# Lightning Interferometry with the Long Wavelength Array
## 1 Introduction  
Interferometers have been used quite successfully to study lightning since the 1970s [1, 2, 3]. These instruments proved to be exceptional tools for the study of lightning due to (1) their ability to capture the whole lightning event, rather than merely the portion of lightning exiting a cloud; and (2) their excellent temporal resolution and relatively good spatial resolution, which is capable of resolving fast lightning processes propagating at large fractions of the speed of light [4, 5]. While the early interferometers were narrowband arrays where the correlation was performed with hardware mixers, the advent of faster digitizers enabled the construction of digital broadband interferometers that used digital Fourier techniques to interfere with the signals. These digital broadband interferometers were able to produce even more detailed pictures of lightning than their narrowband counterparts, especially once their memory buffers were large enough to hold a continuous record of an entire flash [6, 7, 8]. The broadband digital interferometers proved to be affordable and easy to build, resulting in many new scientific findings by multiple research groups [9, 10, 11, 12, 13, 14, 15, 16, 17]. Nearly all lightning interferometric studies performed to date have used relatively sparse arrays containing only a handful of antennas. Consequently, lightning at microsecond timescales has been universally modeled as a single source smaller than the angular resolution of the array (a point source). Sparse arrays are a limitation primarily drivenby cost and complexity; larger arrays are certainly possible and capable of imaging non-point-like sources, as demonstrated by the astrophysical community [18]. In particular, two radio telescopes already exist that use an appropriate frequency range and configuration for the study of lightning: the Low Frequency Array (LOFAR) and the Long Wavelength Array (LWA). LOFAR is a very high frequency (VHF) radio telescope located in the Netherlands and surrounding countries, composed of 40 stations in the Netherlands alone, where each station contains 48 high-band (110-250 MHz) and 96 low-band (30-80 MHz) antennas [19]. LOFAR has been used to detect and map lightning VHF sources using the low-band antennas [20]. The many-kilometer baselines between stations were leveraged to be able to map VHF source locations in three spatial dimensions and time. Further, in [PERSON] et al. [21], [PERSON] et al. [22] and [PERSON] et al. [23], VHF lightning sources were imaged without using a reference feature, with the imaging performed using beam steering. While it should be possible to detect and locate multiple simultaneously emitting lightning VHF sources with LOFAR, all the existing studies model each observation window as a single point emitter [24]. The LWA is a VHF radio telescope designed to study a wide variety of VHF sources, most, but not all, of which are extra-terrestrial [25; 26]. Early studies with the LWA (specifically LWA1, located on the Planes of Agustin, NM, near the Very Large Array) successfully imaged lightning sources with the narrowband transient modes of the array [27; 28; 29]. However, the transient observing modes available in LWA1 only allowed for either 75 kHz of long-duration or 61 ms of full-band observations [25]. This greatly limited the utility of LWA1 in studying lightning; the very narrow-band observations were not capable of achieving the time resolution desired for lightning studies, while the full-band observation duration was not long enough to capture even the majority of a lightning flash. These limitations in lightning observation were intentionally rectified with the advent of the LWA station at Sevilleta (LWA-SV); with the inclusion of a new transient observation mode capable of recording 39.6 MHz of bandwidth for up to 5 s duration, the LWA-SV is capable of imaging multiple and extended lightning sources at sub-microsecond timescales [30; 31].