Universal Behaviour of SelfOrganized Patterns in Planar GasDischarge Systems

1
Universal Behaviour of Self-Organized Patterns
in Planar Gas-Discharge Systems
H.-G. Purwins Institut für Angewandte
Physik Westfälische Wilhelms-Universität,
Münster, Germany 09.08.2005 Developments in
Experimental Pattern Formation Isaac Newton
Institute for Mathematical Sciences Cambridge,
U.K.
2
1. Introduction
3
(No Transcript)
4
First Observation of Microchannel Dielectric
Barrier Discharge
Buss 1932
5
Bifurcation Behaviour of the Positive Column in a
Glow Discharge Tube IExperimental Set-Up
voltage supply and discharge tube
Bödeker, Purwins 2001 (unpublished)
6
Bifurcation Behaviour of the Positive Column in a
Glow Discharge Tube IIElectrical Circuit
discharge column
circuit
parameters electrodes Al, gas Ar, p 0,1 hPa,
d 36 cm,D 4 cm, U0 400-550 V, R0 12.6 kW
Bödeker, Purwins 2001 (unpublished)
7
Bifurcation Behaviour of the Positive Column in a
Glow Discharge Tube IIIBifurcation Diagram (1)
Amplitude square A2 / a.u.
voltage U / V
square of the amplitude of the fundamental
spacial Fourier mode plotted as a function of the
driving voltage U0
Bödeker, Purwins 2001(unpublished)
8
Bifurcation Behaviour of the Positive Column in a
Glow Discharge Tube IIIBifurcation Diagram (2)
Amplitude square A2 / a.u.
voltage U / V
square of the amplitude of the fundamental
spacial Fourier mode plotted as a function of the
driving voltage U0
Bödeker, Purwins 2001(unpublished)
9
Bifurcation Behaviour of the Positive Column in a
Glow Discharge Tube IIIBifurcation Diagram (3)
Amplitude square A2 / a.u.
voltage U / V
square of the amplitude of the fundamental
spacial Fourier mode plotted as a function of the
driving voltage U0
Bödeker, Purwins 2001 (unpublished)
10
Bifurcation Behaviour of the Positive Column in a
Glow Discharge Tube IIIBifurcation Diagram (4)
Amplitude square A2 / a.u.
voltage U / V
square of the amplitude of the fundamental
spacial Fourier mode plotted as a function of the
driving voltage U0
Bödeker, Purwins 2001 (unpublished)
11
Bifurcation Behaviour of the Positive Column in a
Glow Discharge Tube IIIBifurcation Diagram (5)
Amplitude square A2 / a.u.
voltage U / V
square of the amplitude of the fundamental
spacial Fourier mode plotted as a function of the
driving voltage U0
Bödeker, Purwins 2001 (unpublished)
12
CollaboratorsResearch Group Purwins
Münster, past
Münster, present
C. RadehausR. DohmenH. WillebrandM.
BodeF.-J. NiedernostheideE. AmmeltC.P.
SchenkI. BrauerA.W. Liehr many others
S. AmiranashviliJ. BerkemeierH. BödekerS.
GurevichW. ShangL. Stollenwerk
other groups
Yu. Astrov (St. Petersburg)L. Portsel
(St. Petersburg)P. Boeuf (Toulouse)R.
Friedrich (Münster)
13
2. Investigated ExperimentalGas-Discharge Systems
14
Quasi-1-DimensionalDC Gas-Discharge System
cross section
top view
U0 0 1500 V, R0 20 1000 kW, a 3 mm, b
10 mm, d 0.3mm,rSi 0.9 2.6 MW cm, gas Ar,
He air, p 40 100 hPa, l 20 50 mm
Purwins et al. 1987, Willebrand et al. 1990
15
Quasi-2-DimensionalDC Gas-Discharge System
Astrov et al. 1993
16
Quasi-2-DimensionalAC Gas-Discharge System
Ammelt et al. 1993
17
3. Experimental Results forGas-Discharge
Systems Simple Patterns
18
Stationary Periodic Patterns in
theQuasi-1-Dimensional DC Gas-Discharge System
ITuring Bifurcation
U0
decreasing driving voltage
anode Si rSC0.9kW cm bSC0.3mm
aSC12mmcathode Cu gas He p90hPa d4.5mm
UD1500-900V R025kW texp1-10-3 s
Radehaus et al. 1992
19
Stationary Periodic Patterns in
theQuasi-1-Dimensional DC Gas-Discharge System
IIScaling Law for the Turing Bifurcation
square of fundamentalFourier mode / (a.u.)
voltage drop at the device U / V
anode Si rSC0.9kW cm bSC0.3mm
aSC12mmcathode Cu gas He p90hPa d4.5mm
UD1500-900V R025kW texp1-10-3 s
Niedernostheide et al. 1992
20
Stationary Periodic Stripes and Scaling Lawfor
the Bifurcation in the Quasi-2-DimensionalDC
Gas-Discharge System
