The multiscale dynamics of sparks and lightning Ute Ebert CWI Amsterdam and TU Eindhoven TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAA A

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

Lightning: ca. 45 flashes/second worldwide, major source of O 3 and NO x.

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

Lightning – is it possible at all?

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

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

e-e- A A+A+ — — — 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 O 2 -> electron loss Electron number gain larger than loss above ~ V/cm (in air at 1 bar and 300 K) E

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

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:

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

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

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

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

Terrestrial Gamma-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?

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

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

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

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

The multiscale challenge: 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] z r electrons r z net charge

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

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

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

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

Moving Ionization Boundaries Ideal conductor

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

Moving Ionization Boundaries Ideal conductor Air-oil-flow (between glass plates) mathematically equivalent: Viscous oil: v = - r p, incompressible r ∙v = 0 => r 2 p = 0 in oil v = - r p on interface Nonviscous air: p = const.

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

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

From few channels to more. DBM L

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

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

Sprite discharge above a thundercloud

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.

Artikelen voor allgemeen publiek zijn te vinden op b.v. Bliksem boven bliksem Bliksem boven bliksem over reuzenachtige sprite ontladingen boven onweerswolken of Vroege Vonken onder de virtuele microscoop Vroege Vonken onder de virtuele microscoop over simulaties van streamer ontladingen. TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAA A