MASARYK UNIVERSITY
FACULTY OF SCIENCE
DEPARTMENT OF PHYSICAL ELECTRONICS
High-resolution Spectroscopy of
Transient Micro-Plasmas:
Discharge Mechanisms and
Electric Field Determination
Habilitation thesis - Scientific field: Plasma physics
BRNO 2017 MGR. TOMÁŠ HODER, PH.D.
Abstrakt
Předložená habilitační práce se věnuje tématu fundamentálních mechanismů elektrických
výbojů v tlacích blízkých atmosferickému. Shrnuje vědeckou práci autora zaměřenou
na časoprostorově vysoce rozlišenou optickou emisní spektroskopii a elektrickou charakterizaci
plazmatu. V práci je komentováno patnáct vědeckých článků autora. První kapitola
je věnována bariérovým výbojům ve vzduchu podobných plynných směsech a jejich podrobné
parametrické analýze, dále pak nestabilitám a stratifikaci plazmového filamentu ve
výbojích v argonu. V druhé kapitole je popsána metoda pro určení elektrického pole s
rozlišením desítek pikosekund a mikrometrů, která je aplikována na bariérové, koronové
a jiskrové výboje. Věnuje se také sjednocující teorii streamerovského průrazu plynu. V
poslední kapitole je popsána vylepšená metoda pro elektrickou analýzu streamerovského
plazmatu.
Abstract
In the presented habilitation thesis the topic of fundamental gas discharge mechanisms
in high pressure discharges is addressed. The thesis summarises the scientific contribution
of the author which is focused on spatiotemporally high-resolution optical emission
spectroscopy and electrical characterisation of plasmas. Fifteen articles are commented
by the author. In the first chapter, the detailed parametric studies on barrier discharges in
air-like mixtures and contribution to the clarification of instability-driven filament stratification
in barrier discharge in argon is presented. In the second chapter, the method for
high-resolution electric field determination in air-like plasmas is presented and is further
applied to barrier, corona and spark discharges. It addresses the unification theory of
the streamer gas breakdown mechanism, too. In the last chapter, an enhanced method of
electrical characterisation of streamer driven plasmas is described.
– iii –
Contents
Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v
Chapter 1. Advanced spectroscopy: barrier discharge mechanisms . . . . . . . . . . . 1
1.1 The experimental techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 Barrier discharges in air-like gases . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 Barrier discharge channel stratification in argon . . . . . . . . . . . . . . . . . . . 8
Chapter 2. The electric field: a key parameter determination . . . . . . . . . . . . . . . . . 11
2.1 The method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.2 Trichel pulses in negative corona in air: a unification theory of the gas
discharge mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.3 Barrier discharge on the dielectric surface . . . . . . . . . . . . . . . . . . . . . . . 15
2.4 Barrier discharge streamer as an atmospheric lightning analog . . . . . . . . . 16
2.5 The spark discharge mechanism in air . . . . . . . . . . . . . . . . . . . . . . . . . . 17
Chapter 3. Electrical diagnostics: an important supportive method . . . . . . . . . . . 19
3.1 Electrical current probes and their performance . . . . . . . . . . . . . . . . . . . 19
3.2 An equivalent circuit approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
Commented articles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
Introduction
Electrical discharges in high pressure gases have characteristic time scales starting from
picoseconds of electron ensemble relaxation in a given electric field and spatial dimensions
of electrically highly stressed regions go down to tens of micrometers [1, 2]. Whether
industrially applied coronas, sparks and barrier discharges [2, 3], or naturally occurring
lightning and transient luminous events in upper atmosphere [4, 5, 6, 7], all take the form
of relatively thin filaments - compared to their particular length. The whole chain of
physical mechanisms of electrical gas discharges is present, making the selected discharge
investigation a real challenge to experimental as well as theoretical plasma physicist.
Let us consider a gas filled space stressed by an electrical field. The first electrons
generated by the background pre-ionisation (typically radioactivity, cosmic rays or residuals
from a previous electrical gas breakdown) are accelerated and, depending on the gas
type and electric field magnitude, they ionise the neutral surrounding gas and generate
free charge carriers. This process is of statistical nature [8, 9], and depends also on
material properties of electrodes [10] and their mutual spacing (if in laboratory). In barrier
discharges, this process can take several microseconds until the threshold charge amount
is generated and fast gas breakdown is initiated. The classical theory of John S. Townsend
[11] is required in order to describe this pre-breakdown phase of the discharge. The optical
emission of such a discharge-phase is typically very low and advanced sensitive techniques
are necessary to enable the detection on a selected microsecond scale.
As soon as the critical free charge amount is accumulated, a fast ionising wave bridges
the inter-electrode gap. The charge amount threshold is described by the electron multiplication
parameter of the Raether-Meek criterion. This critical amount can be reached in one
strong electron avalanche or by accumulating several sub-critical ones [9]. The breakdown
via such a fast ionising wave is under given conditions named as the streamer mechanism.
The streamer theory was developed independently by Walter Rogowski and Heinz Raether,
in Germany, and Arthur F. Kip and Leonard B. Loeb, in USA, [12, 13, 14, 15] as a direct
reaction to inconsistencies in Townsend’s approach applied to the atmospheric pressure air
sparks [16]. A streamer in close-atmospheric pressure gases is a contracted ionising wave
that propagates into a low- or non-ionised medium exposed to a high electric field. It is
characterised by a self-generated field enhancement at the head of the growing discharge
channel, leaving a trail of filamentary plasma behind [17, 18]. In atmospheric pressure air,
the self-generated electric field manifests itself in a form of an ultra-short electrical current
pulse, typically only few units of a nanosecond.
The streamer head transforms into the cathode layer immediately after its impact onto
the cathode [19, 20] or the cathode layer is created by the, in opposite direction growing,
negative streamer [21]. A transient glow discharge, the third gas discharge mechanism,
– v –
vi Introduction
takes place here. The created plasma channel is fed by a limited electrical current as it
interconnects both electrodes. In barrier discharges, or transient sparks, this mechanisms
has only short duration. In barrier discharges, the electric field in the gap decreases rapidly
due to the electric field screening by the deposited charges on the dielectric surfaces between
the electrodes [22]. Consequently, the discharge channel decays due to the volume and
surface recombination processes, the electrical current exponentially falls down. The whole
process has few tens of nanoseconds duration in atmospheric pressure air. It was shown,
that the deposited surface charges determine the further discharge behaviour [23] and can
last on the surface for several hours. In transient spark discharge, the glow discharge phase
is replaced by the spark mechanism and the process of discharge channel thermalisation
starts. This transition takes hundreds of nanoseconds or few microseconds [24]. Due to the
peaking ionisation the current and the light emission intensities are reaching their maxima
during this phase. In repetitive transient spark, the power supply limits the transferred
charge and stops the discharge after few microseconds.
The above described chain of discharge development can be significantly altered if
inhomogeneous distributionsof freecharges or metastablestates arepresent inthe particular
region. It can be locally enhanced density of free electrons or positive ions from the previous
breakdown caught in the field-free trap and not yet drifted away, respectively. Indeed, this is
the case of Trichel pulses in negative corona [25], highly-repetitive pulsed barrier discharges
or kHz barrier discharges in argon. In atmospheric pressure argon barrier discharge an
instability in cathode layer, caused by the overall increased energy stored in the plasma, can
lead to the stratification of the discharge channel, an unwanted complication for possible
applications of such plasmas. This energy amount, in form of charge or metastable states
enhanced densities, can be detected only indirectly, if using optical emission spectroscopy.
Moreover, one has to deal with extremely low signals, whether of light emission or of the
electrical current. An advanced techniques and methods have to be applied in order to
detect and resolve these phenomena.
The driving force behind all mentioned discharge mechanisms is the local electric field,
whether in the charge free gap or in the streamer head. It is the electric field which accelerates
electrons, enables their further multiplication, thus starting the plasma-chemistry.
