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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 =20m • t = 3.8 ns ICPIG2005_09 • r =60m • r =80m 100 - 1000 (Td) Log scale MIN MAX Iowa State University Optical and Discharge Physics E-FIELD AFTER 80m 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 60m 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 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 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 = 80m) 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 = 80m) 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 = 80m) 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 = 80m) 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 = 60m) 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