This paper is the first in a series of three papers to summarize the recent work of an European-wide collaboration which is ongoing since about one decade using Particle-in-Cell (PIC) methods in low temperature plasma physics. In the present first paper the main aspects of this computational technique will be presented. In the second paper, an overview of applications in low-temperature plasma modelling will be given, whereas the third part will put emphasis on the specific results of modelling ion thrusters.

Several applications of PIC simulations for understanding basic physics phenomena in low-temperature plasmas are presented: capacitive radiofrequency discharges in Oxygen, dusty plasmas and negative ion sources for heating of fusion plasmas. The analysis of these systems based on their microscopic properties as accessible with PIC gives improved insight into their complex behavior. These studies are results of joint efforts over about one decade

This paper provides perspectives on recent progress in the understanding of the physics of devices where the external magnetic field is applied perpendicularly to the discharge current. This configuration generates a strong electric field, which acts to accelerates ions. The many applications of this set up include generation of thrust for spacecraft propulsion and the separation of species in plasma mass separation devices. These "E×B" plasmas are subject to plasma-wall interaction effects as well as various micro and macro instabilities, and in many devices, we observe the emergence of anomalous transport. This perspective presents the current understanding of the physics of these phenomena, state-of-the-art computational results, identifies critical questions, and suggests directions for future research.

In this series of three papers we present results from a combined experimental and theoretical, particle-based study to quantitatively describe capacitively coupled radio-frequency discharges in oxygen. The particle-in-cell Monte Carlo model on which the theoretical description is based is described in this paper. It treats space charge fields and transport processes on an equal footing with the most important plasma–chemical reactions. For given external voltage and pressure, the model determines the electric potential within the discharge and the distribution functions for electrons, negatively charged atomic oxygen and positively charged molecular oxygen. Previously used scattering and reaction cross section data are critically assessed and in some cases modified. To validate our model, we compare the densities in the bulk of the discharge with experimental data and find good agreement, indicating that essential aspects of an oxygen discharge are captured.

Understanding plasma initiation in vacuum arc discharges can help to bridge the gap between nano-scale triggering phenomena and the macroscopic surface damage caused by vacuum arcs. We present a new twodimensional particle-in-cell tool to simulate plasma initiation in direct-current (DC) copper vacuum arc discharges starting from a single, strong field emitter at the cathode. Our simulations describe in detail how a sub-micron field emission site can evolve to a macroscopic vacuum arc discharge, and provide a possible explanation for why and how cathode spots can spread on the cathode surface. Furthermore, the model provides us with a prediction for the current and voltage characteristics, as well as for properties of the plasma like densities, fluxes and electric potentials in a simple DC discharge case, which are in agreement with the known experimental values.

The time-resolved emission of argon atoms in a dusty plasma has been measured with phase-resolved optical emission spectroscopy using an intensified charge-coupled device camera. For that purpose, three-dimensional dust clouds have been confined in a capacitively coupled rf argon discharge with the help of thermophoretic levitation. While electrons are exclusively heated by the expanding sheath (α mode) in the dust-free case, electron heating takes place in the entire plasma bulk when the discharge volume is filled with dust particles. Such a behavior is known as Ω mode, first observed in electronegative plasmas. Furthermore, particle-in-cell simulations have been carried out, which reproduce the trends of the experimental findings. These simulations support previous numerical models showing that the enhanced atomic emission in the plasma can be attributed to a bulk electric field, which is mainly caused by the reduced electrical conductivity due to electron depletion.

Phase resolved optical emission spectroscopy (PROES) was used to determine the spatio-temporal behavior of excitation rates in rf sheaths of capacitively coupled plasmas at 13.56 MHz. The plasmas were ignited in pure oxygen at pressures from 20 to 100 Pa and rf powers from 10 to 100 W. The spatial and phase resolved excitation rates have shown four characteristic patterns, which differing in their spatial and temporal position.PIC-MCC simulations of the oxygen capacitively coupled radio-frequency discharge were used to get a detailed microscopic description of the dynamic processes in rf plasmas. The PIC-MCC simulations reproduced the excitation patterns observed in experiment quite well and allowed to identify the underlying physics.Three excitation patterns appearing in front of the powered electrode were found to be due to electron impact dissociative excitation of molecular Oxygen, whereas the fourth pattern very close to the powered electrode is attributed to collisions of the positive ions with the background gas.

Understanding the mechanism of plasma build-up in vacuum arcs is essential in many fields of physics. A onedimensional particle-in-cell computer simulation model is presented, which models the plasma developing from a field emitter tip under electrical breakdown conditions, taking into account the relevant physical phenomena. As a starting point, only an external electric field and an initial enhancement factor of the tip are assumed. General requirements for plasma formation have been identified and formulated in terms of the initial local field and a critical neutral density. The dependence of plasma build-up on tip melting current, the evaporation rate of neutrals and external circuit time constant has been investigated for copper and simulations imply that arcing involves melting currents around 0.5 − 1 A/μm 2 , evaporation of neutrals to electron field emission ratios in the regime 0.01 − 0.05, plasma build-up timescales in the order of ∼ 1 − 10 ns and two different regimes depending on initial conditions, one producing an arc plasma, the other one not. Also the influence of the initial field enhancement factor and the external electric field required for ignition has been explored, and results are consistent with the experimentally measured local field value of ∼ 10 GV/m for copper.