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 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 University Optical and Discharge Physics Streamer in atmospheric pressure gases. ICPIG2005_03

 Positive corona is sustained between between a rod (r c = 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 University Optical and Discharge Physics ICPIG2005_04

Iowa State University Optical and Discharge Physics N 2 /O 2 /H 2 O = 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. Species: N 2, N 2 (v), N 2 *, N 2 **, N 2 +, N, N*, N +, N 4 +, O 2, O 2 *, O 2 +, O 2 -, O -, O, O*, O +, O 3, H 2 O, H 2 O +, H 2, H, OH, e ICPIG2005_05

TYPICAL STREAMER PARAMETERS: POTENTIAL Iowa State University Optical and Discharge Physics MIN MAX (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 V, 0 – 6 ns ANIMATION SLIDE

TYPICAL STREAMER PARAMETERS: E/N Iowa State University Optical and Discharge Physics  Electric field is high at the streamer tip where ionization occurs.  Electric field is small in the conducting channel. 100 – 1000 (Td) Log scale ICPIG2005_07 MIN MAX V, 0 – 6 ns t = 0 – 6 ns t = 0 – 6 ns ANIMATION SLIDE

TYPICAL STREAMER PARAMETERS: [e], CHARGE, Iowa State University Optical and Discharge Physics x (cm -3 ) (cm -3 )  The electron density behind the streamer front is 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_ V, 0 – 6 ns

E/N BEFORE 20, 60 and 80  m DUST PARTICLE Iowa State University Optical and Discharge Physics (Td) Log scale t = 3.8 ns  Streamer velocity and electric field increase as the streamer approaches the particle. MIN MAX ICPIG2005_ V, 0 – 6 ns No particle r =20  m r =60  m r =80  m E/N

Iowa State University Optical and Discharge Physics E-FIELD AFTER 80  m 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 (Td) Log scale ANIMATION SLIDE

Iowa State University Optical and Discharge Physics E-FIELD AFTER 60  m 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 (Td) Log scale ICPIG2005_11 t = 4.15 t = 4.7 t = 4.15 t = 4.7 ns

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 to (cm -3 ) Log scale t = 4.5 ns MIN MAX ICPIG2005_12

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. E = 5000 V/cm E r  Near the particle ICPIG2005_13

POTENTIAL: DIELECTRIC PARTICLES (r = 80  m) Iowa State University Optical and Discharge Physics t = ns ICPIG2005_14 MIN MAX (Td) Log scale ANIMATION SLIDE

ELECTRIC FIELD: DIELECTRIC PARTICLES (r = 80  m) Iowa State University Optical and Discharge Physics t = 0 – 5.2 ns ICPIG2005_15 MIN MAX (Td) Log scale ANIMATION SLIDE

Iowa State University Optical and Discharge Physics  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 = 80  m) t = 0 – 5.2 ns (Td) Log Scale E/N MIN MAX ICPIG2005_16

Iowa State University Optical and Discharge Physics  Launching of secondary and tertiary streamers with three particles is the same as for two particles. STREAMER INTERACTION: THREE PARTICLES (r = 80  m) (Td) Log Scale MIN MAX E/N ICPIG2005_17 t = 0 – 5.2 ns

Iowa State University Optical and Discharge Physics  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 = 60  m) t = 3.75 t = 4.25 t = 4.6 t = 3.75 t = 4.25 t = (Td) Log Scale MIN MAX E/N ICPIG2005_18

x (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. Iowa State University Optical and Discharge Physics ELECTRON DENSITY FOR THREE 80  m PARTICLES MIN MAX t = 3.45 t = 4.2 t = 4.75 ns ICPIG2005_19

Iowa State University Optical and Discharge Physics PHOTOIONIZATION SOURCE FOR THREE 80  m PARTICLES x10 22 (/cm 3 -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 Iowa State University Optical and Discharge Physics ICPIG2005_21  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. Iowa State University Optical and Discharge Physics ICPIG2005_22