Consequently, new free charges are generated which rearrange the electric field distribution
and so forth. Knowing its instantaneous development in all key coordinates of the
discharge system gives the information necessary to understand the fundamental physics
and, even better, to predict the effects of such a system on its environment. Solving the
Boltzmann equation with appropriate electron and ion scattering cross sections and obtaining
the electron energy distribution function for a given electric field as an input parameter
[26, 27, 28] can give complete information about electron driven processes in the plasma
and finally, using a kinetic model, further development of the plasma-induced chemistry
can be determined [29]. Such information is crucial for optimising the performance of
widely used technology of high-pressure transient plasmas in multiple industrial areas:
ozone production ([30, 31, 32], barrier discharges), surface treatment ([33, 34, 35], barrier
discharges, coronas), environmental uses ([36, 37], barrier discharges, coronas, sparks),
plasma-assisted combustion ([38], barrier discharges, sparks), aerodynamic flow control in
aircraft engineering ([39, 40], barrier discharges, sparks) or newly emerged field of plasma
medicine ([41], barrier discharges, transient sparks). Moreover, the induced charge trans-
Introduction vii
fer and plasma-chemistry in classical lightning or in upper atmospheric transient luminous
events are crucial for understanding of the global electrical circuit [42], the ozone creation
and destruction in the lower stratosphere [43] or the chemistry of transient luminous events
at higher altitudes [44, 45].
The multi-scale nature of the physical and plasma-chemical phenomena described
above truly poses an experimental challenge. The temporal and spatial scales of physical
mechanisms taking place, together with the intensity of the emitted light, non-linearly
change over several orders of magnitude. It requires the application of modern techniques
such as streak cameras or time-correlated single photon counting enhanced spectroscopy.
An advanced methodology for electrical current measurement has to be applied as well.
From above mentioned reasons moreover, a sufficiently sensitive and reliable method
has to be developed in order to quantify the electric field parameter in high resolution.
This habilitation thesis presents the results of the author, combining above mentioned
techniques and methods, and reports his contribution to the high-resolution experimental
investigations of physical mechanisms in high-pressure electrical gas discharges.
It is not the intention of the author to describe the topics in all details here in the commentary
part of the thesis. For more informations the reader is referred to the commented
articles themselves and references therein. The author wishes you a pleasant reading.
Chapter 1
Advanced spectroscopy: barrier
discharge mechanisms
Barrier discharge takes place between two electrodes where at least one of them is covered
by the dielectric barrier [22]. Such a setup in which one of the electrodes is not in direct
contact with the plasma prevents the discharge from sparking and the plasma maintains its
non-thermal character. For barrier discharges in air, the typical temperatures are hundreds
of kelvin for the electrified gas and several thousand kelvin (few units of eV) for the
electrons [46, 34]. The barrier discharge in atmospheric air is typically visible as a thin
violet filament of few tens of microns in diameter and bridging the inter-electrode gap. At
the dielectric surface, a surface discharge spreads as a result of the impact of streamers, see
schematically shown in Fig. 1.1 where the typical discharge current pulses and footprints
on the electrodes are shown as well.
a) b) c)
Figure 1.1: Schematic representation of single filament volume barrier discharge appearance
for the naked eye a), a current pulses in oxygen and air [47] (80 mA/div and 5 ns/div)
b) and Lichtenberg figures created by surface discharges of multiple filaments as recorded
for the first time by Buss [48] c).
First experiments with the barrier discharges were done already by Werner Siemens
[49] in 1857, who used them for generation of ozone gas. In 1932, the electrical signal
was measured by Buss [48] who determined the characteristic timescale to tens of
nanoseconds, took the photographical images of the discharge footprints (see in Fig. 1.1)
and even estimated the electron density in the discharge channel. Later in 1943, Manley
developed a method for the determination of the dissipated power in the plasma based on
– 1 –
2 Chapter 1. Advanced spectroscopy: barrier discharge mechanisms
the construction of charge-voltage diagrams, also called Lissajous figures. This method
has a large influence even today and is still being further improved [50]1. The far history
of barrier discharge investigations and their applications is broad and its exact description
is not within the scope of this work. We refer the reader to the classical texts such as the
review papers of Eliasson and Kogelschatz [47, 22] or the book of Samoilovich, Gibalov
and Kozlov [51].
The new era of the barrier discharge investigation starts with the first use of spatiotemporally
well resolved techniques such as streak cameras [52] (see Fig. 1.2) or cross-correlation
devices [53] and with the implementation of detailed computer modelling [30, 54, 20].
The mechanism of the positive streamer theoretically predicted by the models of Braun
et al. [54, 20] was confirmed and the understanding further improved by spectroscopic
experiments conducted by Kozlov et al. [53, 55, 56].
Figure 1.2: Intensified CCD (left) and streak camera (middle) recordings of the spatiotemporal
distribution of the discharge channel integral luminosity in air at atmospheric
pressure. The cathode directed streamer as well as the transient glow discharge structure
are well visible. The inter-electrode gap is 4 mm and the time interval shown is approx.
20 ns. The picture is taken from [52].
We contributed to the understanding of barrier discharges experimentally, with support
of the theoretical computer modelling. Techniques of the optical signal recording were
significantly improved and mechanisms of barrier discharges in their multiple forms were
clarified. In the next section, the used modern techniques of the plasma induced optical
emission detection will be described. In the second section, several case studies are
presented for sinusoidal and pulse driven barrier discharges in air-like gases. In the third
section of this chapter, the reported studies on an instability-driven discharge channel
stratification in the barrier discharge in argon are presented.
1.1 The experimental techniques
The spatial and temporal occurrence of barrier discharges has a statistical nature based on
the microscopic scale of the physical phenomena taking place. As a result, barrier discharge
breakdown in classical setups takes place spatiotemporally erratically. Therefore a problem
of discharge detection at the right time and in the right place have to be solved. This is an
important task as the signal can be very weak. Therefore, accumulative detection techniques
1We approach this topic in more details in the last chapter where an enhanced methodology for pulsed
barrier discharges is presented.
Chapter 1. Advanced spectroscopy: barrier discharge mechanisms 3
have to be used and a spatiotemporally stable and reproducible discharge operation is
required.
The spatial stability of the discharge was provided by the half-spherical electrodes in
our experiments with volume discharges [56, 57], by deposited parabolic copper films in
the case of coplanar barrier discharge [58, 57] or using syringe needles in the case of
surface barrier discharge [59]. These electrode arrangements created a confined Laplacian
electric field area for the first electrons to be multiplied in. The repetitive discharge then
usually followed this pre-ionised path.
The proper temporal reference to the discharge for exactly timed light detection was
arranged using a master trigger signal in the case of pulsed barrier discharges [60, 61, 62].
The master trigger from the function generator synchronised the power supply and the
recording interval (gate opening) of the detecting system, an intensified CCD camera or
a streak camera, both usually enhanced by a far-field microscope to improve the spatial
resolution. The streak camera images yield the spatiotemporal discharge development
along the discharge axis during rising and falling slopes of the electrical pulse with a high
temporal and spatial resolution of 50 ps and 10 µm, respectively. The spectral resolution
was done using spectral filters.
In the case of sinusoidal driven barrier discharges, the stable temporal occurrence of the
breakdown can not be assured and thus an advanced synchronisation technique has to be
applied. We used the so called time-correlated single photon counting (TCSPC) technique,
where the recorded optical signal is synchronised by the discharge itself. It is also called
cross-correlation spectroscopy when the synchronisation signal is also of an optical nature.
