Heuristic Solution of Langmuir Problem in Arbitrary Domain

  • N. A. Azarenkov V.N. Karazin Kharkiv National University
  • A. V. Gapon V.N. Karazin Kharkiv National University
  • S. V. Dudin V.N. Karazin Kharkiv National University
Keywords: collisionless plasma, Langmuir problem, free fall regime


The Langmuir problem for a collisionless plasma was formulated and solved for some simple domains at 1921. But, for more complicated cases, no robust method is known till now except for the macro particle simulation. We propose a new method applicable to domains with arbitrary boundary shape. The method is based on the solution of the well-known eigenvalue roblem for diffusion-type equations. The comparison of test solutions obtained by this technique with the Particle-In-Cell method demonstrates an acceptable accuracy despite the lack of theoretical validation of this method.


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How to Cite
Azarenkov, N., Gapon, A., & Dudin, S. (2018). Heuristic Solution of Langmuir Problem in Arbitrary Domain. Ukrainian Journal of Physics, 62(1), 33. https://doi.org/10.15407/ujpe62.01.0033
Plasmas and gases