Basic physics of gaseous dielectrics

IEEE Transactions on Electrical Insulation Vol. 25 No. 1, February 1990 55

Basic Physics of Gaseous Dielectrics L. G. Christophorou

and L. A. Pinnaduwage Atomic, Molecular, and HV Physics Group, Oak Ridge National Laboratory, Oak Flidge,

Tennessee, and Department of Physics,

The University of Tennessee, Knoxville, Tennessee

ABSTRACT Basic physical processes involved in the pre-breakdown stages of gaseous dielectrics are discussed, with particular emphasis on electron attachment, electron-molecule scattering and electron impact ionization. Utilization of the understanding of these basic processes for tailoring gases/mixtures with optimum dielectric strengths is indicated.

1. INTRODUCTION 6mm F the four generic insulating media (solids, liquids, 0 gases, and vacuum), specialized compressed gases (e.g.

SFc, mixtures of SF6 with Nz and/or appropriate perfluorocarbons) offer distinct advantages including a very high dielectric strength (Figure 1). The increased demand for higher voltages over the past quarter of century has led to vigorous research in gaseous dielectrics and their wide usage in HV equipment.

Perhaps the most distinct advance concerning the physics of gaseous dielectrics over the past 25 years has been the systematic acquisition of basic knowledge on the relevant fundamental processes, the incorporation of this new knowledge on the elemental microscopic processes into the breakdown process and development, and the resul- tant understanding of discharge phenomena and characteristics from basic principles. Owing to this activity and. the development of the Boltzmann transport and Monte Carlo computational analyses, breakdown phenomena can now be modeled and reasonably well understood, and compressed gaseous dielectrics can now be developed to meet desirable industrial performances.

The early work on the basic physics of gaseous dielectrics is amply described in many books such as those by Townsend [2], Healey and Reed [3], Loeb [4], Loeb and Meek [5], Massey and Burhop [6], Meek and Craggs [7], von Engel [8], Llewellyn-Jones [9], Penning [lo], Raether [ll], Haydon [12], von Hippel [13], and Birks, Schulman and Hart [14], and the recent progress is described in many reviews and books including the reviews by Christo- phorou [15-201, Wootton et al. [21], and Pedersen [22] and the books by McDaniel [23], Nasser [24], Meek and Craggs [25], Hirsh and Oskam [26], and Kunhardt and Luessen

C

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P 300- B C

0 U 1

3

g 200- m

loo -

O O 0.2 0.4 0.6 0.8

C I

1 I I I 0.2 0.4 0.6 0.8 1 .o . _

Electrode separation in inches Figure 1.

Direct current breakdown strength of typical solid, liquid, gaseous, and vacuum insulation in a uniform field [l]. 100 psi= 6 . 8 atm., 1 inch =2.54 cm.

[27]. Recent advances can also be found in the pro-

0018-9367/90/0200-55$1.00 @ 1990 IEEE

56 Christophorou et al.: Basic Physics of Gaseous Dielectrics

ceedings of the many international meetings on the subject, especially the International Symposia on Gaseous Dielectrics [28], and the International Conferences on Gas Discharges and Their Applications [29]. (See also the proceedings of the International Symposia on HV Engi- neering, the International Conferences on Phenomena in Ionized Gases, and the IEEE Conferences on Electrical Insulation and Dielectric Phenomena).

In this paper, after a brief introduction to traditional breakdown concepts, we will discuss some of the basic physical processes which considerably aided our understanding of gaseous dielectrics and their electrical insulating properties. In this, we shall rely heavily on the aforementioned sources, especially on the work carried out a t Oak Ridge National Laboratory; a comprehensive review of the voluminous literature on the subject is beyond the scope of this paper. Our discussion will principally con- centrate on the dielectric properties of gases a t ‘moderately’ high pressures (few kPa to few atmospheres) and under uniform dc (direct current) conditions for which the electrons generated in the gas quickly reach a steady state and thus electron-molecule interactions leading to electrical breakdown can be addressed assuming steady- state conditions even though the breakdown itself is a transient, non-equilibrium phenomenon. Electrode processes, important as they are, especially a t the very low and the very high pressure regimes, will not be consider ed .

2. ELECTRICAL BREAKDOWN OF GASES

2.1 DEFINITIONS AND BREAKDOWN CRITERIA

LECTRICAL breakdown in a gas is a rapid sequence E of irreversible events which quickly lead to a transition of the gas from its ‘normal’ insulating state (conductivity - 10-1461-’m-1) to one of high conductivity (many orders of magnitude larger, depending on the particular conditions; e.g. over 10 orders of magnitude larger for the transition to a glow discharge). Depending on the particular conditions, this transition occurs in times ranging from ns to ms. The voltage value at which breakdown occurs (the ‘breakdown voltage’ V 8 ) depends on the gas, the gas number density N , the separation, geometry, surface condition and composition of the electrodes, and the nature of the applied voltage (dc, ac, impulse). For an applied uniform electric field E , the minimum value, ( E / N ) l i m , of the density-reduced electric field E / N at which breakdown can occur can be used as a working definition of the dielectric strength of a gas (see later this Section). In this case, V, = d(E/N) l i l lLN where d is the electrode gap distance.

In the absence of free electrons, a gas dielectric would remain in its insulating state even when V > V,. When

4.0

7?IN C2F6 f

,e :0 a / N

+ 0

:{ : 0

&A’ , 0.0 -

0 100 200 300 200 E/N (10-17 v C&

Figure 2.

