PHYSICS OF OUR DAYS
`
`Optical discharges
`Yu. P. Ralzer
`
`Institute of Mechanics Problems of the USSR Academy a/Sciences
`Usp. Fiz. Nauk 132, 549-581 (November 1980)
`
`Gas breakdown, steady-state maintenance and the continuous generation of a low-temperature plasma, and
`propagation of the plasma fronts, all are induced by laser radiation. By nature, and in conformity with the
`fundamental laws, these effects are not different from similar processes that occur in constant and alternating
`fields and which are a traditional subject of the study of the physics of gas discharge. In fact, a new chapter
`has been added to the gas-discharge sciences: discharge at optical frequencies. It is a rapidly developing new
`field which encourages both new experiments and applications. It appears useful at this time to characterize
`the position occupied by the new field within the general framework of discharge sciences, and to analyze and
`appraise the latest results.
`PACS numbers: 51.70. + f
`
`1. POSITION OF THE OPTICAL DISCHARGES AMONG
`OTHER DISCHARGE PHENOMENA
`
`(a) Frequency ranges
`During the "pre-laser" era and, more precisely, up
`to the mid-60's, the physics and technology of gas dis(cid:173)
`charge were committed to fields in three basic fre(cid:173)
`quency ranges: (1) constant electric fields with which,
`depending on the nature of interaction, relatively short(cid:173)
`lived pulsed fields and low-frequency oscillating fields
`are partially conformable, (2) high frequencies (called
`"radio frequencies" in the foreign literature), a broad
`range with a mean around 1 MHz, and (3) superhigh
`frequencies, designated SHF (called "microwaves" in
`the foreign literature) and to be found in the gigahertz
`region that corresponds to the centimeter and milli(cid:173)
`meter waves. Beyond these lies the optical region: in(cid:173)
`frared, visible and ultraviolet radiation. However,
`during the pre-laser era-characterized by weak con(cid:173)
`ventional, non-laser, light sources and the fields they
`produced-the possibility of occurrence of gas-dis(cid:173)
`charge effects in the light fields was beyond everyone's
`comprehension.
`
`Historically, gas-discharge phenomena were explored
`in general in the order of ascending frequency ranges.
`Thus, constant or short-lived fields generated by con(cid:173)
`denser discharges were investigated first (hence, in(cid:173)
`cidentally, the term "discharge" which applies to proc(cid:173)
`esses occurring in the gas portion of a circuit). To(cid:173)
`ward the end of the last century and the early part of
`this century, attention had shifted to rf fields. The
`early 1940's and the development of rocket technology
`had advanced the range to microwaves. And, finally,
`the mid-1960's have moved the field into the optical
`range.
`
`The development of relatively powerful pulsed and
`cw lasers had enhanced the discovery and investigation
`of the many new phenomena induced in a gas by laser
`radiation, and the interaction of the latter with ionized
`gases and plasmas. Upon closer examination, it be(cid:173)
`comes evident that among these effects there are spe(cid:173)
`cific processes which naturally and fully belong to gas(cid:173)
`discharge physics. The laser technology has essential-
`
`ly bequeathed to the discharge physics a fourth, optical
`range, thus intrinsically endowing this science with a
`fundamentally new, exceptionally interesting and highly
`applicable chapter that deals with discharges in optical
`fields. Conceivably, the new term-optical discharge(cid:173)
`sounds alien to many at this time, but, in fact, it con(cid:173)
`veys as much sense as the time-honored terms "radio
`frequency" or "microwave" discharges. The new chap(cid:173)
`ter occupies a proper place among the gas-discharge
`sciences, and it entails the same fundamentals as the
`chapters on radio-frequency and microwave discharges.
