In experiments positive streamers can have a feather-like structure, with small hairs connected to the main streamer channel. These feathers were observed in pure nitrogen (with impurities of 1ppm oxygen or less) but not in air. Based on results of numerical simulations, we provide a theoretical explanation for the emergence of these hairs as well as why the hairs are visible in nitrogen, but not in air

Ebert, U. (Ute)

Nijdam, S. (Sander)

Wormeester, G. (Gideon)

English

Wormeester, Gideon

Nijdam, Sander

Ebert, Ute

NARCIS 

Feather-like structures in positive streamers interpreted as electron avalanches

In experiments positive streamers can have a feather-like structure, with small hairs connected to the main streamer channel. These feathers were observed in pure nitrogen (with impurities of 1 ppm oxygen or less) but not in air. We hypothesize that these hairs are individual electron avalanches moving towards the streamer channel. Based on results of numerical simulations, we provide a theoretical explanation why these hairs are visible in nitrogen, but not in air

Wormeester, G.

Nijdam, S.

Ebert, U.

Pure OAI Repository

Feather-like structures in positive streamers

Wormeester, G

Nijdam, S Sander

Ebert, UM Ute

Repository TU/e

Ebert, U.M.

 Feather-like structures in positive streamersCitation for published version (APA):Wormeester, G., Nijdam, S., & Ebert, U. M. (2010). Feather-like structures in positive streamers. In W. G. G. M.Hori, & X. Japan Society of Applied Physics (Eds.), Proceedings of the 63rd Gaseous Electronics Conferenceand 7th International Conference on Reactive Plasmas, Paris, France, 4-8 October 2010 (pp. DTP.00159-).GEC.Document status and date:Published: 01/01/2010Document Version:Publisher’s PDF, also known as Version of Record (includes final page, issue and volume numbers)Please check the document version of this publication:• A submitted manuscript is the version of the article upon submission and before peer-review. There can beimportant differences between the submitted version and the official published version of record. Peopleinterested in the research are advised to contact the author for the final version of the publication, or visit theDOI to the publisher's website.• The final author version and the galley proof are versions of the publication after peer review.• The final published version features the final layout of the paper including the volume, issue and pagenumbers.Link to publicationGeneral rightsCopyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright ownersand it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.            • Users may download and print one copy of any publication from the public portal for the purpose of private study or research.            • You may not further distribute the material or use it for any profit-making activity or commercial gain            • You may freely distribute the URL identifying the publication in the public portal.If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the “Taverne” license above, pleasefollow below link for the End User Agreement:www.tue.nl/taverneTake down policyIf you believe that this document breaches copyright please contact us at:openaccess@tue.nlproviding details and we will investigate your claim.Download date: 15. Jul. 2024Abstract Submittedfor the GEC10 Meeting ofThe American Physical SocietySorting Category: 2.7 (C)Feather-like structures in positive streamers GIDEONWORMEESTER, Centrum Wiskunde & Informatica, SANDER NIJ-DAM, Eindhoven University of Technology, UTE EBERT, CentrumWiskunde & Informatica — In experiments positive streamers can havea feather-like structure, with small hairs connected to the main streamerchannel. These feathers were observed in pure nitrogen (with impuritiesof 1ppm oxygen or less) but not in air. Based on results of numericalsimulations, we provide a theoretical explanation for the emergence ofthese hairs as well as why the hairs are visible in nitrogen, but not inair.Prefer Oral SessionX Prefer Poster SessionGideon WormeesterG.Wormeester@cwi.nlCentrum Wiskunde & InformaticaDate submitted: 12 Jun 2010 Electronic form version 1.4

