The research involves conducting high voltage tests to determine lightning attachment locations on an aircraft model and constructing a streamer discharge simulation model in a 20 cm combined gap. The investigation focuses on the air streamer discharge of a non-uniform electric field in the combined gap through experiments and numerical simulation. The results reveal that the discharge process in the electrode-aircraft model gap closely aligns with the final jump stage of natural lightning. Notably, the surface charge density on the aircraft model exhibits a negative correlation with the radius of curvature. Due to the enhanced electric field strength, the aircraft model tips with bigger curvatures have a greater likelihood of initiating streamer discharge. Once the streamer bridges the electrode-aircraft model gap, the accumulation of space charge results in the aircraft’s surface charge reaching an order of magnitude higher than the initial induced charge.

Ensuring the airworthiness of aircraft and guaranteeing flying safety post-direct lightning strikes is imperative.1 Since lightning tends to target specific regions on an aircraft, varying probabilities exist for different fuselage areas to be struck by lightning channels.1–4 This directly influences the lightning current components encountered by the fuselage and its internal electromagnetic field.5 To determine suitable lightning protection for aircraft structures and electronic systems, it is indispensable to zone the fuselage surface based on the likelihood of lightning attachment—a process known as lightning zoning—which is crucial for civil aircraft to pass airworthiness certification.6 

Once the lightning leader tip and the aircraft connect via the streamer, a lightning strike becomes inevitable, and the lightning strike point is determined in a process known as the final jump, characterized by a striking distance.7 While the streamer zone length in the final jump of a full-scale lightning discharge can exceed 100 m, making it challenging to reproduce in a laboratory setting, the phenomenology of a long air gap discharge in the lab bears similarities to natural lightning.8–10 

Observation serves as the fundamental method for studying the final jump process. In laboratory settings, observations can be conducted at much closer distances and for a more extensive number of events.11–15 In addition, given the intricate nature of streamer discharge, numerical simulations of the physical process of streamer discharge are complicated. The positive streamer development is simulated in the radial direction with the combination of the 2-D Poisson equation and the 1-D transport equation.16 The fluid model is applied to calculate the streamer body propagation.17 In addition, the fluid model is also used to simulate the distorted propagation of streamers in a non-uniform background electric field.18,19 For high frequency discharge, the effect of residual electrons and ions is studied by simulation.20–23 Parallel computing was introduced to calculate the space charge and electric field of streamers in air gaps of 0.5 cm, considering factors like altitude’s impact on streamer bifurcation and propagation velocity.24,25 However, the streamer models related to the final jump are mostly empirical or semi-empirical, with different researchers making assumptions about voltage drop and electric field intensity.26,27

In this paper, we establish a model test platform for aircraft lightning zoning, employing high-speed cameras to observe discharge processes. Based on the fluid model, a numerical simulation model of a 20 cm combined gap is constructed, incorporating an improved plasma model considering photoionization. The study focuses on non-uniform electric field air streamer discharge through simulation, examining space electron density, space electric field, and electric density on different surfaces of the floating model.

The experiment took place at the Anhui Provincial Laboratory of Aircraft Lightning Protection in Hefei, China, at an altitude of ∼0 m. The experimental setup is depicted in Fig. 1. A Phantom V2512 high-speed camera with a frame rate of 660 000, a resolution of 128 × 64 pixels, and an exposure time of 1 µs was utilized to record the discharge process.

FIG. 1.

Schematic diagram of the test platform.

FIG. 1.

Schematic diagram of the test platform.

Close modal

The combined gap configuration featured a rod electrode, a floating aircraft model, and a ground plate. The rod electrode had a hemisphere head with a 2 cm diameter. The metal aircraft model measured 162 cm in wingspan, 160 cm in length, and 45 cm in height. In the experiments, the length of the high voltage electrode-aircraft model gap was H of 155 cm, while the length of the aircraft model-ground gap was G of 90 cm.

The positive lightnings are of higher energies statistically. As a result, positive lightning often causes more severe damage to aircraft than negative lightning.6 In addition, the tests to determine natural lightning attachment locations on aircraft should be conducted with the breakdown occurring in 1–3 µs.10 For the generality of the study, a positive lightning impulse was applied in this paper. The positive lightning impulse, with parameters (1.1/45) µs indicating a rise time of 1.1 µs and a decay time to half value of 45 µs, was generated using a 4800 kV Marx generator.28 The generator was charged at 100 kV per stage. The typical lightning impulse and the recorded test voltage are shown in Fig. 2. The experiment underwent 20 repetitions, with a 10-min interval between each discharge. Table I summarizes the applied voltage and the corresponding standard deviation in experiments.