Electron attachment coefficient TIN (0 , [35]; A, [36]; V, [37]; U, [38]) and ionization coefficient a / N (A [35]; 0 [36]; + [37], o [38]) as a function of E / N for CzFe.

the applied voltage V exceeds V,, gas breakdown can be triggered by a single (initiatory) electron, which, being accelerated by the applied electric field to energies in excess of the ionization threshold energy I of the gas, pro- duces upon impact with the gas atoms or molecules addi- tional free electrons. This, in turn, leads to electron multiplication causing further ionization which leads to formation of an electron avalanche and eventually a highly conductive channel associated with gas breakdown. This process of electron multiplication by electron impact ionization can be represented by

n = no exp(ad) (1) where n is the number of electrons a t the end of a distance z = d resulting from an initial number no of electrons a t z = 0. The coefficient a (known as Townsend’ s primary ionization coefficient) is related to the probability of ionization by a free electron, via collisions with the gas atoms or molecules, per unit distance traveled in the direction of the applied electric field. It is the inverse of the mean distance traversed by an electron in the direction of the field E between ionization events. The density-normalized ionization coefficient a / N depends on the gas and E / N . If, besides electron impact ionization, other (secondary) processes such as collisions of positive ions, photons, and metastable species with the cathode,

IEEE Transactions on Electrical Insulation Vol. 25 No. 1, February l Q S 0 57

Figure 3. Electron attachment coefficient q / N [35] and ionization coefficient a / N (A, [35]; 0, [36], V, [39]) as a function of E/N and gas pressure for n- CrFlo. The dashed line is the electron attachment coefficient when the measurements of [35] were extrapolated to infinite gas pressure. Note that as a consequence of the N-dependence of T I N , the E/N value at which q / N = a / N is now a function of N.

and/or photoionization and Penning ionization in the gas itself also contribute to the electron production, then [2],

where 7 is Townsend's secondary ionization coefficient; for a given gas and electrode system, y is a function of E / N . The transition of the gaseous medium from an insulator to a conductor is postulated to occur (Townsend's breakdown criterion) when n + 00, i.e. when

y[exp(ad) - 11 = 1 (3) or, since a t the values of Q corresponding to breakdown exp(ad) >> 1, when yexp(ad) = 1.

Condition (3) states that unless a new electron is produced by a secondary process for each primary electron, the current in the inter-electrode gap can not be self- sustained and, hence, breakdown can not occur. In view of Equation (3) and the fact that both a / N and y are functions of E / N = V / N d it follows (Paschen's law) that

5 ~~ 0.0 01 02 03 0.4 03 Ob 07 Od 0.V MuNEEcmm -. PI bn

CClF,

I := =

Z M W xa ux) YD xa ax CAS TEYPERATURE T (K)

' Z N l r n C . 3 ./ j; .*-M_LY j ,;:

0 o , > Y l " 1 Y . . 1 I Y u n m o w mmcy ( I 1 (e")

Figure 4. Electron attachment rate constant k, ( q / N a ) w where w is the electron drift velocity, see Section 2.5, as a function of the mean electron energy and temperature [34] (Figures 4a, c). Also given (Fig- ures 4b, d ) are the V,(T), i.e. the uniform field breakdown voltage as a function of gas temperature T (see discussion in [33] and [34]).

(4) v, = V , ( N d ) The aforementioned 'steady-state Townsend' treatment did not consider the crucial role of electron removal from the electrically-stressed gas by electronegative (electron attaching) species. Electronegative gases such as CC4, CC12F2, and SF6 were known to have higher dielectric strengths than air since the late 1930's [30]. Penning [31] discussed the possible role of electron attachment back in 1938, but its incorporation into the Townsend theory only came in the early 1950's when Geballe and Harrison [32] modified the breakdown criterion as

(5) y(exp[(cY - 77)d] - 1) = 1 - 'I

where 'I is the electron attachment coefficient defined as the inverse of the mean distance traversed in the direction of E by a free electron before being attached. Under steady-state conditions q / N , a / N , and ( a - q ) / N ( = & / N , the so-called effective ionization coefficient) are functions of E / N (Figure 2) and in many instances v / N is also a function of N (Figure 3) and T (Figure 4) ([33] and [34]). In Figure 2, v / N is independent of N [35] since for CZF6 electron attachment proceeds solely via dissociative attachment processes. In Figure 3, q / N depends (increases

58

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5 15.0

5! I

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q 10.0

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E w 0.0

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W E E W

Christophorou et al.: Basic Physics of Gaseous Dielectrics

v 1.0 kPa n-C4F10 - -20.0

E/N (10-17 v c&)

Figure 5. The effective' ionization coefficient d / N for CF4, CzFs, C ~ F B , and n-C1Flo as a function of E / N [35]. Note the dependence of (E/N) l i , , , for C3Fe and n-C4Fl" on gas pressure which results from the pressure dependence of q / N . For sufficiently high N , q / N becomes independent of N and so does ( E / N ) t i m .

with) on N and as a consequence of the N-dependence of q /N , the E/N value a t which q / N = a / N is now a function of N. In Figure 4, the low energy electron attachment to C - C ~ F ~ leads predominantly to parent negative ions while that in CClF3 exclusively to dissociative attachment; the cross section decreases with T for the former and increases with T for the latter.

In view of (5), a convenient definition of the static uniform-field breakdown strength, (E/N)lim avails itself, namely: identification of (E/N)i;m with the value of E/N for which the density-normalized effective ionization coefficient equals zero, i.e.

as illustrated in Figures 5 and 6. It should be remem- bered, however, that Equation (6) is a necessary, but not a sufficient condition for breakdown. The fact that the field is sufficiently high for ionization growth does not en- sure that breakdown will occur. Electrical breakdown is a stochastic process and its actual occurrence depends on the probability that an initiatory electron will be available and that it will lead to growth of an avalanche of

IL w - 4 ' 0 ' 100 ' ' 200 ' ' 300 ' ' 400 1 500 ' ' 600 '

E /N ( 1 0 - l ~ Vcm2)

Figure 6. Effective ionization coefficient ( a - q ) / N as a function of the density-reduced electric field E / N . Cur- ves are for the following gases and ( E / N ) i i m (in units of lo-"' V cm'); Nz, 130; V 1% of SFG, 160; + 10% SFG, 235; 0 20% SFs, 269; A, 50% SF.5, 323; and 0 100% SFs, 361 [40].

sufficient size for the development of a conductive breakdown channel in the gas.