`
`(b) Classification of "discharge processes"
`
`For simplicity, and in order to clarify the position
`that effects, arising from the interaction of laser ra(cid:173)
`diation with the ionized gases, occupy among the con(cid:173)
`ventional gas-discharge phenomena, it is expedient to
`classify all gas-discharge phenomena in some meaning(cid:173)
`ful way. Bearing in mind that the interaction of laser
`radiation with a gas is unaffected, as a rule, by the
`presence of solid surfaces, the effects must be classi(cid:173)
`fied according to criteria which are dissociated from
`the effects of electrode-, near-electrode- and bound(cid:173)
`ary-intensive processes. We shall distinguish three
`basic types of spatial gas-discharge processes:
`
`(1) Gas breakdown, development of a turbulent ava(cid:173)
`lanche ionization in it due to an applied external field,
`and conversion of initially non-ionized gas into a plas(cid:173)
`ma.
`
`(2} Maintenance of an unstable plasma by a field, in
`which the temperature of electrons responsible for the
`ionization is sufficiently high, and the gas containing
`atoms, molecules and ions remains cold. Normally,
`this corresponds to a weakly-ionized plasma at fairly
`high pressures, below 100 torr. The degree of ioniza(cid:173)
`tion is, moreover, much lower than a value for a sta(cid:173)
`ble plasma, which corresponds to electron tempera(cid:173)
`ture.
`
`(3) Maintenance of a stable plasma by a field, in
`which the electron and heavy-particle temperatures
`are close, and the degree of ionization is close to that
`of a thermodynamically stable plasma. This is a so-
`
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`0038-5670/80/110789-18$01.10
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`© 1981 American Institute of Physics
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`TABLE I.
`
`Constant electric
`tield
`Radio frequencies
`
`Microwave frequencies
`
`Optical frequencies
`
`Breakdown
`
`Maintenance of an un- Maintenance of a
`stable plasma
`stable plasma
`
`Glow discharge
`
`In interelectrode
`gaps
`Radio frequency, elec- Radio frequency mod- Inductive discharge
`trode or electrode-
`erat~pressure capaci-
`at atmospheric
`less
`tive discharge
`pressure
`
`D.C. arc
`
`In waveguides and
`resonators
`
`In sues, induced by
`a focused laser
`pulse
`
`Pulsed discharges in Microwave plasmo-
`waveguides and
`trons
`resonaton
`Late stages of an
`optical break(cid:173)
`down
`
`~ optical discharge,
`maintained by a
`CO, gas laser radi-
`ation
`
`·
`
`called low-temperature plasma with temperatures of
`the order of 10,000 K, and at pressures normally of
`the order of atmospheric.
`
`Each of these processes may occur in any of the fore(cid:173)
`going frequency ranges. ln fact, nearly all the possible
`alternatives have been investigated experimentally, and
`many of these have been found to have occasionally im(cid:173)
`portant research and engineering applications. Table I
`above illustrates the adopted classification, and indi(cid:173)
`cates typical conditions under which one or another
`process is observed.
`
`(c) Purpose of the paper
`
`Below, we shall consider processes that are induced
`by laser radiation and belong to the category shown in
`the bottom line in the table. Having analyzed the salient
`points, we shall show the gas-discharge nature of these
`processes and verify that, in principle, they hardly dif(cid:173)
`fer from other processes in the same category. We
`shall also review the current status of investigations
`and results in this area. The first problem calls for a
`brief digression into the realm of well-known concepts.
`The second pertains basically to results obtained after
`1972-1973, which were excluded from the author's
`monograph published in 1974 (Ref. 1).
`
`2. OPTICAL GAS BREAKDOWN
`
`(a) Discovery
`
`The instant of birth of the new chapter of gas dis(cid:173)
`charge physics is etched in the memory of many physi(cid:173)
`cists of the present generation. It is associated with
`the discovery of a remarkable effect: optical gas
`breakdown. The first to report this effect were Maker,
`Terhune and Savage in February 1963. 2
`
`The discovery of the effect was made possible by the
`invention of the Q-switched laser, which is capable of
`producing an especially powerful, so-called giant pulse.
