Time resolved 3D interferometric imaging of a section of a negative leader with LOFAR

Abstract

We have developed a three dimensional interferometric beamforming technique for imaging lightning flashes using very-high frequency (VHF) radio data recorded from several hundred antennas with baselines up to 100 km as offered by the Low Frequency Array. The long baselines allow us to distinguish fine structures on the scale of meters, while the large number of antennas allow us to observe processes that radiate at the same intensity as the background when using a time resolution that is close to the impulseresponse time of the system, 100 ns. The new beamforming imaging technique is complementary to our existing impulsive imaging technique. We apply this new tool to the imaging of four stepped negative leaders in two flashes. For one flash, we observe the dynamics of corona bursts that are emitted in the stepping process. Additionally, we show that the intensity emitted in VHF during the stepping process follows a power law over 4 orders of magnitude in intensity for four leaders in two different lightning storms.

Interferometric imaging of Intensely Radiating Negative Leaders

“…With the improved TRI-D formalism, using the data from close to 200 LOFAR antenna-pairs, we can resolve the internal structure of an IRNL. We see that IRNLs are truly completely distinct from normal negative leaders, as a typical negative leader has an almost point-like propagating tip that emits small ( < 5 m) corona bursts in a wellordered fashion [14,15]. As shown in this work, however, an IRNL propagates by creating many corona bursts over a propagating surface of sometimes a square kilometer in size.…”

“…a corona burst) corresponds to an upward current producing a positive pulse for this source location with respect to the broadband antenna (to the north). As argued in [14], a corona burst is followed by a number of streamers that gradually slow-down with limited VHF emission, even though current keeps flowing. In the broadband antenna this gives rise to a broad negative pulse.…”

“…the gain and phase shifts introduced by the antenna electronics that depend on the incoming direction of the radio pulse. This allows us to alleviate the condition that the antennas have to be placed in a relatively small angular range as had to be imposed on the previous version of the TRI-D imager [14]. Even though the formalism is written as a chi-square optimization of the received pulse (in amplitude and polarization) from a point source, the final result is expressed as a weighted coherent sum of the pulses measured in all antennas, very similar to what is obtained in interferometry.…”

“…For reference, note that this impulsive imager has no difficulty mapping many (at least up to 30) simultaneous normal negative leaders. For that reason we use for this work the recently developed time-resolved interferometric 3-dimensional (TRI-D) imaging [14] procedure. In TRI-D the signals from hundreds of antennas are coherently added (beamformed) for each voxel (volumetric pixel) in the imaged volume.…”

“…The main draw-back of the TRI-D imager is that it is much more computing intensive than the impulsive imager. In addition, the TRD-D approach described in our previous work, [14], had another draw back in that the effects of the angle dependent gain and phase-shifts due to the antenna and its electronics (antenna function) were not taken into account in the imaging procedure. This implies that antennas within a relatively narrow viewing cone can be included only in the analysis.…”