2.2 ORIGIN OF INITIATORY ELECTRONS

Where do the initiating ('seed') electrons come from? While radioactive sources, ultraviolet-light irradiation of the cathode (or the gas), and field emission from negative sharp-cathode tips (especially a t high pressures) can be sources of initiatory electrons, the main source of such electrons in gas-insulated equipment is directly or indirectly connected with the ionization of the gas by cosmic and terrestrial radiation. We estimate the contribution from cosmic radiation to be about 2 ~ l O - ~ electrons s-l cm-3 Pa-' by considering that the average dose of cosmic radiation is - 28 mrem yr-' N 2 . 8 ~ lop7 J g-' yr-' [41] and that the average energy to produce an electron-ion pair (Lp.) in most gases of interest is between 25 and 36 eV/i.p. [42, 431. In addition to this, ionization from nat- ural terrestrial sources can produce N electrons s-l cm-3 Pa-l [44]. However, since about 80% of these latter electrons are produced by a- and &particles [44] which normally would not penetrate the metallic enclosures of practical systems, the relevant free electron production rate due to terrestrial radiation is also - 2 ~ l O - ~ electrons s- l cm-3 Pa-l , bringing the total to - 4 ~ 1 0 - ~ electrons s-l cm-3 Pa-'. In nonelectron attaching gases this is the rate at which the free electrons become available for breakdown initiation and its small size clearly indicates a long statistical time lag for breakdown. In electron attaching gases, the electrons produced by cosmic and ter-

IEEE Transactions on Electrical Insulation Vol. 25 No. 1 , February 1990 59

restrial radiation are captured by the gas molecules forming negative ions, and in the case of enclosure dimensions of less than - 10 cm the only significant loss mechanism has been shown [45] to be the diffusion of these ions to the walls. Boggs and Wiegart [45] estimated that the equilibrium concentration of negative ions in SF6 -insulated systems is - lo4 cm-3 by assuming an electron production rate of 4 x lop5 electrons s-l cmP3 Pa-l. It, thus, seems that in electrically-stressed electronegative gases the major source of breakdown-initiating free electrons is electron detachment from these negative ions [46-551 and, therefore, occurs with highest probability in the vicinity of positively-stressed electrodes under nonuniform field conditions. This detachment process is mostly collisional, viz.,

A + B + e

AB + e associative detachment

unassociative detachment

(7) { A - + B +

rather than electric-field induced. Even though the collisional velocities of -4- and B under field-free conditions are too small for collisional detachment (except when reactions 7 - especially 7b - are exoergic), the shift in the velocity distribution of the negative ions to higher velocities under an applied electric field may result in significant collisional detachment. Recent studies [55-571 on 'field- assisted' collisional detachment involving F - , SF5-, and SF6- in SF6, have shown that of these three negative ions the one (F-) with the highest electron affinity ( E A ) [58] and the lowest cross section of formation [33] has the highest electron detachment rate. On the other hand, electric field-induced electron detachment is an unlikely source of initiatory electrons in gas-insulated systems unless negative ions with very small electron binding energies exist in the discharge [46,59]. It has been shown [46] that the probability of electron detachment from anions is very small when E A 2 1.0 eV unless fields 2 10 MV/cm are applied; such fields are well in excess of those leading to gas breakdown. (For a discussion of these and other electron detachment processes see [59-641).

2.3 TIME TO BREAKDOWN

For electrical breakdown to occur, not only must the applied voltage V > V,, but a free electron must be available in the electrically-stressed gas in a suitable location (preferably close to the cathode) for maximum electron amplification. The time lapse between the application of the voltage V 3 V, and the appearance of a suitably- located initiatory electron in the electrically-stressed system is known as the statistical time lag r,. In the absence of field emission from the cathode, r,, is very long (- s) for nonelectron attaching gases, but it can be very short (< s) for electron attaching gases due to the availability of negative ions (and thus free electrons produced

100

80

60

c - - 40

20

0

2 n - 0 5 4 P O L A R I T Y - 3 n - 0 5 4 P O L A R I T Y - 4 n - 0 1 2 P O L A R I T Y -

- I 5 n-0 3 2 P O L A R I T Y -

- 1

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- - -_

2 n - 0 5 4 P O L A R I T Y - 3 n - 0 5 4 P O L A R I T Y - 4 n - 0 1 2 P O L A R I T Y -

- I 5 n-0 3 2 P O L A R I T Y -

- 1

\

- - -_

, , , , 1 n - 0 8 4 P O L A R I T Y f ' 2 " - 0 5 4 P O L A R I T Y -

I 3 n - 0 5 4 P O L A R I T Y - - - 4 n-0 3 2 P O L A R I T Y -

I 5 n-Q 1 2 P O L A R I T Y -

0 20 40 6 0 0 30 6 0 90 120 150

v,, ( * l o )

Figure 7. Formative time lag ~t vs. percentage of overvoltage in Nz and SFs for different field distributions n z E,/E,,, ( E , and E,,, are respectively the average and the maximum field; n values of 0.84, 0.54, and 0.32 correspond, respectively, to approximately homogenous, weakly inhomogenous, and inhomogenous fields); d = 4 mm, and P = 100 kPa.

0 cop

0 HZO

0 0.2 0.8 4.0 4.2 0.4 0.6 (OM (eV)

Figure 8. Electron thermalization times as a function of the mean electron energy < E > M (Pz,, = 130 Pa) [15,79].

by collisional detachment) in the latter especially when electrons are weakly bound to negative ion clusters ([51, 541). For example, it has been observed that even though in large (- few cm) gaps a t atmospheric pressure average


statistical time lags in dry air are - 0.1 s , these could be reduced to - s by the presence of relatively small amounts of water vapor [65]. For both electron attaching and nonelectron attaching gases, the r, is decreased considerably when initiatory electrons can be provided from the cathode by field emission. This can occur in the presence of surface contaminating films and microprojections on the cathode surface, or point cathodes, and under conditions of high overvoltage resulting from impulses.

Once liberated at a suitable location, the free electron undergoes exciting and ionizing collisions, thereby initiating a succession of electron avalanches ultimately leading to breakdown. The time taken for this sequence of events, characterized by the collapse of the applied voltage as a self-sustained glow or arc discharge, is called the formative time lag rj. The magnitude of rj varies from ns to ms depending upon the nature and number density of the gas, the electrode material and polarity, field uniformity, and the amount (‘overvoltage’) by which the applied voltage V exceeds V, (see Figure 7; [66,67]). The data in Figure 7 were obtained [66] with a square impulse gen- erator having - 2 ns rise time and - 150 kV amplitude. It is evident that the higher the overvoltage the shorter the rj a t which breakdown occurs. It is also seen that rj is significantly higher for negative polarity and that it varies considerably with field uniformity, especially for the electronegative gases.