FIG. 2.

The typical lightning impulse and the recorded voltage.

FIG. 2.

The typical lightning impulse and the recorded voltage.

Close modal
TABLE I.

Average breakdown voltage and the corresponding standard deviation.

H (cm)G (cm)Averaged peak voltage (kV)Standard deviation (kV)
155 90 2390 15.5 
H (cm)G (cm)Averaged peak voltage (kV)Standard deviation (kV)
155 90 2390 15.5 

With the development of computer technology, numerical simulation has gradually become one of the most important means of studying gas discharge. The distribution and variation of microscopic parameters such as electron density, electric field, and space charge density during the discharge process can be obtained through simulation calculations, and these data are difficult to obtain in experiments. Most of the previous studies on streamer discharge focused on single gap discharge, and there were few studies on combined gap discharge with floating metal structures. Therefore, in order to study the streamer discharge characteristics in the combined gap and to qualitatively verify the discharge morphology and development process obtained from experiments, we constructed a two-dimensional fluid simulation mode. The innovation of this model is that floating metal is added to the single gap discharge, and the characteristics of floating metal and its effect on streamer discharge are considered. Through such a structure, the streamer discharge process that occurs in aircraft ground lightning zoning tests is simulated.

The fluid model is employed to investigate the streamer discharge process, encompassing the following equations: the electron continuity equation, positive and negative ion continuity equations, and the Poisson equation:29,
net+neμeEDene=Sph+SiSattLep,
(1)
npt+npμpEDpnp=Sph+SilepLpn,
(2)
nnt+nnμnEDnnn=SattLpn,
(3)
2φ=eεnpnenn.
(4)
Here, ne, np, and nn are the electron density, positive ion density, and negative ion density; t is time; μe, μp, and μn are electron, positive, and negative ion mobility; De, Dp, and Dn are the diffusion rates of electrons, positive ions, and negative ions; E is the electric field strength; ε is the permittivity of air; e is the elementary charge; φ is the electric potential; Si is the impact ionization rate; Satt is the electron attachment rate; Sph is the photoionization rate; Lep is the electron–ion recombination rate; and Lpn is the ion–ion recombination rate,30 and the corresponding expressions are as follows:
Si=μeEαne,
(5)
Satt=μeEη2+η3ne,
(6)
Lep=βepnenp,
(7)
Lpn=βpnnpnn.
(8)
Here α is the electron impact ionization coefficient; η2 is the electron two-body attachment coefficient; η3 is the electron three-body attachment coefficient; βep is the electron–ion recombination coefficient; βpn is the ion–ion recombination coefficient. The transport coefficients and the rate coefficients used here are presented in Table II.
TABLE II.

Transport coefficients and rate coefficients used in the model.

ParameterValueReferences
μeN (cm−1 V−1 s−13.74 × 1022 (E/N)−0.25 29  
μpp (cm2 V−1 s−1 Torr) 1846.8 30  
μnp (cm2 V−1 s−1 Torr) 2052 30  
Dep (cm2 s−1 Torr) 1.37 × 106 29  
Dpp (cm2 s−1 Torr) 21.28 30  
Dnp (cm2 s−1 Torr) 32.68 30  
α/N (cm21.4 × 10−16 exp(−660N/E29  
η2/N (cm26 × 10−19 exp(−100N/E29  
η3/N2 (cm51.6 × 10−37 (E/N)−1.1 29  
βepp (cm3 s−1 Torr) 3.8 × 10−5 29  
βpnp (cm3 s−1 Torr) 1.52 × 10−3 29  
ParameterValueReferences
μeN (cm−1 V−1 s−13.74 × 1022 (E/N)−0.25 29  
μpp (cm2 V−1 s−1 Torr) 1846.8 30  
μnp (cm2 V−1 s−1 Torr) 2052 30  
Dep (cm2 s−1 Torr) 1.37 × 106 29  
Dpp (cm2 s−1 Torr) 21.28 30  
Dnp (cm2 s−1 Torr) 32.68 30  
α/N (cm21.4 × 10−16 exp(−660N/E29  
η2/N (cm26 × 10−19 exp(−100N/E29  
η3/N2 (cm51.6 × 10−37 (E/N)−1.1 29  
βepp (cm3 s−1 Torr) 3.8 × 10−5 29  
βpnp (cm3 s−1 Torr) 1.52 × 10−3 29  
The three-exponential Helmholtz equation (9) is employed to calculate the photoionization rate, denoted as Sph,31 and its expression is as follows:
2SphjrλjpO22Sph2r=Ajp2O2Ir,
(9)
where the photon productive rate I(r) is given by
Ir,t=ξ̄vuvipqpq+pSir,t.
(10)
Here, ξ̄ is the average photoionization efficiency of wavelengths between 98 and 102.5 nm. Additionally, υu represents the electron collision excitation frequency of energy level u, υi is the ionization frequency of electron impact, and υu and υi are functions of the reduced field strength. It is noteworthy that υu/υi is a minorant function of the reduced field strength, and in the model, ξ̄υu/υi is set to 0.1.32 

