Download Cosmic Lightning

Scholten
KVI-CART
Lightning project
Lightning Research
Olaf Scholten & Ad van den Berg,
KVI - Center for Advanced Radiation Technology, University of Groningen.
tel: 050 363 3552
e-mail: [email protected]
Lightning is a familiar phenomenon, but still far from being understood. Questions concerning the initiation of lightning as well as the propagation of the discharge are addressed in our
research.
We employ a novel approach using observations made possible by the infrastructure offered
by LOFAR, a new-generation astrophysical radio observatory. We will measure the progress of
the lightning discharge, the streamers and stepped leaders, using dual-polarized broad-band
antennas at nanosecond time resolution over baselines of many tens of kilometers. We have
also developed a new method for determining the electric field in thunder clouds base on the
radio footprint of cosmic-ray induced air showers as measured with LOFAR.
Contents
1
2
1
General physics objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.1
Lightning Imaging with LOFAR. . . . . . . . . . . . . . . . . . . . . . . . . .
1.1.1 Relation to state-of-the-art radio detection of lightning . . . . . . . . .
1.1.2 Proposed project . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.1.3 Computational challenges . . . . . . . . . . . . . . . . . . . . . . . .
1.2
Thunderstorm E-field measurements with cosmic rays . . . . . . . . . . . .
1.2.1 Radio detection of cosmic rays & effects of atmospheric electric fields
1.2.2 Cloud Electric Field Imaging (CEFI) . . . . . . . . . . . . . . . . . . .
1.2.3 Computational challenges . . . . . . . . . . . . . . . . . . . . . . . .
Research group . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1
Collaborating groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2
Selected publications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3
Service to society . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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General physics objectives
Solar radiation drives water evaporation, cloud formation and strongly turbulent convection
within clouds. Below freezing temperature, collisions of water and ice particles in this turbulent
flow can separate electric charges on a large scale, see Fig. (1a). The generated electricpotential differences within thunderclouds drive lightning strokes, see Fig. (1b). However, of
this very common phenomenon, there are still many aspects not understood [3].
1) Lightning initiation: Different mechanisms for lightning initiation have been suggested;
we mention here only two. One is that close to conducting objects, such as graupel in clouds,
the fields are enhanced and thus exceed the background field by such an extent that local
break-down is reached. The other mechanism is based on the fact that Ek , the break-down
field strength, does not need to be reached at all, as energetic cosmic-ray air showers directly create run-away electron avalanches [4], called relativistic runaway electron avalanches
(RREA’s) when the electric field exceeds the run-away threshold of Et = 2 × 105 V/m ≈ Ek /10
(at STP), see Box 1. Different combinations of these processes [5, 6] have also been proposed.
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L
Altitude (Km)
12
8
Emax
4
0
- 0.2
a
Et
- 0.1
0.
0.1
Electric Field (MV/m)
0.2
b
Figure 1: a) Sketch of charge and convection structure within an isolated mature thunderstorm driven
by turbulence in the cloud. Picture is taken from Ref. [1]. b) A balloon measurement of the electric field
E in a thundercloud. The run-away threshold voltage, see Box 1, is indicated by the dotted line and is
proportional to air density. Figure is taken from Ref. [2].
Figure 2:
The Low Frequency Array [8] (LOFAR) is a radio telescope that
is primarily build for astronomy observations. The antennas are arranged in
stations where each of the 24 stations
in the core (∅ ≈ 2 km) contains 96
dual-polarized crossed-dipole low-band
antennas (LBAs) operating in the 10–
90 MHz band. The central core, called
Superterp, has a diameter of 320 m and
contains 6 such stations. Each antenna
is sampled at 200 M samples/s. All antennas are equipped with ring buffers
that can store up to 5 seconds of data
for each single antenna thus allowing for
external triggering. Picture is taken from
our PRL-editors choice paper [9]
A related question is whether right after initiation the discharge usually proceeds in a single direction or if it is bi-directional as recently observed for a single event [7].
By mapping the discharge process we will be able to determine if the discharge initiation occurs at several places scattered over a large volume or is instead relatively localized at a single
moment. If the latter is seen it will be a strong indication of the crucial role played by cosmic
rays.
2) Lightning propagation: Once the discharge process has started the first streamers
form. The field at the tip of these electrically conducting finger-like structures is strong enough
to ionize the air right in front and thus it will grow, see Box 1. While growing, the streamers fork,
a process that is not understood. The streamers draw increasing amounts of electric current
that heats their core, converting them to so-called “leaders”. This mechanism is also still not
understood.