Actually, since secondary ionization processes are responsible for the formative time lag rj , it depends on the particular secondary process(es) which dominate in the prebreakdown stage. If, for example, positive ion impact on the cathode is the most important mechanism of electron generation, rj is inversely proportional to the positive ion drift speed and is thus of the order of - lop5 s. It appears that in general the long 7-j (- 10-1 to - s ) , typical of gases a t moderate pressures under small overvoltages (V/V, 5 1.2), can be accounted for by the Townsend steady-state approach, while the short rj‘ (5 l ov9 s), observed in highly overvoltaged systems, may be explained by several ‘non-steady-state’ descriptions [7, 11,25,27]. In particular, for V/V, values moderately in excess of - 1.2 the ‘streamer’ theory [7,9,68,69] has had considerable success in interpreting breakdown phenomena and rj. In this model, it is assumed that a t a certain stage in the development of a single (initial) avalanche, photoionization of the gas initiates more avalanches which merge to form a streamer in the presence of space charge fields in excess of the applied field. It was argued [68] that such space charge fields would be produced if the initial avalanche contains more than - lo8 electrons and that rj is basically the time taken for the initial avalanche to attain this critical value. The streamer theory requires the generation of electrons ahead of the initial avalanche which are presumed [68] to be produced by

photoionization. However, this mechanism is question- able especially in the case of a pure gas. Lozanskii [70] proposed associative ionization as a mechanism for cre- ating electrons ahead of the initial avalanche, but the involvement of this mechanism in breakdown processes has not yet been confirmed experimentally. Many recent discussions on streamer formation and streamer-to-leader transition for various gaseous dielectrics under a variety of experimental conditions, overvoltages and space-time varying electric fields can be found in the proceedings of the conferences mentioned in the introduction (see also [71-781).

The total time lag from the moment of application of the HV to the occurrence of actual breakdown, qr = r, + Tf.

2.4 STEADY-STATE CO N S I D E RAT1 0 N S

Implicit in the Townsend breakdown theory and the preponderance of the published work on the basic physics of gaseous dielectrics is the assumption that steady-state conditions prevail in the prebreakdown stage. Under these conditions, the kinetic energies of the free electrons in the gas quickly reach a steady-state distribution f (c , E / N ) which is the same everywhere between the electrodes and which, for a fixed temperature T, depends solely on the gas and E / N (see below). The distribution function f (c , E / N ) is normalized by

m r

so that f (c , E / N ) d c is the probability that a given electron will have energy in the range c and 6 + de at the particular E / N value. For the steady-state theory to be valid, the time required for electron energy relaxation, trel << ~j and the function f(c, E / N ) must return to its steady-state value quickly when electrons are added to the system, say by ionization, or removed from it, say by attachment.

We can obtain an idea about the magnitude of trel of dielectric gases by considering another related quantity, namely the mean electron thermalization time t t h , defined as the time needed by electrons of initial energy E ,

to lose energy equal to E , - 1.5 kT and reach thermal equilibrium with the gas. Estimates of the time taken for a swarm of electrons with initial mean energy < c > to thermalize have been made for a number of gases (e.g. see [79-811; also [82,83]) by considering the fact that under steady-state conditions the energy lost per unit time by electrons to elastic and inelastic collisions with the gas molecules is equal to that gained per unit time by the electrons from the applied electric field. These estimated thermalization times for a number of molecular gases a t a

61 IEEE Transactions on Electrical Insulation Vol. 25 No. 1 , February 1990

2 5 1 0 - 2 2 5 la-' 2 5 $00 2 5 $0' ELECTRON ENERGY 1.V)

I -

2

- 100

p 5 .-

0 z

; 2 B

0 i lo-'

c 5

2

10-2

5 2 5 Io-' 2 5 10-1 2 5 IO0 2 5 $0' ELECTRON ENERGY IN)

Figure 9. Normalized electron energy distribution functions f(c) f'(e)e"' for several E / N (in units of lo-" V cm') values in AI and Nz obtained using a two- term Boltzmann solution and the cross sections shown in the Figure [l06].

total pressure of 130 Pa are shown in Figure 8. It is clear from Figure 8 that the thermalization time depends to a large extent on the time taken by the electron to lose the last few tenths of an eV of its energy. In breakdown applications where large applied fields are used, the steady- state mean electron energy is well in excess of thermal and hence the energy loss or gain (which corresponds to transitions to the 'flat' regions of Figure 8), should occur much more rapidly, i.e. trel << t t h . It should also be noted from Figure 8 that the energy exchange occurs faster for

\ . 0 10 20 30 4) YI M 70 10 30 4)

Electron Energy. E . lev1

Figure 10. Normalized electron energy distributions f ( e ) com- puted for the conditions indicated, (a) shows the distinctly different distribution existing in He and SF.5 at the same E / N . Also shown is the f(c) for a 40/60 mixture of SFs/He at the same E / N . (b) shows that in SFs and Nz the distributions are much closer at the same E / N . The mean energies < c > ( F in the Figure) and drift velocities w are shown for each distribution [107]. (Designations such as 1.52(-15) and 3.3(7) mean, respectively, 1.52 x and 3.3 x lo').

large polyatomic molecules (especially those possessing a permanent electric dipole moment) for which the energy levels are much more dense than for smaller molecules. Conversely, the energy exchange occurs slower for inefficient electron thermalizing gases such as the rare gases which have only a few widely-spaced excited states a t low energies. This behavior is expected because the more complex molecules offer more possibilities for inelastic collision processes that result in electron energy loss. To indicate the approximate magnitude of trel for typical gas dielectrics (say, SFG) let us consider the time taken for an electron created with energy E ; to lose a few eV of kinetic energy and reach the steady-state mean energy < E Consider a situation where &,-,tal = 0.13 MPa, E - l o 5 V cm-', w - lo7 cm s-' and I C ; - < E I - 1 eV. Since eEw is the energy gained per second by the electron, trel - s .