This method allows the substitution of the real-time measurement of the discharge event by
a statistically averaged determination of the cross-correlation function between two optical
signals, both originating from the same source. These two signals are the so called main
(spatially and spectrally resolved) and the synchronising signal, see figure 1.3. The time
between the synchronising signal detection and spectrally and spatially resolved singlephoton
count is measured. A complete measurement is supposed to correspond to the
actual light emission of the single micro-discharge. The temporal resolution can go down
to 10 ps in some cases. Using a straightforward optical projection onto the entrance slit
of the monochromator by a UV-achromat lens, the high spatial resolution of 10 µm was
achieved. As the TCSPC technique has a larger dynamic range than the streak camera
used, we applied it for some selected studies also to the pulsed discharges [62].
In summary, the author and his cooperators have achieved a unique spatiotemporal
resolution of up to 10 µm and 10 ps in conducted experiments. These advanced spectroscopy
apparatuses then enabled, in some cases for the first time, to observe the discharge
phenomena in their characteristic spatiotemporal scales and so revealed the microscopical
features of the physical mechanisms taking place.
1.2 Barrier discharges in air-like gases
In this section, some selected results will be commented, which were obtained during
the author’s activity as postdoctoral researcher at the INP Greifswald (Leibniz Institute for
Plasma Science and Technology, Greifswald, Germany, colleagues H. Höft, M. Kettlitz and
R. Brandenburg) and in cooperation with the Institute of Physics, Greifswald University
4 Chapter 1. Advanced spectroscopy: barrier discharge mechanisms
a) b)
Figure 1.3: An outline of the single filament barrier discharge electrode setups a) and
a scheme of the TCSPC apparatus for the case of single filament investigation (here for
the coplanar barrier discharge, b). The imaging optics consists of one lens (UV, achromat);
PMT—photomultiplayer; CFD—constant fraction discriminator; delay—coaxial
delay cable; TAC—time-to-amplitude converter; ADC—analogue-to-digital converter;
MEM—memory block with up to 4096 channels. The pictures are taken from [57, 58].
in Germany (H.-E. Wagner) and Lomonosov Moscow State University in Russia (K. V.
Kozlov). These experimental studies were performed on sinusoidal and pulsed barrier
discharges using the above mentioned devices. The following five articles are commented:
1. Hoder T, Brandenburg R, Basner R, Weltmann K D, Kozlov K V and Wagner H
E 2010 A comparative study of three different types of barrier discharges in air
at atmospheric pressure by cross-correlation spectroscopy Journal of Physics D:
Applied Physics 43 124009 [57]
2. Grosch H, Hoder T, Weltmann K D and Brandenburg R 2010 Spatio-temporal
development of microdischarges in a surface barrier discharge arrangement in air at
atmospheric pressure The European Physical Journal D 60 547–553 ISSN 1434-
6079 [59]
3. Hoder T, Höft H, Kettlitz M, Weltmann K D and Brandenburg R 2012 Barrier
discharges driven by sub-microsecond pulses at atmospheric pressure: Breakdown
manipulation by pulse width Physics of Plasmas 19 070701 [60]
4. Höft H, Kettlitz M, Hoder T, Weltmann K D and Brandenburg R 2013 The influence
of O-2 content on the spatio-temporal development of pulsed driven dielectric barrier
discharges in O-2/N-2 gas mixtures Journal of Physics D: Applied Physics 46 095202
[61]
5. Höft H, Kettlitz M, Becker M M, Hoder T, Loffhagen D, Brandenburg R and
Weltmann K D 2014 Breakdown characteristics in pulsed-driven dielectric barrier
discharges: influence of the pre-breakdown phase due to volume memory effects
Journal of Physics D: Applied Physics 47 465206 [62]
In the first article, the comparison of the coplanar, symmetric and asymmetric volume
barrier discharges in a single filament arrangement in atmospheric pressure air was
Chapter 1. Advanced spectroscopy: barrier discharge mechanisms 5
done using the TCSPC technique. The spatiotemporal development of the light emission
intensity for two distinguished wavelengths were obtained. To be more precise, the intensities
of the spectral bands coming from radiative electronic transitions N+
2 (C3Pu)n0=0 !
N2(B3Pg)n00=0 (band head at 391.5 nm) and N2(C3Pu)n0=0 ! N2(B3Pg)n00=0 (band head
at 337.1 nm) with 0-0 vibrational transitions were measured. These light emission spectral
bands are usually denoted as the first negative (FNS) and the second positive (SPS) systems
of the molecular nitrogen, respectively. The energy level thresholds of the respective
radiative quantum states N+
2 (C3Pu)n0=0 and N2(C3Pu)n0=0 strongly differ and therefore
the electrons responsible for direct impact excitation (as it is the dominant process under
given conditions) have to possess different energies, i.e. 18.7 and 11.0 eV respectively.
Recording the emission intensities of the FNS and SPS, one receives hints on information
about the electron energy distribution in the plasma. Applying a simple kinetic model,
the local electric field strength can be determined, as it is described in detail in the next
chapter.
As a result of recorded FNS and SPS spatiotemporal distributions for given discharges,
we analysed the basic phases of each barrier discharge geometry under investigation in
more details. For the pre-breakdown Townsend phase the contribution of the a and g
processes, together with the charging of dielectric surfaces lead to distinguishable changes
in spatiotemporal discharge development. For example, the charged dielectric cathode in
M+D- (metallic anode and dielectric covered cathode) arrangement of asymmetric volume
barrier discharge is clearly an additional source of 11 eV electrons in comparison to the
M-D+ setup in the next half-period of applied sinusoidal voltage waveform. This leads
to far faster accumulation of the necessary charge threshold for streamer (ionising wave)
propagation. In general, the observed differences between the SPS intensity profiles along
the discharge axis and between the corresponding integral intensity growth rates can be
explained by different boundary and initial conditions of the discharge development. In
the streamer propagation phase, the velocities of the streamer propagation were compared.
The highest positive streamer velocity (determined from the spatiotemporal distributions of
the FNS signal) is observed in the case of the M-D+ electrode arrangement. The streamer
propagates undisturbed towards the metal cathode in the M-D+ arrangement. In all other
cases with dielectric cathodes, the deposited positive ions on the cathode dielectric repulse
the positive head of the CDIW during its propagation resulting in lower velocities. We also
investigated the phase of the transient glow discharge. For the first time, the long lasting
(up to 150 ns) layer of the enhanced electric field at the cathode surface was experimentally
observed for the M-D+ in air at atmospheric pressure. The thickness of the cathode layer
was found to be about 30 µm with the radius of 120 µm. These values supported the
simulations done by Braun et al. in [20]. In the decay phase, the decay of the integral SPS
signal was found to be the slowest one for M+D-, while the decay rates for the other three
electrode configurations were very close to each other. We concluded that the discharge
development during the decay phase is determined by the properties of the anode, i.e. an
accumulation of negative charge on the surface of the dielectric anode results in a fast
decrease in electric field strength within the discharge channel, and consequently, in a
faster decay rate as compared with the M+D- electrode arrangement.
These comparative results were completed by a similar study of the sine driven surface
barrier discharge in the second article. As a result of our effort, all four basic barrier
6 Chapter 1. Advanced spectroscopy: barrier discharge mechanisms
discharges driven by sinusoidal voltage were investigated. The electrical current pulse and
TCSPC measurements, as well as the ICCD imaging showed clearly different mechanisms
in both polarities. In the positive half-period of the applied voltage on the surface electrode
a very similar behaviour of the FNS and SPS emissions was observed in comparison
to the previously discussed paper. The Townsend phase, positive streamer propagation
along the surface and the filament decay were detected. Nevertheless, the transient glow
discharge phase was not present as there is no clearly defined cathode edge. In the negative
half-period, the rather low spatial resolution led to the issue in discharge mechanism
clarification. Only two years later based on the measurements with an improved resolution,
we could clarify this issue applying the unified theory of the streamer breakdown as
published in [63] (see the commented article in the next chapter). As a first the microscopic
positive streamer is created and impacts the cathode. Only then the discharge channel is
created and the cathode layer feeds the negative streamer with sufficient current.
