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There are several approaches to describe the generation of return stroke current in lightning flashes, collectively referred to as return stroke models. Among these, engineering return stroke models are widely used to compute the electromagnetic fields generated by return strokes. These models are typically categorized into three types: current propagation, current generation, and current dissipation models. Each model type can be employed to describe the spatial and temporal variations of the return stroke current. Once these variations are defined, multiple methods are available to calculate the resulting electromagnetic fields, all of which yield equivalent results. One such method involves using electromagnetic field expressions for moving and accelerating charges. This paper illustrates the procedure for calculating the electromagnetic fields of return strokes using this approach. The procedure is demonstrated for all three categories of return stroke models: current propagation, current generation, and current dissipation.

We characterise cortical dynamics using partial differential equations (PDEs), analysing various connectivity patterns within the cortical sheet. This exploration yields diverse dynamics, encompassing wave equations and limit cycle activity. We presume balanced equations between excitatory and inhibitory neuronal units, reflecting the ubiquitous oscillatory patterns observed in electrophysiological measurements. Our derived dynamics comprise lowest-order wave equations (i.e., the Klein-Gordon model), limit cycle waves, higher-order PDE formulations, and transitions between limit cycles and near-zero states. Furthermore, we delve into the symmetries of the models using the Lagrangian formalism, distinguishing between continuous and discontinuous symmetries. These symmetries allow for mathematical expediency in the analysis of the model and could also be useful in studying the effect of symmetrical input from distributed cortical regions. Overall, our ability to derive multiple constraints on the fields - and predictions of the model - stems largely from the underlying assumption that the brain operates at a critical state. This assumption, in turn, drives the dynamics towards oscillatory or semi-conservative behaviour. Within this critical state, we can leverage results from the physics literature, which serve as analogues for neural fields, and implicit construct validity. Comparisons between our model predictions and electrophysiological findings from the literature - such as spectral power distribution across frequencies, wave propagation speed, epileptic seizure generation, and pattern formation over the cortical surface - demonstrate a close match. This study underscores the importance of utilizing symmetry preserving PDE formulations for further mechanistic insights into cortical activity.

An extensive field experiment was conducted to investigate the effects of earth -enhancing compounds on earthing systems. Four identical vertical earth rods were installed, each encased in concrete, Bentonite, and two commercial enhancing materials. Lightning impulse signals were injected into all electrode arrangements, and the measured responses were used to analyse the associated risks of step and touch voltages. The peak voltage values and the corresponding energy dissipation for each measurement were calculated and compared to those of a reference electrode. The analysis of step voltage measurements and the corresponding energy dissipation demonstrated that the use of concrete exhibited greater advantages than the use of Bentonite. However, touch voltage measurements and the associated energy dissipation indicated that despite the lower touch voltage exhibited by Bentonite, its energy dissipation exceeded that of the reference electrode. Consequently, the unique findings reveal that specific variations of earth -enhancing compounds can exhibit reduced earth impedance and lower step or touch voltages while also yielding higher energy dissipation, introducing an unforeseen risk of injury.

An engineering model to represent positive return strokes is introduced as an extension of the Modified Transmission Line model with Linear Current Decay (MTLL). This extension is grounded in experimental data on the electric fields and currents associated with positive return strokes. The core premise of the model is that once the return stroke front reaches the cloud, recoil leader-type activities within the cloud feed the lightning channel with a positive charge. This positive charge then travels to the ground in the form of an M-component, enhancing both the amplitude and duration of the impulse current in the channel and at ground level. The propagation of the return stroke current along the channel follows the MTLL model, while the M-component is treated as a current pulse traveling from the cloud to the ground. At ground level, the M-component current is fully reflected. The model successfully generates electromagnetic fields that resemble those observed from positive return strokes, and it is easily applicable to studies involving the interaction of positive return stroke fields with power lines and the Earth's upper atmosphere.

X-rays have been observed in natural downward cloud-to-ground lightning for over 20 years and in rocket-triggered lightning for slightly less. In both cases, this energetic radiation has been detected during the stepped and dart leader phases of downward negative flashes. More recently, X-rays have also been reported during the dart leader phase of upward negative flashes. In this study, we present the observations of four upward positive lightning flashes from the Santis Tower (2.5 km ASL) in Switzerland. These consist of the simultaneous records of electric current passing through the tower, and electric field strength and X-ray flux 20 m from the tower base. One of the flashes was captured by a high-speed camera operating at 24,000 frames per second, stills from which are also presented. We detected X-rays during the initial phase of upward negative leader propagation, which can be associated with the leader-stepping process from electric field and current waveforms. To the best of our knowledge, this is the first time that such measurements are reported in the literature. The obtained time-synchronised data confirm that the X-ray emissions detected are associated with the initial steps of the upward negative leader. The frequency and energy of X-ray pulses appear to decrease as functions of time, with pulses disappearing altogether within the first millisecond of the leader initiation. X-ray emission also appears to be correlated with the maximum current-derivative and the electric field change of leader steps, consistent with cold electron runaway. These observations contribute to improving our understanding of upward lightning, which is a primary source of damage to tall structures such as wind turbines and telecommunications towers, as well as aircraft during takeoff and landing.