Thus, trel << ~f and with the exception of very large overvoltages, steady-state conditions would normally prevail up to actual breakdown in the preponderance of situations that are of interest to gaseous dielectrics. Notable exceptions to those situations however exist such as the interface regions near an electrode surface or the regions of the discharge when the electric field varies rapidly with distance or time. The effect of such spatial and spatio-

"I 0 - _.. temporal variations in the electron energy distribution


MEAN E L E C T R O N ENERGY. <€>. (ev)

b n-c6FF14 SWARY UNFOLDED

ATCACHYENT CROSS SECTIONS

I 9 2 1 4 9 1 31 - f 00 2 090

>

W 0

- 4, 8

039 A

z 0 x

w a

W

c

i w

a

- a

~~

0 1 2 3 4 5 8 7 8 0 10 ELECTRON ENERGY. E (ev)

Figure 11. (a) Total electron-attachment rate constant, k, as a function of the mean electron energy < E > for the perfluoroalkanes CNFZN+Z ( N = l to 6) and their dc uniform field breakdown voltages relative t o SFs of 1 . (b) Corresponding cross sections [20, 1061.

function and the electron transport parameters has been recognized and studied ([84], [85]; also see Kunhardt and collaborators [86-881 for nonequilibrium descriptions of the dynamics of electrons in a gas under the influence of

space-time varying fields).

A number of (two- and multi-term) Boltzmann equation analysis studies (and Monte Carlo simulations) on gaseous dielectrics have provided electron energy distribution functions for these systems [80,89-1021. Such studies increasingly provide considerable insight into, and understanding of, the development of electron avalanches in gaseous dielectrics and yield calculated values of the electron swarm parameters and collision cross sections

In Figure 9, examples of steady-state electron energy distribution functions f (c , E / N ) are given for Ar and Nz [lo61 a t relatively low fields (low E / N ) . These two gases have been extensively used as buffer gases [33,42] in the measurement of electron attachment coefficients for many electronegative gases. In these experiments the electronegative gas is added to N2 or Ar in such small quantities that f ( ~ , E / N ) is characteristic of the pure N2

or Ar. The f ( e , E / N ) for these two gases are consid- ered to be rather accurate since the relevant cross sections used for their calculation are known with sufficient accuracy for computational purposes. As the E / N increases, the electron energy distribution function shifts to higher energies as expected. Electron energy distribution functions have recently been calculated for a number of dielectric gases and dielectric-gas mixtures, along with self-consistent sets of electron-scattering cross sections, using electron-transport coefficient data and Boltzmann or Monte Carlo analyses. While often the accuracy of those distribution functions is limited, mainly because of insufficient cross section data, they are useful in modeling discharges and in relating the basic physical processes to dielectric gas properties. An example of such approximate electron energy distribution functions is shown in Figure 10 for SFG [107].

[96- 10 1 , 103-1 051.

2.5 THE COEFFICIENTS a AND 77 AND THEIR RELATION T O THE

MICROSCOPIC CROSS SECTIONS

If, for a given gaseous dielectric, the cross sections for the various relevant microscopic processes were known, in principle, they could be integrated over f ( e , E / N ) and could be used, along with the appropriate charge conser- vation equations, to determine the current growth in the gas and predict its breakdown voltage. In practice this is difficult mainly because of lack of knowledge on the required cross sections. One often resorts to the more eas- ily accessible swarm coefficients to predict the discharge development and behavior. The macroscopic coefficients for excitation, dissociation, detachment and ion-molecule reactions (see Section 3) as well as the primary electron- impact ionization coefficient a and the electron attachment coefficient r] are obtained as functions of E / N and

IEEE Transactions on Electrical Insulation Vol. 25 No. I , February 1990 63

h - I

1 2 3 4 5 MEAN ELECTRON ENERGY, (&)(eV)

CROSS SECTtONS

0 a 4 8 8 LO ELECTRON ENERGY E (eV)

Figure 12. (a) Total electron attachment rate constant in SFG as a function of the mean electron energy < e >, measured in the buffer gases Ar (0 , A), N2 (0) and Xe (m). (b) Electron attachment cross section in SFG for SFG-, SFS-, and F-, Fz-, and SFI-, calculated by Hunter et al. (-) [lll] and Kline et al. (. . . [117]).

are quantities representing averages of the respective microscopic cross sections over the electron energy distribution function. For a single gas for example, the relations

of Q and 77 to the total ionization o,(c) (i.e. for all ionization processes) and total attachment U = ( € ) (i.e. for all attachment processes) cross sections and f ( ~ , E / N ) are, respectively,

where w is the electron swarm drift velocity, m is the electron mass, I is the ionization onset energy, and N is the total gas number density.

ELECTRON ENERGY (NI

Figure 13. Total electron impact ionization cross section as a function of electron energy E for (a) Hz, N2, CO2, and SFa and (b) a number of atoms and molecules close t o the ionization threshold energy I (data of [119]; from [118]).

To indicate how relations (9) and (10) were obtained consider an electron with a particular fixed energy e ( > I). The number of ionizing collisions it undergoes per second is u ; ( ~ ) N u = o , ( c ) N ( 2 ~ / m ) ~ / ~ , where U is the electron random velocity. Therefore, the mean number of ionizing events caused by an electron per unit drift distance is

In the case of a component gas j in a multicomponent S,”[ai(€)N(2€/m)l/2]ur-lf(€, E / N ) d € a.

gas mixture

where Nj is the number density of the component gas j , N is the total gas number density (i.e. N = C j N j ) ,

64

,,--I4 I

*-2’ 1 I I I I I I I I 0 2 4 6 8 0 1 2 1 4 16

ELECTRON ENERGY (eV)

Figure 14. Dissociative electron attachment cross sections as a function of electron energy, u d a ( e ) , for a number of molecules. Some of the plotted ( T ~ , , ( E ) were deduced from swarm experiments and are, thus, total cross sections; they are identified with the specific ions as shown because these were the most abundant in mass spectrometric studies. Some of the molecules shown have other resonances which were not plotted for the convenience of display ~ 5 1 .

and w and f ( ~ , E / N ) are, respectively, the electron drift velocity and electron energy distribution function for the gas mixture.

The coefficients a and 7 are related to the corresponding rate constants I C , and I C , for the two processes as:

Measurements of these quantities have been made for many dielectric gases [15-20,28,33-35,42,59,80,106-1171 and in Figures 11 and 12 are shown typical results.

3. BASIC PHYSICAL PROCESSES

3.1 PRIMARY AND SECONDARY INTER ACTIONS

ANY physical processes have been identified which M affect the dielectric properties of gases. These in- volve electrons, positive and negative ions, excited and

with the gas and with the electrodes. In Tables 1 and 2 are listed the principal physical processes which are associated with the gas. The majority of these processes affect the dielectric behavior of the gas directly or indirectly by their effect(s) on the number density and energies of the free electrons which are present in the electrically-stressed system.