anode optically transparent ITO, cathode Si
compensated with Au or ZnrSC105 - 107kWcm,
TSC90K, aSC1mm, gas N2, p140hPa, d1mm,
D20mm,U02142V, R025 - 85kW, ltjgt20mA/cm2
Astrov et al. 1996
21
Stationary Periodic Stripes and Scaling Lawfor
the Bifurcation in the Quasi-2-DimensionalAC
Gas-Discharge System
square of fundamentalFourier mode / (a.u.)
voltage U / V
electrodes optically transparent ITO, dielectric
substrate glass plate, a0.5mm, gas He,
p600hPa, TRT, d0.5mm, D20mm, Û484V,
fsin247kHz, texp2.0ms
Brauer, Thesis, University of Münster 2000
22
Hexagonal Patternin a Quasi-2-DimensionalDC
Gas-Discharge System
cathode Si doped with Zn, ?sc107 109?m,
dsc1.2mm, T 90Kanode transparent ITO glass
gas N2, p129hPa, d0.75mm, R025k?, U01900V
Ammelt et al. 1998
23
Hexagonal Patternin a Quasi-2-DimensionalAC
Gas-Discharge System
electrodes transparent ITO glass plate and a
borosilicate glass plate (0.5mm thick) TRT,
gas He, p63hPa, d0.5mm, D20mm, f90kHz,
Û381V, texp111µs
Brauer et al. 1999
24
Bifurcation Sequence of Current Filaments in a
Quasi-1-Dimensional DC Gas-Discharge System
IIncreasing Voltage
3
1
4
5
2
increasing driving voltage Uo ? 575 775 V
Radehaus et al. 1987 Willebrand et al. 1992
25
Bifurcation Sequence of Current Filaments in a
Quasi-1-Dimensional DC Gas-Discharge System
IIDecreasing Voltage
6
8
9
7
decreasing driving voltage US ? 640 590 V
cathode Cu, anode rSC1.5kW cm, aSC0.3mm,
lx10mm, Si, 1.5k? cm,gas Ar20hPa air,
p170hPa, d3.8 mm, R0164k?
Radehaus et al. 1987 Willebrand et al. 1992
26
Bifurcation Sequence of Current Filaments in a
Quasi-1-Dimensional DC Gas-Discharge System
IIICurrent Voltage Characteristic
I / mA
number of filaments
U / V
cathode Cu, anode rSC1.5kW cm, aSC0.3mm,
lx10mm, Si, 1.5k? cm,gas Ar20hPa air,
p170hPa, d3.8 mm, R0164k?
Willebrand, Radehaus, Purwins 1990
27
Bifurcation Sequence of Current Filamentsin a
Quasi-1-DimensionalAC Gas-Discharge System
gas He-Ar, p1000hPa, electrodes Al-Stripes on
glass, d5.5mm, f16kHz
Guikema et al. 2000
28
Bifurcation Sequence of Current Filamentsin a
Quasi-2-DimensionalDC Gas-Discharge System
anode Si compensated with Au rSC150 kW cm,
aSC0.5mm, TSC4C, cathode optically
transparent ITO, gas He, p300hPa,
d1.5mm, lxly11mm, R086kW, texp20ms
I / mA
U / V
Becker, Ammelt, Purwins 1994 (unpublished)
29
Solitary Current Filamentsin a
Quasi-2-DimensionalAC Gas-Discharge System
electrodes transparent ITO glass plate and a
borosilicate glass plate (0.5 mm thick) TRT,
gas He, p133hPa, d0.5mm, D20mm, f200kHz,
Û380V, texp40ms
Müller et al. 1999 Brauer, Thesis, University of
Münster 2000
30
Spiral Patterns in Quasi-2-DimensionalDC
Gas-Discharge Systems
Movie parameters
U02500 V, rSC1.52 MW cm,SiltZngt, Gas N2, T110
K, p100 hPad0.1 cm, aSC1.3mm, I90 mA,
texp20ms(Gurevich, Astrov, Purwins 2004)
electrodes two glass platesgas He p700hPa,
Û706V, fsin247kHz, d0.5mm, D20mm,
texp2µs(Müller, Purwins 1996 (unpublished))
31
Spiral Patternin a Quasi-2-DimensionalDC
Gas-Discharge System
t80ms
t0ms
t40ms
1cm
t160ms
t200ms
t120ms
parameters U02500 V, rSC1.52 MW cm, SiltZngt,
Gas N2, T110 K, p100 hPa, d0.1 cm,
aSC1.3mm, I90 mA, texp20ms
E. Gurevich, Thesis, University of Münster (2004)
32
Experimental Results for a Target Patternin a
Planar DC SemiconductorGas-Discharge System
t0ms
t40ms
t80ms
t120ms
parameters U02500 V, rSC1.52 MW cm, SiltZngt,
Gas N2, T110 K, p100 hPa, d0.1 cm,
aSC1.3mm, I90 mA, texp20ms
E. Gurevich, Astrov, Purwins 2004 (unpublished)
33
Spiral Patternin a Quasi-2-DimensionalAC
Gas-Discharge System
electrodes two glass plates room temperature,
gas He,p700hPa, d0.5mm, D20mm, f247kHz,
U706V, texp2µs
Brauer, Thesis, University of Münster 2000
34
Experimental Results for a Target and a Spiral
Pattern in a Planar Dielectric Barrier
Gas-Discharge System
electrodes two glass platesroom temperature,
gas He,p600hPa, d0.5mm, D20mm,f247kHz,
U680V, texp2µs