The third article describes the effect of the pulse width on the discharge mechanism in
the repetitive pulsed barrier discharges in atmospheric pressure N2/O2 (0.1 vol. % oxygen
in nitrogen gas) mixture. Barrier discharges were powered by high voltage pulses of widths
between 10 µs and 200 ns and with the rising and falling slopes of the positive pulse voltage
slopes of approximately 250 V/ns. The development of the micro-discharges on rising and
falling slopes was recorded by streak and intensified CCD cameras simultaneously. The
discharge appearance was magnified using a far-field microscopy. It was shown that the
breakdown on the falling slope strongly depends on the selected pulse width. As a result
of pulse width variation the starting point of ignition changes and positive and negative
streamers occur simultaneously in the falling slope. We clarified that the observed effect
is caused by the electric field rearrangement in the gap due to the different positive ion
densities related to their gap crossing times. As the pulse width (i.e. the time between the
rising and the falling slope breakdown) decreased, a higher densities of the positive ions
were still present in the gap from the previous breakdown on the rising slope. The threshold
width interval was 1 µs, where the traditional scheme of the positive streamer creation etc.,
as described in the introduction, completely failed. The free charge was created not at the
anode but in the space, few hundreds of microns close to the cathode. Similarly to the
surface barrier discharge in the negative half-period, microscopic positive and subsequent
negative streamers were detected in the gap, see the figure 1.4. These results delivered
further evidence for the unification theory, as described in the next chapter.
The next high-resolution parametric study we accomplished, was the investigation
of the influence of the oxygen admixture (in nitrogen gas) onto the behaviour of the
filamentary barrier discharges in pulsed regime. The result was published in the fourth
selected article. The setup and techniques of investigation were the same as in previous
article on pulsed barrier discharges. We investigated the spatiotemporal development and
breakdown statistics of filamentary micro-discharges in 1 mm gap. The influence of the O2
admixture was studied for the range of 0.1 to 20 vol% of O2 in N2. Electrical measurements
were recorded, as were simultaneous streak and iCCD images of studied micro-discharges.
Additionally, a newly developed electrical analysis based on the equivalent circuit model of
the discharge was applied (see further in the third chapter). We made following conclusions
based on the detailed quantitative analysis: The pulse current maxima increase with
rising O2/N2 ratio. Under our conditions an O2 concentration above 5 vol% leads to a
Chapter 1. Advanced spectroscopy: barrier discharge mechanisms 7
Figure 1.4: ICCD camera record of the micro-discharge emission during the falling slope
of the square pulse of duration of 1 µs. The first luminosity appears 100 µm in front of the
cathode (part b), it is followed by the creation of the cathode layer due to the impact of the
microscopic positive streamer (part c) and the filament is created by the negative streamer
(part d). The factor K indicates the intensity scaling with respect to the total maximum in
(f). Every picture corresponds to 100 accumulated discharge events. This picture is taken
from [60].
breakdown delay which increases the reduced electrical field strength at ignition. The
discharge current, the emission durations and the transferred charges all decrease with
rising O2/N2 ratio. The discharge channel emission diameter increases with the O2/N2
ratio, the concentration of 5 vol% is also a threshold value here. The streamer propagation
velocities rise with the O2/N2 ratio. Because of the steep voltage rise in pulsed operation
even a short breakdown delay has a strong influence on the reduced electric field strength
in the gap. In other words, an increase in the amount of electronegative O2 - which delays
the breakdown inception - has a significant impact on the discharge physics, apart from
the influence of the effective collisional quenching of excited N2 states by O2. These
results were explained by the properties of oxygen (e.g. electron trapping and collisional
quenching which reduce the background ionisation before breakdown) interplaying with
the rapid voltage increase during the pulse slope.
The last, fifth, article in this section focuses on the memory effects in the pulsed barrier
discharges. We investigated the influence of the pulse width on the pre-phase and the
subsequent breakdown of pulsed barrier discharge in 0.1 vol% O2 in N2 at atmospheric
pressure with a 10 kV pulse amplitude and a 10 kHz repetition rate. This article further
deepened, using the fluid computer modelling (contribution of M. M. Becker and D.
Loffhagen), the understanding of the previously published Letter paper [60], the third
paper in this commented section. The deviations from the classical chain of the gas
breakdown scenario were described and clarified by the gas pre-ionisation. Furthermore,
we completed the experimental analysis by the high-resolution TCSPC and, taking the
advantage of the Poissonian statistical nature of this technique, a signal recording with
uniquely large dynamical range (six orders of magnitude) was constructed. In particular,
this approach enabled a detailed detection of the SPS signal which was locally generated
by the accelerated residual electrons in the first nanoseconds of the falling slope of the
applied voltage for the 10 µs pulse widths. Results of the computer modelling were in
agreement with this hypothesis.
As a result of the quantitative parametrical analysis, four distinct breakdown regimes
were identified, depending on pause times (pulse widths) between the barrier discharges at
the rising and falling slopes (specified by tpulse) and ranging from ‘classical’ mechanism
8 Chapter 1. Advanced spectroscopy: barrier discharge mechanisms
of cathode-directed (positive) streamer propagation, to no streamer propagation at all for
sub-µs pause times. All regimes were determined by their different behaviours in their
pre-phases. For 99.8 µs tpulse 20 µs, no peculiarities in the pre-phase were observed,
while the breakdown featured an exponential increase in the SPS (of N2) emission in
front of the anode, followed by a propagation of a fast cathode-directed streamer. For
pause times between 20 µs and 4 µs a temporally limited (isolated) diffuse SPS emission
was found, as pointed out above. This was correlated to a considerably high residual
electron density in the gap, which led to changes in the spatiotemporal barrier discharge
development - i.e. the propagation velocity, the streamer inception point and the applied
breakdown voltage - but to no general changes in the breakdown characteristics. The
discharge behaviour completely changes for pause times in the range of 2 to 1 µs where
a simultaneous cathode- and anode-directed streamer propagation was observed, starting
directly from the pre-phase near the cathode. When the pause time was below 0.5 µs, no
streamer propagation occurred, but a re-ignition of the afterglow of the previous discharge.
The results of the modelling quantified in details and supported the previously stated
hypothesis that the effects of the pause time are correlated to a change in the pre-ionisation
created by the previous discharge. The pre-ionisation is created especially by the residual
electrons, positive nitrogen N+
2 and oxygen O+
2 ions.
1.3 Barrier discharge channel stratification in argon
Experiments in the asymmetric volume barrier discharge in atmospheric pressure argon
revealed the presence of the discharge channel stratification. The striated column is well
known from the glow discharges in lower pressure gas mixtures. Here however, we
observed a stratification in micrometrical range of the discharge channel created only for
a few units of microseconds [64]. Experimental [64] and theoretical [65] (in cooperation
with C. Wilke and the computer modelling group at INP Greifswald, i.e. M.M. Becker and
D. Loffhagen) efforts were made to clarify this phenomenon in detail. The example of the
visual appearance of the striated discharge with its electrical current development is given
in Fig. 1.5. Following articles are commented in the following text:
1. Hoder T, Loffhagen D, Wilke C, Grosch H, Schäfer J, Weltmann KD and Brandenburg
R 2011 Striated microdischarges in an asymmetric barrier discharge in argon
at atmospheric pressure Physical Review E 84(4) 046404 [64]
2. Becker M M, Hoder T, Brandenburg R and Loffhagen D 2013 Analysis of microdischarges
in asymmetric dielectric barrier discharges in argon Journal of Physics D:
Applied Physics 46 355203 [65]
We applied correlated ICCD imaging and current measurements together with modern
techniques of computer modelling. From the discharge channel images and current
pulse features the characteristic macroscopic parameters were determined. The scaling
law theory known from low-pressure glow discharge diagnostics was applied in order to
describe and explain this phenomenon. The investigated microdischarge is characterized
as a transient atmospheric-pressure glow discharge with a stratified column. It can be
Chapter 1. Advanced spectroscopy: barrier discharge mechanisms 9
Figure 1.5: Correlated intensified CCD camera and current measurements of the channel
stratification in atmospheric pressure argon barrier discharge. The interelectrode gap was
1.5 mm. Argon flow rate is 150 sccm and iCCD gate is 500 ns. This picture is taken from
[64].
described by similarity parameters i/r ⇡ 0.13 A/cm, p · r ⇡ 5 Torr·cm and 3 < l/r < 5
with the current i, pressure p, interval of subsequent striations l and radius of the plasma
channel r. The influence of the small admixture of nitrogen gas was analysed in detail
by spectroscopical means and by computing the electron velocity distribution function
in multi-term approximation (contribution of D. Loffhagen) for the electric field obtained
from the macroscopical parameter l. An attempt to describe the mechanism of creation
of a striated structure is given, based on an established model of the spatial electron relaxation.