5 [ , I I I I I I I I l 5

Christophorou et al.: Basic Physics of Gaseous Dielectrics

I

unexcited atoms and molecules, and photon interactions capability to cause further ionization because ionization

I

I I 1 ‘ 0 2 4 6 8 (0 12 14 I6 18

ELECTRON ENERGY, < i e V l

Figure 15. Ionization cross section U;(.) for Nz and SF6 close to the ionization onset energy I . Electron scattering cross section as a function of E for Nz and electron attachment cross section U , ( € ) for SFs. Normalized electron energy distribution function e l / ’ f ’ ( e , E / N ) as a function of E for Nz at two values of E / N [15,127,128].

Reactions 1 through 5a in Table 1 are responsible for re- moving energy from the free electrons and slowing them down; they are the key processes which determine the electron energy distribution in the gas. The electron slowing-down capability of a gas depends on the cross sections for these processes, especially those involving indirect electron scattering via negative ion resonances [15- 181 which are associated with significant enhancements in inelastic collision cross sections for particular narrowly- defined energy ranges. In the low-energy range (0 to - 20 eV), which is the energy range of principal significance to gaseous dielectrics, such indirect (resonant) processes constitute efficient slowing-down mechanisms (e.g. see the Nz cross section in Figure 9). The effect of these resonances and of the other electron slowing-down processes a t low energies, on the breakdown strength of gaseous media has been amply demonstrated ([15-18,1181).

There are basically three electron-impact ionization processes (6a-6c; Table 1) and two types of electron attachment reactions (5b and 5c; Table 1); the former add and the latter remove electrons (by converting them into heavy slow-moving negative ions) from the dielectric. Once an electron is attached to a molecule it effectively loses its

IEEE Transactions on Electrical Insulation Vol. 25 No. 1, February 1990 65

Table 1. Principal Physical Processes: Primary interactions

Process No. Representation' Description 1

2

3

e + AB -+ AB + e

e + AB -+ AB* + e

e + A B 2 A + B + e

Elastic electron scattering (direct) Inelastic electron scattering (direct)2 Dissociation by electron impact

by electron impact ' * A + B * + e Dissociative excitation

4 e + AB + A+ + B - + e Ion-pair formation 5a e + AB -+ AB-* Elastic (inelastic)

electron scattering (indirect)2

5b + A + + - Dissociative electron attachment

5c -+ A B - + energy3 Parent negative ion for mat ion

6a Ionization by electron impact

6b j A + B+ + 2e Dissociative ionization by electron impact

6c j A* + B+ + 2e Dissociative ionization with fragment excitation'

-+ A B ( A B * ) + e

e + AB -+ AB+ + 2.2

A B ( A ) represents an unexcited and A B * ( A * ) an excited molecule (atom); the double arrow indicates that the reaction can produce a multiplicity of products.

A B * ( A * ) -+ A B ( A ) + hv. excess energy of the metastable AB-" ion must be removed in collisions with other molecules (a much less likely way is radiative stabilization of A B - * ) .

Photon emission may follow these interactions viz.

For the parent negative ion AB- to be formed, the

(or electron detachment) by molecular negative ion collisions is generally very inefficient at the relevant E / N values. While electron impact ionization processes are non- resonant and they extend over a wide energy range above threshold (e.g. see [42,119,120] and Figure 13), electron attachment processes are inherently resonant processes occurring over limited energy ranges typically below - 20 eV (see Figures 11, 12, and 14). The effect of electron attachment on the properties of gaseous dielectrics is pro- found. This has been shown by numerous studies such as those on electron attaching perfluorocarbons [120] which were found to have dielectric strengths higher than SF6 depending on the size of their electron attachment cross section (actually for the strongly electron attaching perfluorocarbons - 2 . 5 ~ higher [120]), and by those on the

dependence of V , on gas number density [121-1241, molecular mass (isotopic dependence) [125] and temperature [34], whenever gas number density, isotopic effects, and temperature introduce corresponding changes in ua(e). The cross sections for electron attachment generally de- crease with increasing electron energy (see Figure 14) and hence low-energy free electrons are usually more efficiently removed from the dielectric (by electron attachment) than higher-energy electrons. Not all gases are electron attaching, however, but gaseous dielectrics with high dielectric strength are, or else contain electronegative additives [15-211.

The 'primary' interactions are followed by a whole host of new interactions which we term 'secondary'. Some of these are listed in Table 2. Each of these interactions may be assigned a coefficient or a rate constant analo- gous to (S), ( lo) , and (13). The relative significance of each of these processes depends on the particular gas. Collectively they influence the number densities of electrons and ions present in the dielectric and affect not only the dielectric strength of the gas, but also its particular behavior under specific situations. For example, the gas dielectric behavior under steep-fronted voltage pulses is affected by the availability of initiating electrons produced by reactions 6 and 7, while corona stabilization is influenced by the electron-ion (reaction 12 in Table 2) and ion-ion (reaction 14 in Table 2) recombination processes. Similarly, electron avalanches are influenced by electron detachment and ion conversion processes [126].

Understanding of the phenomena preceding the transition of the gas from an insulator to a conductor (prebreakdown phenomena) and the mechanism involved in discharge initiation and development invariably requires basic knowledge on a t least some of the processes in Ta- bles l and 2.

3.2 DIELECTRIC PROPERTIES; TAYLORING OF GASEOUS

DIELECTRICS Knowledge on the physical processes in Tables 1 and

2 has been employed to select gaseous media with particular properties and to optimize their dielectric behavior. To illustrate this, let us see how basic knowledge on the electron attaching, electron scattering, and electron impact ionization properties of gases allows one to choose and to tailor gaseous dielectrics for a high V, [15- 20,118,120]. To this end, let us refer to Figure 15 where the ionization cross section U ; ( € ) for N2 and SFs close to the ionization threshold energy I, the electron scattering cross section (total, gt and momentum transfer, c , ~ ) as a function of electron energy E for Nz, and the total electron attachment cross section a,(€) for SF6 are shown, along with the normalized electron energy distribution


Table 2. Secondary Interactions'

Process No. Representation' Description

Phot on-Molecule Interact ions 1 hu + A B -+ AB' Photoabsorp tion 2a h u + A B - + A B t + e Photoionization Zb > A + + + + e Dissociative photoion-

ization 3 hu + A B 3 A + B(*) Photodissociation

with(*)/withont excitation of the fragment(s)