By mapping the propagation of the discharge we will be able to determine the systematics of
the forking structure of the discharges.
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Box-1, Lightning physics: nonlinear and far from equilibrium
Friction force (MeV/m)
The initial plasma channels in lightning, called streamers and leaders, grow when free electrons impact on air molecules and ionize
them thereby creating additional free electrons. These electrons
100
are accelerated by the ambient electric field and simultaneously
Ec=26MV/m
slowed down by inelastic collisions with air molecules, giving rise
10
Stable Ek=3.2MV/m
to the dynamic friction force plotted in Fig. (3). At small energies
Run-away
the attachment rate is larger than the ionization rate and the num1
Et=0.2MV/m
ber of free electrons declines fast. When the electric field exceeds
.1
the break-down field strength (Ek =3 MV/m in air at sea level, decreasing linearly with air density at increasing altitude) the mean
.01
electron energy is such that the creation of additional electrons by
impact ionization dominates over electron losses due to attach.001
ment to oxygen, and ionization avalanches are formed.
Another important field strength is the run-away threshold of
E
Figure 3: Dynamic friction of free elec- t ≈ 0.2 MV/m (in air at sea level). For electrons with an entrons in air at sea level as a function of elec- ergy of about 1 MeV the energy gain from the electric field extron energy. Figure adapted from Ref. [10]. ceeds the friction losses, see Fig. (3), and since at this energy the
attachment rate is negligible, the electrons experience run-away.
A possible source for the necessary 1 MeV seed electrons is a
cosmic-ray air shower.
When run-away or break-down occurs, a conducting plasma is formed by the large number of
free electrons. The plasma forms finger-like structures called streamers. Due to their elongated
form, the ambient electric field at the tip is amplified to above break-down values and the structure
grows. In this way the streamers can penetrate into regions where the background field is well
below the break-down field strength Ek .
While propagating, the structure may split into two or more streamers. In time, increasing
amounts of electric current are drawn which will heat the core, increasing the conductivity which
increases the heating even more. The hot conducting channels (temperatures may rise above
5000 K) are called “leaders”. The precise mechanism that converts streamers to leaders is still not
known and we have presented here only a rough sketch of the process. It is known that leaders
with an excess of negative charge (called negative leaders) often proceed in a step-wise fashion.
It is not understood what causes this stepping and this is one of the questions we will address.
Once leaders begin growing they maintain themselves since the flow of charge to the growing
tip will induce an electric current in the base that keeps it heated and thus conducting. To be able
to understand the development of streamers and leaders it is necessary to measure the underlying
electric currents that drive this process.
3) Electric fields in thunderstorms: Lightning is driven by the electric field in the thundercloud. To understand lightning it is thus imperative to have good data on the strength and
orientation of the electric fields.
We have developed a new, non-intrusive method [9] where the electric field in the cloud is
determined from the radio footprint of cosmic-ray air showers as measured at LOFAR.
At each step in the lightning streamer or leader (see Box 1), a sizable current flows in
short time. By the nature of this process, strong linearly polarized radio-frequency pulses are
emitted at meter wavelengths, making LOFAR, see Fig. (2), an exquisitely suited instrument for
measuring them. The polarization direction of the electromagnetic signal is directly related to
the direction of the leader-step. From the data, a 4D-vector map (space, time and also direction
of the step in the leader) will be built to give the most detailed insight into the spatiotemporal
development of the leaders. From the shape of the measured pulse it is possible to extract the
time profile and the length scale over which the current flows.
It is of prime interest to determine the electric fields existing in the same thundercloud in
which a discharge has been measured. Conventionally this is done by launching an electricpage 3 of 9
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Lightning project
field meter attached to a balloon, however, having such a device in the thundercloud certainly
influences inception of lightning discharges. Recently our group has developed a non-invasive
method for determining the electric-field in thunderclouds [9, 11]. This by measuring the radio
footprint from cosmic-ray air showers at the core of LOFAR.
1.1
Lightning Imaging with LOFAR.
Using LOFAR, a recently built new-generation radio-astronomy observatory, we will construct
a novel system to measure the progress of the electric discharge process that precedes the
main lightning return stroke. This will result in a 4-D vector map of the discharge process.
