Relativistic electron beams

Introduction Conclusions References


even though transient narrow beams of
Published by Copernicus Publications on behalf of the European Geosciences Union.
. A meso-scale convective system is located over France and reaches an area of ∼400×400 km 2 at UTC on 31.08.2008 as inferred from the cloud top infrared brightness temperature. Many negative lightischarges (circles) cluster in the ∼12 km (Tmin = −64 C • ) high convective core of the thunderstorm sured by some positive lightning discharges (crosses). One particular positive lightning discharge (red cross) 52:59.524 UTC causes a sprite discharge above the thundercloud. The size of the red cross indicates the overed by individual sprite elements. 13 Fig. 1. A meso-scale convective system is located over France and reaches an area of ∼400 × 400 km 2 at 01:45 UTC on 31 August 2008 as inferred from the cloud top infrared brightness temperature. Many negative lightning discharges (circles) cluster in the ∼12 km (T min = −64 C • ) high convective core of the thunderstorm surrounded by some positive lightning discharges (crosses). One particular positive lightning discharge (red cross) at 01:52:59.524 UTC causes a sprite discharge above the thundercloud. The size of the red cross indicates the area covered by individual sprite elements. relativistic electrons are now routinely observed in space (Briggs et al., 2011;Cohen et al., 2010;Carlson et al., 2009;Dwyer et al., 2008). Relativistic electron beams are occasionally associated with sprites as inferred from radio remote sensing with low frequency radio signals from ∼40-400 kHz . These radio signals are analyzed here in detail to determine the height of relativistic electron beams above thunderclouds and to determine the associated charge transfer through the middle atmosphere.

The mesocale convective system, lightning discharges and sprites
Thunderstorms and lightning activities in southern Europe have recently attracted special interest because numerous sprites are observed with video cameras above thunderclouds which regularly develop during the summer months from the beginning of May to mid-September (Soula et al., 2009;Neubert et al., 2008  . Two consecutive bursts of electromagnetic radiation in the frequency range ∼40-400 kHz occur at ∼4.4 ms and ∼8.9 ms (bottom panel). These bursts are thought to be caused by relativistic electron beams above the thundercloud.
photometer located at Pic du Midi and vertical electric field recordings with a wideband digital radio receiver (Füllekrug, 2010) located near Bath in South-West England of the United Kingdom (51.35 • N, 2.29 • W). The sprite causing positive cloud-to-ground lightning discharge causes a strong burst of electromagnetic radiation which spans the entire frequency range of the radio receiver. A large fraction of this electromagnetic energy is deposited in the narrow frequency range from ∼5-16 kHz which is typical for cloud-to-ground and intra-cloud lightning discharges  as a result of the large scale quasi-continuous flow of current. Two much smaller consecutive bursts of electromagnetic radiation occur ∼4.4 ms and ∼8.9 ms after the lightning discharge. They do not deposit a large fraction of their electromagnetic energy in the frequency range from ∼5-16 kHz which is untypical for conventional lightning discharges. The first radiation burst coincides with the sprite luminosity at ∼4.4 ms. The second radiation burst shortly follows the sprite luminosity after ∼4.5 ms . Both radiation bursts are thought to be caused by electron beams above the thundercloud resulting from relativistic runaway breakdown .