The term p O2 represents the oxygen partial pressure, and pqpq+p denotes the quenching factor, where p is the air pressure and pq is the quenching pressure of singlet N2. In air, the quenching pressure pq is set to 30 Torr.33 The parameters Aj and λj utilized in Eq. (9) are provided in Table III.31 

TABLE III.

Three exponentials fit the parameters in the Helmholtz equation.

jAj (cm−2 Torr−2)λj (cm−1 Torr−1)
1.986 × 10−4 0.0553 
0.0051 0.1460 
0.4886 0.8900 
jAj (cm−2 Torr−2)λj (cm−1 Torr−1)
1.986 × 10−4 0.0553 
0.0051 0.1460 
0.4886 0.8900 

The simulation model adopts a two-dimensional structure, and the simplified geometry is illustrated in Fig. 3.

FIG. 3.

Geometry diagram of the simplified simulation model.

FIG. 3.

Geometry diagram of the simplified simulation model.

Close modal

As depicted in Fig. 3, the aircraft model is inserted into the conventional needle-plate gap, transforming the single gap structure into a combined gap configuration. This combined gap comprises two distinct gaps: gap H, formed by the needle electrode and the aircraft model, and gap G, formed by the aircraft model and the ground. Consequently, this structure is denoted as the combined gap throughout this paper. To optimize computational resources, the actual discharge distances for gap H and gap G are scaled by factors of 10 and 20, respectively. In other words, the simulated discharge gap is 20 cm, where gap H measures 15.5 cm and gap G is 4.5 cm. The simplified aircraft model features a thickness (D) of 1 cm and a length (L) of 8.1 cm. The simulation time for a complete discharge is ∼180 h. All the simulations are run on a workstation computer (Intel® Xeon® Gold 6226R central processing unit [CPU, (Central Processing Unit)], 2.90 GHz with 16 cores and 64 GB RAM in 64-bit mode, running on Windows 10 Pro).

The voltage applied to the needle electrode follows the lightning waveform used in tests and is expressed as34 
Ut=kUmeAtcosωt+BsinωteCt.
(11)
Here, k is 0.846, Um is the voltage amplitude, A is 22 000, ω is 2 250 000, B is 0.5, and C is 1 080 000. Zero flux boundary conditions are set for the open boundary and the electrode surface, and the following boundary conditions are applied to the floating aircraft model:
ρst=nJi+nJe,
(12)
nD1+D2=ρs.
(13)
Here, n is the unit normal vector, Ji and Je are the ion and electron current densities, ρs is the surface charge density, D is the electric displacement vector, and the aircraft surface charge Q0 is obtained by surface integration of the electric displacement vector,
ΩDndS=Q0
(14)
Additionally, to expedite discharge initiation, an initial plasma with a Gaussian distribution is set in the computational domain,
ne|t=0=np|t=0=n0expxx0sx2yy0sy2.
(15)
Here, n0 = 1014 cm−3, x0 and y0 are the horizontal and vertical positions of the initial plasma, x0 = 10 cm, y0 = 20 cm. sx and sy are the characteristic scales of the initial plasma sx = sy = 500 µm. The initial number value of the negative ion is set to 0.

Within the high voltage electrode-aircraft model gap, the spark arc is consistently attached to the upper fuselage of the aircraft model.10 Notably, some branches of the arc channel extended toward the model’s vertical tail. This observation can be explained by the fact that the streamer consistently attaches to the fuselage before reaching the vertical tail. The arc channel aligns with the leaders, which propagate inside the streamer zone. Essentially, the arc channel remains within the spatial region where the streamer zone has advanced. Due to the closer proximity of the electrode to the fuselage compared to the vertical tail, the field strength is stronger in this direction, leading to an increased streamer propagation velocity. Consequently, the arc striking points consistently attach to the aircraft model’s fuselage.

