# Lightning Interferometry with the Long Wavelength Array
## 4 Summary and Discussion
As interferometer observations increase in sensitivity and resolution, the single point radiator model becomes less and less accurate; this is shown in Figure 7. Here, statistics were computed for the 16 ms period of time between Figure 6a,b, although the results are very similar at other times in the flash. The solid line shows the probability that a source is the brightest in its integration window; for sources below 0 dB\({}_{\rm GB}\), this happens less than 25% of the time. For very sparse arrays, the situation is even worse since, if there is another source close in power, the interference will make location unlikely, as illustrated in Figure 2g. The probability of there not being a second source close in power is indicated by the dotted line in Figure 7, specifically the probability that a source is at least 3 dB brighter than any other sources in the same integration window. In this study, had we not used a multiple-source model to deconvolve the dirty images, significantly less detail would be seen in the lower-power portions of the flash, such as the positive leader tip. Ultimately, using a single source model for the VHF emission from a lightning flash is only valid for the brighter VHF sources. The improved sensitivity and multi-source capability of the LWA open up a new class of lightning observations. As an example of these abilities, we have provided observations of positive leaders in an IC flash. The streamer zone of this positive leader tip radiated at approximately the same brightness as the galactic background and propagated at an unusually quick \(9.4\times 10^{4}\) m/s. The fact that emissions such as this have not been seen in the past is unsurprising, as the received signals would be indistinguishable from noise when measured using a single antenna. The location of these positive leader tip sources is further hampered because sources this faint rarely appear isolated in time. VHF emission on positive leader channels has been routinely observed, but, in almost all cases, the emission was due to needles [36; 52; 53], which have been interpreted as being caused by negative breakdown [14; 39]. Very bright VHF emission from positive streamers, termed fast positive breakdown, has been seen at the beginning of some flashes [10; 13; 54; 55]. Similar fast positive breakdown has also been been reported on lightning channels in the middle of a flash immediately following ground attachment or K/dart leaders, caused by a large potential difference between the leader tip and the cloud [33]. VHF emission from the tips of propagating positive leaders is much more rarely observed. [PERSON] et al. [56] performed VHF interferometer observations of a very nearby positive leader to ground. The VHF emission from this leader tip was impulsive and comparably bright to the negative leader in the same flash--much brighter than the positive leader tip in this study, but substantially less bright than fast positive breakdown. The positive leader also propagated faster than the leader observed in this study, at \(2\times 10^{6}\) m/s as it reared the ground. The authors estimated that the electric field was the positive streamer region \(0.9E_{k}\), substantially higher than that needed for steady positive leader propagation. The leader propagation speed is dependent on the potential at the tip of the leader [57]. Even so, it is usually assumed that the field in the streamer zone is uniform and close to the stability field for positive streamer propagation [58]. The observations indicate that when the tip potential is higher, this may not be true, leading to VHF emission being produced. From this, we surmise that the tip potential of the positive leader in this study was higher than average, possibly because the observations were made during the active phase of the flash [59], when the negative leader maintained higher conductivity in the channel [4; 60], or because the leader was propagating in a higher than average electric field.