A comparison of 3D particle, fluid and hybrid simulations for negative streamers

Abstract

In the high field region at the head of a discharge streamer, the electron\nenergy distribution develops a long tail. In negative streamers, these\nelectrons can run away and contribute to energetic processes such as\nterrestrial gamma-ray and electron flashes. Moreover, electron density\nfluctuations can accelerate streamer branching. To track energies and locations\nof single electrons in relevant regions, we have developed a 3D hybrid model\nthat couples a particle model in the region of high fields and low electron\ndensities with a fluid model in the rest of the domain. Here we validate our 3D\nhybrid model on a 3D (super-)particle model for negative streamers in\novervolted gaps, and we show that it almost reaches the computational\nefficiency of a 3D fluid model. We also show that the extended fluid model\napproximates the particle and the hybrid model well until stochastic\nfluctuations become important, while the classical fluid model underestimates\nvelocities and ionization densities. We compare density fluctuations and the\nonset of branching between the models, and we compare the front velocities with\nan analytical approximation.\n