Understanding lightning initiation is one of the most important questions in atmospheric physics. The heart of the problem of understanding lightning initiation is that, with decades of electric fields measurements, the observed values of detected electric field are not sufficient to create a leader or a stroke propagating on a kilometer(s) scale [1,2]. This could mean that either our understanding of how lightning is initiated or electric field measurements in thunderstorms are inaccurate.
Traditionally, balloons and planes are used to make such measurements. However, there are limitations to obtaining such observations. At first, sending planes, balloons, and launching rockets inside thunderstorms can be quite difficult and dangerous. Moreover, thunderstorms can span up to square kilometers in size, while the electric field measured by airplanes and balloons spans a small region in comparison. To be in the right location at the right time where the electric field and the potential difference are of a high value can be of low probability. Most importantly, the instrument sent inside a thunderstorm might be responsible for discharging the thunderstorm itself before the electric field has the chance to build up.
When cosmic ray particles interact in the atmosphere, they produce a shower of secondary particles. During thunderstorms, these showers of secondary particles would accelerate or decelerate, depending on their charge and magnitude of the electric field they are propagating through. In principle, studying the effect of the electric field on these secondary particles would allow us to measure and model the electric field in their path indirectly.
The effect of thunderstorms on extensive air showers is a hot topic that has been reported on by multiple experiments starting with the Baksan Group in 1985 [3]. They argued that the effect of the observed cosmic ray variations in the hard and soft components of the shower are due to the electric field in the atmosphere. Several studies and observations have followed (EAS-TOP [4], Mount Norikura [5], GROWTH [6], Tibet AS [7], ARGO-YBJ [8], and SEVAN [9]) reporting on the cosmic ray secondary showers (electrons, gamma rays, muons, and neutrons) variation in correlation with thunderstorms. Most recently, a potential difference of greater than 1 GV inside a cloud (predicted by C. T. R. Wilson 90 years ago [10]) was indirectly measured in a storm by the GRAPES-3 Muon Telescope scientists [11]. Such potential difference is almost an order of magnitude larger than the previously reported maximum potential in balloon sounding (0.13 GV) [11,12].
In this work, we will present the effect of the electric field in thunderstorms on the extensive air showers as observed by the Telescope Array Surface Detector (TASD) single count rate. We will report on the observations in the variation of secondary cosmic-ray single-count rate (See the trigger level discussion in Sec. II). The variations are slow, several kilometers square in area, and move together with the thunderstorm on top of the 700 km 2 detector. In comparison to detectors that are spread over less than km 2 in area (i.e., [6]), it is unclear if the gamma ray emission ceases when the thunderstorm disappears, or when the gamma ray source moves away from the detectors observing the rate variation, as the thunderclouds move. We will attempt, to report on this question, for the first time, using a large area coverage of 700 km 2 . Moreover, we will attempt to interpret this variation, by simulating the effect of the electric field in thunderstorms using multiple simple models. The corresponding increase and decrease of the rate variation in correlation with these models is reproduced and discussed.
The Telescope Array (TA) detector is located in the southwestern desert of the State of Utah about 1400 m above sea level. Currently it is the largest Ultrahigh Energy Cosmic Ray (UHECR) experiment in the Northern Hemisphere. The TA detector is comprised of Surface Detectors (SDs) surrounded by three Fluorescence Detectors (FDs). The main goal of the TA detector is to explore the origin of UHECRs using their energy, composition, and arrival direction. The FD, which operates on clear moonless nights (approximately 10% duty cycle) provides a measurement of the longitudinal profile of the Extensive Air Shower (EAS) induced by the primary UHECR, as well as a calorimetric estimate of the EAS energy. The SD part of the detector, with approximately 100% duty cycle, provides shower footprint information including core location, lateral density profile, and timing, which are used to reconstruct shower geometry and energy.
The surface detector utilizes plastic scintillators to observe the EAS footprint produced by primary cosmic ray interactions in the atmosphere. Plastic scintillators are sensitive to all charged particles. The surface detector array part of the TA experiment, is composed of 507 scintillator detectors on a 1.2 km square grid covering 700 km 2 in area shown in Fig. 1. Each surface detector houses two layers of plastic scintillator. Each layer of scintillator has an area of 3 m 2 and a thickness of 1.2 cm. Each plastic scintillator slab has grooves that has 104 WaveLength-Shifting (WLS) fibers running through them collecting light into the photomultiplier tubes (PMTs) they are bundled and connected to. These scintillator layers are separated by a 1 mm stainless-steel plate. The scintillator layers and stainlesssteel plate are housed in light-tight, 1.5 mm thick box made of grounded stainless steel (the top cover is 1.5 mm thick, with a 1.2 mm thick bottom) under an additional 1.2 mm iron roof providing protection from extreme temperature variations [13].
