Electrical characteristics of barrier discharge
Tomáš Hoder
In
I
Department of Physical Electronics Masaryk University, Brno, Czech Republic
Gas Discharges lecture
Historical overview
Q-V plot (aka Lissajous figure)
Simplest equivalent circuit of the barrier discharge
Electrical current in the discharge gap vs. electrical current
measured in the external circuit
Voltage on the gas gap and the electric field parameter
Application of the electrical analysis for the (not only)
spectroscopic plasma investigation
Understanding the plasma chemistry of low pressure volume and for coplanar barrier discharge in atmospheric pressure air
1
Barrier discharge - already Siemens had done it...
Wenn man zwei dünne Glas- und Grlimmerplatten einseitig mit Stanniol belegt und die nicht belegten Seiten so aufeinander legt, dass ein lufterfüllter Zwischenraum von geringer aber gleichmässiger Dicke sich zwischen ihnen befindet, so erhält man bekanntlich eine Lichterscheinung in dem ganzen lufterfllllten Räume, wenn man den so gebildeten Collector durch eine hinlänglich geladene Leydner Flasche ladet. Diese Lichterscheinung wiederholt sich bei der Entladung des Collectors. Das Leuchten des Luftraums tritt nicht ein, wenn die Flasche sehr schwach geladen ist. Es beginnt bei einer ganz bestimmten Ladung und verstärkt sich von diesem Punkte an mit der Vergrösserung der Ladung der Flasche.
fr
*****
^ Nif       &v •
0
Cg = =        ^ l
Uüis
.1
W. Siemens 1857 and Buss 1932, Klemenc 1937, Manley 1943, Samoilovich 1966, Gibalov 1981, Eliasson, Kogelschatz 1983, Heuser 1985, Okazaki 1993, Zhu 1996, Kozlov 2001, Stollenwerk 2007
Current Voltage
GO O
Simplest equivalent circuit of barrier discharge
a macroscopic point of view
Kirchhoff's circuit equations and the result
a macroscopic point of view
0(0 -1 I ■    _ V.
c u*
ud(t) =
Ca
UM) = V(t) - Ud(t)
JR = '(0 ~ jg(t)
jM) = Cg
dUM) dt
	—►	
	node	Cd
	■nal	
	a)	
f	c	
1-		
Jr
gap node   q    q dielectric node
UM) = V(0 -
6(0
Ccell =
Crf + Cg
hit) =
1 + —
((f) - c
g
dV(t) dt
jR(t) =
1 -
Ccell
i(t) - C,
cell
dV(t) dt
q{t) =
Ccell
1 _ Ccell
1 cd
0(0
L Ccell
V(t) \+q0
]
Liu et al. 2003 J. Phys. D: Appl. Phys. Pipa et al. 2012 Rev. Sei. Instrum.
Discharge current correct value?
JR(t) =
C, 1 + —
i(0 - c
8
Tschiersch et al. 2017 J. Phys. D: Appl. Phys. Peeters et al. 2015 Plasma Sources Sci. Technol.
Pipa et al. 2012 Rev. Sci. Instrum. Williamson et al. 2006 J.Phys. D: Appl. Phys. dV(t)     Merbahi et al. 2004 J. Phys. D: Appl. Phys.
Liu et al. 2003 J. Phys. D: Appl. Phys. Bibinov et al. 2001 J. Phys D: Appl. Phys.
^discharge (O — ^meas(0     ^Cgas — ^
meas
(O - c
dVgasCO
gas
gas
dt
Reichen et al. 2010 J. Phys. D: Appl. Phys. Massines et al. 2005 Plasma Phys. Control. Fusion Naude et al. 2005 J. Phys. D: Appl. Phys. Bletzinger et al. 2003 J. Phys. D: Appl. Phys. Lomaev et al. 2001 Atmos. Oceanic Optic.
Electrical current balance equation
a microscopic point of view
U
Cc
C_äl
I
v
=j=Ud
J.