Relativistic electron beams
Seven similar untypical broadband bursts of electromagnetic radiation following sprite-producing lightning discharges have been collected during sprite observations in the years 2008 and 2009 (Table 1). In these two years, a total of ∼140 sprite observations have been examined such that the occurrence rate of the electromagnetic radiation bursts is ∼5 %. These bursts all occured ∼2-9 ms after sprite-producing positive cloud-to-ground lightning discharges. The average spectrum of the seven bursts is relatively flat at frequencies <40 kHz when compared to the average spectrum of their parent lightning discharges (Fig. 4, left). This is consistent with simulations of virgin air high frequency breakdown. The spectral amplitudes of the broadband electromagnetic radiation bursts are as small as ∼100 µVm −1 Hz −1/2 in the frequency range from ∼40-400 kHz, but still ∼1-2 orders of magnitude above an average background spectrum which is recorded 10 ms prior to the causative lightning discharges for reference (Fig. 4,left). This background spectrum exceeds the ultimate sensitivity limit of the wideband digital radio receiver ∼1-2 µVm −1 Hz −1/2 by ∼1 order of magnitude ( Fig. 4, right). Superimposed on the sensitivity limit of the receiver are the omni-present low-frequency, or longwave, radio transmitters in this frequency range, e.g., the United Kingdom radio clock at 60 kHz (the former Rugby MSF signal, now transmitted from Anthorn), France Inter at 162 kHz, Europe 1 at 183 kHz, and BBC radio 4 at 198 kHz. These radio transmitters have a typical narrow bandwidth of ∼10-12 kHz and they exhibit similar spectral amplitudes when compared to the observed broadband (∼40-400 kHz) radiation bursts from electron beams. Numerical simulations of relativistic electron beams above thunderclouds predict theoretically broadband bursts of electromagnetic radiation with a flat spectrum following spriteproducing lightning discharges  in agreement with our experimental observations. These model calculations solve kinetic particle equations on the microscopic scale and Maxwell's equations on the macroscopic scale simultaneously. The causative lightning continuing current drains charge from the thundercloud which exposes the area above the thundercloud to a quasi-static electric field. When this electric field exceeds the runaway breakdown threshold and the continuous flux of high-energy secondary cosmic ray electrons (Daniel and Stephens, 1974, Fig. 2) supplies sufficient energetic seed electrons (Roussel-Dupré et al., 1998, p. 920, eq. in right col.), an electron avalanche above the thundercloud is initiated which quickly develops into an upward propagating relativistic electron beam. The beamed electrons partially discharge the lightning electric field and thereby gain a mean energy of ∼7 MeV with a spread of ∼6 MeV while carrying a total charge of ∼−10 mC upward as inferred from the comparison between the measured and simulated electron beam spectrum (Fig. 4, left and right). Impulsive changes of this downward Table 1. Observations of several electron beams associated with sprites. The date, time, and location of the causative lightning discharges are reported by the French lightning detection system Météorage. The distances between the lightning discharges and the wideband digital radio receiver in South-West England vary between ∼490-1060 km. The electromagnetic radiation bursts from the lightning discharge and the consecutive electron beam exhibit time delays from ∼2-9 ms. The time delays between the direct wave and the sky wave from the electron beam can only be determined for distances up to ∼500 km as a result of the larger signal to noise ratio of the electromagnetic recordings. The observed time delays from ∼25-92 µs indicate that all the electron beams are located at heights between ∼16-72 km, well above the top of the thundercloud at ∼12 km (Fig. 1). The last listed event at 01:29 UTC on 31 August was not associated with any sprite and it indicates that relativistic electron beams may also occur independently of sprites. The full range of techniques described in the methodology section was used during observations from 00:00   (Table 1) is relatively flat at frequencies <4 ne) when compared with the average spectrum of their causative lightning discharges (blue line). Th nd electron beam spectra are ∼1-2 orders of magnitude larger than the average background spectr ne) which is recorded 10 ms prior to the causative lightning discharges for reference. Right: Th om the simulated electron beam is relatively flat at frequencies <40 kHz (red line) when compare  (Table 1) is relatively flat at frequencies <40 kHz (r compared with the average spectrum of their causative lightning discharges (blue line). The lightni on beam spectra are ∼1-2 orders of magnitude larger than the average background spectrum (bla h is recorded 10 ms prior to the causative lightning discharges for reference. Right: The radiati simulated electron beam is relatively flat at frequencies <40 kHz (red line) when compared with  (Table 1) is relatively flat at frequencies <40 kHz (red line) when compared with the average spectrum of their causative lightning discharges (blue line). The lightning and electron beam spectra are ∼1-2 orders of magnitude larger than the average background spectrum (black line) which is recorded 10 ms prior to the causative lightning discharges for reference. (b): The radiation from the simulated electron beam is relatively flat at frequencies <40 kHz (red line) when compared with the simulated spectrum of the causative lightning discharge (blue line). The simulated spectra are ∼2-3 orders of magnitude larger than the sensitivity limit of the wideband digital radio receiver ∼1-2 µVm −1 Hz −1/2 which is inferred from time intervals without any bursts of electromagnetic radiation (black line). Superimposed on this ultimate reference spectrum are the omni-present low frequency, or long wave, radio transmitters, the strongest of which is here the BBC Radio 4 transmitter at 198 kHz, which exhibits spectral amplitudes comparable to the measured and simulated electron beam. current from the electron beam ∼3 × 10 −3 Am −2 , i.e., its displacement current, results in the observed bursts of electromagnetic radiation a few ms after the causative lightning discharge.
The initial lightning discharge and the subsequent electron beam launch electromagnetic waves which can propagate on several paths from the source location to the radio receiver. These propagation paths can be inferred from a detailed analysis of the observed electromagnetic radiation bursts. The burst of electromagnetic radiation from the lightning discharge is composed of two consecutive pulses which are delayed by ∼102 µs (Fig. 5, upper panel) Fig. 5. The burst of electromagnetic radiation from the lightning discharge is composed of two consecutive pulses which are delayed by ∼102 µs (upper panel). The first pulse results from the electromagnetic wave which propagates along the surface of the Earth to the receiver (ground wave). The second pulse results from the electromagnetic wave which is reflected from the ionosphere (sky wave). The burst of electromagnetic radiation from the electron beam is also composed of two consecutive pulses (lower panel). The short time delay of ∼59 µs indicates that the electron beam is located above the thundercloud where it emits an electromagnetic wave which propagates at an angle to the receiver (direct wave).
17 Fig. 5. The burst of electromagnetic radiation from the lightning discharge is composed of two consecutive pulses which are delayed by ∼102 µs (upper panel). The first pulse results from the electromagnetic wave which propagates along the surface of the Earth to the receiver (ground wave). The second pulse results from the electromagnetic wave which is reflected from the ionosphere (sky wave). The burst of electromagnetic radiation from the electron beam is also composed of two consecutive pulses (lower panel). The short time delay of ∼59 µs indicates that the electron beam is located above the thundercloud where it emits an electromagnetic wave which propagates at an angle to the receiver (direct wave).  Fig. 6. The time delay of ∼102 µs between the ground wave and the sky wave from the lightning discharge indicates that the reflecting ionosphere is located at a height of ∼90 km (upper panel). The time delay of ∼59 µs between the direct wave and the sky wave from the electron beam indicates that the electron beam is located at a height of ∼41 km (lower panel). The electron beam does not emit enough photons at visible wavelengths to exceed the sensitivity limit of the charge coupled device chip of the video camera. It is concluded that electron beams above thunderclouds can coincide with sprites but that they independently discharge lightning electric fields above thunderclouds.
18 Fig. 6. The time delay of ∼102 µs between the ground wave and the sky wave from the lightning discharge indicates that the reflecting ionosphere is located at a height of ∼90 km (upper panel). The time delay of ∼59 µs between the direct wave and the sky wave from the electron beam indicates that the electron beam is located at a height of ∼41 km (lower panel). The electron beam does not emit enough photons at visible wavelengths to exceed the sensitivity limit of the charge coupled device chip of the video camera. It is concluded that electron beams above thunderclouds can coincide with sprites but that they independently discharge lightning electric fields above thunderclouds. from the electromagnetic wave which propagates from the lightning discharge to the receiver along the surface of the Earth and is denoted ground wave. The second pulse results from the electromagnetic wave which is reflected from the ionosphere and is denoted sky wave. The time delay between the ground and sky wave determines the ionospheric reflection height (Jacobson et al., 2010) to be ∼90 km for the known distance of ∼571 km between the lightning discharge and the radio receiver as inferred from full wave radio wave propagation simulations with Finite-Difference-Time-Domain (FDTD) modeling. Electromagnetic waves with two or more ionospheric reflections are more strongly attenuated and they are not detected above the background level of the interfering radio transmitters (Smith et al., 2004).
The burst of electromagnetic radiation from the electron beam at ∼4.4 ms is also composed of two consecutive pulses which are delayed by ∼59 µs (Fig. 5, lower panel). The first pulse results from the direct wave which propagates at an angle to the receiver and is denoted direct wave. The second pulse results from the electromagnetic wave which is reflected from the ionosphere and is denoted sky wave. The time delay between the direct wave and the sky wave determines the height of the electron beam to be ∼41 km for the known ionospheric height of ∼90 km (Fig. 6). The electron beam is therefore located well above the thundercloud which terminates at an altitude of ∼12 km. The burst of electromagnetic radiation at ∼8.9 ms emanates from a height of ∼72 km and could result from an independent second electron beam or from the same electron beam. In the the latter case, the second radiation burst is produced by an acceleration of the electrons within the beam, i.e., a displacement current. The electron beam would then propagate with an average velocity of ∼7000 km s −1 (∼0.023c) through the middle atmosphere as inferred from the difference between the two emission heights of ∼31 km and the corresponding time delay ∼4 ms. The heights of two more electron beams associated with other sprite discharges during the same night are determined to be ∼16 km and ∼22 km, both of which are well above the thundercloud.