electrodes two glass platesroom temperature,
gas He,p700hPa, d0.5mm, D20mm,f247kHz,
U706V, texp2µs
Brauer, Theseis, University of Münster2000
35
4. Comparison of Experimental Results for
Various NonlinearDissipative Systems
36
Stripesin Various Nonlinear Dissipative Systems
IPatterns
gas-discharge (ref.1)
chemical solution (ref.2)
fluid (ref.3)
replace by sea fish
optical system (ref4.)
granular medium (ref.5)
37
Stripesin Various Nonlinear Dissipative Systems
IIReferences
(1) Stripe pattern in gas discharge
systemsHexagon and Stripe Turing Structures in a
Gas Discharge SystemYu. Astrov, E. Ammelt, S.
Teperick and H.-G. PurwinsPhys. Lett. A 211 (3),
p. 184 - 190 (1996) (2) Stationary Turing
patterns in a chemical mediumTransition from a
uniform state to hexagonal and striped Turing
patterns Q. Ouyang and H. L. SwinneyNature 352
610-612 (1991) (3) Rayleigh-Benard convection
pattern Nonlinear competition between waves on
convective rolls V. Croquette and H.
WilliamsPhys. Rev. A39 27652768 (1989)
38
Stripesin Various Nonlinear Dissipative Systems
IIIReferences
(4) Optical pattern formed by Fourier
filtering Investigations of pattern forming
mechanism by Fourier filtering Properties of
hexagons and the transition to stripes in an
anisotropic system T. Ackemann, B. Giese, B.
Schäpers and W. LangeJ. Opt. B Quant.
Semiclass. Opt. 1 70 (1999) (5) Stripe pattern
in granular medium vibrated vertically Hexagons,
kinks, and disorder in oscillated granular layers
F. Melo, P. B. Umbanhowar and H. L.
SwinneyPhys. Rev. Lett. 75 3838-3841 (1995)
39
Hexagonsin Various Nonlinear Dissipative Systems
IPatterns
gas-discharge (ref.1)
chemical solution (ref.2)
fluid (ref.3)
optical system (ref.4)
granular medium (ref.5)
mushroom (ref.6)
40
Hexagonsin Various Nonlinear Dissipative Systems
IIReferences
(1) Experimentelle und numerische Untersuchungen
zur Strukturbildung in dielektrische
Barrierenentladungen I. Brauer Dissertation,
Universität Münster 2000 (2) Stationary Turing
patterns in a chemical medium. Transition from a
uniform state to hexagonal and striped Turing
patterns Q. Ouyang and H. L. Swinney Nature 352
610-612 (1991). Image from plate 4 in The
self-made tapestry pattern formation in
nature P. Ball Oxford University Press, Oxford
1999 (3) Rayleigh-Bénard convection of the
nematic liquid crystal 5CB Rayleigh-Bénard
convection in a homeotropically aligned nematic
liquid crystal L. Thomas, W. Pesch and G.
Ahlers Phys. Rev. E, 58, 5885 (1998). Image from
http//www.nls.physics.ucsb.edu/image_pages/pictur
epage1.html
41
Hexagonsin Various Nonlinear Dissipative Systems
IIIReferences
(4) Optical pattern in alkali metal
vapors Optical pattern formation in alkali metal
vapors Mechanisms, phenomena and use Ackemann
T. and W. Lange Appl. Phys. B 72 21-34
(2001) (5) Hexagons, kinks, and disorder in
oscillated granular F. Melo, P.B. Umbanhowar and
H. L. Swinney Phys. Rev. Lett. 75 3838-3841
(1995) (6) Mushroom spore M. Ebert,
Umweltmineralogie, TU Darmstadt image
from http//www.uni-magdeburg.de/abp/picturegalle
ry.htm
42
Solitary Spotsin Various Nonlinear Dissipative
Systems IPatterns
gas-discharge (ref.1)
chemical solution (ref.2)
fluid (ref.3)
nerve pulse (ref.6)
optical system (ref.4)
granular medium (ref.5)
43
Solitary Spotsin Various Nonlinear Dissipative
Systems IIReferences
(1) Localized structure in gas discharge
system Measuring the interaction law of
dissipative solitons, H. U. Bödeker and A. W.
Liehr, T. D. Frank, R. Friedrich and H.-G.
Purwins New Journal of Physics 6 62 (2004) Fig.
6 (2) Localized nonlinear chemical wave Design
and Control Patterns of Wave Propogation Patterns
in Excitable Media T. Sakurai, E. Mihaliuk, F.
Chirila, and K. Showalter, Science 296 2009-2012
(2002) Fig. 2 (3) Localized wave in
binary-fluid convection Localized Traveling-Wave
States in Binary-Fluid Convection J. J. Niemela,