U(t) = ic(x,t) + e(x)e0
dE(x,t) dt
rd+g
Jo
dx
e{x)
pd+g
Jo
e(x)so dt
fd+g
/ E(x, t)dx Jo
l l
+
Cd    Cg I    Ae0 J0 e(x)
dt
jR(t) = Ut) =
1
1 -
Ccell Cd L
l(t) - Cceii
dVjt) dt
Kulikovsky 1994 J. Phys. D: Appl. Phys.
Wang et al. 2006 J. Appl. Phys. Hoder, Bonaventura et al. 2016
Electrical current balance equation + surface charge
a microscopic point of view
U
Cc
C_äl
I
v
=j=Ud
= {ig [R]|i|
J.
it(i) = ic(x,t) + e{x)dE^' = £(i)e0
dEd(t) dt
Mt)
Eg = erEd — o/so
d°L — q
dt ~ Lc
da\ fdg{er - 1)
f^+(w)(W)-
da rerg{g + dh     g + d   ^ dV^ dt L erg + d J    erg + d dt
g + d dV
erg + d dt
1
1 -
c.
cell
Cd L
Bonaventura, Hoder et al. 2017
Limitations: net charge in streamer head and sheath
2D simulation of the volume barrier discharge in atmospheric pressure air
red arrow denotes the streamer impact onto the cathode creating the conductive channel
Braun et al. 1992 Plasma Sources Sei. Technol.
Limitations: net charge in streamer head and sheath
Correlated current and spatiotemporal development of helium line in barrier discharge plasma jet in atmospheric pressure helium
Grounded electrode
0     £     4     6     8    10   12   14   16 18
f t [us]
the streamer impact creating the conductive channel
Sretenovic et al. 2014 J. Phys. D: Appl. Phys.
Limitations of current determination
Coplanar barrier discharge in air at 30 kPa pressure
4000
3000
4000
3> 2000 4,
1000 4
■U(V)
■measured i(t)* 10000 discharge i  (t)* 10000
0
8200  T 8300
T
3000
2000
o o o o
1000
0
8400       8500 8600 time [ns]
8700 8800
red arrow denoting the impact of streamers on the electrodes
jR(t) = jc(t) =
1-
Cgell Cd L
l(t) - Cceii
dV(t) dt
UM) = V(t) -
8(0 Cd
Eft) = Ug(t)/g
11
Hoder, Synek et al. 2016 Plasma Phys. Control. Fusion
Spectroscopic comparison - helium barrier
discharge at 20kPa
Spatiotemporally resolved direct electric field measurement using Stark polarization emission spectroscopy in helium volume barrier discharge
>
03
o
>
UM) =
dř/a(0
L(z) dr
8
6
4
2
0 8
6
4
2
0 8
6
4
|§ 2 O 0 0) 8
Cathode * ♦ ♦♦
I        .......... w
E
o
> 0
-100 ns
Anode
0 ns
Anode
LU
+100 ns
Cathode _I_
Anode
Cathode ♦
+200 ns
Anode
Cathode
+300 ns
Anode
04   -0.02    0.00    0.02    0.04    0.06    0.08    0.10    0.12    0.14    0.16    0.18 0.20
Distance from Cathode (cm)
Figure 8. Development of the electric field spatial distribution in DBD in helium at 200 mbar.
12
Ivkovic et al. 2009 J. Phys. D: Appl. Phys. Liu et al. 2003 J. Phys. D: Appl. Phys.
Spectroscopic comparison - helium at 20kPa
Spatiotemporally resolved direct electric field measurement using Stark polarization emission spectroscopy - comparison
Gas in-
D
0.03mm
=1=
Gas out
M
/g(0=   1 + 7T /t(0-Cg
dt/a(0
at
UM) =
Cd_ C. + G
■i/.W -
dr
-800
-4.0
13
8.0     8.5     9.0     9.5    10.0    10.5    11.0    11.5 12.0
Time (jis)
Figure 10. Comparison of calculated cathode fall voltage Ucai and measured gap voltage Ug in the DBD at 200mbar pressure.