Discussion
A sensitivity analysis of the height determination methodology reveals that a variation of the observed time delay by ∼1 µs corresponds to a ∼1 km vertical height variation such that the height of the electron beam can be determined in a very accurate way. If the observed time delay is interpreted as a variation in the distance between the source and the receiver, ∼1 µs would correspond to a ∼10 km distance difference, such that the source would be well outside the area of the mesoscale convective system. Another sensitivity analysis was performed to determine the optimum distance between the lightning discharge and the radio receiver which maximizes the signals of the ground and sky wave. This distance was found to be ∼300-400 km such that at larger distances, it becomes increasingly difficult to distinguish the ground and sky wave from the background noise of the interfering radio transmitters. Finally, all lightning discharges with a peak current I p > 30 kA reported by Météorage from 00:00-04:00 UTC on 31 August 2008, have been investigated. Only one additional electromagnetic radiation burst with a flat spectrum from ∼40-400 kHz could be found which is similar to the three examples reported here. The burst follows ∼5 ms after two consecutive positive lightning discharges at 01:29:09.785 and 786 UTC (Table 1). This singular observation is indicative of a nonluminous relativistic electron beam without any sprite occurrence as evidenced by the two video cameras. The preliminary result suggests that lightning discharges may also cause relativistic electron beams above thunderclouds without producing sprites because the relativistic breakdown threshold is only ∼1/10 of the conventional breakdown threshold. It is also possible that the observed electromagnetic radiation bursts are related to secondary sprite processes sometimes observed above thundercloud tops Marshall and Inan, 2007;Moudry, 2003). However, these processes remained sub-visual in the optical observations reported in this work, and it is not clear why such a hypothetical process would emit low frequency electromagnetic radiation while the sprite itself does not. It is interesting to note that the low frequency electromagnetic radiation reported here can be observed in space as a result of its transionospheric propagation (Füllekrug et al., 2011(Füllekrug et al., , 2009) and it may be associated with high frequency electromagnetic radiation (Parrot et al., 2008).

