Some results on streamer stagnation
Authors: Chanrion Olivier , Niknezhad Mojtaba , Holbøll Joachim , Neubert Torsten 
Published: March 2022

&lt;p&gt;Streamer discharges are often seen as the building blocks of sparks by playing a major role in their initiation and propagation. The stagnation of streamers is of great interest from the scientific point of view and for industrial applications since it helps defining a maximal length over which a streamer can propagate. Therefore, understanding the stagnation helps the design of high voltage equipment like circuit breakers and gas insulated systems.&lt;/p&gt;&lt;p&gt;In this presentation, we study the stagnation of positive streamers by means of numerical modelling. For negative streamers,&amp;#160;the modelling of the&amp;#160;stagnation mechanism is&amp;#160;relatively&amp;#160;straight forward, since the streamer head enlarges, and the tip electric field vanishes smoothly.&amp;#160;For positive streamers, the modelling is more challenging since a classical&amp;#160;drift-diffusion model&amp;#160;with&amp;#160;the local field approximation&amp;#160;usually leads to an unstable increase of&amp;#160;the streamer tip electric field.&lt;/p&gt;&lt;p&gt;In our&amp;#160;recent results published in [1] and [2], we show&amp;#160;that the instability originates mostly from&amp;#160;the local&amp;#160;field&amp;#160;approximation for the calculation of the ionization source term,&amp;#160;and we show that the non-local&amp;#160;treatment&amp;#160;of the ionization leads to a successful simulation of stagnation. We use&amp;#160;2 different models for the treatment of ionization; the first is&amp;#160;a&amp;#160;classical&amp;#160;model&amp;#160;in which&amp;#160;the ionization source term in the streamer tip is slightly smoothed&amp;#160;[1] and the second, which is based on&amp;#160;an extended model&amp;#160;[3,4].&lt;/p&gt;&lt;p&gt;The successful simulation allows to observe the physical mechanisms behind the stagnation of streamer discharges by showing the role of positive ions and makes it possible to determine the maximal length a streamer can reach.&lt;/p&gt;&lt;p&gt;[1] Niknezhad M, Chanrion O, K&amp;#246;hn C, Holb&amp;#248;ll J&amp;#160;&amp; Neubert T&amp;#160;2021, 'A three-dimensional model of streamer discharges in unsteady airflow: Paper',&amp;#160;&lt;em&gt;Plasma Sources Science and Technology&lt;/em&gt;, vol. 30, no. 4, 045012.&amp;#160;&lt;/p&gt;&lt;p&gt;[2] Niknezhad M, Chanrion O, Holb&amp;#248;ll J&amp;#160;&amp; Neubert T&amp;#160;2021, 'Underlying mechanism of the stagnation of positive streamers',&amp;#160;&lt;em&gt;Plasma Sources Science and Technology&lt;/em&gt;, vol. 30, no. 11, 115014.&lt;/p&gt;&lt;p&gt;[3] Aleksandrov N L and Kochetov I V 1996, &amp;#8217;Electron rate coefficients in gases under non-uniform field and electron density conditions&amp;#8217;, &lt;em&gt;Journal of Physics D: Applied Physics&lt;/em&gt;, vol. 29, no. 6, 1476&amp;#8212;1483.&lt;/p&gt;&lt;p&gt;[4] Li C, Ebert U, Hundsdorfer W 2010, , Spatially hybrid computations for streamer discharges with generic features of pulled fronts: I. Planar fronts', &lt;em&gt;Journal of Computational Physics&lt;/em&gt;, vol. 229, 200-220.&lt;/p&gt;