Ivkovic et al. 2009 J. Phys. D: Appl. Phys. Liu et al. 2003 J. Phys. D: Appl. Phys.
Spectroscopic comparison - N2/H2 mixture at atmospheric pressure in ns-pulsed barrier discharge
Direct electric field measurement in the discharge gap based on coherent anti-Stokes Raman spectroscopy four-wave mixing method
derived within the simplest equivalent circuit approach
Boehm et al. 2016 Plasma Sources Sci. Technol. Kettlitz et al. 2012 J. Phys. D: Appl. Phys. Pipa et al. 2012 Rev. Sci. Instrum.
Spectroscopic comparison - air 30kPa Townsend phase of coplanar barrier discharge prior the breakdown
Effective electric field determined by Townsend alpha coefficient fitting of a(E/N) from high-resolution emission of N2(C-B) in coplanar barrier discharge
0.10
derived within the simplest equivalent circuit approach
applied voltage gap voltage
measured current] 0.08 . riischargp-GUfrenť
- 0.06
o c
-i —1 CD 3
-I 0.04 —
- 0.02
400 600 time [ns]
800
0.00 1000
Electric field at the breakdown instant: 190±30 Td (electrics) and 220±20 Td (fitting) and 210±40 Td from FNS/SPS(E/N)
Pipa et al. 2012 Rev. Sci. Instrum. Hoder, Synek et al. 2016 Plasma Phys. Control. Fusion
Pockels effect comparison - helium barrier discharge at atmospheric pressure
Electric field measurement induced by Pockels effect on deposited surface charge
Glass plate with ITO layer BSO crystal
Isolation plates Aluminium mirror
dt/a(Q ; dt
4«) = ^r\^-V(t)\+qo
1 — ^Cd~ ^ceH
0.8 0.6
-0.6
iiilimHiiiiiiiii|iiiiiiiii|iiiiimniimiiii,
O  Measured surface charge -Temporally integrated net current
0        100      200      300      400 500
t[M5]
Bogaczyk, Sretenovic et al. 2012 Eur. Phys. J. D Liu et al. 2003 J. Phys. D: Appl. Phys.
Determination of capacitances - fully powered large scale reactors (DCSBD, ozonizers,...)
Limited just for full electrode surface /£ /£
coverage by plasma!
E.g. DCSBD at power with full coverage of
electrodes by plasma filaments! Falkenstein et al. 1997 J. Phys. D: appl. Phys.
Manley 1943 Trans. Electrochem. Soc. Peeters et al. 2015 Plasma Sources Sei. Technol.
Pipa et al. 2012 Rev. Sei. Instrum.
Determination of capacitances - pulsed reactors
Low pressure asymmetric barrier discharge in argon at 100 mbar
Atmospheric pressure symmetric barrier discharge in N2-02 mixture
18
i-1-■-1-1-1-1-1-1-1-.-1-1-1-1-1-1-1-r
1    23456789   10 11
V[kV]
115
ßmax — Cd (Vmax 1 Ures)
HV probe
4 6 V/kV
I
Pipa et al. 2012 Rev. Sei. Instrum.
Applicability of the approach - limitations
e.V.
CD
~o o c
15 c
£
C U"
Jr
gap node   g    q dielectric node
V
) =
1
1 -
c
cell
i(0 - c,
dV(0
1 -
6(0
_CCell
Ug(t) = Vit) -
-V(t)
6(0
Limited to barrier discharges which can be
described within a single node approximation - i.e. the radial structure is negligible for given spatial- and temporal-scale:
1. Homogeneous barrier discharges (pulsed or sine applied voltage) 2. Nanosecond pulsed barrier discharges
3. Spatially confined single-filament barrier
discharges
4. Multi-filament plasma sources with full
electrode coverage
Liu et al. 2003 J. Phys. D: Appl. Phys. Pipa et al. 2012 Rev. Sei. Instrum.