4 a hu + A B - ( B - ) + A B ( B ) + e Photodetachment 4b + A - + B Negative ion photodis-

sociation Ion-Molecule (Atom) Interactions

Ion conversion (charge transfer) Collisional detachment

5 A B - ( A - ) + C - A B ( A ) + C-

6 7 A B - ( A - ) + C -+ A B C ( A C ) + e Associative detachment B A B - + n~ -+ A B - C , n 1 cluster formation in-

A B - ( A - ) + C -+ A B ( A ) + C + e

volving negative ions cluster formation involving positive ions

(atom) reactions3

(atom) reactions3

AB+ + n~ -+ A B + C , n 2 1

10 A B - ( A - ) + C D ( C ) 3 products Negative ion-molecule

11 A B t ( A t ) + C D ( C ) 3 products Positive ion-molecule

Electron-Ion and Negative Ion-Positive Ion ' Recornbimation Reactions

12a e + A B t ( A t ) -+ A B ( * ) ( A ( * ) ) Electron-positive ion

recombination with (*)/ without excitation

12b 3 A + d') Dissociative recombination with (*)/ without excited fragment(s)

12c -+ A B ( A ) + hu Radiative recombination 13 A - + e -+ A + 2e Detachment by electron

14 A - + B+ -+ A B ( * ) Negative ion-positive

impact

ion recombimation with (*)/ without excitation

Penning ionization Interactions Involving Excited and Neutral Species

15 16 A ' + B -+ A B + e Associative ionization 17 A B ' ( A ' ) + e ( € ) -+ A B ( A ) + e(€ ' ) e' > E . Superelastic

18 A B ( A ) + C 3 products Chemical reactions

' Not included in the Table are secondary processes involving Electron injection into the gas by impact of positive ions, negative ions, and excited species on the cathode. ' A B ( A , B ) represents an unexcited and A B ' ( A ' , B') an excited ipecies while A B ( * ) ( A ( * ) , B ( ' ) ) represent species in either an Zxcited or an unexcited state; the double arrow indicates that the reaction can produce a multiplicity of products. ' A multiplicity of reactions and products depending on the type

m d state of the reactants.

A B ' ( A ' ) + C -+ A B ( A ) + Ct + e

collision

involving neutral species

f ( ~ , E / N ) E E ' / ' ~ ' ( E , E / N ) for N2 at two values of E / N (0 .124~10- '~ and 1 . 3 ~ 1 0 - ' ~ 2 ( E / N ) l i m V cm'). For the low E / N value the electron energy distribution lies a t low energies and the fraction of the electrons present in the

2.0

1.6

1.2

0.8 W

0.4 k

= o g

t (01 - 0- 0 20 4 0 60 80 100 0 20 4 0 60 80 100

0 % SF, X SF6

CURVE X 1 l-C,F, - 2 1,1,1,-CH3CF3

1 10.00 2 7.52 3 5.02 4 3.76 5 2.51

ol,l - . ~ , 0 20 4 0 60 80 100 0 20 40 60 80 100

% c - C ~ F ~ IN X % SFg IN l-C3F6

Figure 16. Relative breakdown strength of various gas mixtures. In (c), curves 1-4 are for x = 1-C3Fs , l , l , l , -CH~cFa , CHFJ, and CFJ, respectively. In (d) curves 1-6 are for Ntotcl = 10.00, 7.52, 5.02, 3.76, 2.51, and 1.67 x lo" crnv3, respectively, ( P 91 ).

dielectric which are capable of ionizing the gas is negligible (i.e. the gas is an insulator). For the high E / N value a small, but finite fraction of the electrons has sufficient energy to ionize the gas. This is designated in Figure 15 by the shaded area a' which is a measure of the ionization coefficient a / N (Equation (9)). In spite of the fact that only the high-energy tail of f ( c , E / N ) overlaps o,(E), for a nonelectron attaching gas (ua(c) = 0) such as Nz, this can be sufficient t o promote breakdown. In the presence of an electron attaching gas, the free electrons may be effectively prevented from initiating breakdown by being attached to (captured by) the gas molecules forming negative ions. Since the total electron attachment cross section for SF6 (Figures 12 and 15) and for many other electronegative gas dielectrics (Figures 11 and 14; [15-20,28,33,35,106, 111,1201) is large only at low energies, only these very low energy electrons (thermal and epithermal) can be removed efficiently from the dielectric by attachment. The shaded area in Figure 15 that is designated by v' is a measure of the electron attachment coefficient r ] /N [Equation (lo)]. When more than one electron attachment resonance exists (as is usu-

IEEE Transactions on Electrical Insulation Vol. 25 No. 1 , February I990 67

ELECTRON DRIFT/AlTACHMENT CHARACTERISTICS DESIRED IN DIFFUSE-DISCHARGE SWITCHES

AlTACHMENT RATE

CONSTANT (k,)

DRIFT VELOCITY

lw)

= 3 = 120 E/N (10-17 V-cm2)

Figure 17. Schematic illustration of the electron drift veloc- i tytattachment rate constant characteristics desired in diffuse discharge opening switches [135].

ally the case) in the subexcitation energy range (i.e. the energy range below the first excited electronic state of the gas dielectric) and the total electron attachment cross section remains large over a wide range of energies above thermal, the overlap of oa(c) and f (c , E / N ) increases and so does the V, [15-18,1201. Two points need further clar- ification in connection with this discussion: 1.For a strongly electron attaching gas such as SF6 a t

atmospheric pressures, the mean capture time t , 21

(k,N,)-' 5 10W''s and hence both tu and trel are very much shorter than the formative time lag T j ( > s for the cases under discussion in this paper). There- fore, electrons are removed from the dielectric by attachment via the low-energy tail of the electron energy distribution, but the distribution itself relaxes quickly to its steady-state by feeding the depleted low-energy tail from the higher energies. This repetitive deple- tion/feeding of the low-energy electrons does not alter the shape of f ( ~ , E / N ) from its steady state one, but decreases the electron number density over the entire energy range covered by f (c , E / N ) .

