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Runaway Breakdown and its Implications. Gennady Milikh University of Maryland, College Park, MD in collaboration with Alex Gurevich, Robert Roussel-Dupre, Surja Sharma, Parvez Guzdar, Juan Valdivia and Dennis Papadopoulos.

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runaway breakdown and its implications

Runaway Breakdown and its Implications

Gennady Milikh

University of Maryland, College Park, MD

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

Workshop on the multiscale nature of spark precursors & HAL – Leiden, May 2005

  • Basics of Runaway Breakdown
  • Laboratory Experiments
  • Manifestation of R-away Breakdown in the Atmosphere:

- Intracloud X-ray pulses & charge transfer

- Gamma-Ray Bursts

- Terrestrial Gamma-Ray Flashes

- Narrow Bipolar Pulses

  • Theoretical Models
basics of runaway electrons
Basics of Runaway Electrons
  • Cold electrons undergo the dynamical friction force (trace 1)
  • For fast electrons the friction force

(trace 2)


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

basics of relativistic runaway breakdown
Basics of Relativistic Runaway Breakdown

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.

runaway breakdown occurs if
Runaway Breakdown Occurs if
  • The amplitude of electric field exceeds the critical field
  • The e-field stretches along the distance much longer than the avalanche length
  • Fast seed electrons exist with energies
laboratory experiments
Laboratory Experiments
  • The main hurdle in conducting such experiment is the lengthy scale of r-away breakdown. To observe runaway at 1 atm the length of the chamber should be a few times 50 m.
  • One possibility is to conduct it in a dense matter where the avalanche length is a few cm.
  • Another approach [Gurevich et al., 1999] is based on magnetic trapping and cyclotron resonance to accelerate relativistic electrons. After some time delay (100 mcs) a strong X- and gamma-ray emission was detected. Still it is not clear how to distinguish the effect from r-away breakdown from that from a cyclotron resonance.
intracloud observations
Intracloud Observations
  • X-rays were first detected by McCarthy and Parks [1985] from an aircraft
  • Balloon measurements of electric field [Marshall et al., 1996] (the top plate)
  • Balloon measurements of E-field & X-rays made at

4 km [Eack et al., 1996]

(the bottom plate).

ground based observations
Ground-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 continue
Ground-based Observations (continue)
  • 1-2 ms bursts of radiation having energy in excess of 1 MeV was associated with stepped-leaders [Moore et al., 2001]
  • Multiple bursts of 1 mcs detected from rocket triggered lightning with energy in 30-250 keV range [Dwyer et al, 2004], in association with dart leader.
  • On one occasion X-rays up to 10 MeV were detected in association with initial lightning stage (11 kA pulse) preceding the return stroke.
observations of terrestrial gamma ray flashes tgfs
Observations of Terrestrial Gamma Ray Flashes (TGFs)
  • Discovered by Fishman et al. [1994] in data from the Burst and Transient Source Experiment (BATSE) on CGRO.
  • Strongly correlated to thunderstorm activity.
  • Duration ranges from 1 to 10 ms
  • Spectrally harder than cosmic gamma ray bursts.
  • Also detected by LACE located at a low-Earth orbit (525 km) [Feldman et al., 1996a,b].
observations of tgfs by the rhessi spacecraft
Observations of TGFs by the RHESSI 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 between tgfs and sferics
Looking for correlations between TGFs and sferics
  • The Duke University detector collects sferics caused by lightning strokes from a distance 4,000 km
  • In the most cases TGFs preceded lightning strokes by 1-3 ms, although RHESSI has 1-2 ms timing uncertainties
  • The average current moment observed was 49 C-km for +CG or vertical IC.
observations of narrow bipolar pulses nbps
Observations of narrow bipolar 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 breakdown
Theoretical Models of Runaway Breakdown
  • Generation of X-rays due to multiple runaway breakdown inside thunderclouds
  • Models of generation of TGF’s. Beam of runaway electrons caused by:

- Cloud-to-ground discharge

- Intracloud discharge

generation of x rays due to multiple runaway breakdown inside thunderclouds
Generation of X-rays due to multiple runaway breakdown inside thunderclouds

Model Assumptions [Gurevich & Milikh, 1999]:

  • A charge layer within a stratiform cloud has a horizontal extension of tens kms, while its vertical thickness is a few hundred m [Marshall et al., 1995]. Thus we consider 1D model of r-away breakdown
  • The atmosphere is taken as uniform since its density scale is much higher than electron/photon mean free path
  • The breakdown is located at 3-5 km thus the runaway electrons are unmagnetized.
multiple runaway breakdown
Multiple runaway breakdown
  • The total flux of ambient cosmic ray secondary electrons involved in the runaway breakdown
  • The flux of ambient cosmic ray secondary electrons is magnified due to runaway breakdown. The density of runaway electrons:
  • The spectral density of the bremmstrahlung emission:
modeled spectral density of the bremsstrahlung emission
Modeled Spectral Density of the 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 atmosphere
X-ray propagation in the atmosphere
  • X-ray photons experience Compton scattering and loss due to photoionization [Bethe & Ashkin, 1953]. The 1D photon propagation is given by
  • The computed energy spectrum was checked against the balloon observations [Eack, 1996] where X-ray fluxes were integrated over 3 energy channels.

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

fast charge transfer
Fast Charge Transfer
  • Lifetime of free electrons at 4 km is about 70 ns. During this time they are drifting under the action of the thundercloud e-field, which leads to charge transfer
  • A relativistic electron creates 50 slow electrons per 1 cm, the total flux of slow electrons
  • In terms of the charge transferred per unit length during the r-away breakdown process time, t.
model of nbps generation
Model of NBPs Generation
  • Extensive Air Shower (EAS) meets e-field with E in excess of the critical field [Gurevich et al., 2004]
  • Rise time of the pulse
  • Fall time of the pulse
  • Coherent radiation (since
  • Fluxes of 10^18 eV particles are 0.002 part/min km^2
models of tgfs generation
Models of TGFs Generation
  • All models based on runaway breakdown

It is driven by a static electric field due to:

  • Unbalanced charges following a lightning stroke [Bell el., 1995; Lehtinen et al., 1996, 1999, 2001; Taranenko and Roussel-Dupre, 1996; Roussel-Dupre and Gurevich, 1996; Yukhimuk et al., 1999]
  • A static electric field inside a stratified cloud

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

tgfs due to plasma processes in the stratosphere role of whistler waves
TGFs due to plasma processes in the stratosphere: role of whistler waves
  • Runaway breakdown produced by static stratified electric fields creates a magnetized plasma species at altitudes above 15 km.
  • Trapping of the runaway population at these heights can promote the propagation of the electromagnetic pulse associated with thunderstorms as a whistler mode in this region.
  • Sustenance of the ionization driven, self-focusing instability which self-consistently maintains the runaway population and channels the whistler energy along field-aligned ducts all the way to 30 – 35 km.



Runaway Electron Beam


+ + + + +

_ _ _ _ _ _ _


Fig. 1

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

+ + + + + + +

Lightning Stroke


linear stability analysis of dispersion relation
Linear Stability Analysis of Dispersion Relation

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


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


spreading in a volume , thus their density .


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.


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].

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

Computed for:

Red trace – no pumping wave,

Green trace – pumping exists


Cosmic rays can play a surprising role

in the drama of lightning

Gurevich & Zybin, 2005



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