`When the beam of such a (ruby) laser was focused by a
`lens, a spark occurred in the focal region, producing
`a plasma there, as in the case of breakdown in the dis(cid:173)
`charge gap between electrodes {Fig. 1). Very high ra(cid:173)
`diation parameters are required to break down the free
`air by optical radiation. Air breaks down at the peak
`power of 30 MW and when a beam is focused to a spot
`
`FIG. 1. Photograph of a laser spark.
`
`10"2 em in diameter (the typical duration of a giant
`pulse is 30 ns = 3 x 10"8 s; the energy in such a pulse is
`1J). The flux density at the focus for these parameters
`is 105 MW/cm2
`, and the electric field intensity in the
`electromagnetic wave is approximately 6 x 10SV I cm. 11
`The breakdown threshold is well defined, and a small
`decrease in the flux density below a given value will
`preclude breakdown.
`
`The new effect had evoked such broad interest among
`physicists that they literally rushed to investigate it.
`During the next several years, optical breakdown was
`being studied experimentally and theoretically with such
`intensity of detail that today our knowledge about it is
`as extensive as is our understanding of its closest ana(cid:173)
`log, the microwave breakdown, and is certainly super(cid:173)
`ior to our understanding of a more complex process,
`breakdown of a relatively long gap between electrodes.
`The bulk of materials dealing with the optical break(cid:173)
`down was generated during the 1960's, as was also the
`theory of the phenomenon. 1 In recent years; little was
`added to these data in the way of fundamental know(cid:173)
`ledge, although some additional experimental numbers
`have been calculated, refinements of the theory carried
`out, and allowances for certain subtle and understood
`details made.
`
`Figure 23 shows the threshold fields in an optical
`wave E 1, which are required to break down several
`gases by focused radiation from a ruby laser. The
`threshold values were measured over a broad range of
`pressures p. By way of comparison, Fig. 3 shows
`similar data pertaining to breakdown due to micro(cid:173)
`waves.4 The overall similarity of the E 1(p) curves
`should be underscored. As we shall see further, this
`property has a profound physical meaning.
`
`(b) Avalanche ionization in a field
`An electron avalanche develops in a gas under the ef(cid:173)
`fect of an electric field associated with an optical
`wave, as it also does during breakdown in any other
`field. In the case of breakdown induced by ultrashort
`pulses from ruby and neodymium-glass lasers, the
`first, priming electrons appear as a result of a multi(cid:173)
`photon emission from atoms, molecules and, possibly,
`dust which is present in the gas. In this respect,
`
`1) In a constant field, free air breaks down at the field intensity
`of 3X104 V/cm.
`
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`Yu. P. Raizer
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`FIG. 2. Thresholds for a ruby-laser-induced breakdown in Ar,
`He, and N2• Pulse duration 50 ns, focal spot diameter 10-2
`em (Ref. 3).
`
`breakdown in the optical field differs from breakdown
`in fields of lower frequency, in which the first electrons
`appear at random (from cosmic rays). Inside the wave
`field, an electron gradually acquires energy due to col(cid:173)
`lisions with atoms, and it becomes sufficiently energetic
`to ionize an atom and to produce a new electron. This
`is the mechanism of electron multiplication.
`
`Avalanche development is determined by an interplay
`of two opposing processes: energy accumulation by
`electrons due to the field and energy loss by electrons
`due to collisions (elastic and inelastic). It is also de(cid:173)
`termined by a loss of electrons due to diffusion or
`sticking in electronegative gases. Loss of both energy
`and electrons is relatively independent of the nature of
`a field, and it occurs in a manner that is more or less
`the same for all fields. Energy acquisition is the only
`frequency-dependent process whereby singular features
`of the optical breakdown, which are associated with the
`quantum nature of interaction between light and elec(cid:173)
`trons, may be revealed.
