The Particle-In-Cell (PIC) method has been developed by Oscar Buneman, Charles Birdsall, Roger W. Hockney, and John Dawson in the 1950s and, with the advances of computing power, has been further developed for several fields such as astrophysical, magnetospheric as well as solar plasmas and recently also for atmospheric and laser-plasma physics. Currently more than 15 semi-public PIC codes are available which we discuss in this review. Its applications have grown extensively with increasing computing power available on high performance computing facilities around the world. These systems allow the study of various topics of astrophysical plasmas, such as magnetic reconnection, pulsars and black hole magnetosphere, non-relativistic and relativistic shocks, relativistic jets, and laser-plasma physics. We review a plethora of astrophysical phenomena such as relativistic jets, instabilities, magnetic reconnection, pulsars, as well as PIC simulations of laser-plasma physics (until 2021) emphasizing the physics involved in the simulations. Finally, we give an outlook of the future simulations of jets associated to neutron stars, black holes and their merging and discuss the future of PIC simulations in the light of petascale and exascale computing.

Positron beams have been observed by the Fermi satellite to be correlated with lightning leaders, and neutron emissions have been attributed to lightning and to laboratory sparks as well. Here we discuss the cross sections to be used for modeling these emissions, and we calculate the emissions of positrons, neutrons, and also protons from lightning leaders. Neutrons were first erroneously attributed to fusion reactions, but the photonuclear reaction responsible for neutrons should create protons as well. We predict them here; they have not been observed yet. In the paper, we first revisit the model for stepped lightning leaders of Xu, Celestin, and Pasko with updated cross sections, we analyze the spatial and energetic structure of the electron beam, and we calculate the spectrum of the generated gamma ray beam at 16 km altitude. Then we review the scattering processes of photons with emphasis on the processes above 5 MeV, in particular the photon energy losses in Compton scattering events and the generation of leptons and hadrons. We provide simple approximations for photon energy loss and lepton and hadron production for any photon with energy above 5 MeV passing through an arbitrary air layer. Finally, we launch a gamma ray beam with the earlier calculated spectrum of the negative stepped lightning leader from 16 km upward and calculate the production and energy of positrons, neutrons, and protons as well as the propagation of positrons.

Fundamental understanding of the early stages of electrodeposition at the nanoscale is key to address the challenges in a wide range of applications. Despite having been studied for decades, a comprehensive understanding of the whole process is still out of reach. In this work, we introduce a novel modelling approach that couples a finite element method (FEM) with a random walk algorithm, to study the early stages of nanocluster formation, aggregation and growth, during electrochemical deposition. This approach takes into account not only electrochemical kinetics and transport of active species, but also the surface diffusion and aggregation of adatoms and small nanoclusters. The simulation results reveal that the relative surface mobility of the nanoclusters compared to that of the adatoms plays a crucial role in the early growth stages. The number of clusters, their size and their size dispersion are influenced more significantly by nanocluster mobility than by the applied overpotential itself. Increasing the overpotential results in shorter induction times and leads to aggregation prevalence at shorter times. A higher mobility results in longer induction times, a delayed transition from nucleation to aggregation prevalence, and as a consequence, a larger surface coverage of smaller clusters with a smaller size dispersion. As a consequence, it is shown that a classical first-order nucleation kinetics equation cannot describe the evolution of the number of clusters with time, N(t), in potentiostatic electrodeposition. Instead, a more accurate representation of N(t) is provided. We show that an evaluation of N(t), which neglects the effect of nanocluster mobility and aggregation, can induce errors of several orders of magnitude in the determination of nucleation rate constants. These findings are extremely important towards evaluating the elementary electrodeposition processes, considering not only adatoms, but also nanoclusters as building blocks.

When voltage pulses of 1 MV drive meter long air discharges, short and intense bursts of x-rays are measured. Here we develop a model for electron acceleration and subsequent photon generation within this discharge to understand these bursts. We start from the observation that the encounter of two streamers of opposite polarity launches the electrons, that they are further accelerated in the discharge field and then lose their energy, e.g., by photon emission through Bremsstrahlung. We model electron and photon dynamics in space and energy with a Monte Carlo model. Also the detector response to incoming photons is modelled in detail. The model justifies the approximation that the x-ray bursts are isotropic in space; this assumption is used to conclude that x-ray bursts near the high-voltage electrode with 6 ⋅ 10 4 photons and characteristic energies of 160 keV closely reproduce the measured spectra and attenuation curves. The nanosecond duration of the bursts as well as their energy spectrum is consistent with model calculations.

The Atmosphere‐Space Interactions Monitor measures Terrestrial Gamma‐Ray Flashes (TGFs) simultaneously with optical emissions from associated lightning activity. We analyzed optical measurements at 180–230, 337, and 777.4 nm related to 69 TGFs observed between June 2018 and October 2019. All TGFs are associated with optical emissions and 90% of them are at the onset of a large optical pulse, suggesting that they are connected with the initiation of current surges. A model of photon delay induced by cloud scattering suggests that the sources of the optical pulses are from 0.7 ms before to 4.4 ms after the TGFs, with a median of −10 ± 80 µs, and 1–5 km below the cloud top. The pulses have rise times comparable to lightning but longer durations. Pulse amplitudes at 337 nm are ∼3 times larger than at 777.4 nm. The results support the leader‐streamer mechanism for TGF generation.

High‐voltage laboratory experiments show that discharges in air, generated over a gap of one meter with maximal voltage of 1 MV, may produce X‐rays with photon energies up to 1 MeV. It has been suggested that the photons are bremsstrahlung from electrons accelerated by the impulsive, enhanced field during collisions of negative and a positive streamers. To explore this process, we have conducted the first self‐consistent particle simulations of streamer encounters. Our simulation model is a 2‐D, cylindrically symmetric, particle‐in‐cell code tracing the electron dynamics and solving the space charge fields, with a Monte Carlo scheme accounting for collisions and ionization. We present the electron density, the electric field, and the velocity distribution as functions of space and time. Assuming a background electric field 1.5 times the breakdown field, we find that the electron density reaches 2·10²¹ m⁻³, the size of the encounter region is ∼3·10⁻¹² m³ and that the field enhances to ∼9 times the breakdown field during ∼10⁻¹¹ s. We further find that the radial component becomes comparable to the parallel component, which together with angular scattering leads to an almost isotropic distribution of electrons. This is consistent with laboratory observations that X‐rays are emitted isotropically. However, the maximum energy of electrons reached in the simulation is ∼600 eV, which is well below the energies required to explain observations. The reason is that the encounter region is small in size and duration. For the photon energies observed, the field must be enhanced in a larger region and/or for a longer time.