Runaway Breakdown Runaway Breakdown and its Implicationsand its Implications

Gennady MilikhGennady Milikh University of Maryland, College Park, MDUniversity of Maryland, College Park, MD

in collaboration with Alex Gurevich, Robert Roussel-in collaboration with Alex Gurevich, Robert Roussel-Dupre, Surja Sharma, Parvez Guzdar, Juan Valdivia and Dupre, Surja Sharma, Parvez Guzdar, Juan Valdivia and

Dennis PapadopoulosDennis PapadopoulosWorkshop on the multiscale nature of spark precursors & HAL – Leiden, May Workshop on the multiscale nature of spark precursors & HAL – Leiden, May

20052005

OutlineOutline

Basics of Runaway BreakdownBasics of Runaway Breakdown Laboratory ExperimentsLaboratory Experiments Manifestation of R-away Breakdown in the Manifestation of R-away Breakdown in the

Atmosphere:Atmosphere: - Intracloud X-ray pulses & charge transfer- Intracloud X-ray pulses & charge transfer - Gamma-Ray Bursts- Gamma-Ray Bursts - Terrestrial Gamma-Ray Flashes - Terrestrial Gamma-Ray Flashes - Narrow Bipolar Pulses- Narrow Bipolar Pulses Theoretical ModelsTheoretical Models

Basics of Runaway ElectronsBasics of Runaway Electrons

Cold electrons undergo the dynamical friction Cold electrons undergo the dynamical friction force (trace 1)force (trace 1)

For fast electrons the friction forceFor fast electrons the friction force

(trace 2)(trace 2)

vomF

)vv( T

lnv

4v)v(

2

4

m

nemvF

F/e

DE

cnE

c0E

1 2

Tv c min

At Dreicer field the bulk of fully ionized plasma becomes runaway [Dreicer, 1960].

However, even at fast electrons run away.

In the weakly ionized plasma the interactions between high energy electrons and particles obey the Coulomb law. If E-field exceeds the critical value the whole bulk of electrons accelerated [Gurevich, 1961]

For relativistic electrons [Bethe & Ashkin, 1953] the friction force reaches its minimum at

ln4 3

T

neED

nion

mcn k

NZeE

34

12

3

0 ln4

mc

NZeE mc

F/e

DE

cnE

c0E

1 2

Tv c min

20030

2

0

ionc

cn mc

E

E

DEE )/( EET Dc

20/;10 0 thrcthrcn EEEE

Basics of Relativistic Runaway Basics of Relativistic Runaway BreakdownBreakdown

Dynamical friction force as a

function of the Lorentz factor

Although the bulk of secondary electrons caused by the impact ionization of relativistic electrons has low energy, some fast particles with

are also produced. This leads to runaway breakdown.

EEcm cc 2/02

0 2 4 6 8 10

1

1.5

2

2.5

3

3.5

FF nim EEc02

c

Runaway Breakdown Occurs Runaway Breakdown Occurs if if

The amplitude of The amplitude of electric field exceeds electric field exceeds the critical field the critical field

The e-field stretches The e-field stretches along the distance along the distance much longer than much longer than the avalanche length the avalanche length

Fast seed electrons Fast seed electrons exist with energiesexist with energies

5.7/)(0 2.2)(2.2)/( kmzc eatmPcmkVE

)(

150

200

4

42

aval atmPE

Em

E

E

eN

cml cc

m

E

Emc cc 2

02

Laboratory ExperimentsLaboratory Experiments The main hurdle in conducting such experiment is The main hurdle in conducting such experiment is

the lengthy scale of r-away breakdown. To the lengthy scale of r-away breakdown. To observe runaway at 1 atm the length of the observe runaway at 1 atm the length of the chamber should be a few times 50 m. chamber should be a few times 50 m.

One possibility is to conduct it in a dense matter One possibility is to conduct it in a dense matter where the avalanche length is a few cm.where the avalanche length is a few cm.

Another approach [Gurevich et al., 1999] is based Another approach [Gurevich et al., 1999] is based on magnetic trapping and cyclotron resonance to on magnetic trapping and cyclotron resonance to accelerate relativistic electrons. After some time accelerate relativistic electrons. After some time delay (100 mcs) a strong X- and gamma-ray delay (100 mcs) a strong X- and gamma-ray emission was detected. Still it is not clear how to emission was detected. Still it is not clear how to distinguish the effect from r-away breakdown distinguish the effect from r-away breakdown from that from a cyclotron resonance. from that from a cyclotron resonance.