`
`In an alternating field, electrons pursue both oscilla(cid:173)
`tory and random motion. According to classical theory,
`each collision of an electron with a molecule or atom
`results in a transfer of the mean energy of an oscillat(cid:173)
`ing electron A£= e 2E 21m w2 into the energy of random
`motion c (E is the mean-square electric field and w is
`angular frequency). This occurs provided the collisions
`are relatively infrequent. However, if an electron fails
`to undergo many oscillations during a period between
`collisions, i.e., each time oscillations fail to swing
`"fully," energy transfer from the field to electrons is
`slowed down. In the general case, the field imparts the
`following energy per second to an electron
`
`a -Air
`t:J. -Nitrogen
`0 -Oxygen
`
`(1)
`
`where vm is the effective frequency of electron colli(cid:173)
`sions with molecules.
`
`Inasmuch as the collision rate is proportional to gas
`density or pressure, the rate of energy build-up due to
`the field for each frequency w at relatively low pres(cid:173)
`sures is proportional to pressure p, and is determined
`by the ratio E/ w. At relatively high pressures, it is
`inversely proportional to pressure and independent of
`w:
`
`(2)
`
`{c) Threshold field
`
`In order that an avalanche may develop and break(cid:173)
`down take place, energy losses by electrons and a loss
`of electrons must be surmounted. In the case of very
`short field pulses, another requirement is that an ap(cid:173)
`preciable level of ionization must be attained within the
`pulse width, such that a sufficient number of electron
`generations is produced. Clearly, an appropriately
`high rate of energy conversion is required to accom(cid:173)
`plish this, which is sufficient to provide the required
`gas ionization frequency v 1• The latter is the recipro(cid:173)
`cal of time an electron needs in which to attain energy
`greater than the ionization potential and to produce ion(cid:173)
`ization. Thus, the breakdown criterion places a speci(cid:173)
`fic condition on the parameters (dddt)B and E=Et.
`Consequently, at low pressures, when v! « w2
`, the
`breakdown·threshold field Et is proportional to frequen(cid:173)
`cy and decreases with increasing pressure. Converse(cid:173)
`ly, at high pressures, when v!» w2
`, the threshold field,
`grows with increasing pressure and only weakly de(cid:173)
`pends on the frequency. In alternating fields, the
`breakdown threshold is minimal at pressures that ap(cid:173)
`proximately satisfy the condition vm = const P"" w. These
`considerations explain the behavior o{ curve Et(p) in
`Fig. 3 for a microwave breakdown.2 >
`
`The behavior of the optical breakdown curve may be
`explained in the same qualitative way (see Fig. 2). If
`we proceed from the same equation [Eq. (1)], it be(cid:173)
`comes evident why breakdown at optical frequencies re(cid:173)
`quires fields considerably stronger than at microwave
`frequencies (Et- w, threshold intensity of electromag(cid:173)
`netic wave St- E:- w2
`). It becomes clear why the Et(P)
`minimum shifts in the direction of high pressures the
`order of hundreds of atmospheres (the minimum occurs
`atp- w). The main issue is to what extenttheapplicabil(cid:173)
`ity of Eq. (1) is validated for the quantum case of opti(cid:173)
`cal frequencies.
`
`(d) Classics and quanta
`
`The possibility of using a simple and clear formula
`[Eq. (l)J !.n the case of optical frequencies was validated
`
`JJ.Torr
`
`FIG. 3. Breakdown thresholds for N2, 0 2, and air in a micro(cid:173)
`wave field. Frequency 0.994 GHz, diffusion length of discharge
`volume 1.51 em (Ref. 4).
`
`2) Incidentally, the shape of the right-hand side (ascending)
`branch is, in general, similar to the right-hand side (ascending)
`branch of the Paschen curve for the breRkdown of a gap
`between electrodes to which R voltage was :1pplied.
`
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`
`Yu. P. Raizer
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`in one of the first works dealing with the optical break(cid:173)
`down5 in which a quantum theory of this effect was for(cid:173)
`mulated. Actually, an electron absorbs energy in
`quanta, i.e., significant amounts of liw equal to 1.78 eV
`for a ruby laser and 1.17 eV for a neodymium-glass
`laser. Moreover, the actual energy liw acquired by an
`electron during collision with an atom is much greater
`than t::.&=e2E 2/mw2
`, the collisional energy that an elec(cid:173)
`tron would have received according to the classical
`theory. It would seem the latter is totally inapplicable
`under these conditions.