2. For strongly electron attaching gases t , can become comparable to or smaller than trel. In such circum- stances non-equilibrium conditions set in, i.e. f ( ~ , E / N ) can no longer be assumed to have its state-state shape. From the preceding discussion it is apparent that to

optimize the dielectric strength it is desirable that (1) the overlap of a,(€) and f ( e , E / N ) be large, and ( 2 ) the overlap of D ~ ( E ) and f ( ~ , E / N ) be small. Since a, (€) is obviously larger a t high electron energies (Figures 13 and 15) and since a,(€) is generally large a t low electron energies (Figures 11, 12, 14, and 15), in order to

increase the overlap of na(c) and f ( c , E / N ) and to de- crease the overlap of ai(€) and f ( ~ , E / N ) , the electron energy distribution function f (c , E / N ) should be shifted toward low energies as much as possible. Such a shift (re- duction in electron energies) requires large cross sections for elastic and inelastic electron scattering, especially in the subexcitation energy range (impact energies below the energy of the first excited electronic state of the medium). Many studies have demonstrated the significance of electron scattering processes a t these low-energies, and in particular the role of electron slowing down via negative ion resonances [15-18,42,118]. These and other studies, however, clearly showed that high breakdown strengths require large m a ( € ) . Knowledge of ka(< E >) or o,(E) led to the identification of many excellent unitary gas dielectrics such as the perfluorocarbons. The highest known V, (- 2 . 5 ~ higher than in SF6) are exhibited by strongly electron-attaching polyatomic gases such as the perfluorocarbons and other polyhalogenated molecules. Weakly electron-attaching or nonelectron-attaching gases have low V, values. On the other hand, nonelectronega- tive molecular gases with large electron-scattering cross sections have reasonably high V, values compared, for instance, with the rare gases, in which low-energy electron scattering is totally elastic and electron energy losses are associated only with momentum transfer.

A logical conclusion follows the preceding discussion, namely, that the optimum gaseous dielectric in terms of dielectric strength is not a single (unitary) gas but rather a combination of gases (a multicomponent gaseous dielectric) [15-201 designed to provide the best effective combination of the relevant processes given in Tables 1 and 2. For example, and as far as the primary electron- molecule interactions (Table 1) are concerned, the dielectric properties of gases can be optimized by a combination of two or more gases in a multicomponent dielectric gas mixture designed to provide the best effective combination of electron attaching, (electron impact) ionizing and electron-slowing down properties. Basic knowledge on these processes offered several ways to the systematic development of dielectric gas mixtures. Thus, knowledge on the electron-attachment cross section guided the choice of unitary gas dielectrics or electronegative components for dielectric gas mixtures, and knowledge on electron scattering a t low energies guided the choice of buffer gases for mixtures containing electronegative additives. Of practical significance are mixtures of the strongly electron- attaching gases (e.g. SFG, perfluorocarbons) with abundant, inert, and inexpensive buffer gases (e.g. Nz ), with which they act synergistically: the buffer gas(es) scatters electrons into the energy range in which the electronegative gas(es) captures electrons most efficiently.

Examples of the various types of observed uniform-field behavior of the breakdown voltage (V,),n,x of binary gas

68 Christophorou et al. : Basic Physics of Gaseous Dielectrics

mixtures with respect to those (V.,)A,J of the individual components A, B as a function of gas composition are shown in Figure 16.

3.3 GASES FOR SWITCHING OF

CURRENTS EXT E R N A L LY-S U STA I N E D

Even though a gaseous medium by itself is unable to sustain a current below the breakdown voltage, it may act as a conductor of externally-supplied free electrons. For instance, a high-energy external electron beam can be employed to supply substantial electron currents in gases with gains in excess of unity [129-1341. If, then, the discharge is operated well below the breakdown field ( E / N ) l i r n , the current through the discharge can be switch- ed off simply by turning off the external source of electrons. Such externally-sustained gas discharges which do not lead to an arc are known as diffuse gas discharges.

The ability of a gaseous medium to switch large externally-sustained currents appears to be well-suited for fast, high-power repetitive switching and indeed many studies have been conducted to understand and to develop diffuse discharge opening and closing gas switches for pulsed power applications [127-1341. The principle advantages of these switches are: rapid termination of the discharge once the external ionization source is removed, negligible jitter (limited primarily by that of the external source), low inductance, high power handling capacity, and good recovery characteristics (reusability). Of course, many of these advantages are due to the fact that the discharge remains volumetric rather than degenerating into a fila- mentary arc.

The diffuse discharge opening switch in particular, may play a significant role in pulsed power technology employ- ing inductive energy storage [129-1341. Diffuse discharge switches for inductive storage are characterized by two distinct stages: (1) the conducting (storing) stage, when E / N is small (- 3 ~ 1 0 - l ~ V cm’), and (2) the transferring stage (when the stored energy in the inductor is trans- ferred to the load), when E / N is large (2 1 5 0 ~ 1 O - l ’ V cm’). To optimize conduction under the low- E / N conditions of the conducting stage, the electrons produced by the external source (e-beam and/or laser) must remain free (electron losses due to attachment, recombination and diffusion must be kept to a minimum) and must have as large a drift velocity w as possible. To optimize the insulating properties under the high- E / N conditions of the transferring stage, the gas must effectively remove electrons by attachment (have a large attachment rate constant a t high E / N ) . These requirements for the E / N dependence of the electron attachment and drift are schematically illustrated in Figure 17 [135]. Gases with these required properties have been developed [127, 135, 1361.

Finally, the optical modification (enhancement) of the electron attachment properties of gases when irradiated by appropriate laser pulses can be used to change a nonelectron attaching gas into an electron attaching gas and can open up promising possibilities for optical switching/modulation of the dielectric properties of gaseous mat- ter [137-1411. Conversely, laser pulses can be used to change an electron attaching (‘insulating’) gas to a nonelectron attaching (‘conducting’) gas by photodetaching electrons from negative ions present in it [132,142].

4. CONCLUSION URING the past 25 years our knowledge on the basic D physics of gaseous dielectrics has increased substan-

tially and has systematically been applied to the understanding of the dielectric properties of gases from fundamental principles. These basic advances, in turn, have been successfully coupled in many instances to applied research and modern technology. The interdisciplinary character of the international symposia/conferences in the field contributed fundamentally to these developments. The full benefit of this knowledge is yet to be realized.

ACKNOWLEDGMENT This research is sponsored by the U. S. Department of

Energy under contract DE-AC05-840R21400 with Martin Marietta Energy Systems, Inc.

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Basic physics of gaseous dielectrics

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