These computations based on the obtained macroscopic parameters included the
electron-electron interaction, which smoothened the electron mean energy profile. Finally
based on the previous theoretical efforts, we concluded that a transient Franck-Hertz-like
phenomenon takes place [66, 67]. We hypothesised that the source of the non-local electrons
is the electron density gradient instability caused by the channel contraction at the
metallic cathode, similar to [68]. The occurrence of this instability was connected with
the certain over-voltage threshold.
The second article treated the problematic tasks of the channel stratification theoretically
(simulations of M.M. Becker), supported by experimental electrical analysis of
the discharge. Theoretical and experimental studies of two different discharge modes in
asymmetric dielectric barrier discharges in argon at atmospheric pressure have been performed.
The first mode appears to be the well-known filamentary micro-discharge with a
non-striated positive column whereas the second mode is characterised by discharge instabilities
and the appearance of striations. Both experiment and model calculations predict
a transition from the first mode to the second mode when the applied voltage amplitude is
increased above approximately 2 kV. The reliability of the employed fluid model is confirmed
by comparison of the current–voltage characteristics obtained by model calculations
and measurements for different applied voltage amplitudes. In general, the results of the
model calculations point out that in the second discharge mode the ionisation of excited
argon atoms prevents the total recombination of charge carriers between two subsequent
discharge events. This leads to the occurrence of the memory from one discharge to the
following one, which plays an important role in mode transition.
Furthermore, we were able to exclude a false hypothesis previously considered by us
in the first article. The negative differential conductivity action was found by the model
10 Chapter 1. Advanced spectroscopy: barrier discharge mechanisms
contrary to the previous experimental estimations. The negative differential conductivity
is usually a source of the electron ensemble instabilities in gas discharge plasmas [69, 70].
In other words, the theoretical investigations have revealed that the instabilities observed in
the experiment at applied voltages, largely exceeding the burning voltage, are potentially
caused by the occurrence of negative differential conductivity immediately after the first
breakdown in each half-period. It was found that the discharge dynamics at amplitudes in
the range from 2 to 2.5 kV is very sensitive with respect to changes in the reaction kinetics
of metastable argon atoms Ar[1s5] and Ar[1s3] (Paschen notation). We have also shown
that the high rate of chemo-ionisation during the entire temporal evolution prevents the full
plasma recombination between subsequent discharge events. Therefore, the characteristics
of each breakdown is largely affected by the previous one and re-ignition takes place in a
part of the discharge volume only. It has been shown that the role of stepwise ionisation
during discharge events increases and the importance of direct ionisation decreases with
the transition from the low voltage mode to the high voltage mode. Finally, even though the
striations observed in the experiment cannot be reproduced by the fluid model considered,
the interplay of direct ionisation and ionisation processes involving excited particles have
been found to be a possible reason for the striations observed in the experiment under
certain conditions.
Chapter 2
The electric field: a key parameter
determination
Detailed knowledge of the local and instantaneous electric field strength in gas discharges
is crucial for deeper understanding of particular phenomena. The electric field rules the
initiated electron-driven chemistry via statistical effects described by the electron energy
distribution function. This is important for understanding of the plasma-chemical effects
of the particular discharge on its environment. Knowledge of the electric field strength
is therefore important for many applications (air-fed ozonizers, air-pollution treatment,
plasma-medicine etc.) but also for understanding the atmospheric electricity. In the
following sections, the used enhanced method for E/N (gas density reduced electric
field strength) determination will be presented together with several case studies of its
implementation. The presented and commented work was accomplished by the author
during his activities at the INP Greifswald in Germany, Academy of Sciences of the Czech
Republic in Prague, Instituto de Astrofísica de Andalucia Granada in Spain, as well as at
the Department of physical electronics of the Masaryk University in Brno, Czech Republic.
This work was done also in cooperation with Ecole Polytechnique Paris and Pau University
in France, as well as Comenius University in Slovakia.
2.1 The method
Researchers have been trying to estimate the mean electron energy or the electric field
strength in air-like plasmas already for decades. Typically, the estimation of basic parameters
of practically all nitrogen-containing plasmas at different pressures was widely based
on the emission of the two above mentioned nitrogen spectral systems, FNS and SPS dominantly
due to the large difference in their excitation potentials which determine their
excitation rate coefficients. Thus, also for discharge in atmospheric pressure air, these
emissions have been in the focus for a long time as well, especially for streamer discharges
[71]. The kinetic scheme enabling the determination of the electric field strength in the discharge
using the ratio of FNS and SPS intensities has already been applied by Gallimberti
et al. [71] and was further used by others (see [72] and references therein).
The radiation kinetics of these spectral indicators (FNS and SPS) in air at atmospheric
pressure is determined dominantly by the following elementary processes: direct elec–
11 –
12 Chapter 2. The electric field: a key parameter determination
tron impact excitation/ionisation (equations 2.1,2.2), spontaneous radiation (2.3,2.4) and
collisional quenching (2.5,2.6) [55, 56]:
e+N2(X1
S+
g )u=0 ! N+
2 (B2
S+
u )u0=0 +2e, 4E = 18.7 eV; (2.1)
e+N2(X1
S+
g )u=0 ! N2(C3
Pu)u0=0 +e, 4E = 11.0 eV; (2.2)
N+
2 (B2
S+
u )u0=0 ! N+
2 (X2
S+
u )u00=0 +hn, l = 391.5 nm,tB
0 = 64.0 ns (2.3)
N2(C3
Pu)u0=0 ! N2(B3
Pg)u00=0 +hn, l = 337.1 nm,tC
0 = 36.6 ns (2.4)
N+
2 (B2
S+
u )u0=0 +N2/O2 ! products, tB
eff = 0.045 ns (2.5)
N2(C3
Pu)u0=0 +N2/O2 ! products, tC
eff = 0.640 ns (2.6)
In these equations, teff stands for the effective lifetime of a given radiative state. It
is given by the reduction of the original radiative lifetime t0 by collisional quenching
[73, 74, 75]. Under the assumption that the direct electron impact excitation process is
dominant for the N+
2 (B2S+
u )u0=0 and the N2(C3Pu)u0=0 state, simple balance equations for
the densities of the radiative states nB and nC can be written. After division and substitution
of the densities for measured intensities IFNS and ISPS, one obtains
dIB(r,t)
dt
+
IB(r,t)
tB
eff
dIC(r,t)
dt
+
IC(r,t)
tC
eff
tB
eff
tC
eff
= RFNS/SPS(E/N). (2.7)
Here, RFNS/SPS(E/N) is the ratio, which is an unambiguous rising function of E/N.
This calibration curve, connecting the measured intensities and the electric field, can be
determined theoretically or experimentally [76, 77].
