22nd International Symposium on Plasma Chemistry
July 5-10, 2015; Antwerp, Belgium
Optical emission from spark discharge in water: evaluation of plasma
temperature
I.V. Timoshkin1, M.J. Given1, M.P. Wilson1, T. Wang1, S.J. MacGregor1 and N. Bonifaci2
1
2
University of Strathclyde, Department EEE, 204 George Street, Glasgow G1 1XW, U.K.
The G2E Laboratory, 25 rue des Martyrs, P.O. Box 166, FR-38042, Grenoble Cedex 09, France
Abstract: High voltage spark discharges in water are characterised by intensive light
emission which can be used for evaluation of plasma temperature in the discharge cavity.
This paper presents a study of the plasma temperature of spark discharges in tap and
distilled water as a function of the inter-electrode distance. The results show that plasma
temperature reaches its maximum at a specific inter-electrode gap.
Keywords: spark discharge in water, plasma temperature, Boltzmann’s plot
2. Optical emission spectra of sparks in water
In the present paper spark discharges were initiated in
distilled and tap water (with conductivities of ~0.3 µS/cm
and ~60 µS/cm correspondingly) and optical emission
spectra of these discharges have been obtained.
A cylindrical test cell filled with water houses two
movable, horizontally orientated 3 mm in diameter copper
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rods (HV and ground electrodes). Four inter-electrode
distances, 0.5 mm, 1 mm, 1.5 mm and 2 mm were used in
the present tests. The high tension electrode was stressed
with HV impulses with a rate of rise of ~0.45 kV/ns
generated by Blumline pulsed power system. The applied
voltage was measured using a Tektronix P6015A high
voltage probe (division ratio 1:1000, bandwidth of
75 MHz) coupled with a Tektronix TDS 2024 digitising
oscilloscope (bandwidth of 200 MHz).
A typical
breakdown event in distilled water (0.5 mm gap) is shown
in Fig. 1.
10
0
Voltage, kV
1. Introduction
Impulsive spark discharges in liquid water have been
extensively studied over the past decades as water is used
in pulsed power systems and technologies which require
controllable spark discharges such as water-filled plasma
closing switches and sources of high intensity underwater
acoustic impulses. Plasma acoustic sources have many
practical applications which include: water treatment;
waste recycling and utilisation; mineral engineering and
drilling applications and bio-medical applications. High
voltage impulsive breakdown in water is a complex
physical phenomenon which includes initiation and
propagation of plasma streamers in the inter-gap,
formation of the conductive plasma channel and the
development of an underwater plasma-filled cavity which
drives a powerful acoustic impulse into the bulk liquid
water [1].
There is a strong interest in further
understanding the energy characteristics of underwater
sparks which is driven by the development of novel
applications of spark discharges including practical
applications in the field of plasma medicine,
environmental protection and by the continuing
development of already established applications. One of
the important parameters which characterises the energy
delivered to the spark discharge is the electrical
conductivity of the plasma in the discharge cavity. The
conductivity of plasma depends on its temperature which
can be determined from the optical emission spectra of
spark discharges. The aim of the present work is to
investigate the plasma temperature of spark discharges
initiated in tap and distilled water by high voltage
impulses.
-10
-20
-30
Breakdown
-40
40
60
80
100
120
Time, ns
Fig. 1. Breakdown event (voltage collapse) in distilled
water.
Optical emission from the plasma channel formed
between the electrodes was monitored using an Ocean
Optics HR4000 spectrometer. No significant difference
between optical emission spectra for spark discharges in
tap and distilled water has been observed. A typical
emission spectrum from the spark discharge in distilled
water (1.5 mm inter-electrode gap) is shown in Fig. 2.
1
6500
6250
Temerature, K
6000
5750
5500
5250
5000
Fig. 2. Optical emission spectra from spark discharge in
distilled water.
3. Time-averaged plasma temperature
Depending on the state of plasma, plasma components
can be characterised by different temperatures. However,
if plasma is in the state of local thermodynamic
equilibrium (LTE), all particles in such plasma have
approximately the same temperature. Assuming that
plasma of underwater spark discharges is in its LTE state,
the Boltzmann’s plot method can be used for calculation
of the time-averaged plasma temperature [2]. In this
method the peak intensities of specific spectral lines
(which belong to the same element), I i , are obtained.
Then data points on a plot of log (I i λ i /g iu A i ) as a function
of the corresponding excitation energy, E iu , are fitted with
a straight line (λ i is excitation wavelength, A i is the
transition probability and g iu is the statistical weight of
the upper level). Therefore, the plasma temperature, T,
can be calculated from the slope, - (k B T)-1:
 Iλ
λn i i
 Ai g iu



=−
Eiu
+ const
k BT
(1)
The validity of the assumption that plasma of the
underwater spark discharge is in the state of local
thermodynamic equilibrium is discussed below. In the
present work intensities of Cu I lines were used to plot
Boltzmann’s graphs for different inter-electrode distances.
The transition probabilities and corresponding statistical
weights of the upper levels for Cu I lines used in this
study were taken from database [3].