`
`However, analysis of the quantum kinetic equation
`for the electron energy distribution function shows that
`Eq. (1) may be used anyway, even if the actual classical
`condition li w «A.& is not satisfied. This requires a
`much less stringent condition liw« &, where & is the
`actual electron energy. In the microwave range, even
`the trivial requirement li w «A.& is satisfied and the
`question of quantum effects does not generally arise.
`Conversely, in the optical range, A.&-10-2 eV«Iiw
`-1 eV; however, the mean energy of electron spectrum
`is of the order of the ionization potential, i.e., 10 ev
`and, therefore, the condition li w « & may be cons ide red
`satisfied, at least for the frequencies of ruby and neo(cid:173)
`dymium-glass lasers.
`
`Thus, in the case of optical fields, Eq. (1) roughly
`holds, although it should be treated statistically. Let,
`for example, t::.& = 0.011iw. An electron, of course, may
`not receive a hundredth of a photon from the field dur(cid:173)
`ing collision. This means that, roughly speaking, it
`gains nothing in the first 99 collisions, and in the hun(cid:173)
`dredth collision it absorbs a full photon all at once.
`Strict calculations of the electron avalanche and break(cid:173)
`down threshold are normally carried out on the basis
`of the kinetic equation. Calculations carried out in Ref.
`5 and subsequent works (see Ref. 1) are in satisfactory
`agreement with experimental results.
`
`Alongside the many classical characteristics, cer(cid:173)
`tain new details also appear at optical frequencies,
`which are associated with the quantum nature of inter(cid:173)
`action between the optical radiation and matter. Thus,
`for example, ionization of excited atoms is possible by
`means of two- or three-photon emission of electrons
`and this sometimes significantly affects the multiplica(cid:173)
`tion rate for electrons. However, the avalanche mech(cid:173)
`anism of the optical breakdown is neither different in
`principle from a mechanism responsible for microwave
`breakdown, nor from a spatial breakdown at lower fre(cid:173)
`quencies, including the Townsend (not streamer) gas
`discharge between electrodes.
`
`(e) A link between microwaves and light
`A particularly convincing experimental result in this
`respect is the fact that the classical laws Et- worSt
`- w2 are satisfied for the threshold values over a broad
`range of optical frequencies, up to the microwave
`range. As far as the latter is concerned, the law Et- w
`is theoretically valid only at low pressures that corre(cid:173)
`spond to the left-hand side of the curve Et(p). However,
`even the atmospheric pressure in the optical region is
`"low" in this sense.
`
`10-5 to-4 to-J 10-2 to-' 10°
`..!,em
`
`FIG. 4. Thresholds for atmospheric-pressure air breakdown
`induced by various lasers. Dashed line corresponds to the clas(cid:173)
`sical function s, ~ ( tJ + v~) which, with the exception of very
`long-wave region, yields a laws,~ w2, i.e., a straight line in
`the logarithmic scale.
`
`To validate the law, we have numerous data for the
`air breakdown by ruby (X=0.694 J.Lm), neodymium-glass
`(>.=1.06 J.Lm) andC02(X=10.6J.Lm) lasers. Quite re(cid:173)
`cently, other results were obtained in the intermediate
`infrared range by means of HF (X= 2.7 J.Lm) and DF (X
`= 3. 8 J.Lm) lasers, 6 and a heavy water laser (>. = 385 J.Lm
`= 0. 38 mm) was used to establish a point in the broadest
`unknown region of the spectrum between the infrared
`and microwave regions (the submillimeter region).7
`
`Threshold intensities are shown on a logarithmic
`scale in Figure 4; the experimental data points are
`plotted on the curve which follows the law St- w2. As
`can be seen, data points bunch closely near the curve,
`although strict obedience of the law is never expected.
