelectrode itself, i.e., there is no potential jump betweenthe high-voltage electrode and the wall, necessary forthe primary breakdown and excitation of the ioniza-tion wave. On the other hand, the high electron den-sity and the wall charge caused by them concentratethe electric field lines inside the tube and create a lon-gitudinal field in it, as it occurs in a steady-state dis-charge [3]. In such a field, the discharge can be ignitedwithout an IW, by the ionization multiplication ofresidual electrons. In this case, the voltage for dis-

1032 IONIKH

Fig. 20. Breakdown voltages in the 1st and 2nd pulses of apair at various intervals between pulses; vertical strokesshow boundaries of scatter in a series of 50 measurements.Argon, 5 Torr [88].

0 200 400 600 8000

2

4

6

8

Ub, kV 1st pulse

2nd pulse

�, msFig. 21. Time dependences of voltage and current duringbreakdown in nitrogen by periodic pulses; U0 is the voltagepulse amplitude [90]; р = 1 Torr.

0

2

4 U0

0 5 10 15 200

3

6

9

t, ms

U, k

Vi,

mA

Fig. 22. Breakdown voltages in the 1st and 2nd pulse of apair at different intervals between pulses. The repetitionperiod of pairs is 200 ms. Argon, 5 Torr [87].

0 10 20 30 40 500

1

2

3

Ub, kV

�, ms

1st pulse

2nd pulse

charge ignition without the participation of an IW canbe higher than that with an IW, because of a less effi-cient (from the point of view of ionization) potentialdistribution along the tube.

Note that, in the works [56–58, 60], devoted tobreakdown in argon or in its mixtures, the pulse repe-tition rate was 5 Hz. From the data of Figs. 20 and 22,it follows that, under these conditions, a very strongmemory effect can be expected.

4.5. Initiation of Breakdown by Visible Radiation

In [60], it was mentioned that the external illumi-nation of a discharge tube can change the ignitionvoltage. Therefore, the shielding of the tube wasintended to protect it from this influence as well.Its mechanism was not discussed. The effect on thebreakdown of UV, X-ray, and gamma radiation is wellunderstood [8] and its mechanism is clear: this is pho-toionization of gas or photoelectric effect from thesurface of electrodes. For visible radiation, these pro-cesses are usually impossible and the mechanism mustbe different. For the ignition of a low-pressure glowdischarge during a Townsend breakdown, there arepublications [91–94] by the aforementioned Serbiangroup. In these studies, the breakdown time delay tdwas measured. In [91], a breakdown in neon was stud-ied at a pressure of 10 Torr and the interelectrode gapwas illuminated by the radiation of a tunable laser at awavelength of 614.3 nm, corresponding to the transi-tion 1s5–2p6 in the Ne atom. In [92–94], a breakdownin nitrogen at a pressure of 1 Torr was studied, and thegap was illuminated with radiation from a nitrogendischarge. In all cases, irradiation changed the delaytime, but the sign of this change was different: in [91–93], td increased and, in [94], decreased. In explainingthe result, in the first case, an assumption is made thatthe radiation destroys the metastable states Ne(1s5)

P

and N2( ) and thereby reduces the rate of ioniza-tion processes occurring with their participation,which leads to an increase in td. The authors of [94]relate their result to photoelectric effect from the cath-ode surface. They had to assume the presence on thecathode surface of a microfilm of iron oxide with alonger photoelectric threshold wavelength than that ofthe metal.

In long tubes, the effect of illumination by visiblelight on the breakdown was observed in [95–97]. Thesource of irradiating light was a tungsten halogen lampwith a power of 150 W. Standard f luorescent lampswere studied, which contained an Hg–Ar mixture at apressure of 150–500 Pa and had a length of 50 cm anda diameter of 28 mm without the f luorescent coating.In [97], the lamp was installed in a metal housing withan aperture for irradiation with light. Voltage pulseshad the shape

(6)

+Σ3 uА

( )[ ]= τ0 1 – exp – /U U t

LASMA PHYSICS REPORTS Vol. 46 No. 10 2020

ELECTRIC BREAKDOWN IN LONG DISCHARGE TUBES 1033

Fig. 23. Discharge ignition voltage under illumination ofthe tube at different points and at different parameters ofthe voltage pulse; white dots: in darkness. Fluorescentlamp, Ar–Hg mixture, p = 350 Pa [97].

450

U0,

V

400

3500 5 10

Distance from anode, cm15 20 25

with τ ≈ 10 ms and a repetition rate of 10 Hz. The valueof U0 was chosen so as the discharge ignition