Figs. 3 and 4 show the temperature of underwater
plasma discharges as a function of the inter-electrode
distance for tap (Fig. 3) and distilled (Fig. 4) water.
2
1.0
1.5
2.0
Inter-electrode gap, mm
Fig. 3. Plasma temperature as a function of the
inter-electrode distance for tap water.
6500
6250
Temperature, K
As it can be seen from Fig. 2, the most prominent line
in the emission spectra is the hydrogen Balmer series line,
H α , at 656.28 nm. The oxygen line, O I, at 777 nm and
several copper lines (Cu I at 510.554 nm, 515.324 nm,
521.820 nm, 529.25 nm, 578.213 nm) also can be clearly
identified in this spectrum.
0.5
6000
5750
5500
5250
5000
0.5
1.0
1.5
2.0
Inter-electrode distance, mm
Fig. 4. Plasma temperature as a function of the interelectrode distance for distilled water.
Each point in these graphs is the mean value of
15 temperatures obtained from the Boltzmann’s graphs
plotted using optical emission data registered from
different breakdown events, the error bars indicate
standard deviation for each mean value.
It can be seen from Figs. 3 and 4 that the temperature
changes with the inter-electrode gap and both “types” of
water show a non-linear behaviour of the plasma
temperature.
The plasma temperature reaches its
maximum at a specific inter-electrode distance, in the
present experimental conditions this distance is ~1.5 mm.
No significant difference between the plasma temperature
for discharges in tap and distilled water has been
observed, maximum temperature in both cases is ∼0.5 eV.
As mentioned above, this temperature was calculated
using Cu I line parameters taken from [3]. However, in
the case when transition probabilities and statistical
weights for Cu I lines were taken from database [4], the
calculated time-averaged temperature is higher,
∼(0.8-0.9) eV. This discrepancy is required further
analysis.
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The plasma of underwater spark discharges contains
hydrogen atoms, which is confirmed by the high intensity
of H α line in the optical emission spectra, Fig. 1. This
line can be used for evaluation of the electron density in
plasma due to Stark’s broadening of hydrogen spectral
lines.
As was stated above, the Boltzmann’s plot approach
can be used assuming that plasma is in the state of its
local thermodynamic equilibrium. The assumption that
plasma of underwater spark discharges is close to its LTE
state can be validated using a criterion discussed in [5].
This criterion states that the electron density, N e , of
plasma in the state of LTE should satisfy the following
relationship:
N e ≥ 9.2⋅ 1017
k BT  ∆E 


E H  E H 
3
(2)
5. References
[1] I.V. Timoshkin, R.A. Fouracre, M.J. Given and
S.J. MacGregor. J. Phys. D: App. Phys., 39,
4808-4817 (2006)
[2] C. Enghelhard, G. Chan, G. Gamez, W. Buscher and
G. Hieftje. Spectrochim. Acta B, 63, 619-629
(2008)
[3] www.nist.gov
[4] http://cfa-www.harvard.edu
[5] H.R. Griem. Phys. Rev. E, 131, 1170-1176 (1963)
[6] D. Dobrynin, Y. Seepersad, M. Pekker,
M. Shneider, G. Friedman and A. Fridmam.
J. Phys. D: Appl. Phys., 46, 105201 (2013)
[7] A. Denat, N. Bonifaci and O. Lesaint. in: XIX
Europhysics Conference on Atomic and Molecular
Physics of Ionised Gases. (Spain) 1-77 (2008)
where E H is the ionisation potential of hydrogen, ΔE is
the difference between ground and first excited states of
hydrogen atoms, k B is Boltzmann’s constant. According
to this criterion, hydrogen-rich plasma with an average
temperature of ∼0.5 eV has an electron density of
~7⋅1016 cm-3.
The electron density can also be evaluated using the
width of the H α line, this estimation gives the same order
of magnitude for N e , ~ 3⋅1016 cm-3. Thus, according to
criterion (2) plasma in the underwater spark discharge
cavity is close to its LTE state. This evaluation of
electron density is in a reasonable agreement with
estimations by other authors, [6], however in paper [7]
higher values of N e were reported for positive super-sonic
pre-breakdown streamers in water: ~1017 cm-3 for
streamers with velocities of 1-2 km/s and ~5⋅1018 cm-3 for
streamers with velocity of ~30 km/s. As it is suggested in
[7], this difference in the electron density can indicate a
difference in the degree of ionisation in transient
underwater plasma structures.
4. Conclusion
It has been shown that the underwater spark discharges
can produce plasma which is close to its LTE state in both
tap and distilled water. An average plasma temperature
evaluated using the Boltzmann’s method for both cases,
distilled and tap water, shows a non-linear behaviour as a
function of the inter-electrode distance. In the present
experimental conditions the temperature has its maximum
value of ∼0.5 eV at the inter-electrode gap of 1.5 mm.
The obtained time-averaged plasma temperature can be
used for calculation of the electrical conductivity of
plasma and the energy delivered into the underwater spark
discharge. Thus, this method of evaluation of the plasma
temperature can help in optimisation of the electrode
topologies and electric driving circuits used in practical
applications of the underwater spark discharges.
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