The problem is that for precise determination of the electric field strength in a streamer
discharge a sub-nanosecond-resolved recording of the FNS and SPS emissions is necessary
[78, 79, 80, 72, 81]. These emissions have an ultra-short shift between their maxima,
given by the electric field waveform and, of course, the different excitation potentials of
the radiative states. This has to be taken into account when applying this method for
the electric field determination in fast discharges (coronas, barrier discharges or Sprite
streamers in air). We clarified this issue in detail in the following commented article:
• Hoder T, Bonaventura Z, Bourdon A and Šimek M 2015 Sub-nanosecond delays
of light emitted by streamer in atmospheric pressure air: Analysis of N+
2 (C3Pu)n0=0
and N2(C3Pu)n0=0 emissions and fundamental streamer structure Journal of Applied
Physics 117 073302 [72]
In this article, theoretical analysis of ultra-short phenomena occurring during the
positive streamer propagation in atmospheric pressure air is presented. Motivated by our
experimental results obtained using TCSPC with a precision of tens-of-picoseconds and
tens-of-microns, it is shown that, when the streamer head passes a spatial coordinate,
emission maxima from N+
2 (C3Pu)n0=0 and N2(C3Pu)n0=0 radiative states follow with
different delays. We reported that these different delays are caused by differences in the
Chapter 2. The electric field: a key parameter determination 13
dynamics of populating the radiative states, due to different excitation and quenching rates.
Associating the position of the streamer head with the maximum value of the self-enhanced
electric field, a delay of 160 ps was experimentally found for the peak emission of the first
negative system of N+
2 ion. In surprising contrast to the highly nonlinear behaviour of
streamer events, a linear dependence was found using 2D axi-symmetric simulations as well
as 1D analytic models (contributions of Z. Bonaventura and A. Bourdon) for the emission
maxima delays as a function of the streamer radius to velocity ratio r/v. We concluded that
the coupling of the delay and the r/v parameter represents an intrinsic characteristic of the
streamer head and we proposed an analytical model for this coupling. A delay dilatation
of few tens of picoseconds was observed experimentally on early-stage streamers and the
general mechanism of this phenomenon is clarified theoretically. The dilatation of these
delays of few tens-of-picoseconds during the early-stage streamer evolution was obtained
using the proposed model in good agreement with experimental findings. We have shown
that the SPS delay can reach the value of up to 400 ps at given conditions, which can
cause an error in the discharge analysis by correlating electrical measurements (current
and voltage waveforms for instantaneous power and energy estimation) to the early-stage
streamer emission development only. As we have shown in this article, the detected
emission only represents populations of excited states formed behind the running streamer
head, giving only delayed information about the streamer head position. We concluded
that it is reasonable to expect that similar phenomena occur in other streamer-mechanism
driven discharges, too (e.g. plasma jets or transient sparks in helium or argon mixtures
with air).
Furthermore, for the first time, based on the results of a 2D axi-symmetric model, a
spectrometric representation of the whole streamer head area was visualised for subsequent
picosecond moments (contribution of M. Šimek). It is shown that for short delays, the
FNS emission peaks at the axis of the streamer, while several tens of picoseconds later
more complex FNS intensity distributions appear. Also, by understanding the structure
of emission spectra in the streamer head, one can assess that the radial averaging of
the streamer emission will cause smaller distortion of the further processed signal in
comparison with the axial signal integration. This last finding is important for further data
processing of spectroscopic data for E/N determination through the ratio method.
2.2 Trichel pulses in negative corona in air: a unification
theory of the gas discharge mechanism
In this section, the issue of the discharge mechanism of negative corona Trichel pulses
is addressed [25, 82]. The mechanism of Trichel pulses in negative corona discharge in
atmospheric pressure air has been a controversial topic already for decades. It was also
one of the last critical issues to be understood for the completion of the unification model
of high-pressure gas breakdown. At gas pressures above roughly 10 kPa, the sequence of
events leading to an arc formation consists of the bridging of the gap by primary streamers,
and the subsequent heating of the initial channel created by the streamers [1, 82]. The
transition between these two stages is determined by the formation of an active cathode
spot capable of feeding an increasing current of electrons into the discharge channel.
14 Chapter 2. The electric field: a key parameter determination
The mechanism for cathode spot formation still remains somewhat obscure, and it is
the important and still missing segment in a unified theory consistently integrating the
extensive results pertaining to the streamer-initiated breakdown phenomena: Except for
the pre-breakdown phenomena in negative corona gaps and for cathode spot formation
by a breakdown of cathode sheaths of pulsed high-pressure discharges [83], the primarystreamer
arrival to the cathode is accepted to be a turning point in the streamer-initiatedbreakdown
development leading to the final arc formation. In the exceptional cases
mentioned, cathode spot formation is related to fast phenomena (⇠ 0.1–1 ns) inside of
a narrow (⇠ 0.1 mm) high-field region in the cathode vicinity. Because of an apparent
technical difficulties of viewing such a microscopic area with a sub-nanosecond time
resolution, the formation of cathode-directed streamers in such very narrow cathode regions
is obviously not considered. This causes the mentioned inconsistency in theory concerning
cathode spot formation in high pressure discharges. We approached this topic in the
following two papers:
1. Hoder T, Černák M, Paillol J, Loffhagen D and Brandenburg R 2012 High-resolution
measurements of the electric field at the streamer arrival to the cathode: A unification
of the streamer-initiated gas-breakdown mechanism Physical Review E 86(5) 055401
[63]
2. Hoder T, Loffhagen D, Voráč J, Becker M M and Brandenburg R 2016 Analysis
of the electric field development and the relaxation of electron velocity distribution
function for nanosecond breakdown in air Plasma Sources Science and Technology
25 025017 [84]
In the first article, from the measured FNS and SPS recordings with spatiotemporal
distribution of 10 ps and 10 µm, we revealed a fast microscopical streamer process including
both positive and negative streamer occurrence. We estimated the velocity of the positive
and negative streamers to be 6⇥104 and 7⇥105 m/s, respectively. The positive streamer
electric field was determined to be 8⇥106 V/m and even a higher field at the created cathode
layer, both in agreement with results of numerical modelling [19, 20]. The characteristics
of the cathode-directed streamer as well as the measured spatiotemporal development of
its electric field, indicated that the ionisation processes leading to the fast current rise to
the Trichel pulse maximum are associated with the formation of a microscopic positive
streamer in the immediate vicinity of the cathode. It is important to mention that this
fact was not considered in a great majority of recent computer simulations. We have
supposed that such phenomena occur in many practical situations and their consideration
offers the attractive feature of the theoretical unification of all streamer-initiated breakdown
processes. As a first step to such unification we claimed that the results presented here
indicate that any streamer-initiated breakdown phenomenon in a discharge gap with a highly
stressed cathode (e.g. negative corona gap) is always associated with the positive-streamer
formation in the vicinity of the cathode surface. This was confirmed by the author for
barrier discharges with different pulse width in [60] and sinusoidal driven surface barrier
discharges [59].
In the second article (invited contribution), we improved the above mentioned approach,
confirmed the previously obtained findings and clarified the effect of the gas heating using
Chapter 2. The electric field: a key parameter determination 15
SPS spectra thermometry (spectroscopic simulation contributed by J. Voráč). Also the
charge transfer in the gap and in the direct microscopic vicinity of the negative electrode
was clarified using analytical models and also using computer simulations (contribution
of M.M. Becker). Finally, the spatiotemporal relaxation of the electron velocity distribution
function for electric fields obtained in the experiment was computed (contribution of
D. Loffhagen) using unique multi-term solving of the Boltzmann equation. These simulations
confirmed the local field approximation for the electron ensemble which is crucial
for the application of the ratio method for E/N determination in highly transient plasmas
with strong electric field gradients.
2.3 Barrier discharge on the dielectric surface
Coplanar barrier discharge is widely used for surface treatment of various materials.