CWI's Institutional Repository

DTP-159Feather-like structures in positive streamersGideon Wormeester  1 , Sander Nijdam2, Ute Ebert1,21 Centrum Wiskunde & Informatica (CWI), PO Box 94907, 1090 GB, Amsterdam, NetherlandsPhone/FAX: +31205924208/+31205924199 E-mail:G.Wormeester@cwi.nl2 Department of Applied Physics, Eindhoven University, PO Box 513, 5600 MB, Eindhoven, Netherlands.In experiments of positive streamers, feather-like structures were observed in N2 mixtures with an impurity level below 1 ppm, e.g. when the  N2 contains 1 ppm O2 or less. These feathers did not appear in streamers in air. Based on numerical simulations, we provide a possible explanation for the difference in feather-formation in these mixtures.1. IntroductionStreamers  are thin channels  of  ionized gas  that  are of significant  importance  in  processes  of  atmospheric electricity (for example lightning and sprites) as well as in industrial applications such as lighting and disinfection. We distinguish  between  positive  and  negative  streamers. Negative streamers propagate in the direction of the electron drift,  while  positive  streamers  move  against  the  drift direction and therefore require a source of electrons ahead of the streamer head.In recent experiments by Nijdam  et al [1], small hairs were  observed  connecting to  the  main  streamer  channels, giving  the  entire  channel  a  somewhat  feather-like appearance. These feathers were visible in “pure” nitrogen with at most 1 ppm contamination of oxygen, as can be seen in figure 1, and in pure argon. In air, no such feathers were observed.Fig.  1.  Zoom to segments of  positive streamers  in nitrogen  at  200  mbar.  Hairs  are  inside  the rectangular boxes. The picture is from [1].2. Hypothesis on the origin of feathersWe hypothesize  that  the  feathers  are  separate  electron avalanches moving towards the streamer. Free electrons in front of the streamer head drift towards the streamer due to the enhanced electric  field  generated by the  space  charge layer  in  the  streamer  head.  Once  the  electrons  enter  the region  where  the  electric  field  is  above  the  breakdown value,  where  the  impact  ionization  rate  exceeds  the attachment rate, more free electrons are created than there are lost. This results in an avalanche that drifts towards the streamer head. This can be seen schematically in figure 2. If the  avalanche  is  created  directly  in  front  of  the  streamer head, it will be overtaken by the propagating streamer and will therefore not be visible in experiments. Avalanches seen in  experiments  start  away  from  the  path  of  streamer propagation.Fig.  2.  Schematic  representation  of  a  positive streamer propagating from left to right as found in [2] and many other papers and textbooks.If  at  the  critical  electric  field,  where  the  impact ionization  and  attachment  rates  are  equal,  the  electron denisty  is  low,  one  expects  that  these  avalanches  do  not overlap and can be seen as distinct structures. On the other hand, if the electron density is already high enough so that the average distance between free electrons is much smaller than the dimensions of the streamer, one expects so many avalanches that they will overlap and can no longer be seen as separate entitites, but only as a whole, being part of the propagating streamer.The source of electrons in front and to the sides of the streamer head is assumed to be photo-ionization. An excited nitrogen molecule falls back to the ground level emitting a photon with the right energy to ionize an oxygen molecule. The characteristic ionization length of these photons scales inversely with the oxygen density and as a consequence, the density  of  free  electrons  in  the  region  away  from  the streamer head are expected to be orders of magnitude higher in  air  than  in  nitrogen  with  only  a  very  small  oxygen admixture. Therefore we expect avalanches to overlap more easily  in  air,  while  in  nitrogen  with  a  1  ppm  oxygen admixture, the avalanches are more likely to be distinct.3. Numerical simulations and resultsNumerical  simulations  were  performed  with  a  code using an adaptive grid refinement scheme [3].  The model consists  of  a  fluid description for  the densities  with drift, 7th ICRP and 63rd GEC, October 4-8, 2010, Paris, Francediffusion and reaction terms. Included reactions are impact ionization,  attachment,  detachment  and  recombination. Photo-ionization  is  included  as  described  in  [4].  The electrode  configuration  is  needle-plane.  Simulations  are done at 300 K and 1 bar, using a voltage of 24 kV with an 8 mm  gap  between  the  tip  of  the  needle  and  the  planar electrode. Since we use a fluid approximation, our code can not  be  used  to  model  individual  avalanches.  For  this,  a particle  code  or  a  hybrid  code  such  as  [5]  is  needed. However, we can still use results from the fluid code to draw conclusions  on  whether  the  presence  of  hairs  and  the corresponding feather structure can be expected or not.The left panel of figure 3 shows the electron density and the boundary of the region where the electric field exceeds the critical field and avalanches can occur; the simulation is in air. With the rate coefficients from BOLSIG+ [6] for impact ionization  and  attachment,  as  they  were  used  in  the simulation, this critical field is 32 kV/cm. It is immediately obvious that at the outer boundary, the electron density is already 105  mm-3.  