In the case of the aircraft model-ground gap, the spark arc is consistently attached to the aircraft model’s nose or engine nacelles, with several unsuccessful discharge channels attached to the fuselage. As shown in Fig. 4, both the nose and engine nacelles can be treated as structure tips, sharing the same distance to the ground. Once the high voltage electrode-aircraft model gap broke down due to the streamer, the floating aircraft model assumed an equipotential conductor status. Streamers would initiate earlier from the nose or nacelles than from other flatter regions on the conductor surface.8,9 When one streamer bridged the aircraft model-ground gap, the attachment point for the spark arc was determined, causing the velocity of other streamer channels to decrease until they ceased altogether.

FIG. 4.

Typical spark channels in the combined gap.

FIG. 4.

Typical spark channels in the combined gap.

Close modal

In this study, a high-speed camera was employed to capture the discharge processes within the electrode-aircraft model gap. Two selected images illustrate the discharge paths, representing the commencement and conclusion of the final jump phase.

As depicted in Fig. 5, the bright white region corresponds to the leader, while the dim white region signifies the streamer propagation area. The appearance of the bright leader on the rod electrode indicates that the high voltage electrode-aircraft model gap has been bridged by the dim streamer region. Following the streamer breakdown of the gap, it was observed that the leader continued to propagate inside the streamer zone from the original leader tip. This observation suggests that the final spark arc attachment point coincides with the initial contact point of the streamer with the aircraft model.

FIG. 5.

Typical discharge process in the combined gap.

FIG. 5.

Typical discharge process in the combined gap.

Close modal

In Fig. 6, the high-voltage gap discharge initiates at the high-voltage rod electrode, displaying a typical streamer shape reminiscent of classical non-uniform electric field single-gap streamer discharge. The streamer head, slightly inclined to the left during propagation, is attributed to the asymmetry between the left and right sides of the simplified simulation model. This asymmetry results in a slightly smaller distance between the left side of the model and the high voltage electrode compared to the right side. Consequently, the field strength on the left side is marginally larger, leading to increased ionization intensity and causing the streamer head to skew leftward.

FIG. 6.

Spatial distribution of electron density.

FIG. 6.

Spatial distribution of electron density.

Close modal

Once the streamer head reaches the upper surface of the simulation model, signifying the end of the streamer discharge in the electrode-aircraft model, the streamer discharge occurs between the two endpoints of the aircraft and the ground electrode. The right endpoint, with a smaller curvature radius, becomes the initial point of the streamer discharge in the aircraft-ground gap, referred to as the right branch, while the left branch originates from the left endpoint. The completion of the streamer discharge in the right branch indicates the breakdown of the entire combined gap. Subsequently, the surface electric potential of the aircraft model experiences a significant decrease. When the electric field intensity at the left endpoint drops below the discharge threshold, the streamer propagation velocity of the left branch decreases significantly until it halts.

In addition to electron density, electric field intensity is a crucial parameter. As shown in Fig. 7, a high field intensity region is consistently present near the high voltage electrode. As the streamer moves away from this region, it enters a stable propagation stage, and the field intensity of the streamer head remains almost unchanged. When the streamer head approaches the upper surface of the aircraft model, there is a slight increase in field intensity due to the “proximity effect.”

FIG. 7.

Spatial distribution of the electric field strength.

FIG. 7.

Spatial distribution of the electric field strength.

Close modal

After the completion of the streamer discharge in the electrode-aircraft model gap, the smaller curvature radius causes the maximum spatial field intensity to transfer to the right endpoint. The electric field then acts as the driving force of the discharge, resulting in a higher propagation velocity for the right branch compared to the left branch. After the right branch reaches the ground, the field intensity of the left branch head gradually decreases until it falls below the discharge threshold. This indicates that the tip with a smaller curvature radius is more prone to initiating the discharge and becoming the spark arc attachment point for the floating conductor.

Figure 8 presents the spatiotemporal evolution of the charge density on the aircraft surface, with the left endpoint specified as the starting point and clockwise considered the positive direction. Before the streamer bridges the electrode and the aircraft model, the charge distribution on the aircraft model surface is primarily due to electrostatic induction. However, after the streamer bridges the electrode and the aircraft model, the conduction of the high-voltage gap triggers the beginning of the aircraft model-ground gap discharge. Positive charge accumulates at 270°, the center of the upper surface of the aircraft model, while the left and right streamer branches initiate at the endpoints of the left and right sides (0° and 180°), leading to the gradual accumulation of negative charge with streamer propagation. The accumulation of space charges results in an aircraft surface charge an order of magnitude larger than the induced charge before streamer breakdown.