It is a discharge generated on the surface of dielectrics in which both electrodes are
embedded. The so called Diffuse Coplanar Surface Barrier Discharge developed at the
Department of Physical Electronics in the team of prof. M. Černák is applied in several
plasma related research and development areas. As the coplanar discharge propagates
dominantly on the surface, the created residual surface charge has a strong influence on
the subsequent discharge propagation [23, 85, 86, 87]. We approached this topic using
discharge arrangement which modelled such situation. There, two surface streamers of
the same polarity propagated on the dielectric surface close to each other. The following
invited article described our results:
• Hoder T, Synek P, Chorvát D, Ráhel J, Brandenburg R and Černák M 2017 Complex
interaction of subsequent surface streamers via deposited charge: a high- resolution
experimental study Plasma Physics and Controlled Fusion 59 074001 [88]
We have recorded the development of two subsequent surface microdischarges in air by
TCSPC and intensified CCD camera technique with high spatiotemporal resolution. We
performed also a precise electrical measurements. Using special current probe inspired
by setup from [89] and implementing the method of Pipa et al. [90, 91] (see also the last
chapter) we quantified the transferred charge to the dielectric surface. The deposited surface
charge from the first microdischarge significantly affects the pattern of the second event.
Subsequently, the residual charge remaining behind the massive second microdischarge
significantly biases the effective electric field in the gap as it was obtained from the
precise electric measurements. We have observed multiple phenomena of surface streamer
branching, reconnection and deceleration of streamer propagation on surfaces charged
with the same polarity. A unique spatiotemporal distribution of the reduced electric field
strength was obtained using the FNS/SPS ratio method which can be further used for the
determination of the streamer-initiated surface plasma-chemistry similarly as we have done
for volume streamers in [92]. The peak values of the positive streamers were 1200 Td for the
presumably uncharged dielectric surface and even higher for the charged one. These high
values were recently obtained also using hybrid and fluid modelling [93]. We hope that
the understanding of such discharge behaviour and of the generated close-surface plasmachemistry
may lead to better design of surface barrier discharges used for industrial plasma
treatment in air.
16 Chapter 2. The electric field: a key parameter determination
2.4 Barrier discharge streamer as an atmospheric lightning
analog
In our further application of the electric field determination method from the spectroscopic
signatures of FNS and SPS, we approached the topic of streamer dynamics at
lower pressures - similar to the lower stratosphere where the ozone layer is placed. Such
early stage streamers are the first stages of the larger discharges, they are preceding the
creation of the leader discharge which creates the lightning phenomena [6, 7]. We experimentally
determined the electric field radially and temporally resolved and computed
the generated plasma-chemistry using plasma-chemical kinetic model (contribution of
F.J. Gordillo-Vázquez). Our results are described in detail in the following article:
• Hoder T, Šimek M, Bonaventura Z, Prukner V and Gordillo-Vázquez F J 2016 Radially
and temporally resolved electric field of positive streamers in air and modelling
of the induced plasma chemistry Plasma Sources Science and Technology 25 045021
[92]
The reduced electric field strength distribution peaked at 500 Td, with a temporal profile
corresponding to the classical theoretical results on streamer structure by Kulikovsky
et al. [94], which is also used as a tool for extrapolation to low field values, see Fig. 2.1.
Kulikovsky’s analytical model was confirmed both numerically [79, 72, 94] and experimentally
[95]. The influence of the different sets of quenching constant on the resulting
electric field strength is presented on sub-nanosecond resolved data for the first time, further
improving the art of implementation of the ratio method.
Figure 2.1: Recorded FNS and SPS sub-nanosecond signals for the 4 torr streamer in air,
reconstructed E/N waveform and the extrapolation according to the Kulikovsky analytical
model [94]. This picture is taken from [92].
Analysing the results of kinetic modelling we found that the production of ozone is
negligible, while that of nitride oxide was considerably enhanced with respect to its ambient
value. We found that streamers produced under given conditions (4 torr or 37 km altitude)
are able to seed the air ahead of Blue Jets (a type of stratospheric transient luminous event)
Chapter 2. The electric field: a key parameter determination 17
with significant transient concentrations of chemical species such as O(1D) and N(2D),
which contribute to fast heating and, ultimately, to the streamer to leader transition.
2.5 The spark discharge mechanism in air
Another discharge mechanism we addressed in our experiments was the spark discharge, as
it is the direct transition between the non-thermal streamer-ruled and thermalised arc-like
discharge mechanisms. In our investigations, apart from the SPS and FNS signals, the
emission of the atomic lines of oxygen and nitrogen were recorded by the TCSPC, too. We
published our findings in the following article:
• Janda M, Hoder T, Sarani A, Brandenburg R and Machala Z 2017 Cross-correlation
spectroscopy study of the transient spark discharge in atmospheric pressure air
Plasma Sources Science and Technology 26 055010 [96]
We obtained the spatiotemporal distribution of the reduced electric field strength during
the primary streamer phase of the transient spark peaking at approx. 300 Td. This value
is considerably lower than that in the previous case. We concluded that this is due to the
higher residual ionisation of the gas after it has been exposed to the thermalised plasma at
high repetition frequency. Typically, in pre-ionised gas sufficient amount of electrons is for
disposal and so a high electric field gradient does not develop. The transition from streamer
to spark proceeds very fast within about 10 ns for the case with a current pulse repetition
rate in the range 8-10 kHz. This is attributed to memory effects, leading to a low net
electron attachment rate and faster propagation of the secondary streamer. We concluded
that gas heating, accumulation of species such as oxygen atoms from the previous spark
pulses, as well as the generation of charged particles by stepwise ionisation can play an
important role contributing to this fast streamer-to-spark transition. The emission of the
atomic spectral lines of nitrogen and oxygen was detected dominantly during the phase of
discharge channel thermalisation indicating an increasing dissociation level of originally
molecular gas.
Moreover, we addressed the issue of the secondary streamer and tried to determine also
the electric field in it. The conditions created by the primary streamer however, prevented
our method to work with sufficient precision, so we could only comment on the maximum
threshold which was not exceeded.
Chapter 3
Electrical diagnostics: an important
supportive method
Electrical measurement of discharge current and voltage waveforms is a classical and
sometimes the easiest way to access the dissipated energy or estimate the electron density
in the generated plasma [48]. In the case of streamer-initiated discharges however, the
temporal timescales go to the sub-nanosecond level and the current amplitude in some
pre-breakdown phenomena is in the order of few units of micro-amperes. In the following
sections, we briefly describe some enhanced methodology and techniques we applied as
supportive means which can confirm spectroscopically obtained results.
3.1 Electrical current probes and their performance
The first problem, as noted above, is the design of the proper setup which is able to detect
low and fast changing signals. We adopted the methodology proposed in [89, 97] where a
so called coaxial design of the current probe was used. Similar experiments were done also
in [98] or [99] where it was further improved with the statistical analysis. Coaxial setup
minimises the noise and oscillations in the signal due to the external influences. Only such
an enhanced setup combined with high-tech oscilloscopes with sufficient bandwidth can
lead to results capturing the fine features of the current signal under investigation. Such a
setup was applied in our experiments also, during the investigation of both coronas [63],
and barrier discharges [88, 92]. The step at the leading edge of the current pulse of negative
corona Trichel discharges in atmospheric pressure air can be resolved, which is a sign of
well adjusted electrical measurements [63, 72]. Study of this extremely fast feature of the
current pulse enabled a deeper analysis of the fundamental mechanism of the Trichel pulse
[82]. We correlated the current measurements with optical recordings and electric field
development for the first time in [63] and contributed to the experimental understanding
of the Trichel pulse corona discharge.