The elementary physics issue concerns the
mechanisms that drive the branching and stepping
process. This process is a combination of three
Cloud
mechanisms: electron multiplication near the tip
of the ionized leaders; space charge effects; and
possible photo-ionization at larger distances which
creates free electrons. The balance among these
mechanisms is poorly understood [12, 13]. This
Stepped leader
physics is reflected in the forking structure of the
i+1
stepped leaders (see Fig. (4)). Further insight can
1
be obtained by analyzing the statistics of the mea2
sured angles between different steps, the number
3 •••
of branches and their relative angles.
Ground
Apart from the pure physics perspective, the
branching process is also of interest from the perFigure 4: Schematic indication of a spective of lightning protection [12, 14] since this
stepped leader development. A typical determines the effective cross section of the dislength for a single step is 10 to 50 m. Fig- charge process which is an important input in
lightning-protection calculations.
ure adapted from Ref. [13].
Another issue of interest is the time-dependence
of the charge flows in a single step of the lightning
discharge. Measurements [15, 16] of radio emission indicate that the discharge proceeds with
a speed of about half the light velocity. Following arguments similar to those we have used for
the interpretation of the radio-signal emitted by cosmic rays [17], the polarization of the signal can be used to extract the orientation of each leader step while the pulse shape provides
information on the time dependence of the current. With LOFAR we combine polarization sensitivity with a high temporal resolution making it unique. This combination will help to unravel
the individual steps.
1.1.1
Relation to state-of-the-art radio detection of lightning
There are several Lightning Mapping Arrays (LMA) [18] in operation that detect radio pulses
emitted in the discharge process. These allow for an accurate mapping in time and space
of each step in the discharge by using the time-of-arrival (TOA) method, see Fig. (5). In this
method the timing of the signals in a number of distant antennas is used to reconstruct the
position of the source. This has resulted in detailed maps of leader development that have
contributed much to a better understanding of the physics of lightning. However, no information
is obtained about the charge flow between the dots in Fig. (5) which is necessary to grasp the
physics at the microscopic level.
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KVI-CART
Lightning project
Figure 5:
Following
extensive intra-cloud (IC)
activity (colored blue), a
cloud-to-ground (CG) flash
occurred, initiated by the
stepped leader whose radio source locations are
shown in orange. The time
and position of the event
is determined using the
time-of-arrival (TOA) method
deploying a series of distant
antennas. This has resulted
in detailed maps of leader
developments. Figure taken
from Ref. [3]
1.1.2
Proposed project
The data accumulation (data pipeline) will be very similar in structure to the one that is presently
in operation for measuring cosmic-ray air showers, with some noticeable differences. For the
lightning observations we need to include antenna stations that are many kilometers away from
the core. Knowing the LOFAR architecture this will not be much of an issue by itself, however,
an accurate timing calibration will necessary. A second point to consider is that a trigger needs
to be developed to read out the memory of each antenna (TBB, Transient Buffer Board) that
contains the digitized signal of the previous 5 seconds. The radio signal of the lightning return
stroke (the main lightning flash) can be used as a trigger to freeze the TBB memory and read
out the radio signals emitted in the 5 seconds preceding the big flash that contains the physics
we are after. In the new LOFAR-Lightning pipeline all these features have to be combined.
The polarization direction of the signal lies in the plane spanned by the emitting current
and the direction of the radiation. This well known fact from electromagnetism has proven to
be a very powerful basis for the interpretation of radio emission from cosmic-ray induced air
showers [17, 19, 9]. From the preliminary data we know that the lightning pulses are strongly
polarized where the polarization direction varies strongly for the individual peaks that form the
total pulse. Combining the intensity and polarization information from many different antennas
at different viewing angles with respect to the discharge, the time structure and direction of each
step can be determined. This forms the input for building a 4-D vector map of the complete
discharge current showing for every step the position in space as well as the direction of the
electric current and therefore giving detailed insight into the spatiotemporal development of the
leaders (see Fig. (4)). The shape of each pulse is related to the time-dependence and the
distance over which the current flows.
1.1.3
Computational challenges
The time trace of each antenna is densely packed with partially overlapping pulses of varying
strength so we are operating close to the confusion limit. The strength and polarization of a
pulse in the time trace will depend on the viewing angle to the source. Each pulse may (will)
have a different source location where the sources could be separated by any distance between
10 m to a few km. In a neighboring antenna the relative position of the various peaks will thus
be different as it is governed by the distance of the antenna to the sources. For the imaging it is
important to trace the pulses coming from the same source in all antennas to be able to make
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an accurate Time of Arrival (ToA) reconstruction to determine the 3-D location of the source as
well as time of emission. The polarization of the signal gives spatial orientation of the emitting
current. The fine-structure (separation of positive and negative peak) are measure of the step
length. We are still searching for an efficient algorithm to meet this challenge.