Intracloud ObservationsIntracloud Observations X-rays were first X-rays were first

detected by McCarthy detected by McCarthy and Parks [1985] from and Parks [1985] from an aircraftan aircraft

Balloon measurements Balloon measurements of electric field [Marshall of electric field [Marshall et al., 1996] (the top et al., 1996] (the top plate)plate)

Balloon measurements Balloon measurements of E-field & X-rays made of E-field & X-rays made at at

4 km [Eack et al., 1996]4 km [Eack et al., 1996] (the bottom plate).(the bottom plate).

Ground-based ObservationsGround-based Observations

The electric field (the top Plate), the soft component (electrons, 10-30MeV) of cosmic rays (second from the top) observed during the thunderstorm on 09/07/00. The arrows show lightning strokes. The largest pre-lightning enhancement lasts about 0.5 min (after Alexeenko et al, 2002).

Ground-based Observations Ground-based Observations (continue) (continue)

1-2 ms bursts of radiation having energy 1-2 ms bursts of radiation having energy in excess of 1 MeV was associated with in excess of 1 MeV was associated with stepped-leaders [Moore et al., 2001]stepped-leaders [Moore et al., 2001]

Multiple bursts of 1 mcs detected from Multiple bursts of 1 mcs detected from rocket triggered lightning with energy in rocket triggered lightning with energy in 30-250 keV range [Dwyer et al, 2004], in 30-250 keV range [Dwyer et al, 2004], in association with dart leader.association with dart leader.

On one occasion X-rays up to 10 MeV were On one occasion X-rays up to 10 MeV were detected in association with initial detected in association with initial lightning stage (11 kA pulse) preceding lightning stage (11 kA pulse) preceding the return stroke. the return stroke.

Observations of Terrestrial Observations of Terrestrial Gamma Ray Flashes (TGFs)Gamma Ray Flashes (TGFs)

Discovered by Discovered by Fishman et alFishman et al. [1994] in data from . [1994] in data from the Burst and Transient Source Experiment the Burst and Transient Source Experiment (BATSE) on CGRO. (BATSE) on CGRO.

Strongly correlated to thunderstorm activity. Strongly correlated to thunderstorm activity.

Duration ranges from 1 to 10 msDuration ranges from 1 to 10 ms

Spectrally harder than cosmic gamma ray bursts.Spectrally harder than cosmic gamma ray bursts.

Also detected by LACE located at a low-Earth Also detected by LACE located at a low-Earth orbit (525 km) [orbit (525 km) [Feldman et alFeldman et al., 1996a,b]. ., 1996a,b].

Observations of TGFs by the Observations of TGFs by the RHESSI spacecraftRHESSI spacecraft

The map shows the global thunderstorm activity, while the crosses reveal where the TGFs were observed.

[Smith et al., 2005]

Examples of TGFs and their energy spectrum.

Looking for correlations Looking for correlations between TGFs and sfericsbetween TGFs and sferics

The Duke University detector collects The Duke University detector collects sferics caused by lightning strokes from sferics caused by lightning strokes from a distance 4,000 kma distance 4,000 km

In the most cases TGFs preceded In the most cases TGFs preceded lightning strokes by 1-3 ms, although lightning strokes by 1-3 ms, although RHESSI has 1-2 ms timing uncertaintiesRHESSI has 1-2 ms timing uncertainties

The average current moment observed The average current moment observed was 49 C-km for +CG or vertical IC. was 49 C-km for +CG or vertical IC.

Observations of narrow bipolar Observations of narrow bipolar pulses (NBPs)pulses (NBPs)

Positive NBP (left) and negative NBP (right) observed by Los Alamos Sferic Array [Smith et al., 2002] (and the FORTE satellite). Time is given in mcs.• NBPs are bipolar EM-pulses of large amplitude observed at 0.2-0.5 MHz

• The mean rise time 1-2 mcs, fall time 5-10 mcs

• Negative polarity NBPs are located at 15-20 km, Positive NBPs – at 7-15 km

• Generated by an unipolar current pulse of 30-100 kA, with M= 0.2-0.8 C-km

• Its average propagation velocity is c/2 and the average length is 3.2 km

• NBPs are accompanied by intensive radio emission in the frequency range up to 500 MHz.

