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STREAMER DYNAMICS IN A MEDIA CONTAINING DUST PARTICLES* Natalia Yu. Babaeva and Mark J. Kushner

This study investigates the dynamics of streamers in the presence of aerosols and dust particles, exploring their effects on streamer behavior. The model incorporates various parameters to analyze the interactions between streamers and particles.

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STREAMER DYNAMICS IN A MEDIA CONTAINING DUST PARTICLES* Natalia Yu. Babaeva and Mark J. Kushner

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  1. 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 natalie5@iastate.edu mjk@iastate.edu http://uigelz.ece.iastate.edu July 2005 * Work supported by the National Science Foundation and Air Force Research Lab ICPIG2005_01

  2. 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 Iowa State University Optical and Discharge Physics ICPIG2005_02

  3. 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. •Streamer in atmospheric pressure gases. Iowa State University Optical and Discharge Physics ICPIG2005_03

  4. 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. Iowa State University Optical and Discharge Physics ICPIG2005_04

  5. DESCRIPTION OF THE MODEL: BASIC EQUATIONS • Poisson’s equation, continuity equations and surface charge are simultaneously solved using a Newton iteration technique. • 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 Iowa State University Optical and Discharge Physics ICPIG2005_05

  6. MINMAX 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) Iowa State University Optical and Discharge Physics ICPIG2005_06

  7. MINMAX 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 • t = 0 – 6 ns 100 – 1000 (Td) Log scale Iowa State University Optical and Discharge Physics ICPIG2005_07

  8. MINMAX 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. Log scale 1010 - 3 x 1014 (cm-3) 1011 - 1013 (cm-3) Iowa State University Optical and Discharge Physics t = 5.0 ns ICPIG2005_08

  9. MINMAX E/N BEFORE 20, 60 and 80 m DUST PARTICLE E/N 15000 V, 0 – 6 ns • Streamer velocity and electric field increase as the streamer approaches the particle. • No particle • r =20m •r =60m• r =80m •t = 3.8 ns 100 - 1000 (Td) Log scale Iowa State University Optical and Discharge Physics ICPIG2005_09

  10. MINMAX 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. ANIMATION SLIDE • t = 0 – 5 ns • t = 0 – 5.2 ns 100 - 1000 (Td) Log scale Iowa State University Optical and Discharge Physics ICPIG2005_10

  11. MINMAX E-FIELD AFTER 60m PARTICLE E/N • 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). • t = 4.15 • t = 4.7 • t = 4.15 • t = 4.7 ns 100 - 1000 (Td) Log scale Iowa State University Optical and Discharge Physics ICPIG2005_11

  12. MINMAX 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 • t = 4.5 ns Iowa State University Optical and Discharge Physics ICPIG2005_12

  13. r E 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. • Near the particle • E = 5000 V/cm Iowa State University Optical and Discharge Physics ICPIG2005_13

  14. MINMAX POTENTIAL: DIELECTRIC PARTICLES (r = 80m) ANIMATION SLIDE • t = 0 - 5.2 ns Iowa State University Optical and Discharge Physics 100 - 1000 (Td) Log scale ICPIG2005_14

  15. MINMAX ELECTRIC FIELD: DIELECTRIC PARTICLES (r = 80m) ANIMATION SLIDE • t = 0 – 5.2 ns Iowa State University Optical and Discharge Physics 100 - 1000 (Td) Log scale ICPIG2005_15

  16. MINMAX 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. • This process is repetitive for particles of the same size and evenly spaced. • t = 0 – 5.2 ns 100 - 1000 (Td) Log Scale Iowa State University Optical and Discharge Physics ICPIG2005_16

  17. MINMAX 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 100 - 1000 (Td) Log Scale Iowa State University Optical and Discharge Physics ICPIG2005_17

  18. MINMAX 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 particles. • t = 3.75• t = 4.25 • t = 4.6 • t = 3.75• t = 4.25 • t = 4.6 100 - 1000 (Td) Log Scale Iowa State University Optical and Discharge Physics ICPIG2005_18

  19. MINMAX ELECTRON DENSITY FOR THREE 80 m PARTICLES • 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. • t = 3.45 • t = 4.2 • t = 4.75 ns 1012 - 6 x 1014 (cm-3) Log Scale Iowa State University Optical and Discharge Physics ICPIG2005_19

  20. MINMAX 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. • A relay-like process results in which streamer is handed off between particles. • t = 2.95 • t = 3.95 • t = 4.25 • t = 4.8 ns 109 - 7x1022 (/cm3-s) Log Scale Iowa State University Optical and Discharge Physics ICPIG2005_20

  21. 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 Iowa State University Optical and Discharge Physics ICPIG2005_21

  22. 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

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