G. Ahlers and D. S. Cannell Phys. Rev. Lett. 64
1365-1368 (1990)
44
Solitary Spotsin Various Nonlinear Dissipative
Systems IIIReferences
(4) Localized structure in an optical
system Interaction of Localized Structures in an
Optical Pattern-Forming System B. Schäpers, M.
Feldmann, T. Ackemann and W. Lange Phys. Rev.
Lett. 85 748751 (2000) (5) Solitary structure
in granular materials Localized excitations in a
vertically vibrated granular layer P. B.
Umbanhowar, F. Melo and H. L. Swinney Nature 382
793-796 (1996) Scientific American, November 1996
p. 28 image from http//chaos.ph.utexas.edu/resear
ch/granular/sci_am.html (6) Nerve pulse Keynes,
in Spektrum der Wissenschaften 1979
45
Spiralsin Various Nonlinear Dissipative Systems
IPatterns
dc gas-discharge (ref.1)
semiconductor (ref.3)
chemical solution (ref.2)
optical system (ref.4)
Ca-waves on frog egg (ref.6)
social amoebae (ref.5)
46
Spiralsin Various Nonlinear Dissipative Systems
IIReferences
(1) Dynamisches Verhalten in strukturbildenden
planaren Gasentladungssystemen I.Müller,
Diplom-Arbeit, Universität Münster, p.56,
1996 (2) The Structure of the Core of the
spiral Wave in the Belousov-Zhabotinskii
Reaction S. C. Müller. T. Plesser and B.
Hess Science 230 661-663 (1985) (3)
Electro-luminescence in AC thin-film
devices Domain electro-luminescence in AC
thin-film devices H. Rüfer, V. Marrello and A.
Onton J. Appl. Phys. 51 1163-1169 (1980)
47
Spiralsin Various Nonlinear Dissipative Systems
IIIReferences
(4) Optical spiral pattern in a single-mirror
feedback scheme Optical target and spiral
patterns in a single-mirror feedback scheme F.
Huneus, B. Schäpers, T. Ackemann and W.
Lange Appl. Phys. B 76 191 (2003) (5) Spiral
formed in bacteria colony (amoeba of
Dictyostelium discoideum) image
from http//www.uni-magdeburg.de/abp/picturegaller
y.htm (6) Spiral waves of calcium across the
surface of fertilized frog eggs David Clapham,
Mayo Foundation, Rochester Image from Fig. 3.30
(p 76) in The self-made tapestry pattern
formation in nature P. Ball, Oxford University
Press, Oxford 1999
48
Fractalsin Various Nonlinear Dissipative Systems
IPatterns
gas-discharge (ref.1)
electrochem. Deposition (ref.2)
Hele-Shaw cell (ref.3)
lung (ref.5)
bacteria growth (ref.6)
viscous fingering (ref.4)
49
Fractalsin Various Nonlinear Dissipative Systems
IIReferences
(1)Lichtenberg pattern Lichtenberg
1780 Experimental result from a Lichtenberg
figure produced with the original equipment of
Lichtenberg Photostudio Wilder Göttingen (2)Branc
hing produced by electrochemical deposition onto
a central electrode Fig. 5.6 (a) (p 113) in
The self-made tapestry pattern formation in
nature P. Ball, Oxford University Press
1999 Mitsugu Matsushita, Chuo University (3)Visco
us fingering in the Hele-Shaw cell Eshel
Ben-Jacob, Tel Aviv University Image from Fig.
5.4 (c) (p 112) in The self-made tapestry
pattern formation in nature P. Ball, Oxford
University Press, Oxford 1999
50
Fractalsin Various Nonlinear Dissipative Systems
IIIReferences
(4)Viscous fingering produced when air displaces
oil in a model porous medium Roland Lenormand,
Institut Francais du Petrole, Rueil-Malmaison. Fig
. 5.13 (p 118) in The self-made tapestry
pattern formation in nature P. Ball, Oxford
University Press 1999 (5)The highly branched
bronchial structure of a lung Martin Dohrn, Royal
College of Surgeons, Science Photo Library Fig.
5.2 (p 111) in The self-made tapestry pattern
formation in nature P. Ball, Oxford University
Press 1999 (6) Generic modeling of cooperative
growth-patterns in bacterial colonies E.
Ben-Jacob (Benjacob), O. Schochet, A. Tenenbaum,
I. Cohen, A. Czirok and T. Vicsek Nature 368
46-49 (1994) Image from http//star.tau.ac.il/in
on/T_Nature.jpg
51
5. Experimental Results forGas-Discharge
Systems Complex Patterns
52
Periodic Patterns in Quasi-1-DimensionalDC
Gas-Discharge Systems I Survey