FIG. 8.

Spatiotemporal evolution of charge density on aircraft surface.

FIG. 8.

Spatiotemporal evolution of charge density on aircraft surface.

Close modal

In this study, we established an aircraft lightning zone model test platform and constructed a combined gap discharge model with a magnitude of 20 cm. The experimental results reveal that the aircraft lightning zone model test effectively simulates the final jump process of an aircraft struck by lightning in the air. Before the leader propagation, the streamer bridges the electrode and the aircraft model, and the discharge enters the final jump stage. The simulation results reveal that the development of the streamer tends to favor the direction of higher average field strength in the gap between the high voltage electrode and the aircraft model. However, without enough propagation distance, the streamer did not attach to the aircraft model tips in the simulation. The streamer propagation is accelerated by the enhanced electric field around the aircraft model tips, which become the preferred initiation point of the next streamer discharge. Before the streamer breakdown in the rod electrode-aircraft model gap, the accumulation of space charges results in an aircraft surface charge an order of magnitude larger than the induced charge.

This work was supported by the Ministry of Industry and Information Technology of the People’s Republic of China (Grant No. MJZ5-2N22).

The authors have no conflicts to disclose.

Our work did not use any human or animals.

G.S. and Z.Z. contributed equally to this work.

Guoqing Sun: Conceptualization (equal); Formal analysis (lead); Investigation (lead); Methodology (equal); Software (equal); Validation (equal); Visualization (equal); Writing – original draft (lead); Writing – review & editing (equal). Zhihang Zhao: Data curation (equal); Formal analysis (equal); Software (equal); Visualization (equal); Writing – original draft (supporting); Writing – review & editing (equal). Zemin Duan: Conceptualization (equal); Funding acquisition (lead); Investigation (equal); Project administration (lead); Supervision (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.

