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STREAMER DYNAMICS IN A MEDIA CONTAINING
DUST PARTICLES*
Natalia Yu. Babaeva and Mark J. Kushner
Iowa State University
Department of Electrical and Computer Engineering
Ames, IA 50011, USA
[email protected] [email protected]
http://uigelz.ece.iastate.edu
July 2005
* Work supported by the National Science Foundation and Air Force Research
Lab
ICPIG2005_01
AGENDA
 Streamer dynamics through aerosols and dust particles
 Description of the model
 Effect of dust particles on streamer dynamics
 Dynamics before and after particles
 Multiple particles
 Summary
ICPIG2005_02
Iowa State University
Optical and Discharge Physics
STREAMER DYNAMICS
 Streamers are ionization
waves having a high electric
field at the avalanche front.
 Air or other gases can be
contaminated with particles
or aerosols having sizes of
10s to 100s μm.
 The intersection of
propagating streamers with
particles can significantly
perturb streamer dynamics.
ICPIG2005_03
• Streamer in atmospheric
pressure gases.
Iowa State University
Optical and Discharge Physics
DESCRIPTION OF THE MODEL: GEOMETRY
 Positive corona is sustained between
between a rod (rc= 0.07 cm) at 15 kV and a
grounded surface separated by 0.2 cm.
 2-d unstructured mesh is produced with
Skymesh2.
ICPIG2005_04
Iowa State University
Optical and Discharge Physics
DESCRIPTION OF THE MODEL: BASIC EQUATIONS
 Poisson’s equation, continuity equations and surface charge are
simultaneously solved using a Newton iteration technique.
       N j q j   s
j
N j
t

    j  S j

 s
   q j (   j  S j )    ( ())
t
j
• N2/O2/H2O = 79.5/19.5/1.0
• Species:
N2, N2(v), N2*, N2**, N2+, N, N*, N+, N4+,
O2, O2*, O2+, O2-, O-, O, O*, O+, O3,
H2O, H2O+, H2, H, OH, e
ICPIG2005_05
Iowa State University
Optical and Discharge Physics
TYPICAL STREAMER PARAMETERS:
POTENTIAL
15000 V, 0 – 6 ns
 Potential is compressed
in front of the streamer
head.
 Potential drop inside the
streamer is small.
 Streamer is analogous to
the metal rod on the axis.
ANIMATION SLIDE
• t = 0 – 6 ns
• t = 0 – 6 ns
0 - 15000 (V)
ICPIG2005_06
MIN
MAX
Iowa State University
Optical and Discharge Physics
TYPICAL STREAMER PARAMETERS:
E/N
15000 V, 0 – 6 ns
 Electric field is high
at the streamer tip
where ionization
occurs.
 Electric field is
small in the
conducting
channel.
ANIMATION SLIDE
• t = 0 – 6 ns
ICPIG2005_07
• t = 0 – 6 ns
100 – 1000 (Td) Log scale
MIN
MAX
Iowa State University
Optical and Discharge Physics
TYPICAL STREAMER PARAMETERS: [e], CHARGE,
[e]
Space Charge
15000 V, 0 – 6 ns
 The electron density behind
the streamer front is 1013-1014
cm-3 .
 The plasma in the inner part
of the streamer channel is
quasi-neutral.
 Positive space charge is
concentrated at the streamer
boundary.
MIN
MAX
Log scale
1010 - 3 x 1014 (cm-3) 1011 - 1013 (cm-3)
t = 5.0 ns
ICPIG2005_08
Iowa State University
Optical and Discharge Physics
E/N BEFORE 20, 60 and 80 m DUST PARTICLE
15000 V, 0 – 6 ns
E/N
 Streamer
velocity and
electric field
increase as
the streamer
approaches
the particle.
• No particle • r =20m
• t = 3.8 ns
ICPIG2005_09
• r =60m
• r =80m
100 - 1000 (Td) Log scale
MIN
MAX
Iowa State University
Optical and Discharge Physics
E-FIELD AFTER 80m PARTICLE
E/N
 The conical streamer head
develops into a concave tip.
 A new streamer starts from the
bottom side facing the grounded
electrode. The two streamers
eventually merge.
 If the particle has sharp features ,
electric field enhancement
launches a secondary streamer
that does not merge with the
primary streamer.
• t = 0 – 5 ns
ICPIG2005_10
• t = 0 – 5.2 ns
100 - 1000 (Td) Log scale
MIN
MAX
ANIMATION SLIDE
Iowa State University
Optical and Discharge Physics
E-FIELD AFTER 60m PARTICLE
E/N
 The conical
streamer head
develops into a
concave tip.
 The streamer
compresses the Efield field between
its tip and the
particle surface
facing the front.
 Plasma envelopes
smaller particles
(20 µm, 60 µm).
• t = 4.15
ICPIG2005_11
• t = 4.7
• t = 4.15
• t = 4.7 ns
100 - 1000 (Td) Log scale
MIN
MAX
Iowa State University
Optical and Discharge Physics
SURFACE AND SPACE CHARGE FOR 80m PARTICLE
 Streamer delivers a substantial
positive charge to top of particle.
 Charging of particle occurs within
1 ns.
 In a repetitively pulsed system, the
charge accumulated on a particle
can influence subsequent
streamers.
1012 to 1013 (cm-3) Log scale
MIN
• t = 4.5 ns
ICPIG2005_12
MAX
Iowa State University
Optical and Discharge Physics
ELECTRIC FIELD NEAR SPHERE IN EXTERNAL E-FIELD
 Solution of Laplace’s equation outside a conducting particle
of radius a in an external electric field.
r

