Runaway Breakdown and its Implications

1
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
2
Outline

• 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

3
Basics of Runaway Electrons

• Cold electrons undergo the dynamical friction
  force
  (trace 1)
• For fast electrons the friction force
• 
  (trace 2)

4
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
5
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.
6
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

7
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.

8
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).

9
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).
10
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.

11
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.

12
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.
13
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.

14
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.

15
Theoretical Models of Runaway Breakdown

• Generation of X-rays due to multiple runaway
  breakdown inside thunderclouds
• Models of generation of TGFs. Beam of runaway
  electrons caused by
• - Cloud-to-ground discharge
• - Intracloud discharge

16
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.

17
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

18
Modeled Spectral Density of the Bremsstrahlung
Emission
Computed for z4 km, unidirectional differential
intensity of cosmic ray secondary from Daniel and
Stephens 1974, and E/Eco2.
19
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.

20
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.

21
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 1018 eV particles are 0.002 part/min
  km2

22
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.

23
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.

24
B
e
Runaway Electron Beam
Whistlers

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

Lightning Stroke
Ground
25
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.
• Here

Fig. 2a,b
26
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.
27
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 .
28
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.
29
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.
30
Runaway in the presence of e.m. waves (nonlinear
model)
Computed for
Red trace no pumping wave, Green trace
pumping exists
31

• Cosmic rays can play a surprising role
• in the drama of lightning
• Gurevich Zybin, 2005

32

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