The multiscale dynamics of sparks and lightning

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The multiscale dynamics of sparks and
lightning
Ute Ebert
CWI Amsterdam and TU Eindhoven http//homepages.cw
i.nl/ebert/
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The multiscale dynamics of sparks and
lightning
Puzzles in lightning Physical mechanisms Computati
ons and Analysis
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Sparks and lightning evolve in three stages 1.
Charge separated -gt voltage builds up 2.
Streamer/leader conducting channels grow 3.
Short circuit Ohmic heating, visible stroke
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Lightning is it possible at all?
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100 MV
100 MV on 10 km 10 kV/m electric
breakdown of air requires 30 kV/cm
A field paradox?
10 km
-gt average field 100 MV/10 km 100 V/cm
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100 MV
100 MV on 10 km 10 kV/m electric
breakdown of air requires 30 kV/cm
A field paradox?
10 km
-gt average field 100 MV/10 km 100 V/cm Highest
field measured inside thundercloud 3 000 V/cm
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Free electrons, if present,
drift and diffuse in local E-field like a
ball jumping down a slope. Collisions with
neutral molecules Impact ionization -gt
electron gain Attachment to O2 -gt electron
loss Electron number gain larger than loss
above 30 000 V/cm
(in air at 1 bar and 300 K)
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100 MV
100 MV on 10 km 10 kV/m electric
breakdown of air requires 30 kV/cm
A field paradox?
10 km
-gt 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!
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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
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Self-organized
plasma reactor dots produce
O, X-rays(?),
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Terrestrial Gamma-Ray Flashes, gt
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?

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Hypothesis Enhanced field region at
streamer tip electron accelerator -gt
Bremsstrahlung -gt gamma-rays Gamma-ray bursts
now also observed in MV-lab discharges
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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 lt 10-4.

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Fluid approximation with Impact ionization e
A ? 2 e A Ohms law j ne
E Coulombs law n ne div E

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? Minimal streamer model for electron density s,
ion density ? and electric field E
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Streamer mechanism

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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)
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The multiscale challenge
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Numerical decoupling of domains and moving local
grid refinement
Coupling of the computational grids
s, ?
E
C. Montijn et al., J. Comp. Phys. 2006, Phys.
Rev. E 2006
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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
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Periodic array of negative streamers in 2D
Anode
Direction of propagation
Cathode
Charge distribution and (electro-)dynamics
different from single streamer!
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Periodic array of negative streamers in 2D
Anode
Direction of propagation
Cathode
Thin front structure, almost a moving boundary
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The electric potential f around a conducting
body (solutions of f 0 with boundary
conditions) Electric field slope of f - r f
Coordinates around body uncharged body
in an external field
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Air-oil-flow (between glass
plates) mathematically equivalent Viscous oil
v -rp, incompressible rv 0 gt
r2p 0 in oil v -rp on
interface Nonviscous air p const.
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Hele-Shaw Flow
Radial Symmetry
Hole
Glycerol
Channel configuration
Saffman-Taylor finger
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An array of streamers (2D, fluid-model)
Saffman-Taylor finger with ?½! Mathematics of
selection?
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From few channels to more.
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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
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Elves, sprites, jets
correlated with lightning
strokes Predicted 1925, observed since 1989.
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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.
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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
microscoop over
simulaties van streamer ontladingen.
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