• single patterns
• stationary travelling
  oscillatory
• X -
  -
• - X
  -
• - -
  X
• coexisting
  patterns
• stationary travelling oscillatory
  counter-propag.
• X X
  - -
  
• X -
  X -
  
• - X
  X X
  
• - -
  -

53
Periodic Patterns in Quasi-1-DimensionalDC
Gas-Discharge Systems II Coexistence of
Stationary and Travelling Patterns

• cathode Cu, anode Si, ?SC 1.5 kOcm, l 38
  mm, a 12.5 mm, b 0.3 mm
• gas He, p 51 hPa, d3.1 mm, U0 1086 V,
  R023,5 k O texp10 ms

Willebrand et al.1991
54
Periodic Patterns in Quasi-1 DimensionalDC
Gas-Discharge Systems III Coexistence of
Stationary and Oscillatory Patterns

• cathode Cu, anode Si, ?SC 1.9 kO cm, l 38
  mm, a 12.5 mm, b 0.3 mm
• gas He, p 21 hPa, d 4.1 mm, U0 770 V,
  R026,6 k O, texp1,5 ms

Willebrand et al.1991
55
Dynamics of Defects in a Periodic Pattern in a
Quasi-2-DimensionalDC Gas-Discharge System
Movie anode optically
transparent ITO, cathode Si compensated with Zn
or Zn, ?SC108Ocm, TSC130K, aSC1mm, gas Ar,
p340hPa, d0.5mm, D30mm,U05000V, R0 5MO
Bödeker, Purwins 2005 (unpublished)
56
Dynamics of Defects in a Periodic Pattern in a
Quasi-2-DimensionalDC Gas-Discharge System
Movie anode
optically transparent ITO, cathode Si
compensated with Zn or Zn, ?SC108Ocm, TSC130K,
aSC1mm, gas N2, p280hPa, d0.5mm,
D30mm,U03000V, R0 1MO
Bödeker, Purwins 2005 (unpublished)
57
Coexistence of Stripes and Dense Filamentsin a
Quasi-2-DimensionalDC Gas-Discharge System
Movie anode
optically transparent ITO, cathode Si
compensated with Zn or Zn, ?SC108Ocm, TSC130K,
aSC1mm, gas N2, p280hPa, d0.5mm,
D30mm,U02700V, R0 1MO
Bödeker, Purwins 2005 (unpublished)
58
Zigzag Instability of Stationary Periodic
Stripes in the Quasi-2-DimensionalAC
Gas-Discharge System

