Streamer discharges are often operated in a repetitively pulsed mode and are therefore influenced by species left over from the previous discharge, especially free electrons and ions. We have investigated these effects by applying two consecutive positive high voltage pulses of 200-700 ns duration to a point-plane gap in artificial air, pure nitrogen, other nitrogen-oxygen mixtures and pure argon at pressures between 67 and 533 mbar. The pulses had pulse-to-pulse intervals ( t) between 200 ns and 40 ms. We imaged both discharges with two ICCD cameras and combined this to a compound image. We observe for values of t below 0.5-15 µs (at 133 mbar, with t depending on gas mixture) that during the second pulse the streamers continue the paths of the first-pulse streamers. We call the maximal time for which this continuation still occurs the continuation time. For N 2 -O 2 mixtures, this time has a maximum at an oxygen concentration of about 0.2%. According to our plasma-chemical modelling this maximum is determined by the electron loss rate which has a minimum around this oxygen concentration. Depending on oxygen concentration the dominant recombining positive ion is N + 4 , O + 2 or O + 4 where O + 2 dominates around 0.2% O 2 and recombines slowest. For increasing values of t we observe that after the continuation phase first no new streamers occur at all, then new streamers show up that avoid the entire pre-ionized region. Next we see new thin streamers that follow the edges of the old channels. For larger t (10-200 µs) the new streamers start to increase in size and move to the centre of the old channels. Finally, around millisecond timescales the new channels are completely independent of the old channels.Together this points to the combination of two mechanisms: streamers search the proximity of regions with increased electron density, but cannot penetrate regions with very high electron density.

Abstract. Streamer discharges pose basic problems in plasma physics, as they are very transient, far from equilibrium and have high ionization density gradients; they appear in diverse areas of science and technology. The present paper focuses on the derivation of a high order fluid model for streamers. Using momentum transfer theory, the fluid equations are obtained as velocity moments of the Boltzmann equation; they are closed in the local mean energy approximation and coupled to the Poisson equation for the space charge generated electric field. The high order tensor in the energy flux equation is approximated by the product of two lower order moments to close the system. The average collision frequencies for momentum and energy transfer in elastic and inelastic collisions for electrons in molecular nitrogen are calculated from a multi term Boltzmann equation solution. We then discuss, in particular, (1) the correct implementation of transport data in streamer models; (2) the accuracy of the two term approximation for solving Boltzmann's equation in the context of streamer studies; and (3) the evaluation of the mean-energy-dependent collision rates for electrons required as an input in the high order fluid model. In the second paper in this sequence, we will discuss the solutions of the high order fluid model for streamers, based on model and input data derived in the present paper.PACS numbers: 52.25. Dy, 52.65.Kj, 52.25.Fi, 52.25.Jm Submitted to: J. Phys. D: Appl. Phys.

We evaluate the performance of three plasma fluid models: the first order reaction-drift-diffusion model based on the local field approximation; the second order reaction-drift-diffusion model based on the local energy approximation and a recently developed high order fluid model by Dujko et al (2013 J. Phys. D 46 475202) We first review the fluid models: we briefly discuss their derivation, their underlying assumptions and the type of transport data they require. Then we compare these models to a particle-in-cell/Monte Carlo (PIC/MC) code, using a 1D test problem. The tests are performed in neon and nitrogen at standard temperature and pressure, over a wide range of reduced electric fields. For the fluid models, transport data generated by a multi-term Boltzmann solver are used. We analyze the observed differences in the model predictions and address some of the practical aspects when using these plasma fluid models.

The high-order fluid model developed in part I of this series is employed here to study the propagation of negative planar streamer fronts in pure nitrogen. The model consists of the balance equations for electron density, average electron velocity, average electron energy and average electron energy flux. These balance equations have been obtained as velocity moments of Boltzmann's equation and are here coupled to the Poisson equation for the space charge electric field. Here the results of simulations with the high-order model, with a particle-in-cell/Monte Carlo (PIC/MC) model and with the first-order fluid model based on the hydrodynamic drift-diffusion approximation are presented and compared. The comparison with the MC model clearly validates our high-order fluid model, thus supporting its correct theoretical derivation and numerical implementation. The results of the first-order fluid model with local field approximation, as usually used for streamer discharges, show considerable deviations. Furthermore, we study the inaccuracies of simulation results caused by an inconsistent implementation of transport data into our high-order fluid model. We also demonstrate the importance of the energy flux term in the high-order model by comparing with results where this term is neglected. Finally, results with an approximation for the high-order tensor in the energy flux equation is found to agree well with the PIC/MC results for reduced electric fields up to 1000 Townsend, as considered in this work.