This  will  generate  so  many avalanches that they will overlap and are no longer distinct.Running the same simulation on a mixture of N2 with 1 ppm O2 gives completely different results. As can be seen in the right panel of figure 3, the electron density away from the  streamer  head  is  around  102 mm-3.  Additionally,  the density  of  the  attaching  oxygen  has  been  reduced  by  5 orders of magnitude, so the critical field is lower than in air,  which  in  turn  means  that  avalanches  can  be formed at  a greater distance from the streamer head. At these levels of electrons, the number of avalanches in this nitrogen mixture will  be  low  enough  in  number  to  be  visually  distinct, resulting in observable hairs in experiments.Fig.  3.  left:  Electron density in mm-3 of a positive streamer  in  air.  Black  line  indicates  where  the electric  field exceeds  the  breakdown value.  Right: Electron densities on the axis of positive streamers in air (solid line) and N2 with a 1 ppm O2 admixture (dashed line).We  can  estimate  the  number  of  hairs  per  mm  of streamer length by counting the number of free electrons in the region where the field is above the breakdown field. As a first estimate, we obtain 400 electrons per mm in 2 boxes parallel to the streamer channel as depicted in figure 1.In experiments  in nitrogen at  200 mbar,  1.5 hairs per mm of streamer length were observed. Applying similarity laws for streamers [7], this corresponds to 7.5 hairs per mm at  1  bar.  However,  our  simulations  have  a  much  higher background  electric  field  and  therefore  electron  densities will be much higher than in experiments.  In addition, the precise  level  of  O2 contamination  in  the  experiment  is unknown. The 1 ppm level that we used in our simulations is an  upper  bound  for  the  experimental  value.  Lower  O2 concentrations result in less free electrons and a lower hair density. Finally, not every free electron will end up forming a distinct avalanche. Indeed, electrons that are closer to the streamer may already be part of an ongoing avalanche, while we count them as source of their own avalanche.Since our numerical code assumes cylindrical symmetry, a  streamer can only be followed up to the point  where it branches. This limits the length of streamers in nitrogen that we can simulate and therefore we can't  directly match the parameters used in experiments.4. ConclusionWe  have  proposed  that  the  feather-like  structures  in positive streamers are due to individual avalanches created by  photo-ionization.  They  are  visible  only  in  nitrogen mixtures with a very small admixture of oxygen, and not in air,  since  in  air  the  avalanches are  too dense  and  largely overlap.  The  numerical  simulations  with  a  fluid  model, while  not  suited  for  simulation  of  individual  hairs,  have provided reasonable estimates  of the avalanche density  to support our hypothesis. Our estimate is an upper limit for the number of hairs. This number is lower in experiments because the local electric fields in the experiments are lower and the oxygen content is below 1 ppm, while 1 ppm was used in the simulations.References[1]  S.  Nijdam,  F.M.J.H.  van  de  Wetering,  R.  Blanc,  E.M.  van Veldhuizen,  U.  Ebert  :  J.  Phys.  D:  Appl.  Phys.  43 (2010) 145204.[2] L. Niemeyer, L. Ullrich, N. Wiegart: IEEE Trans. Elec. Ins. 24 (1989) 309-324.[3]  C.  Montijn,  W.  Hundsdorfer,  U.  Ebert:  J.  Comp.  Phys.  219 (2006) 801-835[4] A. Luque, U. Ebert, C. Montijn, W. Hundsdorfer: Appl. Phys. Lett. 90 (2007) 081501[5] C. Li, U. Ebert, W. Hundsdorfer: J. Phys. D: Appl. Phys.  42 (2009) 202003[6] G. J. M. Hagelaar, L. C. Pitchford: Plasma Sources Sci. & Tech.  14 (2005) 722-733[7] U. Ebert, S. Nijdam, C. Li, A. Luque, T. M. P. Briels, E. M. van Veldhuizen:  J.  Geophys.  Res.  [in  press]  (2010) doi:10.1029/2009JA0148677th ICRP and 63rd GEC, October 4-8, 2010, Paris, France

Feather-like structures in positive streamers.

 
  In experiments positive streamers can have a feather-like structure, with small hairs connected to the main streamer channel. These feathers were observed in pure nitrogen (with impurities of 1 ppm oxygen or less) but not in air. We hypothesize that these hairs are individual electron avalanches moving towards the streamer channel. Based on results of numerical simulations, we provide a theoretical explanation why these hairs are visible in nitrogen, but not in air. 
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Gideon Wormeester

Sander Nijdam

Ute Ebert

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Japanese Journal of Applied Physics

Feather-Like Structures in Positive Streamers Interpreted as Electron Avalanches

Feather-like structures in positive streamers.

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