22nd International Symposium on Plasma Chemistry
July 5-10, 2015; Antwerp, Belgium
An ion-electron recombination in hydrogen/helium plasma at low temperatures
R. Plašil, P. Dohnal, Á. Kálosi, P. Rubovič, M. Hejduk and J. Glosík
Charles University in Prague, Faculty of Mathematics and Physics, Department of Surface and Plasma Science,
V Holešovičkách 2, CZ-18000 Prague, Czech Republic
Abstract: We present a study of ion-electron recombination in low temperature
hydrogen/helium plasma. A near infrared cavity ring-down spectrometer has been used to
measure decay of H 3 + ions in afterglow plasma. The main aim of the study was to
understand ternary processes that govern an evolution of hydrogen/helium plasma
composition at higher pressures.
Keywords: ion-electron recombination, hydrogen plasma, absorption spectroscopy
1. Introduction
Hydrogen plasma is present in many technological
applications and also in many astrophysical environments.
It may be found in hydrogen dominated atmospheres of
Jovian planets and in cold interstellar clouds. The
important constituent of typical hydrogen plasma is H 3 +
ion. H 3 + is the most abundantly produced molecular ion in
interstellar space and it stands on the beginnings of many
reaction chains. As proton affinity of H 2 molecule is low,
H 3 + starts a tree of ion-molecular reactions leading to
formation of other astrophysically significant molecules
[1].
One of its important destruction mechanisms is
recombination with electrons. We have been studying the
recombination of H 3 + with electrons for several years and
we found agreement between results of plasma and beam
experiments. We explained discrepancies among most of
the other plasma afterglow experiments by unexpectedly
fast helium-assisted ternary recombination channel in
hydrogen/helium plasma [2]. At 300 K, the rate
coefficients of helium-assisted ternary recombination
overtop by more than two orders of magnitude expected
value of such processes [3].
H 3 + + e– → H 3 #
(1)
H 3 + M → H 2 + H (or 3 H) + M
#
(2)
#
In this scheme highly excited neutral molecule H 3 in
Rydberg state is formed and it is consequently stabilized
by collision with neutral molecule M. In our recent
publication we identified also ternary recombination
channel enhanced by H 2 at 300 K [4] with ternary rate
coefficient 9×10–23 cm6 s–1. We observed a saturation of
the ternary recombination process due to finite rate of
Equation (1). At higher number densities of H 2 the overall
rate coefficient is driven only by the formation of the
highly excited neutral molecule H 3 #.
The independence of measured recombination rate
coefficient in saturated region may clarify data measured
by Amano [5] that presented three times higher binary
recombination rate of H 3 + than the most of other
experiments. We want to study the hydrogen-assisted
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ternary recombination further below 300 K to understand
this extremely fast process.
2. Experiment
Measurements took place in stationary afterglow with
time-resolved cavity ring-down spectrometer [6]. Pulsed
microwave discharge was periodically ignited in a
mixture of He, Ar and H 2 gas. Helium was used to ensure
thermalization of ions and electrons and to reduce
diffusion of plasma. Trace of argon was added to remove
metastable helium atoms and to enhance production of
H 3 +. Details about chemical kinetics were given in [7].
Fast switch allowed us to turn off the incident microwave
power within 30 µs. The kinetic temperature was
measured from the Doppler broadening of absorption
lines of neutral molecules and ions and it was found to be
close to the temperature of the wall of the apparatus
within few kelvins.
To measure decay curves of the lowest rotational
energy levels of H 3 + we used a near infrared cavity ringdown spectrometer with synchronous detection
capabilities. For each ring-down event the time of data
acquisition start was recorded, relative to the discharge
cycle. More detailed description of the used apparatus can
be found in [6,8] and in references therein.
For this measurement the second overtone transitions
originating from the ground vibrational level of H 3 + were
used. The lowest rotational levels (1,1) (para, transition
3v 2 1(2,1)←0v 2 0(1,1)) and (1,0) (ortho, transition
3v 2 1(2,0)←0v 2 0(1,0)) of the vibrational ground state were
monitored. For evaluation of rotational temperature we
also probed another state (3,3) (ortho, transition
3v 2 1(4,3)←0v 2 0(3,3)).
