Modeling multiple time scales in streamer discharges

Bibliografical information

Title                Modeling multiple time scalesin streamer discharges

Author            A. Markosyan

                         U.M. Ebert (Promotor)

                         S. Dujko (Co-promotor)

Publisher        Eindhoven : Technische Universiteit Eindhoven, 2014

Pages               171 p.

ISBN               978-94-6259-167-7

PDF                 Download (14.9 MB)

Promotion     Doctoral degree 19-05-2014; Department of Applied Physics

Links               TU/e library

Media              at CWI (english, dutch), at (dutch

Conclusions and Outlook

Conclusions and suggestions for future work have been given at the end of each chapter in the thesis. The main findings of this thesis are summarised here.

High order fluid model

We have derived a new high order fluid model for streamer discharges, based on first principles. The high order fluid model employs the first four moments of the Boltzmann equation. The system is closed by approximating the highest order tensor with lower order moments, namely the average electron density and the average electron energy, in the last equation. We also have sketched the derivation of the lower order models. The source terms of the high order fluid model are evaluated using momentum transfer theory. We have calculated transport data using a multi term Boltzmann solver and the publicly available two term solver (BOLSIG+). The non-local efects in the profile of the average electron energy are present both in the Particle-in-Cell Monte Carlo model and in the high order model, but are missing in the first order model due to the local field approximation. The slope of the average electron energy in the region ahead of the streamer is related to the spatial variation of the average electron energy in the avalanche phase of the streamer development. These observations are consistent with those made by Li et al. [ J. Appl. Phys., 101(12):123305, 2007]. In chapter 4 we discussed fluid models for streamer discharges of arbitrary order. In particular, we summarised the origins and the assumptions underlying each fluid model, including the second order model. We compare them with Particle-in-Cell Monte Carlo in Ne under varying externally applied electric fields. We have concluded that the high order fluid model must be used in order to accurately simulate the streamer head and the region ahead of the streamer. Our comparisons show that the second order model describes very well the electron density and the average electron energy in a streamer channel, although it largely underestimates streamer front propagation velocity.

We have derived a high order fluid model in three spatial dimensions, and we have simulated the streamers in one dimension. The resulting hyperbolic system should be investigated in higher spatial dimensions. The mathematical properties of the system are currently under investigation. The high order model should be extended even further to include the ion motion and the chemistry in the streamer channel, which will also allow the investigation of the heating dynamics. The temperature and pressure efects on the properties of streamers should be investigated. Furthermore, the assumptions on the isotropy of the temperature tensor and absence of the super-elastic collisions, metastables and photo-ionization could be eliminated. Besides, the high order model has never been tested to simulate positive streamers. We have shown that the high order fluid model simulates the streamer head with great accuracy. This fact can be used to couple the high order fluid model with Particle-in-Cell Monte Carlo in a hybrid framework similar to the model developed by Li et al. [ J. Phys. D, 42(20):202003, 2009]. The region ahead of the streamer head is lacking electrons and only few highly energetic ones are present. This means, generally speaking, the in this region the fluid approximation is failing. Here is where Particle-in-Cell Monte Carlo can be used to capture the electron dynamics properly. The other parts of the streamer body can be accurately represented by the fluid description.

Plasma chemistry

S. Nijdam and E. Takahashi have performed experiments in N2:O2 mixtures and argon to investigate the efects of a preceding streamer discharge on a subsequent discharge by applying two positive high voltage pulses in succession with pulse-to-pulse intervals (dt) between 200 ns and 40 ms. They observed that the value of dt for which we can still observe continuation of the first-pulse streamers during the second pulse depends on the oxygen concentration in nitrogen-oxygen mixtures and has a maximum at an oxygen concentration of about 0.2%. Our zero dimensional plasma-chemical model reproduces and explains the experimental results.

We have developed a tool, called PumpKin, to find the dominant pathways in plasma chemical models. The tool is based on the algorithm proposed by R. Lehmann [Journal of Atmospheric Chemistry, 47(1):45–78, 2004]. PumpKin is user friendly tool publicly available under the license GNU GPL (version 2), and it can be obtained from the website

PumpKin is a new tool and many possible use-cases are still unknown even for me. Publicity will help to reveal many applications from different fields. On my behalf, the graphical user interface (GUI) is presently in the development stage and before printing this thesis it will be realised. Another important component to be added is the visualisation of results using the open source tool called Graphviz. The philosophy (or the license) behind of PumpKin assumes that the scientist-enthusiasts will include many other features and improve the user’s experience.

Copyright © 2012-2017 Aram H. Markosyan. All rights reserved.