E
40
Z' axis, micrometers
30
20

U
a3 
Er  
 E0 1  2 3  cos ,
r
r 

for r  a
 a3 
1 U
E  
  E0 1  3  sin  ,
r r
 r 
for r  a
10
0
 Near the particle
-10
Er  3E0 cos ,
-20
-30
-40
-40 -30 -20 -10
0
10
20
30
40
E  0,
for r  a
for r  a
Z axis, micrometers
• E = 5000 V/cm
ICPIG2005_13
Iowa State University
Optical and Discharge Physics
POTENTIAL: DIELECTRIC PARTICLES (r = 80m)
 5
 5
 5
  25
ANIMATION SLIDE
• t = 0 - 5.2 ns 100 - 1000 (Td) Log scale
ICPIG2005_14
MIN
MAX
Iowa State University
Optical and Discharge Physics
ELECTRIC FIELD: DIELECTRIC PARTICLES (r = 80m)
 5
 5
 5
  25
ANIMATION SLIDE
• t = 0 – 5.2 ns 100 - 1000 (Td) Log scale
ICPIG2005_15
MIN
MAX
Iowa State University
Optical and Discharge Physics
STREAMER INTERACTION: TWO PARTICLES (r = 80m)
E/N
 Streamer dynamics for
the upper particle are
similar to a single
isolated particle.
 A second streamer is
launched from the
bottom of the first
particle. A third
streamer is launched
from the lower surface
of the second particle.
• t = 0 – 5.2 ns
ICPIG2005_16
100 - 1000 (Td) Log Scale
MIN
MAX
 This process is
repetitive for particles
of the same size and
evenly spaced.
Iowa State University
Optical and Discharge Physics
STREAMER INTERACTION: THREE PARTICLES (r = 80m)
E/N
 Launching of
secondary and
tertiary streamers
with three
particles is the
same as for two
particles.
• t = 0 – 5.2 ns
ICPIG2005_17
100 - 1000 (Td) Log Scale
MIN
MAX
Iowa State University
Optical and Discharge Physics
STREAMER INTERACTION: THREE PARTICLES (r = 60m)
E/N
 The initial
process for
60 m
particle is
the same as
for 80 m.
 The
secondary
streamers
can merge
sooner than
with the
larger
• t = 3.75 • t = 4.25 • t = 4.6 • t = 3.75 • t = 4.25 • t = 4.6 particles.
ICPIG2005_18
100 - 1000 (Td) Log Scale
MIN
MAX
Iowa State University
Optical and Discharge Physics
ELECTRON DENSITY FOR THREE 80 m PARTICLES
 Electron flow
envelopes the
particles.
 Plasma density
is larger near
the particle
surfaces.
• t = 3.45
ICPIG2005_19
• t = 4.2
• t = 4.75 ns
1012 - 6 x 1014 (cm-3) Log Scale
MIN
MAX
 A wake of
smaller electron
density above
the particle is
due to electron
flow around the
particle.
Iowa State University
Optical and Discharge Physics
PHOTOIONIZATION SOURCE FOR THREE 80 m PARTICLES
 Photoionization is
enhanced in
regions of high
electric field.
 For two or more
particles there are
bursts of
photoelectrons.
• t = 2.95
• t = 3.95
• t = 4.25
• t = 4.8 ns
109 - 7x1022 (/cm3-s) Log Scale
ICPIG2005_20
MIN
MAX
 A relay-like
process results in
which streamer is
handed off
between particles.
Iowa State University
Optical and Discharge Physics
STREAMER VELOCITY VS PARTICLE NUMBER AND SIZE
 Streamer velocity
increases in the
presence of dust
particles.
 There exist an
optimum for particle
size and particle
separation at which
the streamer velocity
is maximal.
 Particles are separated by gaps
of 3 particle diameter
ICPIG2005_21
Iowa State University
Optical and Discharge Physics
CONCLUDING REMARKS
 The intersection of propagating streamers with particles not only
charges the particles but can also significantly perturb the
streamer dynamics:
 Loss of charge
 Electric field enhancement
 Secondary processes.
 The interaction between the streamer electric field and the local
(surface) electric field dominates the dynamics.
 The particle size and dielectric constant (capacitance) and
conductivity modify interaction due to charge accumulation and
shorting of field.
 Streamer–particle interactions are more complex for more
random assemblies of particles having different sizes.
ICPIG2005_22
Iowa State University
Optical and Discharge Physics