In this study, microwave radiation pulses emitted from natural lightning have been found to interfere with the Fourth Generation Long Term Evolution (4G LTE) mobile communication data transmission. Two sets of measurement instruments have been synchronized where lightning electric field sensor together with 4G LTE network were evaluated its performance under two conditions namely fair-weather (four cases) and storm (four lightning cases). The microwave radiation emitted from lightning was directly measured without the use of a mixer and down-convertor to ensure the preservation of information such as the number of pulses and amplitude. A client-server architecture has been set up for data transmission utilizing User Datagram Protocol (UDP) where the packets have been generated by using Internet Performance Working Group Third Version (Iperf3) platform. Under fair-weather conditions, the 4G LTE connection at both the client and server nodes demonstrated stability and experienced minimal impact. On the other hand, natural lightning electromagnetic interference disrupted the 4G LTE communication links. Among the four reported storms, three storms have affected the 4G LTE data transmission. The first and fourth storms resulted in a complete connection drop to zero, lasting for 4 minutes and 2 seconds and for 44 seconds, respectively. The observation of hundreds microwave radiation pulses, each characterized by individual oscillating features suggests a potential disruption to packet transmission. Moreover, negative could-to-ground (-CG) and intra-cloud (IC) lightning flashes have been identified as the primary sources of interference to the 4G LTE data transmission. This information could be useful for future studies and for developers working on improving the reliability and performance of 4G LTE networks, particularly in areas prone to thunderstorms.

This study investigates the occurrence of chaotic pulse trains (CPTs) and regular pulse trains (RPTs) in tropical positive cloud-to-ground (CG) lightning flashes. These flashes are categorized into four types based on the initial polarity of the initial breakdown (IB) pulses and their relationship to the first return stroke (RS). A total of 71 positive CG flashes from five thunderstorm events were analyzed. The analysis reveals instances of CPTs and RPTs both before and after the first positive RS, along with the occurrence of mixed polarities in RPTs. Variations in IB pulse polarities and the presence of CPTs and RPTs before the first positive RS were observed, contrasting with previous findings in negative CG flashes. All positive CG flashes have been detected when cloud top height occurrences were between 12 and 18 km. In contrast, for negative CG flashes with CPTs and RPTs the cloud top height occurrences were between 5 and 12 km. It is interesting that CPTs and RPTs can be detected during IB process of positive CG flashes at relatively high altitude in the thundercloud. Perhaps due to low pressure at higher altitudes in the cloud, electrical process associated with CPTs and RPTs are easily discharged before the occurrence first positive return stroke. The altitudes of cloud top heights for the inverse polarity of IB pulses were located between 16 and 18 km. This research enhances the understanding of positive CG lightning initiation process and their relationship with CPTs and RPTs, as well as the occurrence of recoil leaders.

The occurrence of positive cloud-to-ground (CG) lightning flashes proves to be a challenging task when compared to the negative CG flash which common happen in tropical region. This due to the positively charged clouds to reach higher altitudes to enable the transfer of electrical charges to the Earth's surface. With several sensors that deployed in the Malacca region (2.314077 degrees N, 102.318282 degrees E) such as the wide band fast and slow antenna, magnetic field sensors, and the electric field mill (EFM-100). This research study focuses on the temporal characteristics of positive CG lightning activity in the tropical region during September and October 2021. A total of 203 positive cloud-to-ground flashes were meticulously analyzed in the context of 16 thunderstorm events. Key findings highlight the consistent initiation of positive cloud-to-ground flashes through initial breakdown (IB) pulses, followed by the development of stepped leaders and subsequent return strokes. Notably, most positive cloud-to-ground events (72%) were observed as single strokes and the maximum multiplicity recorded being four subsequent return strokes. Furthermore, the analysis focuses into the temporal aspects of these lightning events, revealing average durations for various parameters, including rise-time (6.26 mu s), zero-crossing (26.43 mu s), pulse duration of the first RS (139.76 mu s), and the interval from the first IB to the first return stroke (134.19 ms). Additionally, the recorded data from the Electric Field Mill (EFM) instruments together with Constant Altitude Plan Position Indicator (CAPPI) radar demonstrate a notable correlation. Specifically, the electric field (E-field) values exhibit a discernible increase when positive cloud-to-ground lightning events are detected near the lightning sensor.

In this paper, Very -High Frequency (VHF) radiation pulses associated with 11 negative Narrow Bipolar Events (NBEs) produced by a tropical storm over Malacca Strait are examined. The lightning data were recorded from a measurement station (ST) which consisted of a fast antenna (FA) and three VHF sensors (two 5 m perpendicular baselines interferometer). The average rise time (RT), average zero -crossing time (ZCT), average pulse duration (PD), and range of peak currents of the negative NBEs were 1.4 +/- 0.4 mu s, 2.7 +/- 1.0 mu s, 12.0 +/- 6.9 mu s, and -10 to -64 kA, respectively. The key finding is that all VHF radiation pulses have been found to precede the negative NBEs with an average lead time of 0.7 +/- 0.3 mu s. An interferometer map for one negative NBE (labelled as NBE10) detected at 35.7 km from ST has shown a characteristic of mixed propagation direction of fast streamers. The first VHF radiation source was detected at 12.4 +/- 0.4 km above sea level. The total length and estimated velocity of the main propagation of the VHF radiation sources were 2.2 +/- 0.7 km and between 1.4 x 10 8 and 2.8 x 10 8 ms -1 , respectively. Moreover, based on the Himawari satellite image, the maximum extent of the cloud top height was estimated to be around 20.9 km over sea level (over Malacca Strait). All the VHF radiation sources associated with NBE10 were suggested to be detected above the main negative charge region (6 km altitude that corresponds to -10 degrees C). Thus, it could be suggested that NBE10 was initiated most likely in the environment of the ice crystals alone, based on the first altitude of the VHF radiation source and maximum extent of cloud top height.

A current propagation type return stroke model which is consistent with the estimated distribution of the charge on the leader channel is described. The model takes into account the dispersion of the return stroke current along the return stroke channel. The model is capable of generating lightning return stroke electromagnetic fields that are in close agreement with experimental observations. The model could also be used to estimate the electric fields from the leader-return stroke combination at any given distance.