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The multiscale dynamics of sparks and lightning

The multiscale dynamics of sparks and lightning. Ute Ebert. CWI Amsterdam and TU Eindhoven http://homepages.cwi.nl/~ebert/. TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: A A A A A. The multiscale dynamics of sparks and lightning.

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The multiscale dynamics of sparks and lightning

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  1. The multiscale dynamics of sparks and lightning Ute Ebert CWI Amsterdam and TU Eindhoven http://homepages.cwi.nl/~ebert/ TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAA

  2. The multiscale dynamics of sparks and lightning Puzzles in lightning Physical mechanisms Computations and Analysis TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAA

  3. Lightning: • ca. 45 flashes/second worldwide, • major source of O3 and NOx.

  4. Sparks and lightning evolve in three stages: 1. Charge separated -> voltage builds up 2. Streamer/leader: conducting channels grow 3. Short circuit: Ohmic heating, visible stroke

  5. Lightning – is it possible at all?

  6. 100 MV 100 MV on 10 km = 10 kV/m … electric breakdown of air requires 30 kV/cm A field paradox? 10 km -> average field 100 MV/10 km = 100 V/cm TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAA

  7. 100 MV 100 MV on 10 km = 10 kV/m … electric breakdown of air requires 30 kV/cm A field paradox? 10 km -> average field 100 MV/10 km = 100 V/cm Highest field measured inside thundercloud 3 000 V/cm TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAA

  8. e- Free electrons, if present, drift and diffuse in local E-field – like a ball jumping down a slope. Collisions with neutral molecules: Impact ionization -> electron gain Attachment to O2 -> electron loss Electron number gain larger than loss above ~30 000 V/cm (in air at 1 bar and 300 K) + + + + + + - - - - - + - - + + - E - + A+ + - + - + A - - + - + - - - + + - + — — — — — —

  9. 100 MV 100 MV on 10 km = 10 kV/m … electric breakdown of air requires 30 kV/cm A field paradox? 10 km -> average field 100 MV/10 km = 100 V/cm Highest field measured inside thundercloud 3 000 V/cm Electric breakdown of air requires ~30 000 V/cm Hammer, nail and wall: field focussing! TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAA

  10. Movie of Lightning leader[G.M. McHarg, US Air Force Academy, summer 2007] shows how the lightning leader searches its way to the ground. The total duration of the movie is only 3.5 milliseconds, time steps are 5 microseconds. Not the total channel is illuminated, but only the actively propagating tip. In this tip electrical forces are focused, similarly to the focusing of mechanical forces in the tip of the nail. But the “lightning nail” is not pre-fabricated, but self-organized. We later will see how. Similar glowing tips are seen on smaller scale in the lab:

  11. Air, +28 kV on 40 mm, exposure 0<t<300ns

  12. Air, +28 kV on 40 mm, exposure 46<t<47 ns

  13. Air, 1 bar, +28 kV pulse on point above, 40 mm gap to plate below 50 ns (50 ns < t < 100 ns) 10 ns (50 ns < t < 60 ns) 300 ns (0 ns < t < 300 ns) exposure: 1 ns (46 ns < t < 47 ns) [Ebert et al., PSST 06, Briels et al., J Phys D 2006]

  14. Self-organized plasma reactor dots produce O*, X-rays(?), …

  15. TerrestrialGamma-Ray Flashes, > 50/day [discovered 1994, here RHESSI satellite data 2006] correlated with lightning strokes There are puzzles in cosmology, but do we understand our own earth?

  16. 12 stage 2.4MV Marx generator Hypothesis: Enhanced field region at streamer tip = electron accelerator -> Bremsstrahlung -> gamma-rays Gamma-ray bursts now also observed in MV-lab discharges

  17. e— Fast processes in the ionization front (in pure N2 or Ar for simplicity): 10-9 m: 10-6 m: Electrons drift and diffuse in local E-field. Elastic, inelastic and ionizing collisions with neutral molecules. Degree of ionization < 10-4. + + + + + + - - - - - + - - Fluid approximation with Impact ionizatione—+ A →2 e—+ A+ Ohm’s lawj ~ neE Coulomb’s lawn+— ne= div E + + - E - + A+ + - + - + A - - + →Minimal streamer model for electron density σ, ion density ρ and electric field E: - + - - - + + - + — — — — — —

  18. E Nonionized Region E - - - charge layer - - - - + - - - + - - + - - - + Ionized Region + - - + - + - + + - e- - - + - + + + - - + - - + - - + - + + + + + + - + + Streamer mechanism + + + + + + E A+ A A* — — — — — —

  19. Propagating streamer Strong local field enhancement Net charge n+ - ne Electric field Negative electrons ne Positive ions n+ z (mm) r (mm) r (mm) r (mm) r (mm)

  20. Solve Poisson equation everywhere. Solve densities in ionized region. Resolve steep density gradients with high accuracy. Do not exceed computational memory. [Montijn et al., 2006, Luque et al., 2008] electrons net charge z z r r The multiscale challenge:

  21. Whole computational domain Grids for Poisson equation Grids for densities ¢x=4 ¢x=2 ¢x=1 ¢x=1/2 ¢x=1/4 ¢x=1/8 Numerical decoupling of domains and moving local grid refinement Coupling of the computational grids σ, ρ E [C. Montijn et al., J. Comp. Phys. 2006, Phys. Rev. E 2006]

  22. 2 interacting streamers in 3D: Surfaces of equal electron density Electrostatic repulsion versus attraction through photoionization Quasispectral method for the Poisson equation [Luque et al., PRL 08, Research Highlight Nature 08]

  23. L Periodic arrayof negative streamers in 2D: Anode Direction of propagation Cathode Charge distribution and (electro-)dynamics different from single streamer!

  24. L Periodic arrayof negative streamers in 2D: Anode Direction of propagation Cathode Thin front structure, almost a moving boundary

  25. Moving Ionization Boundaries Ideal conductor

  26. The electric potential φ around a conducting body (solutions of ¢φ = 0 with boundary conditions) Electric field = slope of φ = - rφ Coordinates around body uncharged body in an external field

  27. Moving Ionization Boundaries Ideal conductor Air-oil-flow (between glass plates) mathematically equivalent: Viscous oil: v = -rp, incompressible r∙v = 0 => r2p = 0 in oil v = -rp on interface Nonviscous air: p = const.

  28. Colored Water Hele-Shaw Flow Radial Symmetry Hole Glycerol Channel configuration Saffman-Taylor finger

  29. L An array of streamers (2D, fluid-model): Saffman-Taylor finger with λ=½! Mathematics of selection?

  30. L DBM From few channels to more.

  31. 5 µs 5 ns Computational Science: adaptive grids, hybrid (MC-continuous) Nonlinear Dynamics: Fronts and interfaces, model reduction Spark formation in Nature and Technology geophysics: Sprite discharges Physics/electroengineering.: Streamer discharges: experiments and applications

  32. Elves, sprites, jets correlated with lightning strokes Predicted 1925, observed since 1989.

  33. Sprite discharge above a thundercloud

  34. 4 cm Telescopic images of sprite discharges [Gerken et al., Geophys. Res. Lett. 2000] 4 cm 1 bar Approximate similarity between different gas densities, better than theory predicts.

  35. Artikelen voor allgemeen publiek zijn te vinden op http://homepages.cwi.nl/~ebert/PublPubl.html, b.v. Bliksem boven bliksem over reuzenachtige sprite ontladingen boven onweerswolken of Vroege Vonken onder de virtuele microscoopover simulaties van streamer ontladingen. TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAA

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