Streamers, sprites, leaders, lightning:

from micro- to macroscales

Workshop, Oct. 8-12, 2007, Lorentz Centre

Organizers: Ute Ebert (CWI Amsterdam, TU Eindhoven),

Davis D. Sentman (Fairbanks, Alaska)

Many disciplines:

Applied math, computational science, theoretical physics,

applied physics, electrical engineering, industry,

geophysics on atmospheric electricity:

lightning, transient luminous events, terrestrial gamma ray flashes

Avoid terminology slang

that other disciplines might not be familiar with!

Many disciplines – but common subjects:

Streamer-like discharges in various media:

Air at a large range of pressures, argon, nitrogen, air-fuel-mixtures, combustion gases, supercritical fluids, liquids, solids

Dependence on electric circuit (voltage, polarity, …) and on magnetic field

Streamer ignition, streamer to leader transition

Leaders, lightning

Many disciplines – but common subjects:

Complex subject: very many scales in space and time,

from microscopic cross sections up to macroscopic streamers.

Input: electric power into a given medium,

Output: distribution of conductivity, chemical excitations, X-rays

Major challenge for observations and modeling!

Join forces!

Why?Basic physical interest in start up of sparking

● Spark plug in car engine● Ozone generation for disinfection● Start of energy saving lamps● Lightning …

+28 kV

4 cm

300 ns

Streamer discharge in ambient air (TUE):

4 cm

Telescopic images of sprite discharges [Gerken et al., Geophys. Res. Lett. 2000]

4 cmSimilarity law: 1 bar versus 10-5 bar … even 30 bar in lamps and spark plugs!

What can we learn from each other?

Air, 40 mm,

exposure 2 ns54 kV 28 kV

A phase transition???

Air, 40 mm,

exposure 50 ns54 kV 28 kV

A phase transition???

No, continuous.[T. Briels et al., J. Phys. D 39, 5201 (2006)]

Experiments show many unexpected features,

also when changing polarity and gas composition.

Theory???

54 kV 28 kV

+

- - - -+

++

++++

+

+

+

--

-

--

-

-

--

--

-+-

-

e—

A

A+E

— — — — — —

+ + + + + +

Fast processes in the ionization front:

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.

Continuum approximation with

Impact ionization e— + A 2 e— + A+

Ohm’s law j ~ ne E

Coulomb’s law n+— n e = E

The multiscale challenge:

Solve Poisson equation everywhere.

Solve densities in ionized region.

Resolve steep density gradients with high accuracy.

• Do not exceed computational memory.

[U. Ebert et al., Plasma Sources Sci. Technol. 15, S118 (2006)][C. Montijn et al., Phys. Rev. E 73, 065401 (2006)][C. Montijn et al., J. Comput. Phys. 219, 801 (2006)][A. Luque et al., Appl. Phys. Lett. 90, 081501 (2007)]

z

r

electrons

r

z

net charge

The multiscale challenge:

Solve Poisson equation everywhere.

Solve densities in ionized region.

Resolve steep density gradients with high accuracy.

• Do not exceed computational memory.

3D, interacting streamers: [A. Luque et al., proceedings ICPIG 2007 and in preparation]

z

r

electrons

r

z

net charge

The multiscale challenge:

Solve Poisson equation everywhere.

Solve densities in ionized region.

Resolve steep density gradients with high accuracy.

Take particle nature into account locally!

[C. Li et al., J. Appl. Phys. 101, 123305 (2007) and submitted]

Explain chemical processes and X-ray emission from lightning?

z

r

electrons

r

z

net charge

Streamers, sprites, leaders, lightning:

from micro- to macroscales

Let’s try to make progress this week!