Theoretical Models of Runaway Theoretical Models of Runaway BreakdownBreakdown

Generation of X-rays due to multiple Generation of X-rays due to multiple runaway breakdown inside runaway breakdown inside thundercloudsthunderclouds

Models of generation of TGF’s. Beam Models of generation of TGF’s. Beam of runaway electrons caused by:of runaway electrons caused by:

- Cloud-to-ground discharge- Cloud-to-ground discharge

- Intracloud discharge- Intracloud discharge

Generation of X-rays due to multiple Generation of X-rays due to multiple runaway breakdown inside runaway breakdown inside

thundercloudsthunderclouds Model Model Assumptions Assumptions [Gurevich & Milikh, 1999]:[Gurevich & Milikh, 1999]: A charge layer within a stratiform cloud has a A charge layer within a stratiform cloud has a

horizontal extension of tens kms, while its vertical horizontal extension of tens kms, while its vertical thickness is a few hundred m [Marshall et al., thickness is a few hundred m [Marshall et al., 1995]. Thus we consider 1D model of r-away 1995]. Thus we consider 1D model of r-away breakdownbreakdown

The atmosphere is taken as uniform since its The atmosphere is taken as uniform since its density scale is much higher than electron/photon density scale is much higher than electron/photon mean free pathmean free path

The breakdown is located at 3-5 km thus the The breakdown is located at 3-5 km thus the runaway electrons are unmagnetized.runaway electrons are unmagnetized.

Multiple runaway breakdownMultiple runaway breakdown

The total flux of ambient The total flux of ambient cosmic ray secondary cosmic ray secondary electrons involved in the electrons involved in the runaway breakdownrunaway breakdown

The flux of ambient cosmic The flux of ambient cosmic ray secondary electrons is ray secondary electrons is magnified due to runaway magnified due to runaway breakdown. The density of breakdown. The density of runaway electrons: runaway electrons:

The spectral density of the The spectral density of the bremmstrahlung emission: bremmstrahlung emission:

),(

),(

s

dJdamb

clzN avalambe

1}/exp{

dNNI me rfv

Modeled Spectral Density of Modeled Spectral Density of the Bremsstrahlung Emissionthe Bremsstrahlung Emission

Computed for z=4 km, unidirectional differential intensity of cosmic ray secondary from Daniel and Stephens [1974], and E/Eco=2.

X-ray propagation in the atmosphereX-ray propagation in the atmosphere

X-ray photons experience X-ray photons experience Compton scattering and loss Compton scattering and loss due to photoionization [Bethe & due to photoionization [Bethe & Ashkin, 1953]. The 1D photon Ashkin, 1953]. The 1D photon propagation is given bypropagation is given by

The computed energy The computed energy spectrum was checked against spectrum was checked against the balloon observations [Eack, the balloon observations [Eack, 1996] where X-ray fluxes were 1996] where X-ray fluxes were integrated over 3 energy integrated over 3 energy channels. channels.

Here red points show the real Here red points show the real measurements, blue – model at measurements, blue – model at 70 m from the sources, green – 70 m from the sources, green – model at 420 m from the model at 420 m from the source.source.

),(/2

2

zQ

n

cz

nD

t

n

Fast Charge TransferFast Charge Transfer

Lifetime of free electrons at Lifetime of free electrons at 4 km is about 70 ns. During 4 km is about 70 ns. During this time they are drifting this time they are drifting under the action of the under the action of the thundercloud e-field, which thundercloud e-field, which leads to charge transferleads to charge transfer

A relativistic electron creates A relativistic electron creates 50 slow electrons per 1 cm, 50 slow electrons per 1 cm, the total flux of slow the total flux of slow electronselectrons

In terms of the charge In terms of the charge transferred per unit length transferred per unit length during the r-away during the r-away breakdown process time, t.breakdown process time, t.

lifedrift tm

eEl

}/exp{50 avalambsl lzz

mCtleQ driftsl /10 4

Model of NBPs GenerationModel of NBPs Generation Extensive Air Shower (EAS) Extensive Air Shower (EAS)

meets e-field with E in meets e-field with E in excess of the critical field excess of the critical field [Gurevich et al., 2004][Gurevich et al., 2004]

Rise time of the pulse Rise time of the pulse Fall time of the pulseFall time of the pulse Coherent radiation (since Coherent radiation (since