Measured data show good kinetic and rotational
thermalization of H 3 + ion in the discharge and in the
afterglow because at used conditions prior recombination
with electron, H 3 + undergoes many collisions with
hydrogen and helium. Electrons are hot during the
discharge, but they are thermalized within few
microseconds in the afterglow. We found that electron
temperature also corresponds to neutral gas temperature at
similar conditions [9].
1
From time resolved measurement of spectral lines we
derived decays of H 3 + number density n. If the
recombination process is dominant we can write the
following equations.
d𝑛
d𝑡
1
𝑛
= 𝛼eff 𝑛2
=
(3)
1
+ 𝛼eff
𝑛(𝑡=0)
𝑡,
(4)
where α eff denotes measured binary rate coefficient of
recombination. Examples of measured decays are plotted
in Figure 1. Reciprocal value of ion number density is
used for clarity.
1/n (10–11 cm3)
8
273 K
7 α = 3.0×10–7 cm3 s–1
eff
6
5
4
3
effective binary recombination rate coefficients at 273 K
are plotted in Figure 2.
The plotted statistical errors of the rate coefficients are
given by used fit procedure. A systematic error of our
experimental setup consists mainly in an uncertainty of
the dimension of the plasma column in the resonator and
it is less than 10 %.
Measured α eff consists of binary recombination rate
coefficient 6×10–8 cm3 s–1 and comparable addition of
helium-assisted ternary recombination (~5×10–8 cm3 s–1
between 900 Pa and 1800 Pa) with rate coefficient in the
order of 10–25 cm6 s–1. The increase of measured effective
recombination rate coefficient on the left side of Figure 2
for [H 2 ] < 1016 cm–3 is caused by hydrogen-assisted
ternary recombination characterized by rate coefficient
9×10–23 cm6 s–1.
The obvious difference between data measured at
300 K and 273 K is brought out by a formation of H 5 +
and its relatively fast recombination with electrons. The
pressure dependence at 273 K is induced by smaller
proportion of H 5 + in equilibrium at lower pressure. The
losses of ion number density caused by recombination of
H 5 + are comparable to all other channels even at 273 K.
4.0
2
300 K
αeff = 2.1×10–7 cm3 s–1
0
0
100
time (µs)
200
300
Fig. 1. Examples of measured plasma decays in afterglow
plasma plotted in reciprocal graph at two temperatures.
These plots illustrate the dominance of recombination
process at used conditions, [H 2 ] = 3×1016 cm–3 and
overall pressure 1800 Pa.
3.0
2.5
2.0
3. Results and conclusions
In our experiment we decreased temperature of the wall
of the apparatus to 273 K. At high number densities we
observed increase of measured binary recombination rate
coefficient due to formation of H 5 + ions. At high number
densities of H 2 and sufficiently low temperature H 5 +
cluster may be formed and it keeps chemical equilibrium
described by ratio [H 5 +]/[H 3 +] that depends on
temperature.
H 3 + + H 2 + He → H 5 + + He
(5)
H 5 + He → H 3 + H 2 + He
(6)
H 5 + e → neutral products
(7)
+
+
–
300 K
1800 Pa
900 Pa
1.5
1.0
To obtain more accurate values of recombination rate
coefficient we included also diffusion losses in the
evaluation, for details see reference [10].
+
273 K
1800 Pa
900 Pa
3.5
αeff (10–7 cm3 s–1)
1
0
1
2
3
16
4
5
6
–3
[H2] (10 cm )
Fig. 2. Measured binary recombination rate coefficients at
273 K at two pressures. The comparison with rate
coefficients measured at 300 K [4] shows substantial
difference caused by the formation of H 5 +.
To determine dependence of hydrogen-assisted ternary
recombination rate coefficient we need to separate
influence of H 5 + clusters from hydrogen-assisted ternary
recombination. Therefore we will need to study formation
of H 5 +/ H 3 + equilibrium and the influence of H 5 +
recombination with electrons at temperatures below
300 K.
At our conditions, model based on [7,11,12] shows that
ratio between H 5 + and H 3 + is very close to equilibrium
taking the Equations (5 – 7) into account. Measured
2
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Acknowledgements
This work was partly supported by Grant Agency of
Czech Republic GACR P209/12/0233 and GACR 1414649P and GAUK 692214.
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