There are a total of three trigger data levels-Level-0, Level-1, and Level-2. Charged particles triggering a single counter (both the upper and the lower scintillators) with an energy above approximately 0.3 Minimum Ionizing Particles (MIPs) (∼0.75 MeV) are stored in a memory buffer on CPU board as Level-0 trigger data-the trigger rate is approximately 750 Hz. Charged particles triggering the detector with an energy above approximately 3 MIPs are stored as a Level-1 trigger event-the trigger rate is approximately 30 Hz. When three adjacent detectors trigger with an energy above 3 MIPs within 8 μs the data is saved as a Level-2 trigger-1 the trigger rate is approximately 0.01 Hz. The Level-2 trigger is the one used to study UHECRs and Level-0's main goal is to monitor the health of the detector. In this work we are using the rate of the detected particles every ten minutes recorded by the Level-0 trigger dominated by the single particles with primary energy ranging between ∼2 eV × 10 10 -10 13 eV.
The TASD is designed to detect the charged components (primarily electrons, positrons, and muons) of the Extensive Air Shower (EAS). The response of the detector has been discussed in detail in [13,14]. Mostly muons and electrons are detected above approximately 30 MeV. Below this, the total energy deposited by muons and electrons falls off rapidly; below 1 MeV there is no detectable energy deposit as the electrons fail to penetrate a significant depth into the scintillator [14].
The Telescope Array detector has been in operation since 2008. Thunderstorms continuously pass on top of the Telescope Array detector. In this work, we searched for possible variation in the cosmic ray single count rate using Level-0 trigger in correlation with National Lightning Detection Network (NLDN) activity. There are typically about 750 NLDN recorded flashes (intracloud and cloudto-ground) per year over the 700 km 2 TASD array. Due to the large number of flashes only days with thunderstorms including a high recorded peak currents (>90 kA) are incorporated in the current search. For the Level-0 trigger data collected between 2008-2011, several thunderstorms were observed to produce a variation in the cosmic ray single count rate, the variations were observed during lightning events and in correlation with thunderstorms in the absence of lightning.
As an example, we chose an event observed on September 27, 2014 shown in Fig. 2. In Fig. 2, each frame lasts for ten minutes in duration. The time of the start of each frame is denoted on each frame in UTC. The color scale represents the change of the rate in Level-0 trigger of the current frame N c from the ten-minute frame right before it N p divided by N p ( N c -N p N p ) or (ΔN=N). Lightning events reported by the NLDN locations are also added in each of the frames in Figs. 2 and6 in the Appendix. Intracloud in black and cloud-to-ground in gray. It is worth noting that three Terrestrial Gamma-Ray Flashes (TGFs) were reported in [14] on this day. One of these TGFs was reported at 07∶54∶35 (during the first frame in Fig. 2).
One can see a movement of a deficit in the intensity variation ΔN=N for 30 min (from 7:50-8:20 in UTC) in correlation with lightning activity. In addition, an excess was also found for 30 min (from 19:00-19:30 in UTC) in the intensity variation ΔN=N during which no lightning activity was reported by NLDN (Fig. 6 in the Appendix). These variations are both seen in correlation with lightning (using NLDN) and thunderstorms (using radar images as shown in Fig. 9 in the Appendix) in addition or in the absence of lightning [see Supplemental Material Videos (SM4, SM5) in [15] ]. The variations correlation with pressure is not available at the current time resolution at the ground level. However, the variations were found to be not correlated with temperature changes at the ground level as shown in Figs. 3 and7 in the Appendix. The size of the variation ranged for this thunderstorm from 6 km to 24 km in diameter on the ground. The variations were observed in excess and deficit modes over ten minutes in duration, mostly between AEð0.5-1Þ% and can reach up to 2% in magnitude.