`The fact is that work with different lasers is performed
`under different experimental conditions. The pulse
`width of ruby and neodymium-glass lasers is approxi(cid:173)
`mately 30 ns; C02 laser, in this case, 80ns; HF,
`120ns; DF, 90ns; and 0 20, 75ns. The focal spot diam(cid:173)
`eters are also different (10- 2-10-3 em). At the long
`wavelength, threshold essentially depends on either
`presence of dust particles in the air or the preioniza(cid:173)
`tion conditions, since the occurrence of priming elec(cid:173)
`trons in these cases is difficult. Deviation of a point at
`>.=0.38mm from the curve st- w2 is associated with the
`fact that the frequency w is already comparable with
`collisional frequency lim and the law must be corrected
`for the latter (St- ( w2 + 11!)]. Allowance for this makes
`the theory more compatible with experiment.
`The law St- w2 is violated significantly in the short(cid:173)
`wave region of the spectrum as a result of breakdown
`by the second harmonics of neodymium-glass and ruby
`lasers. Instead of increasing, the threshold intensity
`decreases sharply with increasing frequency (quantum
`growth). Here, quantum effects are fully in evidence;
`the second harmonic of a ruby laser is very large,
`3.56 eV.
`
`(f) A long spark
`
`At a moderately high intensity above threshold, laser
`radiation must be sharply focused to produce break(cid:173)
`down, which occurs only in a small focal region. How(cid:173)
`ever, at very high intensities in the case of a beam
`
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`weakly collected by a long-focus lens, the intensity is
`sufficient to produce air breakdown over a long dis(cid:173)
`tance along the lens axis and beyond. This results in
`an extended optical breakdown, a highly impressive
`phenomenon called the "long spark."
`
`A two-meter long spark was observed for the first
`time in 1967, when a 1-GW 18-ns giant-pulse neodymi(cid:173)
`um-glass laser was focused through an f= 2.5-m lens. 8
`Two years later, a 25-m spark was produced [by a 90-
`J 4-GW(peak) neodymium-glass laser, with a beam di(cid:173)
`vergence of 4 x lo-s rad and focused by a/= 28-m lens}-9
`A 15-m section of the spark extended in front of the
`focus and a 10-m section, behind. A record-length
`spark-longer than 60 m-was obtained in 1976 by
`means of a two-stage neodymium-glass laser setup,
`with the combined energy of 160J and average power of
`5GW, using an f= 40m lens. 10 The spark, produced in
`a courtyard (at an institute) is well defined against the
`background of a building (Fig. 5). Long sparks are
`never continuous, but consist of ionized sections alter(cid:173)
`nating with those unaffected by breakdown. Clearly,
`this is associated with the statistical origin of the prim(cid:173)
`ing electrons which occur at selected points and, prob(cid:173)
`ably, the time-dependent variations in the field at vari(cid:173)
`ous points due to a complex spatial-temporal and angu(cid:173)
`lar structure of the intense light beam.
`
`Long sparks were also obtained in air by means of
`12 (of the
`high-power electroionization C02 lasers11
`•
`order of 1 m11
`). The purpose of one work12 was to es(cid:173)
`tablish the maximum power and intensity of the C02
`laser radiation that can be propagated through air, a
`problem of considerable importance. The laser output
`was 160J, of which 30J was produced during 50 ns and
`the remainder, 130J, during J..LS; the peak power was
`0.56 GW. The longest spark (7 .5m) was achieved by
`expanding the initial beam by means of a telescope to
`be 40 em in diameter and, subsequently, focusing it by
`means of a long-focus mirror (f= 54m) directly out(cid:173)
`doors; the angle of beam convergence (dlf) was 11135
`and the least cross-section diameter, 0.5 em. The
`spark occurred at intensities of 1-2 Xl08Wicm 2
`• A
`considerable portion of radiation (of the order of tens
`of percent) was absorbed in the process by the plasma.
`Both the plasma generation threshold and amount of
`
`FIG. 5. Photograph of a long spark obtained by means of a neo(cid:173)
`dymium-glass laser. Spark length 8 m, focal length of lens 10
`m (Ref. 10).