Another issue is to find the most efficient way to display the final results. Projection on
different planes is the first thing to do and let the picture unfold in time, like a lightning movie.
The picture will be rather dense. Are there better ways to get insight in the physics by plotting
angle changes of the progress, opening angles between forkings, intensity of the current?
1.2
Thunderstorm E-field measurements with cosmic rays
Very recently we have developed a non-invasive method for determining the electric-field in
thunderclouds [9, 11] by measuring at the core of LOFAR the radio footprint from cosmic-ray
air showers. The obtained resolution of the radio footprint is sufficient to deduce the electric
currents induced in the shower plasma by the ambient electric field. Essential for being able
to do this is the very detailed understanding of the mechanisms behind radio emission from air
showers [20] as well as having a good calibration of the LOFAR antennas.
1.2.1
Radio detection of cosmic rays & effects of atmospheric electric fields
Cosmic rays are energetic particles that have their source outside the Earth. At low energies,
below 1010 eV, they are ejected by the Sun. At higher energies, up to about 1017 eV, they are
probably ejected by supernova explosions within our own Galaxy and at even higher energies
they are created by even more energetic extra-galactic events.
When a high-energy cosmic ray with an energy of, say 1017 eV, impinges on the atmosphere
it will, through collisions with air molecules, create a cascade of secondary particles called
an extensive air shower. Since electrons and positrons are the lightest particles that can be
created, they are overwhelmingly abundant in the air shower. These light particles are deflected
in opposite directions by the Lorentz force induced by the geomagnetic field. This creates a
macroscopic current in the atmosphere transverse to the direction of the shower, ~v , and the
~ which is the main driving term for radio emission which is polarized along the
magnetic field B
~ direction [17].
induced current, in the ~v × B
~ the total force on the electrons is instead F~ =
In the presence of a large electric field E
~ + E).
~ For E
~ > 10 kV/m it considerably changes the direction of the induced current
q(~v × B
and thus the polarization of the radio waves. For the interpretation one should distinguish
~ parallel, Ek , and perpendicular, E
~ ⊥ , to the shower direction. The latter
the component of E
changes the direction of the induced current as well as its magnitude. The change in direction is
observed through a deviation of the polarization direction from the fair weather expectation [9].
The height dependence of the electric current is directly reflected in the intensity of the radiation as function of distance to the shower. Under fair weather conditions the electric current
is proportional to the number of electrons. This lies at the basis of the analysis presented
in Ref [20] where we showed that from the radio emission the shower properties can be determined with an accuracy that competes with the method of fluorescence emission that is
currently used most. Since atmospheric electric fields depend strongly on height the strength
of the height-dependence of the induced current will change and can be unfolded from the
radio footprint [9].
1.2.2
Cloud Electric Field Imaging (CEFI)
Following up on the proof of concept [9] imaging of the thunder-cloud electric field imaging
(CEFI) should be performed by combining the observations of several cosmic ray taken within
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a narrow time-span. Since the cosmic rays come at random angles this will greatly increase the
accuracy of the field measurement. Errors will cancel because of the random sampling of the
cloud. A complicating factor will be that clouds are highly dynamic. One has to determine the
appropriate time and length scales for its variability. This probably can be done from the data
itself by checking the consistency of the results for two events where the angle of incidence is
similar.
Important to be able to perform CEFI is thus to increase the detection efficiency of cosmic rays at LOFAR to allows for reducing the time interval between two events. This can be
achieved in two ways and both should be followed. One is to increase the area covered by
scintillator plates that act as a trigger for LOFAR cosmic-ray observations. The other, more
promising method, is to lower the threshold energy. As the flux is inversely proportional to energy to the third power, lowering the energy strongly increases the rate of events. At too low
energies the radio-signal strength will however be too small to detect so one should find an
optimum.
The data on the distribution of the charges should be coupled to the structure of the cloud.
A possibility is for example to install a dedicated cloud-laser [21]. This we will be investigated
in collaboration with the Dutch weather service (where we have contacts already).
In a later stage, when the mapping has been proven, it will be most interesting to combine
these measurements with those of the discharge process for a single cloud.