What about not fully powered barrier discharge reactors ... ?
or middle-sized multifilament discharges without full surface coverage by plasma - what to do?
V(t) i(t)
raq
diel.
* n -L
1
aQ
Ml
ßCgap X
J plasma ( V
I UJifí
plasma (0 —
1
1 — Qell/Qiel L &
fdß(0 dV(0l
-r--(-cell-7.—
čí }
-(■
0(0 =  1 -
<-cell Cdiel
ô plasma (0 + CcellV(í)
^(0 = 11 + 1^)^(0-
P Cdiel
0(0-
o
1.5 1.0 0.5
— 00 O -0.5
-1.0
-1.5
I      I      I      I I	1     1     1     1 1 / //, / /s' /J*
1      , 1	'/ Voltage amplitude (kV) _ -4.2 -----8.4 -------10.1 -----11.1 -11.6 i.i.
■15 -10
10 15
diel
V(kV)
Peeters et al. 2015 Plasma Sources Sei. Technol.
How to use this? What parameters can be approached..
... besides the cases for mentioned spectroscopy and Pockels effect cases
*(0 =
1
1 -
c,
cell
[
i(0 - c
cell
dV(t) dt
The upper estimate of the electron density development within the established discharge channel
JRit)
eE(t)ße{E{t)/N)
UM) = V(t) -
Q(t)
P(t)=jR(t)Ug(t)
Instantaneous discharge power development
Averaged, spatially unresolved, electric field strength development
E(t) = U/t)/g
Effective electric field and power in ns-pulsed single-filament coplanar barrier discharge
Complete analysis of macroscopic parameters of nanosecond pulsed plasma in atmospheric pressure argon
4500
n—1—i—1—i—1—i—1—i—1—i—1—i—1—i—1—i—1—i—'—i—1—i—<-
1500 1000-500-0
gap voltage (left) and reduced el. field (right) current in the gap
o
a> o C
=1 m 3
-40 -20   0   20   40   60   80  100 120 140 160 180 200
- 180
- 160
- 140
- 120
- 100 -80 -60 -40 -20 -0
n
Q-C
o
CD D-
2.
D-
H o.
-40 -20 0
- 6
- 2
" - 0
- -2
-i—i—|—i—|—i—|—i—|—i—|—i—|—i—|—i—r
20   40   60   80  100 120 140 160 180 200
-o
o
4 n
3
time [ns]
time [ns]
Gap voltage, effective reduced electric field and internal discharge current development
Instantaneous development of the internal transferred charge, energy and power in the discharge
Compare to Leiweke et al 2013 J. Appl. Phys. 22       Dedrick et al. 2012 Plasma Sources Sci. Technol
V
Hoder, Simek et al. 2017
Electron density in ns-pulsed single-filament coplanar barrier discharge
Rough estimate of lower and upper limit of electron density by line-ratio and electrical methods
a
T3
Ö
O H
O
3
10 -
breakdown process  c«  established channel
-i-1-1-r
-i-1-1-r-
-I-1-1-r-
80
20
25
30 time [ns]
35
40
Other limitation of the method probably reached -plasma channel with high electron density would have less capacitive behaviour as Cg
Hoder, Simek et al. 2017
Compare to Walsh et al 2010 Eur. Phys. J. D     Zhu and Pu 2010 J. Phys. D: Appl. Phys.