The main goal of this simulation work is to quantify the electric field inside thunderstorms resulting in the observed variations in the single count rate by the TASD detector. To do this we need to learn the conversion of the observed (ΔN=NÞ into the equivalent potential model. This is done by inserting the atmospheric electric field model into the CORSIKA simulations. Here the CORSIKA package used in this simulation work is 7.6900 [17], where cosmic rays and their extensive air shower particles propagate through the atmosphere and through the implemented electric field model. Both the electromagnetic and the muonic components of the showers are traced through the atmosphere and the implemented electric field model until they reach the detector observational level (∼1400 m).
As a start, two electric field models are used. Note that both models chosen are the simplest electric field models that allow us to reproduce the main observed (ΔN=NÞ values. Both models use a uniform electric field layer. The first model uses a uniform electric field 2 km inside the thundercloud that is located 2 km above ground level. The second model uses a uniform electric field between the thundercloud base and the ground. Both models are illustrated in the Appendix (Fig. 8). In this second model the thundercloud base is 2 km in height from the detector. While thunderstorm structures are known to be complex, both the thundercloud length and height from the ground used in this work are reasonably representative of thunderstorms at the Southwestern desert of Utah [14].
Primary cosmic ray particles composed of protons were generated between 20 GeV-10 TeV. SIBYLL2.3c [18] is used for the high-energy interaction (>80 GeV). While, GHEISHA [19], URQMD [20], and FLUKA [21] FIG. 3. Rate variation vs time and temperature variation vs time for two detectors numbered (1516 and 1015). Here 1516 shows a deficit in the rate variation (-0.8%) and 1015 shows an excess in the rate variation (þ1.3%). are used for the low-energy model (< 80 GeV). The zenith and azimuth range from 0°≤ θ ≤ 60°and 0°≤ ϕ ≤ 360°. The energy threshold of secondary particles were traced until they reach the following energies; 0.05 GeV for hadrons, 0.5 GeV for muons, 0.001 GeV for electrons, and 0.001 GeV for gammas.
The simulation was curried out first with no electric field for background. Second, by applying an electric field value that ranges between -2000 and þ2000 V=cm (-200 and þ200 kV=m). Figure 4 shows the distribution of the electromagnetic (γ; e AE ) and muonic shower components (μ AE ) on the ground at 1400 m propagated through the atmosphere with electric field at AE2000 V=cm and without an electric field from cloud to ground. The air shower particles (γ; e AE , and μ AE ) are then propagated through the SD detector using an energy dependent response function derived from GEANT4 simulation of the surface detector [14] and following the same trigger condition as the Level-0 trigger. The dependence of ðΔN=NÞ on the potential inside the thunderstorms is shown in Fig. 5 using both thunderstorm electric field models described in this section. Note that, the direction of the electric field follows CORSIKA's definition, where positive electric field direction is pointing upwards.
The simulation results shown in Fig. 5 presents (ΔN=N) vs the potential difference (ΔV) for both investigated electric field models. The first model included a uniform electric field inside a cloud (IntraCloud model: Fig. 8, Left) with 2 km in thickness and two kilometers in height from the ground. This model produced both the excess and deficit observed in the variation in the cosmic ray single count rate. While we are unable to distinguish the type of triggering particle from plastic scintillators, simulations show that the deficit observed by the TASD is dominated by muons. In a negative electric field, an average deficit using the low energy models (GHEISHA, URQMD, and FLUKA), is 0.75 AE 0.28% obtained at -0.2 GV. In a positive electric field, an average deficit of 1.3 þ1.17 -1.38 % is obtained at þ0.2 GV. As shown in Fig. 2 the deficit observed by the TASD is mostly between 0.5% and 1% and can go up to 2%. This observed deficit is reproduced around AE0.2 GV, using this model.