• anode high resistivity SiltZngt, decrease of ?SC
  with increasing light intensity,
• ?sc 108 Ocm, TSC90 K, b 1.0 mm, gas N2, p
  174 hPa, d 0.8 mm, D20mm,
• U0 2.48 kV, ltjgt4.8 57.6 µA/cm2

Astrov et al. 1997
59
Solitary Current Filamentsin a
Quasi-2-DimensionalDC Gas-Discharge System
non-ocillatory tails
oscillatory tails
parameters U0 3,6 kV,rSC 3,05 MW cm, R0
4,4 MW, Gas N2, T100 K, p 279 hPa, D30 mm,
d 500 mm, aSC1 mm, I 200 mA, texp20 ms
parameters U0 2,74 kV, rSC 4,95 MW cm, R0
20 MW, Gas N2, T100 K, p 280 hPa, D30 mm, d
250 mm, aSC1 mm, I 46 mA, texp20 ms
Bödeker et al. 2003
60
Propagating Current Filament in a
Quasi-2-DimensionalDC Gas-Discharge System
1 cm
real time
Movie parameters
U02,7 kV, rSC4,95 MW cm, R020 MW, Gas N2,
T100 K, p280 hPa, D30 mm, d250 mm, aSC1 mm,
I46 mA
Bödeker et al. 2003
61
Drift Bifurcation of a Filamentin a
Quasi-2-DimensionalDC Gas-Discharge System
parameters U03,7 kV, R010 MW, Gas N2, T100
K, p286 hPa, D30 mm, d750 mm, aSC1 mm, I107
mA, texp20 ms, frep50 Hz
square of the intrinsic velocity as a function of
the specific resistivityof the semiconductor
wafer and typical experimental trajectories
Bödeker et al. 2003
62
Drift Bifurcation of a Filament in
aQuasi-2-Dimensional AC Gas-Discharge System
ITypical Trajectories
classical Brownianmotion Û 660 V
active Brownianmotion Û 750 V
gas He, p200hPa, d0.5mm, a1mm, D40mm,
f200kHz, texp200µs
Stollenwerk, Purwins 2005
63
Drift Bifurcation of a Filament in
aQuasi-2-Dimensional AC Gas-Discharge System
IIBifurcation Diagramm
Stollenwerk, Purwins 2005
64
Rotating Filament Clusterin a Quasi-2-Dimensional
DC Gas-Discharge System
parameters U0 1.9kV, rSC 4.510-8W cm, gas
N2, T90 K, p 2hPa, dgap0.8 mm, dSC
1 mm, aSC20 mm, texp20 ms
Liehr et al. 2004
65
Filament Clustersin a Quasi-2-DimensionalAC
Gas-Discharge System
change of voltage
Ueff438V
Ueff495V
D13mm a0.55mm b0.7mm c0.3mmp419hPa
gas He f200kHz T40ms
Ammelt, Schweng, Purwins 1993
66
Experimentally Observed Hierarchyof Filamentary
Patterns in Quasi-2-Dimensional DC Gas-Discharge
Systems I
Research Group Purwins, University of Münster
67
Experimentally Observed Hierarchyof Filamentary
Patterns in Quasi-2-DimensionalDC Gas-Discharge
Systems II
Research Group Purwins, University of Münster
68
Experimentally Observed Hierarchyof Filamentary
Patterns in Quasi-2-Dimensional DC Gas-Discharge
Systems III
Research Group Purwins, University of Münster
69
Experimentally Observed Hierarchyof Filamentary
Patterns in Quasi-2-DimensionalAC Gas-Discharge
Systems I
Research Group Purwins, University of Münster
70
Experimentally Observed Hierarchyof Filamentary
Patterns in Quasi-2-DimensionalAC Gas-Discharge
Systems II
Research Group Purwins, University of Münster
71
Experimentally Observed Hierarchyof Filamentary
Patterns in Quasi-2-DimensionalAC Gas-Discharge
Systems III
Research Group Purwins, University of Münster
72
Zigzag Instability of Targets and Spirals in the
Quasi-2-DimensionalDC Gas-Discharge System
t
anode high resistivity SiltZngt, ?SC 108 Ocm,
TSC90 K, b1.0 mm, gas N2, p150 hPa, d0.8 mm,
D30mm, U0 2.6 kV, ltjgt 6.5 µA/cm2,
texp4?10-4 s, Dt(a,e)10 s
Astrov et al. 1998
73
6. Modelling Charge Transportin Gas-Discharge
Systems Using Drift-Diffusion Equations
74
Relevant Scales for Charge Transport in
Gas-Discharge Systems