1.
V.
Mazur
and
L. H.
Ruhnke
,
J. Geophys. Res.
98
,
12913
12930
, (
1993
).
2.
V.
Mazur
,
B. D.
Fisher
, and
J. C.
Gerlach
,
J. Aircr.
21
,
607
611
(
1984
).
3.
J. A.
Plumer
,
J. Atmos. Electr.
12
,
83
96
(
1992
).
4.
C.
Pavan
,
P.
Fontanes
,
M.
Urbani
,
N. C.
Nguyen
,
M.
Martinez-Sanchez
,
J.
Peraire
,
J.
Montanya
, and
C.
Guerra-Garcia
,
J. Geophys. Res.: Atmos.
125
,
e2019JD031245
, (
2020
).
5.
J. A.
Plumer
,
N. O.
Rasch
, and
M. S.
Glynn
,
J. Aircr.
22
,
429
433
(
1985
).
6.
V.
Mazur
,
L. H.
Ruhnke
,
T. A.
Warner
, and
R. E.
Orville
,
J. Electrost.
71
(
4
),
763
768
(
2013
).
7.
S.
Visacro
,
M.
Guimaraes
, and
V. H.
Murta
,
J. Geophys. Res.: Atmos.
122
,
13356
13369
, (
2017
).
8.
A.
Castellani
,
A.
Bondiou-Clergerie
,
P.
Lalande
,
A.
Bonamy
, and
I.
Gallimberti
,
IEE Proc. - Sci., Meas. Technol.
145
,
185
192
(
1998
).
9.
A.
Castellani
,
A.
Bondiou-Clergerie
,
P.
Lalande
,
A.
Bonamy
, and
I.
Gallimberti
,
IEE Proc. - Sci., Meas. Technol.
145
,
193
199
(
1998
).
10.
J. A.
Plumer
, in
Proceedings of the 2012 International Conference on Lightning Protection, Vienna, Austria
(
IEEE
,
2012
), pp.
1
17
.
11.
A. Y.
Kostinskiy
,
V.
Syssoev
,
N.
Bogatov
,
E.
Mareev
,
M.
Andreev
,
M.
Bulatov
,
L.
Makal’sky
,
D.
Sukharevsky
, and
V.
Rakov
,
J. Geophys. Res.: Atmos.
121
,
9756
9766
, (
2016
).
12.
W.
Lu
,
L.
Chen
,
Y.
Ma
,
V.
Rakov
,
Y.
Gao
,
Y.
Zhang
,
Q.
Yin
, and
Y.
Zhang
,
Geophys. Res. Lett.
40
,
5531
5535
, (
2013
).
13.
A.
Gürlek
, “
Breakdown process on rod–rod air gap under oscillating lightning impulse voltage
,”
High Voltage
5
,
319
326
(
2020
).
14.
V.
Rakov
and
M.
Tran
,
Electr. Power Syst. Res.
173
,
122
134
(
2019
).
15.
Z.
Wang
,
C.
Zhuang
,
Y.
Zhang
, and
R.
Zeng
,
High Voltage Eng.
344
,
920
925
(
2018
).
16.
R.
Morrow
and
J.
Lowke
,
J. Phys. D: Appl. Phys.
30
(
4
),
614
627
(
1997
).
17.
C.
Li
,
J.
Teunissen
,
M.
Nool
et al,
Plasma Sources Sci. Technol.
21
,
055019
(
2012
).
18.
X.
Li
,
D.
Wang
,
J.
Chen
,
J.
Wu
,
N.
Zhao
,
P.
Jia
, and
K.
Wu
,
Phys. Fluids
34
,
027112
(
2022
).
19.
P.
Jia
,
W.
Wan
,
L.
Zhang
,
J.
Ran
,
K.
Wu
,
J.
Wu
,
X.
Pang
, and
X.
Li
,
AIP Adv.
13
,
065005
(
2023
).
20.
A.
Schmidt-Bleker
,
S. A.
Norberg
,
J.
Winter
,
E.
Johnsen
,
S.
Reuter
,
K. D.
Weltmann
, and
M. J.
Kushner
,
Plasma Sources Sci. Technol.
24
,
035022
(
2015
).
21.
L.
Nie
,
L.
Chang
,
Y.
Xian
, and
X.
Lu
,
Phys. Plasmas
23
,
093518
(
2016
).
22.
Y.
Xian
,
X.
Lu
,
J.
Liu
,
S.
Wu
,
D.
Liu
, and
Y.
Pan
,
Plasma Sources Sci. Technol.
21
,
034013
(
2012
).
23.
X.
Li
,
J.
Chen
,
K.
Wu
,
J.
Wu
,
F.
Zhang
,
N.
Zhao
,
P.
Jia
,
Z.
Yin
,
Y.
Wang
, and
C.
Ren
,
Phys. Plasmas
28
,
103507
(
2021
).
24.
Y.
Zhang
,
R.
Zeng
,
X.
Li
et al,
Proc. CSEE
2828
,
6
12
(
2008
).
25.
Z.
Zhao
,
X.
Wei
,
Y.
Yao
,
B.
Zhu
,
H.
Nie
, and
Y.
Li
,
Proc. CSEE
43
(
10
),
4034
4045
(
2023
).
26.
F.
Rizk
,
IEEE Trans. Power Delivery
10
,
1360
1370
(
1995
).
28.
D.
Zemin
,
S.
Xiaoliang
,
F.
Jie
,
D.
Jingbo
,
N.
Youyuan
,
L.
Xin
,
C.
Rongbao
, and
S.
Anhong
,
IEEE Trans. Dielectr. Electr. Insul.
20
,
1112
1116
(
2013
).
29.
A.
Kulikovsky
,
J. Phys. D: Appl. Phys.
30
,
441
(
1997
).
30.
P.
Dordizadeh
,
K.
Adamiak
, and
G. S.
Peter Castle
,
J. Phys. D: Appl. Phys.
48
,
415203
(
2015
).
31.
A.
Bourdon
,
V.
Pasko
,
N.
Liu
,
S.
Célestin
,
P.
Ségur
, and
E.
Marode
,
Plasma Sources Sci. Technol.
16
,
656
(
2007
).
32.
A.
Kulikovsky
,
J. Phys. D: Appl. Phys.
33
,
1514
(
2000
).
33.
P.
Ségur
,
A.
Bourdon
,
E.
Marode
,
D.
Bessières
, and
J.
Paillol
,
Plasma Sources Sci. Technol.
15
,
648
(
2006
).
34.
S.
Okabe
,
T.
Tsuboi
,
G.
Ueta
,
J.
Takami
, and
H.
Hirose
,
IEEE Trans. Dielectr. Electr. Insul.
17
,
2
4
(
2010
).