Electric field in Townsend phase of coplanar barrier discharge in atmospheric pressure air
Electric field prior the breakdown from Townsend a(E/N) coefficient fitting on N2(C-B) spectra emission
100
1-r
fita(E/N)/N = 3.7-10"18cm2 resulting in E/N = 185 Td
80
2 60
o
• —
S* 40 a
H 20-
m
o
cathode
anode
0
—T—'—T—
0.26 0.28
0.30 0.32 0.34 0.36 interelectrode axis [cm]
0.38 0.40
Electric field in the gap from electrical analysis
24
Electric field at the breakdown instant: 180±30 Td (electrics) and 185±20 Td (fitting) and 200±40 Td from FNS/SPS(E/N)
Hoder, Jánsky, Bessiéres et al. 2016
Importance of basic plasma parameters for long-term chemistry (4torr volume BD streamer)
E(x,t)      EVDF(x,t)     rate coefficients (x,t) [^> electron, radical, metastable densities (x,t)
electric field
electrons
10
25
-5 0 5 radial position [mm]
oxygen atoms
NO molecules
-5 0 5 radial position [mm]
Hoder, Bonaventura et al. 2016 Plasma Sources Sei. Technol.
Although spatially unresolved and approximative, the electrical analysis according to the simplest equivalent circuit approach can give important informations about the
plasma for (not only) low-density confined plasmas.
It can gives information about temporal development of the effective electric field in the discharge gap, about the net transferred charge or electron density within the plasma channel or the instantaneous consumed power in the plasma.
All these derived informations can support other methods applied to investigation of the plasma. For precise analysis an, at least, 2D numerical model for given conditions
has to be utilised.
Single-filament coplanar barrier discharge was studied numerically and experimentally resulting in electric field high-resolution records in quantitative agreement. We plan to compute the generated surface gas chemistry using novel kinetic model of Zdenek Bonaventura including usage of sensitivity analysis.
27
Thank you for your attention!
3
Z. Bonaventura, P. Synek,
V
^wers/>   J. RáheP and M.Cernák
■s-
OH
If
^^y
J. Jánský
M. Simek
D. Bessieres and J. Paillol
A. Pipa
Greifswald
F.J. Gordillo-Vazquez
in
IVERSITE
DE PAU ET DES PAYS DE L'ADOUR
... and thanks to my colleagues and collaborators for the fruitfull discussions and their contribution!
Streamer impact and channel current
2D simulation of the volume barrier discharge in atmospheric pressure air
red arrow denotes the streamer impact onto the cathode creating the
conductive channel
Braun et al. 1992 Plasma Sources Sei. Technol.
Pre-breakdown phase of pulsed BDs: different pulse widths
Electrical characteristics
TC-SPC recording at the anode
60 80 t/ps
»> new-found local maximum emerging prior to the breakdown of the gap
6
Hoeft et al. 2014 J.Phys.D:Appl.Phys.
Emission spectra and E/n determination
nHHHHHHHHBHHHHH
50000 -
300        320        340        360        380        400        420 440
wavelength (nm)
FNS
SPS
N+(B2E+)^=0 -	^N+(X22^=0 + mv
A =	391.5 nm
N2(c3nj^0 -	+ N2(B3n9V=0 + hz/
A =	337.1 nm
Intensity ratio FNS/SPS = f(E/n)
0.001
0.0001
0.01
100
1000   E/AMO-.Vm* 10000
Paris et al. 2005 J.Phys.D:Appl.Phys.
9
—► access to the electric field determination
without any distortion of the discharge - just from its emission
Experimental setup
Without use of theoretical computations we used single-table setup including:
• Corona discharge as a subject of investigation
• Optical setup with monochromator, photomultipliers and TC-SPC module (resolution of almost 10 ps and 10 urn)
• Townsend discharge for electric field calibration
UV lamp 253.8 nm □
adjustable mirror
corona discharge
Townsend discharge
a
PMT2
lens
monochromator
PMT1
	
	c
m	o
	b
	£
	o
	o
B	
ICCD
TC-SPC
Hoder et al. 2012 Phys.Rev.E Hoder et al. 2016 Plasma Sources Sci. Technol.