• Molecular dynamical approach
• electron collision time 0.1 ps
• electron free path 1 µm
• ion collision time 10 ps
• ion free path 1 µm
• Drift-diffusion approach (introduction of mean
  velocity)
• discharge length 1 mm
• electron travel time 10ns
• ion travel time 1µs
• Reaction-diffusion approch
• space scale separation for the charge density
  variation in z- and x-, y-direction)
• observation radial drift small with respect to
  radial diffusion
• current relaxation time (reaction, diffusion) 10
  µs
• Maxwell time of the high ohmic semiconductor 10
  µs

75
Model Equation for the Planar DC Semiconductor
Gas-Discharge System IGas-Discharge Space (-d lt
z lt 0)
ne , np electron/ion density Se, Sp
electron/ion source term ,
electron/ion particle current density me, mp
electron/ion mobility electrical
field De, Dp electron/ion diffusion
constant n ionisation rate b
recombination rate j electrical
potential Te, Tp electron/ion temperature
global electrical current density
Amiranashvili, Purwins 2003 (unpublished)
76
Model Equation for the Planar DC Semiconductor
Gas-Discharge System II Semiconductor Wafer (0
lt z lt dSC)
global electrical current density l
specific electrical conductivity
electrical field j electrical
potential e dielectric constant of the
semiconductor
Amiranashvili, Purwins 2003 (unpublished)
77
Model Equation for the Planar DC Semiconductor
Gas-Discharge System IIIBoundary Conditions Gas
Semiconductor at z0
s surface charge DS diffusion
constand of surface charge unity
vector in z-direction e dielectric
constant of the semiconductor ve, vp thermal
electron/ion speed g g
-Townsend-coefficient k
Boltzmann-constant me, mp electron/ion mass U
voltage drop at the component z0
gas/semiconductor surface z-d metallic anode
Amiranashvili, Purwins 2003 (unpublished)
78
Evolution of a Spot Pattern in aQuasi-2-Dimension
alAC Gas-Discharge System I Parameters
Experimental (theoretical)parameters
Numericalparameters
gas He13hPa air (He)p 133hPa (300) a
0.5mm (0.5) d 0.5mm (0.5) D 20mm
(8) fsin200kHz (200) Û767V (700) texp2.5ms
(? 0,05) (a, µ from tables)
grid points 100 x 50 x 48 10mm x 5mm x
1,5mmNeumann boundary conditions
Stollenwerk, Boeuf, Purwins 2005 (to be
published)
79
7. Modelling Charge Transportin Planar
Gas-Discharge SystemsUsing 3-ComponentReaction-D
iffusion Equations
80
Qualitative Description of Pattern Formation in
Planar DC Gas-Discharge Systems IActivator and
Inhibitor
Purwins, Klempt, Berkemeier 1987
81
Qualitative Description of Pattern Formation in
Planar DC Gas-Discharge Systems IIEquivalent
Circuit
Purwins, Klempt, Berkemeier 1987, Bode et al. 2002
82
Qualitative Description of Pattern Formation in
Planar DC Gas-Discharge Systems IIIThe
3-Component Reaction-Diffusion Equation
Bode et al. 2002
83
Qualitative Description of Pattern Formation in
Planar DC Gas-Discharge Systems IV Relevance of
the 3-Component R-D-System

• Relatively simple structure
• Concept of activator and inhibitor
• Solutions reflect many of the experimentally
  observed patterns
• Theoretical prediction could be varified
• Insight into mechanisms of the formation of
  pattern
• Bridge from gas-discharge to reaction-diffusion
  system
• Kind of normal form
• Universality