Simulations [11] show that by extending the observations of cosmic ray footprints to lower
frequencies the sensitivity to the components of the electric field is enlarged. It is thus very
advantageous to extend the measurements to this frequency range. Because of the relevant
length scales in the shower one does not gain by going to even lower frequencies.
1.2.3
Computational challenges
At present there does not exist a direct mapping to extract from the radio footprint the atmospheric electric field. The procedure followed it to make an electric field configurations, take
these as an input in a cosmic-ray air shower simulation that yields a radio footprint. An extensive search is performed on possible field configurations and the one that compares best with
the data is used. The complicating facts are two fold. Firstly, a single calculation of a radio footprint is very computer intensive, about 1 day CPU time. Secondly, the air-shower calculation is
based on Monte-Carlo techniques to simulate its evolution. This means that when varying the
field configuration also the air-shower evolution will change which will also affect the footprint.
An efficient approach to control these issues is being looked for.
2
Research group
2.1
Collaborating groups
Prof. Stijn Buitink (Vrije Universiteit Brussel).
Prof. Ute Ebert (CWI & Eindhoven)
Prof. Heino Falcke (Nijmegen & Bonn & Astron & Nikhef)
2.2
Selected publications
(i) Coherent Cherenkov Radiation from Cosmic-Ray-Induced Air Showers.
K.D. de Vries, A.M. van den Berg, O. Scholten, and K. Werner, Phys. Rev. Lett. 107,
061101 (2011); arXiv:1107.0665.
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(ii) Method for high precision reconstruction of air shower Xmax using two-dimensional radio
intensity profiles.
S. Buitink, et al. [O. Scholten], Phys. Rev. D 90, 082003 (2014); arXiv:1408.7001.
(iii) Probing the radio emission from air showers with polarization measurements.
A. Aab, et al. (The Pierre Auger Collaboration) [O. Scholten], Phys. Rev. D 89, 052002
(2014); arXiv:1402.3677.
(iv) Prediction of Lightning Inception by Large Ice Particles and Extensive Air Showers.
Anna Dubinova, Casper Rutjes, Ute Ebert, Stijn Buitink, Olaf Scholten, and Gia Thi Ngoc
Trinh Phys. Rev. Lett. 115, 015002 (2015).
(v) Probing Atmospheric Electric Fields in Thunderstorms through Radio Emission from CosmicRay-Induced Air Showers.
P. Schellart, Gia Thi Ngoc Trinh, et al. (O. Scholten) Phys. Rev. Lett. 114, 165001 (2015);
arXiv:1504.05742.
2.3
Service to society
First of all, we address fascinating scientific questions in an interdisciplinary project. The general public and especially high-school pupils are usually fascinated with spectacular phenomena like thunder and lightning which is central to this proposal. This we see in the many articles
in newspapers and even a TV appearance, see [23], that were inspired by our work. This general public interest can be triggered even more by developing a special user-friendly web-based
interface to view recent lightning discharges. It will be equipped with a module that teachers
can use in the classroom to teach high school students the basics of lightning and let them
create their own movies of lightning discharges.
As mentioned in the proposal, see also Refs. [12, 13, 14], a better understanding of the
branching and stepping process in lightning leaders will lead to a better understanding of its
effective cross section, the lateral distance over which the discharge is attracted to conducting
bodies, and thus improved modeling of lightning protection.
References
[1] M. Stolzenburg and T.C. Marshall, Charge Structure and Dynamics in Thunderstorms, Space Sci.
Rev. 137, 355 (2008).
[2] M. Stolzenburg et al. , Electric field values observed near lightning flash initiations, Geophys.
Res. Lett. 34, L04804 (2007).
[3] J.R. Dwyer and M.A. Uman, Phys. Rep. 534, 147 (2014).
[4] A.V. Gurevich, G.M. Milikh, R. Roussel-Dupre, Runaway electron mechanism of air breakdown
and preconditioning during a thunderstorm, Phys. Lett. A 165, 362 (1992); L.P. Babich, et al. ,
New data on space and time scales of a relativistic runaway electron avalanche for thunderstorms
environment: Monte Carlo calculations, Phys. Lett. A 245, 460 (1998); G. Milikh, R. RousselDupre, Runaway breakdown and electrical discharges in thunderstorms, J. Geophys. Res. 115,
A00E60 (2010); J.R. Dwyer, The relativistic feedback discharge model of terrestrial gamma ray
flashes, J. Geophys. Res. 117, A02308 (2012).