Summary
In summary, relativistic electron beams above thunderclouds have been detected in association with sprites. The electron beams can coincide with sprites but they are then located above the thundercloud and below the main body of sprites. The electron beams can also occur shortly after the sprite luminosity. Both results suggest that non-luminous electron beams and luminous sprites independently discharge lightning electric fields in the middle atmosphere. The observed relativistic electron beams above thunderclouds occur simultaneously with ∼5 % of all optically observed sprites and they are thus very rare. The small number of photons possibly emanating from non-luminous relativistic electron beams and sub-visual streamers may be identified in future studies by combining more sensitive optical observations with interferometric radio recordings to map the low-frequency radio sky above thunderclouds. However, the relativistic electron beams are a new form of impulsive energy transfer between thunderclouds and the middle atmosphere which need to be considered as a novel element in the global atmospheric electric circuit (Rycroft and Odzimek, 2010;Rycroft, 2006;Rycroft et al., 2000).

Methods
The Meteosat Second Generation satellite measures the thermal infrared radiation of the Earth from 10.5-12.5 µm with a Ritchey-Chrétien telescope connected to a HgCdTe detector. This passive imaging radiometer is calibrated with two black bodies at 290 K and 340 K and it scans the full Earth disk every 15 min. The optical camera system on Pic du Midi consists of a wide-angle, low-light, video camera and a high-speed photometer mounted on a pan-tilt unit. The camera is equipped with a 16 mm, f 1.40 lens with a field of view of 31 • and it has an exposure time of 40 ms for one image. The photometer counts photon emissions at a sampling rate of 20 kHz with a time resolution of 50 µs. The camera system is synchronized to UTC with a Global Positioning Satellite (GPS) receiver with an absolute timing accuracy <1 ms. The optical camera system in Sant Vicenç de Castellet is a Watec 902H2 equipped with a 12 mm, f 0.8 lens with a field of view of 31 • and an exposure time of 20 ms. The French lightning detection system Météorage covers southwestern Europe and the western Mediterranean Sea. The radio detection system of 18 sensors reports cloudto-ground lightning discharges with a detection efficiency of ∼90 %, peak current accuracy of ∼5 %, location accuracy <4 km, and timing accuracy <1 ms. The wideband digital radio receiver near Bath in the UK measures the vertical electric field strength by use of a capacitive probe with a sampling frequency of 1 MHz, frequency response from ∼4 Hz to ∼400 kHz, amplitude resolution of ∼35 µV, and timing accuracy of ∼12 ns. Numerical simulations of relativistic electron beams are performed with the transient, multimaterial, compressible, fluid dynamics code CAVEAT which was adapted to solve the electromagnetic equations and their effect on the electron and ion populations in a selfconsistent way on the Los Alamos National Laboratory supercomputer facility. The Finite-Difference-Time-Domain (FDTD) method dynamically solves Maxwell's equations on a spatial grid using equivalent vertical current sources representing the relativistic electron beam and the causative lightning discharge and propagates the full wave radio electromagnetic fields to the wideband digital radio receiver.