84
Solutions of the 3k-Reaction-Diffusion Equation
Fronts
u cos t cont. tanh k(x-ct)
85
Solutions of the 3k-Reaction-Diffusion Equation
Stripes and Hexagons
Koch, Purwins, et al. 1994 (unpublished)
86
Solutions of the 3k-Reaction-Diffusion Equation
Dissipative Soliton
Liehr et al. 2003
87
Solutions of the 3k-Reaction-Diffusion Equation
Rotating Molecule
Liehr et al. 2003
88
Solutions of the 3k-Reaction-Diffusion Equation
Target Pattern
Koch, Purwins, et al. 1994 (unpublished)
89
Solutions of the 3k-Reaction-Diffusion Equation
Spirals
Koch, Purwins, et al. 1994 (unpublished)
90
Reduction of the Drift-Diffusion Equation to a
Reaction-Diffusion Equation I Relevant Scales

• Molecular dynamical approach
• electron collision time 0.1 ps
• electron free path 1 µm
• ion collision time 10 ps
• ion free path 1 µm
• Drift-diffusion approach (introduction of mean
  velocity)
• discharge length 1 mm
• electron travel time 10ns
• ion travel time 1µs
• Reaction-diffusion approch
• space scale separation for the charge density
  variation in z- and x-, y-direction)
• observation radial drift small with respect to
  radial diffusion
• current relaxation time (reaction, diffusion) 10
  µs
• Maxwell time of the high ohmic semiconductor 10
  µs

91
Reduction of the Drift-Diffusion Equation to a
Reaction-Diffusion Equation IIThe Equation

• conditions
• current density ltlt critical current density
• vicinity of ignition voltage
• axial scale ltlt radial scale, 2 scale expansion
• adiabatic elimination of electron dynamics
• normalized equations

u current densityv (gap voltage) -
(ignition voltage) extended Fischer equation
Amiranashvili et al. 2005
92
8. Summary and Conclusions
93
Experimentally Observed Patterns

• Simple experimental systems, near to practical
  devices
• Elementary structures as generic patterns
• fronts
• periodic patterns
• well localized solitary patterns (dissipative
  solitons, DS)
• spirals
• fractals
• Universal behaviour
• Large variety of unexplored static and dynamic
  complex patterns
• gas-, liquid- and solid-like many-body systems
• chains, domains
• internal degrees of freedom of DS
• zigzag destabilization
• all kinds of defect structures etc

94
Challenges ITheoretical Concepts and
Understanding

• Theoretical approach
• point of view Nonlinear Dynamics and Pattern
  Formation
• particle in cell approach (PIC)
• drift-diffusion approach
• reaction-diffusion approach
• time scales
• particle description of dissipative solitons
• Understanding
• mechanisms on a mesoscopic or macroscopic level
• bridge to chemical and biological systems
• bridge to universality

95
Challenges IIClassical Problems in Plasma
Physics

• Technical Problems
• electrode preparation
• time scales
• Improvement of existing devices
• Environmental protection (dcstreamers, ac
  micro-discharge)
• Light technology (patterns in discharge tubes)
• Welding and cutting (confinement in arc
  discharge)
• Suppression of patterns
• Electrical break down in solids
• Cathode spots (dissipative solitons)
• Fluorescence tubes (oscillations)
• Display technology (filamentation)
• IR-converter

96
Challenges IIIPossible New Perspectives

• Material preparation by self-organization
• Manipulation and control of patterns
• Information technology devices
• Generation of complex patterns in hierarchically
  coupled systems
• Dissipative solitons as particle like objects
• Many-body systems consisting of dissipative
  solitons
• Voronoi-diagrams as an examples for unpredictable
  application

97
Voronoi Diagrams in Quasi-2-DimensionalAC
Gas-Discharge System ISelf-Organized Filaments
1cm
1cm
parameters gas N2, p122 hPa, d2.6 mm, D40mm,
a10.5 mm, a21 mm, Û2050 V, texp40 ms, f50 kHz
Zanin et al. 2002
98
Voronoi Diagrams in Quasi-2-DimensionalAC
Gas-Discharge System IIPredefined Filaments
1cm
cross section
top view
parameters gas N2, p122 hPa, d3.0 mm (1mm
inner isolating layer), D40mm, a10.7 mm, a20.1
mm, Û2100 V, texp40 ms, f50 kHz
Zanin et al. 2002