Transcript - Lorentz Center

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
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

Basics of Runaway Electrons
Cold electrons undergo the dynamical friction
F  m o v
force
(trace 1)
 For fast electrons (v  v ) the friction force
4 e n
F  mv( v) v 
ln 
(trace 2)
mv

T
4
2
F/e
ED
E cn
2
1
E c0
vT   c
 min

At Dreicer field the bulk of fully ionized plasma becomes runaway [Dreicer, 1960].
However, even at
4e 3 n
ED 
ln 
T
E  ED fast electrons
   c  T ( ED / E ) 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]
Ecn 
4 e3 Z N m
 ion
kn
For relativistic electrons [Bethe & Ashkin, 1953] the friction force reaches its
minimum at
F/e
4 Ze3 N m
Ec 0 
mc2
Ecn
mc2

 200
Ec 0 30 ion
ln 1
ED
E cn
2
1
Ecn  10 Ethr ; Ec 0  Ethr / 20
E c0
vT 
c
min

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    c  mc 2 Ec 0 / 2 E
are also produced. This leads to runaway breakdown.
Runaway Breakdown Occurs if
The amplitude of
electric field exceeds E (kV / cm)  2.2P(atm)  2.2e
the critical field
 The e-field stretches
Ec 0
m 2 c 4 Ec 0
1
along the distance
laval 

50
m

4
2

N
e
E
E P(atm)
m
much longer than the
avalanche length
2
mc
Ec 0
 Fast seed electrons
  c 
2E
exist with energies

 z ( km ) / 7.5
c0
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

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
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)
1-2 ms bursts of radiation having energy in
excess of 1 MeV was associated with steppedleaders [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)

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
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
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)
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

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

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



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:
 amb   d

 J ( ,  )d
s ( , )
N e   amb exp{ z / laval }
I  N e N m    vf r d
1
c
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 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 Xray 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.
n
 2 n  n
D 2 
 Q( z, )
t
z  / c 
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.
eE
ldrift 
tlife
m
 sl  50 z amb exp{ z / laval }
Q  e sl ldrift t  104 C / m
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

laval    600  1500m)

Fluxes of 10^18 eV particles
are 0.002 part/min km^2
 r  laval / c  1s
 f  (5 1018 cm3 / Nm )2 s
2J 2
P
 100  300GW
3c
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

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 fieldaligned ducts all the way to 30 – 35 km.
30 km
B
Z0
  rays
Z0
e
Runaway Electron Beam
Whistlers
20 km
_ +_ +_ +_ +
_ _+ _
Thundercloud
+ + + + + + +
Lightning Stroke
Ground
Fig. 1
Gamma-ray bursts
in the presence of
thunderclouds
[Milikh et al., 2005]
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:
(eh / e ) 2  0.1; (ec / e ) 2  3,400;
 h / e  0.5; c / e  30,000
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
E  Ec
When it reaches magnetization height the instability develops.
nh  10 cm 3
is needed
in order to provide:
  10 4 s 1
4 1
and   0.5 10 s i.e. the burst-time of gamma-ray flashes.
The runaway breakdown starts with a primary particle  0 (eV )
which generates
N f  109  0 (eV ) MeV particles [Gurevich et al., 1999].
Then runaway develops and produces N R  N f exp{z /  ( )} relativistic
electrons
 3  2 ( )
spreading in a volume V  z
, thus their density
3
4
nR  NR / V .
The energy of a primary cosmic particle needed to generate
nh  10 cm 3
versus the distance.
Thus
 0  1018  1019 eV ,   1.5 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  0  1018  1019 eV [Gurevich et al., 2004].
Runaway in the presence of e.m.
waves (nonlinear model)
Computed for:
 0.7;
c0
k  0.1 / c
E /E  0.1
0 c0
E/E
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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