– 19 –
20 Chapter 3. Electrical diagnostics: an important supportive method
3.2 An equivalent circuit approach
In the case of electrical characterisation of barrier discharges, one has to deal with the
capacitive nature of the system. The current and voltage measured in the external circuit are
not the real values physically present in the gas gap as a plasma parameters [50, 100]. This
makes the analysis more complex in comparison to the corona or spark discharges where
the electrodes are in direct electrical contact with the plasma. Typically, an equivalent
circuit has to be applied using the Kirchhoff equations to decouple the net discharge
characteristics from the recorded signals [100, 101]. The net discharge current, gas gap
voltage, net transferred charge and instantaneous power can be obtained. The gas gap
voltage is of special importance, as it gives the temporal development of the value of the
average electric field in the gas gap, if divided by the gap size. This fact can be used to
calibrate the electric field determined spectroscopically using FNS/SPS ratio method as
described earlier in this text. The spectroscopically obtained spatiotemporal distribution
of the electric field strength can be integrated over the space for each time giving temporal
development to the field comparable to electrical measurements. This was successfully
applied by the author and his colleagues in [88, 92]. For the above described approach
however, one has to know all the parameters of the analysed equivalent circuit. The
effective capacitances of the discharge system are of the main importance.
With A. V. Pipa, we presented such an approach for pulsed barrier discharges and improved
the methodology for the necessary parameter determination - the effective discharge
capacitances. It was published in the following articles:
1. Pipa A V, Hoder T, Koskulics J, Schmidt M and Brandenburg R 2012 Experimental
determination of dielectric barrier discharge capacitance Review of Scientific
Instruments 83 075111 [90]
2. Pipa A V, Koskulics J, Brandenburg R and Hoder T 2012 The simplest equivalent
circuit of a pulsed dielectric barrier discharge and the determination of the gas gap
charge transfer Review of Scientific Instruments 83 115112 [91]
The determination of electrical parameters (such as instantaneous power, transferred
charge, and gas gap voltage) in barrier discharge reactors relies on estimates of key capacitance
values (and their accuracy, see Fig. 3.1 [102], contribution of the author). We
addressed this topic in the first article.
In the classic large-scale sinusoidal-voltage driven discharges, also known as silent
or ozonizer discharge, capacitance values can be determined from a charge-voltage (QV)
plot, also called Lissajous figure. For miniature laboratory reactors driven by fast
pulsed voltage waveforms with sub-microsecond rise time, the capacitance of the dielectric
barriers cannot be evaluated from a single Q-V plot because of the limited applicability
of the classical theory. Theoretical determination can be problematic due to electrode
edge effects, especially in the case of asymmetrical electrodes. We stress the fact that the
lack of reliable capacitance estimates leads to a “capacitance bottleneck” that obstructs
the determination of other discharge electrical parameters in fast-pulsed reactors. We
suggest to obtain the capacitance of dielectric barriers from a plot of the maximal charge
versus maximal voltage amplitude (Qmax-Vmax plot) in a manner analogous to the classical
Chapter 3. Electrical diagnostics: an important supportive method 21
approach. We examined this method using measurements of current and voltage waveforms
of a coaxial discharge reactor in argon at 100 mbar driven by square voltage pulses with
a rise time of 20 ns and with different voltage amplitudes up to 10 kV. Additionally, we
confirmed the applicability of the method also for the data reported in literature measured
at 1 bar of nitrogen-oxygen gas mixtures and xenon.
Figure 3.1: The influence of the effective capacitance values onto the further discharge
parameters using the simplest equivalent circuit. Gas gap voltage Ug(t), discharge current
jR(t), instantaneous electrical power P(t) and energy E(t) coupled into discharge for fast
and slow nanosecond applied voltage switches. See [102] for more details. This picture is
taken from [102], contribution of the author.
In the second article, we have reviewed the concept of the simplest equivalent circuit for
barrier discharges in general. We show that the approach is consistent with experimental
data measured either in large-scale sinusoidal-voltage driven or miniature pulse-voltage
driven discharges. An expression for the charge transferred through the gas gap q(t) is
obtained with an accurate account for the displacement current and the values of discharge
reactor capacitance. This enabled (1) a significant reduction of experimental error in the
determination of q(t) in pulsed barrier discharges, (2) the verification of the classical electrical
theory of ozonizers about maximal transferred charge qmax, and (3) the development
of a graphical method for the determination of qmax from charge-voltage characteristics
measured under pulsed excitation.
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Commented articles
On the next pages the original authors’s work is presented as a collection of in the text
commented 15 reviewed scientific articles. They are listed in following order:
1. Hoder T, Brandenburg R, Basner R, Weltmann K D, Kozlov K V and Wagner H
E 2010 A comparative study of three different types of barrier discharges in air
at atmospheric pressure by cross-correlation spectroscopy Journal of Physics D:
Applied Physics 43 124009
2. Grosch H, Hoder T, Weltmann K D and Brandenburg R 2010 Spatio-temporal
development of microdischarges in a surface barrier discharge arrangement in air at
atmospheric pressure The European Physical Journal D 60 547–553 ISSN 1434-
6079
3. Hoder T, Höft H, Kettlitz M, Weltmann K D and Brandenburg R 2012 Barrier
discharges driven by sub-microsecond pulses at atmospheric pressure: Breakdown
manipulation by pulse width Physics of Plasmas 19 070701
4. Höft H, Kettlitz M, Hoder T, Weltmann K D and Brandenburg R 2013 The influence
of O-2 content on the spatio-temporal development of pulsed driven dielectric barrier
discharges in O-2/N-2 gas mixtures Journal of Physics D: Applied Physics 46 095202
5. Höft H, Kettlitz M, Becker M M, Hoder T, Loffhagen D, Brandenburg R and
Weltmann K D 2014 Breakdown characteristics in pulsed-driven dielectric barrier
discharges: influence of the pre-breakdown phase due to volume memory effects
Journal of Physics D: Applied Physics 47 465206
6. Hoder T, Loffhagen D, Wilke C, Grosch H, Schäfer J, Weltmann KD and Brandenburg
R 2011 Striated microdischarges in an asymmetric barrier discharge in argon
at atmospheric pressure Physical Review E 84(4) 046404
7. Becker M M, Hoder T, Brandenburg R and Loffhagen D 2013 Analysis of microdischarges
in asymmetric dielectric barrier discharges in argon Journal of Physics D:
Applied Physics 46 355203
8. Hoder T, Bonaventura Z, Bourdon A and Šimek M 2015 Sub-nanosecond delays
of light emitted by streamer in atmospheric pressure air: Analysis of N+
2 (C3Pu)n0=0
and N2(C3Pu)n0=0 emissions and fundamental streamer structure Journal of Applied
Physics 117 073302
– 31 –
32 Commented articles
9. Hoder T, Černák M, Paillol J, Loffhagen D and Brandenburg R 2012 High-resolution
measurements of the electric field at the streamer arrival to the cathode: A unification
of the streamer-initiated gas-breakdown mechanism Physical Review E 86(5) 055401
10. Hoder T, Loffhagen D, Voráč J, Becker M M and Brandenburg R 2016 Analysis
of the electric field development and the relaxation of electron velocity distribution
function for nanosecond breakdown in air Plasma Sources Science and Technology
25 025017
11. Hoder T, Synek P, Chorvát D, Ráhel J, Brandenburg R and Černák M 2017 Complex
interaction of subsequent surface streamers via deposited charge: a high- resolution
experimental study Plasma Physics and Controlled Fusion 59 074001
12. Hoder T, Šimek M, Bonaventura Z, Prukner V and Gordillo-Vázquez F J 2016 Radially
and temporally resolved electric field of positive streamers in air and modelling
of the induced plasma chemistry Plasma Sources Science and Technology 25 045021
13. Janda M, Hoder T, Sarani A, Brandenburg R and Machala Z 2017 Cross-correlation
spectroscopy study of the transient spark discharge in atmospheric pressure air
Plasma Sources Science and Technology 26 055010
14. Pipa A V, Hoder T, Koskulics J, Schmidt M and Brandenburg R 2012 Experimental
determination of dielectric barrier discharge capacitance Review of Scientific
Instruments 83 075111
15. Pipa A V, Koskulics J, Brandenburg R and Hoder T 2012 The simplest equivalent
circuit of a pulsed dielectric barrier discharge and the determination of the gas gap
charge transfer Review of Scientific Instruments 83 115112