`
`energy absorbed in the plasma depend on the dust con(cid:173)
`tent of air, the presence in air of sub-micron size
`aerosol particles, and humidity. In purified air, the
`threshold increases to 3 x 109 WI cm2
`• Schlieren pho(cid:173)
`tography shows that each particle serves as a plasma
`focus from which an optical detonation wave propagates
`(see below) and leaves an absorbing plasma cloud be(cid:173)
`hind it.
`
`Actually, the plasma generation threshold measured
`in the experiment ( 108 WI em 2
`) is not the same as the
`breakdown threshold, i.e., occurrence of avalanche
`ionization in a gas induced by a priming electron; the
`latter is an order of magnitude higher. Instead, it
`represents a threshold at which the plasma foci occur
`as a result of heating of gas particles and the subse(cid:173)
`quent ionization of ambient air by laser radiation. The
`question of what is the real mechanism for breaking
`down dusty air by C02 laser radiation remains unclear.
`Citations concerning this subject may be found in Refs.
`12 and 13. The breakdown threshold is further reduced
`15
`if the radiation is focused near a solid surface. 14
`•
`<and
`reterencee therein)
`
`(g) Discharge initiation by a laser spark
`
`It was observed some time ago that concurrent inter(cid:173)
`action of the laser radiation and other fields-micro(cid:173)
`wave, constant-with a gas considerably enhances its
`breakdown by the other field. In this manner, directed
`breakdown is achieved between electrodes under a con(cid:173)
`stant potential: The spark discharge develops along the
`optical channel and may be directed either at an angle
`to the constant field or even be fractured (for refer(cid:173)
`ences see Refs. 1 and 11). The lowering of the electric
`breakdown threshold and a very rapid laser interaction
`effect have contributed to the development of laser-fixed
`dischargers. 16 The long laser spark has been used ef(cid:173)
`fectively to initiate discharge in long interelectrode
`gaps.U• 17
`19 This procedure may replace the conven(cid:173)
`-
`tional method of using thin exploding wires for initiating
`electrical discharges, which has many disadvantages.
`The long laser-spark path provides a conduit for the
`electrode gap discharge. Moreover, breakdown elec(cid:173)
`tric field intensity is reduced considerably to 250V I
`cm. 19 Normally, electric breakdown of long gaps is
`due to a leader mechanism: A bright channel leader,
`propagates from the anode, and is preceded by a darker
`streamer. The dense portion of a long laser spark,
`which lies relatively close to the focus, is an equiva(cid:173)
`lent of a leader thus formed. 19
`
`3. MAINTENANCE OF AN UNSTABLE PLASMA
`
`Glow discharge is one of the most common discharge
`processes in a constant field at pressures below tens
`of torr. Unstable, weakly-ionized stationary plasmas
`may be produced at both radio and microwave frequen(cid:173)
`cies at low pressures. At optical frequencies, how(cid:173)
`ever, the steady -state process is totally atypical; in(cid:173)
`stead, it calls for much higher radiation intensities.
`The power of currently available cw lasers is suffi(cid:173)
`cient, as a rule, to maintain a stable plasma only.
`
`Steady-state maintenance of an unstable plasma al-
`
`793
`
`Sov. Phys. Usp. 23(11). Nov. 1980
`
`Yu. P. Raizer
`
`793
`
`Energetiq Ex. 2058, page 5 - IPR2015-01375
`
`

`
`ways requires electric fields that are considerably
`stronger than those used to maintain a stable plasma.
