STREAMER DYNAMICS IN A MEDIA CONTAINING DUST PARTICLES* Natalia Yu. Babaeva and Mark J. Kushner Iowa State University Department of Electrical and Computer

STREAMER DYNAMICS IN A MEDIA CONTAINING DUST PARTICLES*

Natalia Yu. Babaeva and Mark J. Kushner

Iowa State UniversityDepartment 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

Iowa State University

Optical and Discharge Physics

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

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.

Iowa State UniversityOptical and Discharge Physics

• Streamer in atmospheric pressure gases.

ICPIG2005_03

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.

DESCRIPTION OF THE MODEL: GEOMETRY

Iowa State UniversityOptical and Discharge PhysicsICPIG2005_04



• N2/O2/H2O = 79.5/19.5/1.0

DESCRIPTION OF THE MODEL: BASIC EQUATIONS

Poisson’s equation, continuity equations and surface charge are simultaneously solved using a Newton iteration technique.

j

sjjqN jj

j St

N

jjjj

s Sqt

))(()(

• 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

TYPICAL STREAMER PARAMETERS: POTENTIAL

Iowa State UniversityOptical and Discharge PhysicsMIN MAX

0 - 15000 (V)

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.

ICPIG2005_06

• t = 0 – 6 ns • t = 0 – 6 ns

15000 V, 0 – 6 ns

ANIMATION SLIDE

TYPICAL STREAMER PARAMETERS: E/N


Electric field is high at the streamer tip where ionization occurs.

Electric field is small in the conducting channel.

100 – 1000 (Td) Log scaleICPIG2005_07 MIN MAX

15000 V, 0 – 6 ns

• t = 0 – 6 ns • t = 0 – 6 ns

ANIMATION SLIDE

TYPICAL STREAMER PARAMETERS: [e], CHARGE,


1010 - 3 x 1014 (cm-3) 1011 - 1013 (cm-3)

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.

[e] Space Charge

Log scale

MIN MAX

t = 5.0 ns ICPIG2005_08

15000 V, 0 – 6 ns

E/N BEFORE 20, 60 and 80 m DUST PARTICLE


100 - 1000 (Td) Log scale

• t = 3.8 ns

Streamer velocity and electric field increase as the streamer approaches the particle.

MIN MAX ICPIG2005_09

15000 V, 0 – 6 ns

• No particle • r =20m • r =60m • r =80m

E/N



E-FIELD AFTER 80m PARTICLE

• t = 0 – 5 ns • t = 0 – 5.2 ns

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.

ICPIG2005_10

E/N

MIN MAX 100 - 1000 (Td) Log scale

ANIMATION SLIDE



E-FIELD AFTER 60m PARTICLE

The conical streamer head develops into a concave tip.

The streamer compresses the E-field field between its tip and the particle surface facing the front.

Plasma envelopes smaller particles (20 µm, 60 µm).

E/N

MIN MAX 100 - 1000 (Td) Log scale

ICPIG2005_11

• t = 4.15 • t = 4.7 • t = 4.15 • t = 4.7 ns



SURFACE AND SPACE CHARGE FOR 80m 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

• t = 4.5 ns

MIN MAX

ICPIG2005_12



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.

-40 -30 -20 -10 0 10 20 30 40

Z axis, m icrom eters

-40

-30

-20

-10

0

10

20

30

40

Z' a

xis,

mic

rom

eter

s

• E = 5000 V/cm

arforr

aE

r

UEr

,cos213

3

0

arforr

aE

r

U

rE

,sin11

3

3

0

E

r

Near the particle

arforEEr ,cos3 0

arforE ,0

ICPIG2005_13

POTENTIAL: DIELECTRIC PARTICLES (r = 80m)


• t = 0 - 5.2 ns

5 5 5 25

ICPIG2005_14 MIN MAX 100 - 1000 (Td) Log scale

ANIMATION SLIDE

ELECTRIC FIELD: DIELECTRIC PARTICLES (r = 80m)


• t = 0 – 5.2 ns

5 5 5 25

ICPIG2005_15 MIN MAX 100 - 1000 (Td) Log scale

ANIMATION SLIDE



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.

This process is repetitive for particles of the same size and evenly spaced.

STREAMER INTERACTION: TWO PARTICLES (r = 80m)

• t = 0 – 5.2 ns

100 - 1000 (Td) Log Scale

E/N

MIN MAX ICPIG2005_16



Launching of secondary and tertiary streamers with three particles is the same as for two particles.

STREAMER INTERACTION: THREE PARTICLES (r = 80m)

100 - 1000 (Td) Log Scale MIN MAX

E/N

ICPIG2005_17

• t = 0 – 5.2 ns



The initial process for 60 m particle is the same as for 80 m.

The secondary streamers can merge sooner than with the larger particles.

STREAMER INTERACTION: THREE PARTICLES (r = 60m)

• t = 3.75 • t = 4.25 • t = 4.6 • t = 3.75 • t = 4.25 • t = 4.6

100 - 1000 (Td) Log Scale MIN MAX

E/N

ICPIG2005_18

1012 - 6 x 1014 (cm-3) Log Scale

Electron flow envelopes the particles.

Plasma density is larger near the particle surfaces.

A wake of smaller electron density above the particle is due to electron flow around the particle.


ELECTRON DENSITY FOR THREE 80 m PARTICLES

MIN MAX

• t = 3.45 • t = 4.2 • t = 4.75 ns

ICPIG2005_19



PHOTOIONIZATION SOURCE FOR THREE 80 m PARTICLES

109 - 7x1022 (/cm3-s) Log Scale

Photoionization is enhanced in regions of high electric field.

For two or more particles there are bursts of photoelectrons.

A relay-like process results in which streamer is handed off between particles.

MIN MAX

• t = 2.95 • t = 3.95 • t = 4.25 • t = 4.8 ns

ICPIG2005_20

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

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.


Documents

STREAMER DYNAMICS IN A MEDIA CONTAINING DUST PARTICLES* Natalia Yu. Babaeva and Mark J. Kushner Iowa State University Department of Electrical and Computer