Fluxes of 10^18 eV Fluxes of 10^18 eV particles are 0.002 part/min particles are 0.002 part/min km^2km^2

sclavalr 1/

sNcm mf 2318 )/105(

)1500600 mlaval GW

c

JP 300100

3

2 2

Models of TGFs GenerationModels of TGFs Generation All models based on runaway breakdownAll models based on runaway breakdown

It is driven by a static electric field due to:It is driven by a static electric field due to: Unbalanced charges following a lightning Unbalanced charges following a lightning

stroke [stroke [Bell elBell el., 1995; ., 1995; Lehtinen et alLehtinen et al., ., 1996, 1999, 2001; 1996, 1999, 2001; Taranenko and Roussel-Taranenko and Roussel-Dupre,Dupre, 1996; 1996; Roussel-Dupre and GurevichRoussel-Dupre and Gurevich, , 1996; 1996; Yukhimuk et alYukhimuk et al., 1999] ., 1999]

A static electric field inside a stratified A static electric field inside a stratified cloud cloud

[Gurevich et al, 2004; Milikh et al., 2005]. [Gurevich et al, 2004; Milikh et al., 2005].

TGFs due to plasma processes in the TGFs due to plasma processes in the stratosphere: role of whistler wavesstratosphere: role of whistler waves

Runaway breakdown produced by static stratified Runaway breakdown produced by static stratified electric fields creates a magnetized plasma electric fields creates a magnetized plasma species at altitudes above 15 km. species at altitudes above 15 km.

Trapping of the runaway population at these Trapping of the runaway population at these heights can promote the propagation of the heights can promote the propagation of the electromagnetic pulse associated with electromagnetic pulse associated with thunderstorms as a whistler mode in this region. thunderstorms as a whistler mode in this region.

Sustenance of the ionization driven, self-focusing Sustenance of the ionization driven, self-focusing instability which self-consistently maintains the instability which self-consistently maintains the runaway population and channels the whistler runaway population and channels the whistler energy along field-aligned ducts all the way to 30 energy along field-aligned ducts all the way to 30 – 35 km. – 35 km.

+ + + + + + +

+ + + + + _ _ _ _ _ _ _

Lightning Stroke

Thundercloud

Runaway Electron Beam

0Z0Zkm 30

Ground

km 20

B

Whistlers

e

rays

Fig. 1Gamma-ray bursts in the presence of thunderclouds [Milikh et al., 2005]

Linear Stability Analysis of Linear Stability Analysis of Dispersion RelationDispersion Relation

shows that an shows that an instability can instability can develop in the develop in the system driven by system driven by the relative drift the relative drift between the hot between the hot and cold electrons.and cold electrons.

Here:Here:

000,30/;5.0/

;400,3)/(;1.0)/( 22

eceh

eeceeh

Fig. 2a,b

Fig. 3. The behavior of the peak growth rate as a function of altitude. Maximum is at about 30 km.

Fig. 4. The dependence of the peak growth rate upon the number density of the hot electrons.

Some Estimates

Runaway beam starts at a certain height and moves up if

When it reaches magnetization height the instability develops.

is needed in order to provide:

and i.e. the burst-time of gamma-ray flashes.

The runaway breakdown starts with a primary particle

which generates MeV particles [Gurevich et al., 1999].

Then runaway develops and produces relativistic

electrons

spreading in a volume , thus their density .

cEE

310 cmnh 1410 s14105.0 s

)(0 eV

)(10 09 eVN f

)}(/exp{ zNN fR

4

)(

3

23 zV VNn RR /

The energy of a primary cosmic particle needed to generate

versus the distance.

Thus is required, and the length of the r-away

discharge is 2.5 km.

310 cmnh

5.1,1010 19180 eV

Such conditions for runaway breakdown are similar to those leading to generation of strong bipolar pulses [Smith et al., 2002; Jacobson, 2003]. The latter are a manifestation of runaway breakdown occurs at 18-20 km simulated by a cosmic particle of [Gurevich et al., 2004].

eV19180 1010

Runaway in the presence of Runaway in the presence of e.m. waves (nonlinear model)e.m. waves (nonlinear model)

Computed for:

Red trace – no pumping wave,

Green trace – pumping exists

0.1c0

/E0E

c0.1k

0.7;c0

E/E

/

Cosmic rays can play a surprising Cosmic rays can play a surprising role role in the drama of lightningin the drama of lightning

Gurevich & Zybin, 2005Gurevich & Zybin, 2005

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