The case of streamer discharge in air
SPS
e + N2(XlY+)v=0     N2(C3nu)^=0 + e (AE = ll.OeV),
N2(C3nu)u,=0^ N2(B3ng) (A.c = 337.1 nm),
^-J* Products,
N2(C3nu)l/=0 + N2/O2
dnc(r,t) (E\ /ic(r, -j-= Arc   — I n^nc(r, t)--«-
*        V" /
1        c c 1
—q- — Kx2nft2 + K^nOi + —
rcff To
c 00 1
t)
C
FNS
e + N2(X 1 Y+)v=0 -+ NjCB 2£u+)U'=o + 2e (AE = 18.7 eV).
NJ(B2ElJ')l/=o N+(X2X2;)^+Av (A.B = 391.5 nm).
N}(B 2E+)„m) + N2/02 Products.
——— = Atb I —  «N2wc(r, /)--=-
* W Tcff
lcff
*6
oo
= ^N2WN2 + ^o2/i02 + j] —
^=0 T0u"
6
Kozlov et al. 2005 J.Phys.D: Appl.Phys
Kinetic scheme, light intensities and ratio
SPS
FNS
;(r,t) /E\ 1 he Ic(r,t) d/B(r,Q , (E\ ST 1 he lB(r, I) -r-= *c I — ) nn2nc(r, t)Tc-~----r— —T.— = *B I — I nn2nc(r, O'B-g-----g—
( ^FNs/re™s	+ dl^s/dt^	i rFNS	
			[x] The image pari with relationship ID rld7 was not found in the tile.
V ^SPs/^effS	+ dlsps/dt j	J _SPS	
		Teff	
R(x,t) = f(E/n(x,t))
Paris et al. 2005 J.Phys.D:Appl.Phys.
7
Time-correlated single photon counting technique,
cross-correlation spectroscopy
MAIN-Signal:
• random single photons
• spatially resolved
• spectrally resolved
micro-discharge
■<=n
SYNC-Signal:
• represents shape of the full light pulse
• giving a time reference
STOP
ruuU
Delay
relative \J time information ^
single photon accumulation
first counted photon
High temporal resolution, but especially high dynamic range and perfect correlation to the studied emission event - the time reference (trigger) is set on the discharge itself!
time
Ikuta and Kondo 1976 IEE W. Becker 2005 Advanced time-correlated single-photon counting techniques
LFA - collision frequencies
For justification of local field approximation the approach of analysis of the energy-resolved collision frequencies for momentum and energy dissipation as well as the energy-resolved mean free path and energy dissipation length.
U [eV] u [eV]
Quasi-stationary evolution of the distribution function of the electrons takes place and electrons can be assumed to be in equilibrium with the
local field.
Hoder, Loffhagen et al. 2012 Phys. Rev.
LFA - relaxation
U [eV]
EBE and MC results agree well and coincide with the corresponding steady-state electron distribution function components ^ equilibrium values are reached after 10 ps and 5 urn.
14
of EVDF
Other approach is the study of the electron relaxation in time and space for different reduced electric field strengths E/N:
lines represent f0, f1 after 10 ps of the temporal electron relaxation (solution of the electron Boltzman equation in multi-term approximation).
symbols denote f0, f1 for the ID spatial relaxation of electrons after a distance of 5 jim using the Monte Carlo method.
Hoder, Loffhagen 2016 PSST
E[kVcm-i] v*x ^k[1013R]       Sources [1023 crtrV1] Density [1013 cm"3]
M     4^     01     CO     O     M   °       °       0      0       0       POPWUJiCJIOlvlODMPOPMUJiUlOlO     H>     1*0     CO     .p.     Ol Ol
oooooob    ro 'o    co bbbbbbbbbbbbbbbbbbbbbbbbbb
um{v) = NvQT(v)
Am (v)
1
NQT(v)
K(v) = Xm(v)
\J 3ue(v]
VM = Nv ( ^Qd(v)
vT
Lofihagen2015