Page 94 - Academic Press Encyclopedia of Physical Science and Technology 3rd InOrganic Chemistry

P1: GLM/GLT P2: FQP Final Pages
Encyclopedia of Physical Science and Technology En004F-171 June 8, 2001 17:11

Dielectric Gases 361

FIGURE 1 Ionization cross section σ i (ε) for N 2 and SF 6 close to the ionization onset I . Electron-scattering cross
section as a function of ε for N 2 and electron-attachment cross section σ a (ε) for SF 6 . Normalized electron energy
distribution function ε 1/2 f (ε, E /N) as a function of ε for N 2 at two values of E /N. [From Christophorou, L. G., et al.
(1984). IEEE Trans, Elect. Insul. El-19, 550–566.]

electron produces a successor, the current maintains itself Thus (see Fig. 2) for pure SF 6 , (E /N) lim = 3.61 ×
2
and becomes independent of γ . 10 −15 V cm , and it decreases as N 2 is added in the binary
For an electronegative gas the situation is different be- mixture.
cause in this case the free electrons can be effectively pre- For nonuniform fields, ¯α is a function of the position
ventedfrominitiatingbreakdowniftheyattachthemselves between the electrodes, and the breakdown voltage V s can
to gas molecules and form stable negative ions. The total be calculated from the so-called streamer criterion,
attachment cross section σ a (ε) for SF 6 is shown in Fig. 1.

x 0
In general, σ a (ε) is large at very low energies, and thus ¯ α(x) dx = k , (6)
only electrons with energies at the extreme low-energy 0
range can be removed efficiently by electron attachment.
where x 0 is the length at which the electron avalanche
The shaded area in Fig. 1 that is designated by η is a mea- 8
reaches the critical number of electrons (∼10 ) in the
sure of the effective electron attachment coefficient η/N a
avalanche tip for causing streamer formation. The k is a
[Eq. (2)]. Knowledge of α/N and η/N a allows one to pre-
constant characteristic of the gas. It is generally accepted
dict (E /N) lim , which for static uniform fields and a unary
that photoionization processes play a role in the propaga-
gas is defined as the value of E /N at which α = η, namely,
tion of the streamer.
γ [exp{(α − η)d }− 1] = 1 − η/α. (4) For the gas dielectric strength to be optimized, not only
must σ i (ε) be small and σ a (ε) be large [and extend to high
Both α/N and η/N a are functions of E /N (see Figs. 2
energies to maximize the overlap of σ a (ε) and f (ε, E /N),
and 3). Most often, one measures the so-called effective
as in Eq. (2)], but the electron energies must be as low as
ionization coefficient (α − η)/N (see Fig. 2), and the static
possible because a low-lying f (ε, E /N) minimizes α and
uniform field breakdown strength (E /N) lim is defined as
maximizes η. Many studies, however, clearly show that
the value of E /N for which
high breakdown strengths require large σ a (ε). This can be
(α − η)/N ≡ ¯α/N = 0. (5) seen from the examples in Fig. 3. As the attachment-rate