`This applies in general to all frequency ranges includ(cid:173)
`ing the optical. Actually, energy which an electron re(cid:173)
`ceives from the field is transported without delay to
`atoms, molecules and ions. The electron temperature
`T. rapidly assumes a steady-state value which is de(cid:173)
`termined by a balance between an average energy ac(cid:173)
`quisition from the field, and transfer to heavy particles
`during each collision:
`
`<'~·f k(T,-T);
`
`(3)
`
`where T is temperature of heavy-particle gas, and 6 is
`average portion of energy given up by an electron to
`heavy particles when T 0 » T. In an atomic gas, 6= 2m/
`M-10-5 -10-4 (M is atomic mass); in a molecular gas,
`because of inelastic processes of excitation of vibra(cid:173)
`tions and rotations' 6- 10-3 -10-2
`•
`
`In order that the electron-shock ionization of atoms(cid:173)
`the rate of which rapidly increases with T .-could make
`up for electron losses and the plasma remain intact,
`the electron temperature in any discharge, both stable
`and unstable, must be maintained at approximately l(cid:173)
`eV level. In a stable plasma, for which T •- T « T. and
`the energy exchange between electrons and molecules
`is bilateral, the required field is much smaller than in
`an unstable plasma, where T • » T and the electrons
`only yield energy to molecules and receive nothing
`from them. In the unstable case, Eq. (3) defines the
`field required to maintain a plasma. In the stable case,
`field is defined by the overall energy balance of the en(cid:173)
`tire plasma (see Section 4), and Eq. (3) fixes only a
`small detachment of temperature ( T •- T) being estab(cid:173)
`lished. Equation (3) may be used to estimate the re(cid:173)
`quired C02-laser radiation intensity readily for the
`steady-state maintenance of an unstable plasma with
`T.» T. We have w=1.78 xlQ14 rad/s, and for p<lO
`atm, w2 » v!, i.e., E and S=cE 2/471' are independent of
`pressure. Let T. = 1.5 eV; 6 = 2. 7 x 10·5 and S= 3 x 108
`w/cm2 in argon and -0.8 xl0-2 and -109 w/cm 2 in air,
`respectively. These values are very high for cw la(cid:173)
`sers, the latter even exceeding the breakdown threshold
`for natural free air. However, in order that a dis(cid:173)
`charge be prevented from spontaneously becoming sta(cid:173)
`ble, rapid extraction of energy from the gas is neces(cid:173)
`sary, for which lower pressures are preferred (as also
`3
`in the case of all unstable discharges). 20
`•
`
`Thus, although there exists in principle a possibility
`of a steady -state maintenance of an unstable plasma by
`light, application of this process is difficult. The proc(cid:173)
`ess is also "unprofitable:" A weakly-ionized plasma
`absorbs only a small portion of radiation, unless it is
`produced along a very long and powerful optical beam.
`
`3) The fact that E~nstable » EJtable does not mean that more
`energy is relased in an unstable plasma than in a stable pl(cid:173)
`asma. The energy yield density is proportional not only to
`E 2, but also the electron density n 0 • The unstable plasma
`is always weakly ionized:
`In the case of strong ionization
`the energy yield is somewhat large, the heat transfer is un(cid:173)
`able to prevent heating of the gas to the electron temperature
`level, and the plasma becomes stable.
`
`Although experiments of this kind have not been tried,
`the effect occurs automatically for short periods of
`time in the terminal stage of the optical breakdown at
`near-threshold powers.
`
`4. STEADY·STATE MAINTENANCE OF A STABLE
`PLASMA
`
`(a) Continuous optical discharge and the optical
`plasmotron
`
`Discharges of the arc type, in which a stable plasma
`is maintained in a steady state by a field, have broad
`application in physical research and engineering. Gen(cid:173)
`erators which produce dense low-temperature plas(cid:173)
`mas-plasmotrons-are built on this basis. In a plas(cid:173)
`motron, cold gas is blown through a steadily burning
`discharge. The gas is heated to temperatures of 5000-
`10,000 K, and flows out as a continuous plasma jet,
`more often at atmospheric pressure. Today, fields
`are used in laboratories and industrial equipment which
`fall into three frequency ranges: constant, rf and
`microwave. Accordingly, there are three types of
`plasmotrons: arc, induction and microwave.
`
`In 1970, the possibility of steady-state maintenance
`of a plasma by cw laser radiation was articulated and
`theoretically validated, and thoughts conc