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Mountaintop towers are highly exposed to self-initiated upward lightning flashes. Accurate estimation of their effective height-the equivalent flat-ground height yielding the same lightning exposure-is essential for reliable exposure assessment, for interpreting and calibrating measurement data at instrumented mountaintop towers, and for comparison with established protection guidelines. This study applies a two-step numerical framework that couples finite-element electrostatic simulations with a leader-inception and propagation model for representative tower-terrain configurations reflecting reference instrumented mountaintop sites in lightning research. For each configuration, the stabilization field, the minimum background electric field enabling continuous upward leader propagation to the cloud base, is determined, from which effective heights are obtained. The simulated results agree with the analytical formulation of Zhou et al. (within similar to 10%), while simplified or empirical approaches by Shindo, Eriksson, and Pierce exhibit larger deviations, especially for broader mountains. A normalized analysis demonstrates that the tower-to-mountain slenderness ratio (h/a) governs the scaling of effective height, following a power-law dependence with exponent -0.17 (R² = 0.94). This compact relation enables direct estimation of effective height from geometric parameters alone, complementing detailed leader-inception modeling. The findings validate the proposed physics-based framework, quantify the geometric dependence of effective height for mountaintop towers, and provide a foundation for improving lightning-exposure assessments, measurement calibration and design standards for elevated structures.

These new findings provide detailed understanding into how seasonal monsoon patterns shape the characteristics and behaviour of isolated breakdown pulse (IBP) train discharges and their co-occurrence with ground flashes. Using high-resolution broadband electric radiation field measurements (12.5 to 25 nanoseconds) over a twosecond duration, we identified key influences of monsoon variations. Notably, the ground-level cool condition and high humidity during the Northeast monsoon coincided with the IBP train activity. Among 90 samples analysed, most positive IBP train discharges occurred between late evening (6 PM) and midnight (12 AM), while negative IBP train discharges were rare, with only six cases recorded across all monsoon periods. We categorized IBP trains into two types: type-i, consisting of uniform polarity pulses with an average of 19 pulses, and type-ii, featuring a higher average of 95 pulses, followed by sequences of composite bipolar pulses. Interestingly, the occurrence of positive IBP train discharges during storms influenced the production of cloud-to-ground (CG) flashes. Storms with frequent positive IBP train discharges exhibited the highest number of positive CG flashes. Conversely, increased positive IBP train activity corresponded to a reduced percentage of negative CG flashes. These results enhance our understanding of storm electrification dynamics in tropical regions.

Without loss of generality, the return stroke can be treated as a current pulse propagating along the leader channel while undergoing attenuation and dispersion. According to the measurements, the return stroke travels along the leader channel with a speed less than the speed of light. However, if the return stroke speed were to be lower than the speed of light, the propagating return stroke would generate an electric field traveling ahead of the return stroke front with the speed of light. Since the leader channel is conducting and finite in thickness, the electric field that extends ahead of the return stroke front would interact with the leader channel generating currents that effectively push the return stroke front speed to the speed of light. In this paper we will make a case for the fact that the return stroke speed is actually equal to the speed of light. The slower return stroke speeds obtained in experimental investigations are shown to be caused by the rapid dispersion of the return stroke current as it propagates along the leader channel. The analysis presented in the paper is restricted to the lightning subsequent return strokes but the conclusions are also valid for lightning first return strokes.

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.

Observations and theoretical principles indicate that electromagnetic waves, including light, propagate more slowly in dielectric media than in a vacuum. This behavior is elegantly described by Maxwell's equations, which account for material-specific permittivity and permeability. According to the principle of superposition, the net electromagnetic wave within a dielectric medium results from the combination of the incident wave and secondary waves generated by the medium's interaction with the incident wave. Notably, both the incident wave and the secondary waves propagate at the speed of light in a vacuum. The Ewald-Oseen extinction theorem explains that secondary waves, emitted by atoms in the dielectric medium, interfere with the incident wave in such a way that they cancel the original wave and produce a resultant wave propagating at a reduced speed determined by the dielectric constant of the medium. In this paper, we extend the application of the Ewald-Oseen theorem to electromagnetic wave propagation in transmission lines and demonstrate that the principles used to model lightning return strokes align closely with those predicted by the theorem.

Macroscopic studies of cortical tissue reveal a prevalence of oscillatory activity, that reflect a fine tuning of neural interactions. This research extends neural field theories by incorporating generalized oscillatory dynamics into previous work on conservative or semi-conservative neural field dynamics. Prior studies have largely assumed isotropic connections among neural units; however, this study demonstrates that a broad range of anisotropic and fluctuating connections can still sustain oscillations. Using Lagrangian field methods, we examine different types of connectivity, their dynamics, and potential interactions with neural fields. From this theoretical foundation, we derive a framework that incorporates Hebbian and non-Hebbian learning - i.e., plasticity - into the study of neural fields via the concept of a connectivity field.

Understanding how the path of streamers is influenced by background electric fields is crucial in leader progression models and electrical breakdown models in long gaps. While numerous advanced models of streamers exist, applying them to leader progression models to track streamer movement remains computationally intensive and impractical. In this study, we employ one of the simplest streamer models available in the literature to investigate how streamers are deflected in the presence of background electric fields. Our analysis identifies the key parameters that govern this interaction. Additionally, we estimate the time and length scales over which streamers are diverted by a background electric field of a specified strength.