Chemistry Reference
In-Depth Information
detected outside the plasma. Even if self-absorption does occur, the spectral distribu-
tion of the emitted light still carries information on the plasma conditions. It contains
information about the different kinds of plasma species, their number density and
temperature, as well as about the strengths of internal or external electric fields.
The intensity of the spontaneous emission from molecules can be expressed as
the number of photons emitted by a unit volume per second over all solid angles. The
intensity of a spectral line from the
n
,
v
,
N
−→
n
,
v
,
N
rovibronic (rotational
vibrational electronic) transition may be written as
I
n
ν
N
N
n
ν
N
A
n
ν
N
n
ν
N
=
n
ν
N
,
(6.17)
where
n
are the quantum numbers describing an electronic state of the molecule
ν and
N
are the corresponding vibrational and rotational quantum numbers,
respectively
By convention the initial state is denoted by primes and the final state by double
primes.
N
n
ν
N
is the population density of the initial rovibronic level and
A
the
corresponding transition probability for spontaneous emission.
A plasma diagnostic technique based on emission spectroscopy has the charac-
teristics of an inverse problem. Usually, integral intensities of emission lines in the
line of sight are measured within a solid angle with a certain spectral resolution. A
local value of the intensity can be determined only if the plasma under investigation
is homogeneous over the solid angle. Otherwise theoretical inversion methods have
to be applied, such as Abel inversion in the case of cylindrical or spherical symmetry,
or tomography. Measurements of spectrally, spatiotemporally, and phase-resolved
emission of statistically generated discharges succeeded by the technique of cross
correlation spectroscopy (CCS) [154]. The main advantage of this method is its high
sensitivity(singlephotoncounting)combinedwitharesolutioninthesub-nanosecond
and sub-millimeter range. On the basis of the measured spatiotemporally emission
structure and a suitable modeling, conclusions are possible on the chemistry as well
as on electrical fields and density of electron gas. Above all, the CCS was applied
to study the microdischarges of dielectric barrier discharges in air at atmospheric
pressure. This is illustrated in Section 8.1.1 on ozone generation. Other emission
spectroscopic methods are successfully applied for determination of electron energy
distribution function and electron density, also [155-157].
Gans et al. [156] determined the electron energy distribution function in a H
2
capacitively coupled 13.56 MHz discharge at 148 Pa time and space resolved (
5ns,
0.5 mm) by using an analytical model of the excitation population dynamics and
spectroscopic measurements of the excited state population of admixed rare gas
atoms with known data for excitation and de-excitation processes, as excitation cross
sections, cascading contributions from higher electronic states.
Measurements of Stark broadening of spectral lines can be used for determina-
tion of electron densities. This broadening is caused by a local perturbation of the
electric field and therefore determined by the electron density
N
e
. The theory of Stark
broadening is mostly developed for hydrogen atoms [158,159]. The half width
<
λ
S
