Derivation of a merging condition for two interacting streamers in air

TL;DR

This paper presents a numerical study on the interaction of two air streamers, deriving a merging condition based on their width-to-distance ratio, which is consistent across various parameters.

Contribution

It introduces a new merging criterion for two interacting streamers in air, validated through detailed numerical simulations.

Findings

Streamers tend to merge when width-to-distance ratio reaches ~0.35 for positive and ~0.4 for negative streamers.

The merging ratios are independent of electric field, initial seed configuration, and pressure.

The study provides a quantitative criterion for streamer merging in air.

Abstract

The simulation of the interaction of two simultaneously propagating air streamers of the same polarity is presented. A parametric study has been carried out using an accurate numerical method which ensures a time-space error control of the solution. For initial separation of both streamers smaller or comparable to the longest characteristic absorption length of photoionization in air, we have found that the streamers tend to merge at the moment when the ratio between their characteristic width and their mutual distance reaches a value of about 0.35 for positive streamers, and 0.4 for negative ones. Moreover it is demonstrated that these ratios are practically independent of the applied electric field, the initial seed configuration, and the pressure.