We present and compare six simulation codes for positive streamer discharges from six different research groups. Four groups use a fully self-implemented code and two make use of COMSOL Multiphysics ®. Three test cases are considered, in which axisymmetric positive streamers are simulated in dry air at 1 bar and 300 K in an undervolted gap. All groups use the same fluid model with the same transport coefficients. The first test case includes a relatively high background density of electrons and ions without photoionization. When each group uses their standard grid resolution, results show considerable variation, particularly in the prediction of streamer velocities and maximal electric fields. However, for sufficiently fine grids good agreement is reached between several codes. The second test includes a lower background ionization density, and oscillations in the streamer properties, branching and numerical instabilities are observed. By using a finer grid spacing some groups were able to reach reasonable agreement in their results, without oscillations. The third test case includes photoionization, using both Luque's and Bourdon's Helmholtz approximation. The results agree reasonably well, and the numerical differences appear to be more significant than the type of Helmholtz approximation. Computing times, used hardware and numerical parameters are described for each code and test case. We provide detailed output in the supplementary data, so that other streamer codes can be compared to the results presented here.

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Using theoretical and experimental methods, the electric field and the electron multiplication in direct vicinity of a sharp cathode is analysed. The development of the electric field in the pre-breakdown phase of the atmospheric pressure air negative DC corona discharge in the Trichel pulse regime is determined. During the following ultra-fast electrical breakdown, the emission of selected spectral bands of the nitrogen molecule is recorded with high spatiotemporal resolution using the time-correlated single photon counting method. The emission of a Townsend discharge is used to calibrate the setup for the quantitative determination of electric field. Therefore, the Trichel pulse corona and Townsend discharge cell are arranged in the same single-table setup. This direct calibration procedure is described step-by-step including the discussion of known limitations. Finally, the electric field development of the positive streamer passing the 160 μm distance in less than two nanoseconds is determined.Due to the high spatiotemporal gradients of the electric field strength within the streamer breakdown, the local field approximation of the electron component is analysed by investigating numerically the temporal and spatial electron relaxation by means of the solution of the electron Boltzmann equation and Monte Carlo simulation. Results of these computations are given for several reduced electric field values and prove that the electrons are in a hydrodynamic equilibrium state for experimentally given space and time scales for reduced fields above 100 Td.

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A time-correlated single-photon counting technique was used to verify the formation of a cathode-directed streamer inside the narrow cathode region following the interpulse phase of regular negative corona Trichel pulses in ambient air. A purely experimental approach was used to determine the spatiotemporal development of the electric field during the Trichel pulse rise with an extremely high resolution of 10 μm and tens of picoseconds. The results confirm the positive-streamer mechanism for Trichel pulse formation and provide supportive evidence for the hypothesis that the formation of a primary cathode-directed streamer occurs always in any streamer-initiated breakdown and prebreakdown phenomena associated with cathode spot formation.

The local-mean-energy approximation (LMEA) and the local-field approximation (LFA) are commonly applied to include the electron properties like transport and rate coefficients into a hydrodynamic description of gas discharge plasmas. Both the approaches base on the solution of the stationary spatially homogeneous Boltzmann equation for the electron component, but the consequences of these approaches differ drastically. These consequences of using both the approaches are studied and discussed on a kinetic level and by comparison of results of hydrodynamic investigations of low-pressure glow discharge plasmas. It is found that the LMEA is to be strongly recommended for the application to a hydrodynamic description of dc as well as rf discharge plasmas, while the LFA is conditionally suitable to describe dc glow discharges with rough reaction kinetics only and its application to rf discharge plasmas is inappropriate.

Solids facing a plasma are a common situation in many astrophysical systems and laboratory setups. Moreover, many plasma technology applications rely on the control of the plasma-surface interaction, i.e. of the particle, momentum and energy fluxes across the plasma-solid interface. However, presently often a fundamental understanding of them is missing, so most technological applications are being developed via trial and error. The reason is that the physical processes at the interface of a low-temperature plasma and a solid are extremely complex, involving a large number of elementary processes in the plasma, in the solid as well as fluxes across the interface. An accurate theoretical treatment of these processes is very difficult due to the vastly different system properties on both sides of the interface: quantum versus classical behavior of electrons in the solid and plasma, respectively; as well as the dramatically differing electron densities, length and time scales. Moreover, often the system is far from equilibrium. In the majority of plasma simulations surface processes are either neglected or treated via phenomenological parameters such as sticking coefficients, sputter rates or secondary electron emission coefficients. However, those parameters are known only in some cases and with very limited accuracy. Similarly, while surface physics simulations have often studied the impact of single ions or neutrals, so far, the influence of a plasma medium and correlations between successive impacts have not been taken into account. Such an approach, necessarily neglects the mutual influences between plasma and solid surface and cannot have predictive power.In this paper we discuss in some detail the physical processes a the plasma-solid interface which brings us to the necessity of coupled plasma-solid simulations. We briefly summarize relevant theoretical methods from solid state and surface physics that are suitable to contribute to such an approach and identify four methods. The first are mesoscopic simulations such as kinetic Monte Carlo (KMC) and molecular dynamics (MD) that are able to treat complex processes on large scales but neglect electronic effects. The second are quantum kinetic methods based on the quantum Boltzmann equation that give access to a more accurate treatment of surface processes using simplifying models for the solid. The third approach are ab initio simulations of surface process that are based on density functional theory (DFT) and time-dependent DFT. The fourths are nonequilibrium Green functions that able to treat correlation effects in the material and at the interface. The price for the increased quality is a dramatic increase of computational effort and a restriction to short time and length scales. We conclude that, presently, none of the four methods is capable of providing a complete picture of the processes at the interface. Instead, each of them provides complementary information, and we discuss possible combinations. PACS numbers: