{"abstracts":[{"sha1":"ab8b81bcaacf012c8fc83162edc126cbb5ff0ed6","content":"We propose a new approach to unambiguous determination of parameters of\npositive and negative electric streamer discharges. From hydrodynamic\nequations, in the assumption of a solution in the shape of a streamer, it is\npossible to derive several relations between streamer parameters, which form a\nsystem of algebraic equations (SAE). Because of the made approximations, the\nerror in the solution of this system is expected to be probably up to a few\ntens of percent. Solving the SAE allows us to express all streamer parameters\nin terms of the streamer length L, the constant uniform external electric\nfield E_e, and the streamer radius. The solutions with different radii are\nvalid solutions of the hydrodynamic equations, and are analogous to the\npropagation modes of flat-front perturbations with different transverse\nwavelengths. We interpret the streamer as a nonlinear instability, whose\nbehavior is determined by choosing the radius at which the velocity is\nmaximized, because, as we show, the velocity plays the same role as the\nexponential growth rate in the case of linear instabilities.\n Thus, streamer behavior is unambiguously determined by E_e and L, in a\nrelatively computationally economical way. In contrast, numerical methods of\nsolving the microscopic equations, such as hydrodynamic simulations, are more\ncomputationally demanding, and the preferred solution in them arises\nautomatically because of numerical fluctuations. The calculations for air at\nsea level conditions produce reasonable values for commonly observed streamer\nparameters. The calculated positive streamer velocities and negative threshold\nfields are compatible with experimental measurements. The physical reason for\nthe positive threshold fields is also discussed. A much simplified analytical\nmodel (Appendix B) reproduces many of the presented results, at least\nqualitatively.","mimetype":"text/plain","lang":"en"},{"sha1":"8f0296be5fdf279be7be236d232463cace25ac04","content":"We propose a new approach to unambiguous determination of parameters of\npositive and negative electric streamer discharges. From hydrodynamic\nequations, in the assumption of a solution in the shape of a streamer, it is\npossible to derive several relations between streamer parameters, which form a\nsystem of algebraic equations (SAE). Because of the made approximations, the\nerror in the solution of this system is expected to be probably up to a few\ntens of percent. Solving the SAE allows us to express all streamer parameters\nin terms of the streamer length $L$, the constant uniform external electric\nfield $E_e$, and the streamer radius. The solutions with different radii are\nvalid solutions of the hydrodynamic equations, and are analogous to the\npropagation modes of flat-front perturbations with different transverse\nwavelengths. We interpret the streamer as a nonlinear instability, whose\nbehavior is determined by choosing the radius at which the velocity is\nmaximized, because, as we show, the velocity plays the same role as the\nexponential growth rate in the case of linear instabilities.\n Thus, streamer behavior is unambiguously determined by $E_e$ and $L$, in a\nrelatively computationally economical way. In contrast, numerical methods of\nsolving the microscopic equations, such as hydrodynamic simulations, are more\ncomputationally demanding, and the preferred solution in them arises\nautomatically because of numerical fluctuations. The calculations for air at\nsea level conditions produce reasonable values for commonly observed streamer\nparameters. The calculated positive streamer velocities and negative threshold\nfields are compatible with experimental measurements. The physical reason for\nthe positive threshold fields is also discussed. A much simplified analytical\nmodel (Appendix B) reproduces many of the presented results, at least\nqualitatively.","mimetype":"application/x-latex","lang":"en"}],"refs":[],"contribs":[{"index":0,"raw_name":"Nikolai G. Lehtinen","role":"author"}],"license_slug":"ARXIV-1.0","language":"en","version":"v1","ext_ids":{"arxiv":"2003.09450v1"},"release_year":2020,"release_date":"2020-03-20","release_stage":"submitted","release_type":"article","webcaptures":[],"filesets":[],"files":[{"release_ids":["lytmgp5urjakvat6fzg23zadeu"],"mimetype":"application/pdf","urls":[{"url":"https://arxiv.org/pdf/2003.09450v1.pdf","rel":"repository"},{"url":"https://web.archive.org/web/20200325050014/https://arxiv.org/pdf/2003.09450v1.pdf","rel":"webarchive"}],"sha256":"9efd29bfbe8ddde4da52d9ad210ba97ee701b3dde9bb4fd94c8b57a3f1d4a488","sha1":"98c66df7fb3924185e944b7c02b7891b880604b4","md5":"45b16eb46f149f1467ee1d9b32b3132a","size":1009816,"revision":"3bd62ae6-87a5-4c76-bf73-27a932bf1c1f","ident":"gl33scqclrgkfl4bkykonumasu","state":"active"}],"work_id":"bil6fbfgtbdeloknbiufcopcim","title":"Electric streamers as a nonlinear instability: the model details","state":"active","ident":"lytmgp5urjakvat6fzg23zadeu","revision":"7bf30f96-a7de-48b5-90f7-8d51aed0f88b","extra":{"arxiv":{"base_id":"2003.09450","categories":["physics.plasm-ph","physics.ao-ph"],"comments":"25 pages, 10 figures, submitted to PRE"}}}