As the potential difference increases above 0.3 GV so does the variation in the cosmic ray single count rate turns from deficit to excess. The excess in the variation of ΔN=N strongly depends on the polarity of the electric field inside the thunderstorm in addition to the magnitude of the electric field. Simulations show that while the deficit in muons is stronger with a larger potential, an excess in the total number of particles observed by the TASD is expected as the variation of the soft components of the cosmic ray air shower dominates the total number of the observed particles. It also shows that the observed excess can be obtained depending on the low energy model and polarity. The TASD observed excess is mostly between 0.5% and 1% and can go up to 2%. In a negative electric field an average excess of 1.36 þ1. 18 -0.44 % is obtained at -0.4 GV. In the positive electric field, an average excess of 0.5%-2% is obtained with a potential between 0.3 GV and 0.4 GV. For the most part, the magnitude of ΔV needed to obtain the same observed variation is larger in the negative than in the positive electric field. This asymmetry is due to the fact that the number of electrons exceeds the number of positrons in the extensive air showers. This, in addition to the fact that, there are higher numbers of electrons with lower energies than positrons. Thus the effect of positive fields (accelerating electrons) is larger than the negative field (accelerating positrons) [8].
The second model included a uniform electric field of 2 km in length from the cloud to the ground (Cloud-to-Ground model: Fig. 8, right). This model produced only the excess in the variation in cosmic ray air single count rate (for the simulation sets produced). As in the first model, the excess in the total number of particles observed by the TASD is expected as the variation of the soft components of the cosmic ray air shower dominates the total number of observed particles. In a negative electric field, an average excess of 1.40 þ0. 4 -0.2 % can be produced by a potential difference of -0.2 GV. In a positive electric field, an excess of 0.5%-2% can be produced by a potential difference of less than 0.2 GV. The excess at a potential difference of -0.4 GV and 0.4 GV is 20% and 40% consecutively (much larger than the maximum observed excess of 2%). Therefore, we conclude that any observed excess resulting from this model is reproduced close to AE0.2 GV in potential.
It is important to note that, the interpretation of both models to the observations in the TASD single count variations is based on the assumption that the duration of the electric field inside the thunderstorm matches that of the duration of the ten minutes recorded observations by the Level-0 filter. However, the duration of the electric field could, in principle, be shorter than ten minutes and therefore we can assume that our current electric field interpretation is a lower limit value to the possible electric field magnitude that is responsible for the single rate observed variations.
Variation in the flux of secondary low-energy cosmic ray counting rate in association with thunderstorms is reported in this work by the Telescope Array Surface Detector. The surface detector utilizes plastic scintillators to observe the charged components (primarily electrons, positrons, and muons) of the cosmic ray air shower. The variation in secondary low-energy cosmic-ray counting rate magnitude mostly ranges between (0.5% and 1%) and can reach up to 2%, both in excess and deficit, with a size that range from 6 km-24 km in diameter. This is the first observation of the variation in the secondary cosmic ray air showers covering 700 km 2 in size. Due to the large size of the TASD detector, we can clearly state that the intensity variations in the single count rates observed move in the same direction as the thunderstorms for tens of minutes at a speed of ∼20 km=10 min. These variations are both seen in correlation with lightning (using NLDN) and thunderstorms (using radar images) in the absence of lightning.
To interpret the effect of the electric field inside thunderstorms on the variation of the cosmic ray secondary shower flux, Monte Carlo simulations are performed with CORISKA. First, cosmic rays air showers are propagated in multiple electric field models, then the secondary shower particles (both soft and hard components of the shower) are propagated through the detector following the same trigger condition of the data used in this analysis. The total number of particles is then recorded and compared to simulation sets with no electric field. This simplified models used reproduced both the excess and deficit observed in the variation in the cosmic ray air shower flux. The electric field magnitude found to reproduce the observed intensity variations was approximately between 0.2 GV-0.4 GV, depending on the electric field model used and the direction of the electric field. Compared to previous observations, the potential difference recorded by TASD is larger than the reported maximum potential in balloon sounding (0.13 GV) [12]. However, the largest potential difference observed by a cosmic ray detector, thus far, was reported by the GRAPES-3 Muon Telescope, with a potential difference of 1 GV [11].
In order to interpret the observations of ΔN=N by the TASD, more precisely, it is clear that we need to know the polarity of the thunderstorm. This could in principle be achieved by implementing an array of Electric Field Mills (EFMs) at the Telescope Array site. This will allow us to better understand the polarity of the observed thunderstorms and therefore model them. Currently, an Electric Field Mill remote station has been installed approximately in the middle of the Telescope Array site for testing. This will enable us to study the relation between SD observations and the development of thunderstorm's electric field as it progresses on top of the Telescope Array detector.
* rabbasi@luc.edu † Present address: University of Californa-Santa Cruz and Flatiron Institute, Simons Foundation.‡ Deceased