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Encyclopedia of Physical Science and Technology En004F-171 June 8, 2001 17:11

360 Dielectric Gases

(reaction 12) or positive and negative ions (reaction 13); η E 2 1/2 −1 ∞ E 1/2
can collisionally detach electrons from negative ions (re- = w f ε, ε σ a (ε) d ε,
N a N m 0 N
actions 14 and 15) or convert one ionic species to another
(reaction 16) (and thus change its stability); or can change (2)
the ion’s size (and thus its mobility) by clustering (reac- where I is the ionization onset energy, N the total gas
tion 17). While the role of these processes may be less ob- number density, and N a the attaching gas number density;
viousthantherolesofgroupsAandB,itcan,dependingon for a unary electronegative gas dielectric N = N a , but for
the prevailing conditions, be most significant. For exam- mixtures containing electronegative and nonelectronega-
ple, the gas dielectric behavior under steep-fronted voltage tive components N a < N.
pulses is affected by the availability of “initiating” elec-
trons produced by reactions 14 and 15. Similarly, corona
B. Dielectric Properties
stabilization (Section III.B) is influenced by the electron–
ion (12) and ion–ion (13) recombination processes. Having elaborated briefly on the basic physical processes
Understanding of the phenomena preceding the tran- occurring in electrically stressed dielectric gases, we can
sition of the gas from an insulator to a conductor (pre- appropriately ask the question: How can the dielectric
breakdown phenomena) and the mechanisms involved in properties of a gaseous medium be optimized based on
discharge initiation and development invariably requires knowledge of such processes? To illustrate the type of
basic knowledge on at least a fraction of the processes in answer one can get to this question let us see how knowl-
Table I. This knowledge comes from two sources: low- edge of the electron-attaching, electron slowing-down,
pressure beam experiments and high-pressure swarm ex- and electron impact-ionization properties of gases allows
periments.Inhigh-pressureswarmexperiments,asinelec- one to choose and to tailor gaseous dielectrics. This can be
trically stressed gas dielectrics, the free electrons attain an seen by referring to Fig. 1. When the value of E /N is low
equilibrium energy distribution f (ε, E/N), and the mea- (e.g., 1.24 × 10 −16 V cm in Fig. 1 for N 2 ), f (ε, E /N) lies
2
sured electron trasport coefficients (the electron drift ve- at low energies, and the number of electrons capable of
locity w and the ratio D T /µ of the transverse diffusion ionizing the gas is negligible (i.e., the gas is an insulator).
coefficient D T to the electron mobility µ) are related to As the voltage is increased, however, f (ε, E /N) shifts to
the cross sections for the microscopic electron–molecule higher energies, and for sufficiently high E /N values the
interactions through f (ε, E/N). In principle, from a mea- number of electrons capable of ionizing the gas is such that
surement of w(E/N) and D T /µ(E/N) and a knowledge the gas makes the transition from an insulator to a conduc-
of the electron scattering cross section, f (ε, E/N) can be tor. In Fig. 1, f (ε, E /N) is shown for N 2 at the limiting
2
calculated through the Boltzmann transport equation or by value of E /N , (E /N) lim (
1.3 × 10 −15 V cm ) (i.e., the
Monte Carlo methods. If, then, for a given gas dielectric value of E /N at which breakdown occurs). Even at this
the various cross sections are known, they can be inte- high E /N value only a small fraction of electrons possess
grated over f (ε, E/N) and used along with the appropri- sufficient energy to induce ionization, which, nonetheless,
ate charge conservation equations to determine the current for a non-electron-attaching gas such as N 2 , is sufficient
growth in the gas and predict its breakdown voltage. In to promote gas breakdown. This is designated in Fig. 1 by
practice this is difficult because neither the cross sections the shaded area α, which is a measure of the ionization
nor f (ε, E /N) is known for the majority of the dielectric coefficient α/N [Eq. (1)].
gases or gas mixtures, so one resorts to the more easily For a non-electron-attaching gas and a uniform field,
accessible swarm coefficients to predict the discharge de- knowledge of α provides a measure of (E/N) lim through
velopment and behavior. the so-called Townsend breakdown criterion,
From high-pressure swarm studies, the coefficients for αd
γ (e − 1) = 1. (3)
excitation, detachment, and ion–molecule reactions are
obtained as functions of E /N, as well as the primary ion- In Eq. (3), αd is the number of electrons generated by an
ization coefficient α and the effective electron attachment electron leaving the cathode and arriving as an electron
coefficient η. Most of the data are on the latter two coeffi- avalanche at the anode (at a distance d from the cath-
cients.Thecoefficients α and η aremostsignificantandare ode), and γ is the so-called secondary ionization coeffi-
related to the respective ionization, σ i (ε), and attachment, cient, defined as the number of secondary electrons pro-
σ a (ε), cross sections and f (ε, E /N) by duced perprimary ionization. These secondary-electron
processes include (1) electron emission from the cathode
1/2

α E 2 −1 ∞ E 1/2 as it is struck and photons, positive ions, and metastable

= w f ε, ε σ i (ε) d ε,
N N m I N molecules and (2) gas processes such as photoionization
(1) of the gas. Physically, Eq. (3) states that when each initial