[5] A. Gurevich, A. Karashtin, Runaway Breakdown and Hydrometeors in Lightning Initiation,
Phys. Rev. Lett. 110, 185005 (2013).
[6] Anna Dubinova, Casper Rutjes, Ute Ebert, Stijn Buitink, Olaf Scholten, and Gia Thi Ngoc
Trinh, Prediction of Lightning Inception by Large Ice Particles and Extensive Air Showers.,
Phys. Rev. Lett. 115, 015002 (2015).
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[7] Joan Montanyà, Oscar van der Velde, and Earle R. Williams, The start of lightning: Evidence of
bidirectional lightning initiation, Nature Scientific Rep.5, 15180 (2015).
[8] M. P. van Haarlem, et al. , A & A 556, A2 (2013); arXiv:1305.3550; LOFAR Wikipedia page.
[9] P. Schellart et al. , Probing Atmospheric Electric Fields in Thunderstorms through Radio Emission
from Cosmic-Ray-Induced Air Showers, Phys. Rev. Lett. 114, 165001 (2015); arXiv:1504.05742.
[10] G.D. Moss, et al. , Monte Carlo model for analysis of thermal runaway electrons in streamer tips
in transient luminous events and streamer zones of lightning leaders, J. Of Geophys. Res. 111,
A02307 (2006).
[11] G. Trinh, O. Scholten, et al. , Influence of Atmospheric Electric Fields on the Radio Emission
from Extensive Air Showers., Accepted for publication in Phys. Rev. D; arXiv:1511.03045.
[12] P. Lalande, V. Mazur, A Physical Model of Branching in Upward Leader, J. Aerospace Lab. 5,
AL05-07 (2012);
M. Vargas, H. Torres, On the development of a lightning leader model for tortuous or branched
channels Part II: Model results, Journal of Electrostatics, 66, 489 (2008).
[13] Wei Shi, Qingmin Li, and Li Zhang, A stepped leader model for lightning including charge distribution in branched channels, J. App. Phys., 116, 103303 (2014).
[14] Y.Z. Xu and M.L. Chen, A 3-D Self-Organized Leader Propagation Model and its Engineering
Approximation for Lightning Protection Analysis, IEEE trans. on power delivery, 28, 2342 (2013)
and many other similar references.
[15] J. Jerauld, et al. , Electric and magnetic fields and field derivatives from lightning stepped leaders and first return strokes measured at distances from 100 to 1000 m, J. Geophys. Res., 113,
D17111 (2008).
[16] J. Howard, et al. , Measured close lightning leader-step electric-field-derivative waveforms, J.
Geophys. Res. 116, 2156 (2011).
[17] O. Scholten, K. Werner, and F. Rusydi, A Macroscopic Description of Coherent Geo-Magnetic
Radiation from Cosmic Ray Air Showers, Astropart. Phys. 29, 94 (2008), arXiv:0709.2872;
Klaus Werner and Olaf Scholten, Macroscopic Treatment of Radio Emission from Cosmic Ray Air
Showers based on Shower Simulations, Astropart. Phys. 29, 393-411 (2008), arXiv:0712.2517;
K. Werner, K.D. De Vries, O. Scholten, A Realistic Treatment of Geomagnetic Cherenkov Radiation from Cosmic Ray Air Showers, Astropart. Phys. 37, 5 (2012); arXiv:1201.4471.
[18] Some links to Lightning Mapping Array, Oklahoma LMA; SPORT; New Mexico; Ebro Valley; J.D.
Hill, et al. , Correlated lightning mapping array and radar observations of the initial stages of three
sequentially triggered Florida lightning discharges, J. of Geoph. Res.: Atm 118, 8460 (2013).
[19] P. Schellart, et al. , Polarized radio emission from extensive air showers measured with LOFAR,
J. Cosm. Astrop. Phys. 10, 014 (2014); arXiv:1406.1355.
[20] S. Buitink, et al. , Method for high precision reconstruction of air shower Xmax using twodimensional radio intensity profiles., Phys. Rev. D 90, 082003 (2014); arXiv:1408.7001.
[21] see for example link to ceilometer.
[22] S. Nijdam, et al. , Streamer discharges can move perpendicularly to the electric field, New J. of
Phys. 16, 103038 (2014)
[23] Science News, April 23, 2015; Nature News, April 23, 2015; APS Focus, April 24, 2015; see
https://www.kvi.nl/~scholten/media.pdf for a more complete overview.
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