Flat background probe in the mode of the continuous environment

Mathematics. Physics. Mechanics


Kotel'nikov V. A.*, Kotelnikov M. V.*

Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia

*e-mail: mvk_home@mail.ru


Consider a flat wall surface probe in the form of an elongated rectangle, located on a streamlined dense plasma surface. The problem is non-stationary two-dimensional, multi-parameter if the flow velocity is parallel to this surface and perpendicular to the long side of the rectangle.

Mathematical model of the problem includes the equation of continuity for ions and electrons and the Poisson equation for the self-consistent electric field. Total speed of charged particles vector consists of three components: convective, diffusive and a component that is associated with mobility. Convective component is determined from the solution of gas dynamic part of the problem and is considered a given.

Numerical model of the problem is based on the method of successive iterations in time. In particular, the continuity equation is solved by Davydov method of large particles, and the Poisson equation — by spectral methods.

Sets of current-voltage characteristics (CVC), sufficient for practice within limits of geometrical dimensions of the probe and values of directed plasma flow velocity, were obtained in numerical experiments. This set of CVC allows you to refine the results of processing the characteristics of probes installed on the surface of hypersonic aircraft (HA), as well as in plasma jets flowing out of technological plasmatrons in various applications (plasma chemistry, plasma spraying, plasma processing of surfaces, plasma electronics and etc).

In addition to probe characteristics profiles, the self-consistent electric fields, the concentrations of ions and electrons, evolutionary curves for streams of charged particles upon a plane probe and information about the role of nonlinear finite and edge effects are described in article. This information is necessary for analysis of heat, charge, mass flows and momentum flux from plasma upon the surface of HA.


electric probe, voltage-current characteristic, flat wall surface probe, continuity equation, Poisson equation, finite effect, edge effect


  1. Chan P., Telbot L., Turyan K. Elektricheskie zondy v nepodvizhnoi i dvizhushcheisya plazme. Teoriya i primenenie. (Electric probes in stationary and moving plasma. Theory and application), Moscow, Mir, 1978, 202 p.
  2. Alekseev B.V., Kotel’nikov V.A. Zondovyi metod diagnostiki plazmy (Probe method of plasma diagnostics), Moscow, Energoatomizdat, 1988, 239 p.
  3. Shan’kov A.V. Matematicheskoe modelirovanie protsessov perenosa vblizi ploskikh pristenochnykh zondov (Mathematical modeling of transfer processes near plane wall probes), Doctor’s thesis, Moscow, MAI, 1955, 218 p.
  4. Ul’danov S.B. Matematicheskoe modelirovanie protsessov perenosa vblizi zaryazhennykh tel v turbulentnom potoke plazmy (Mathematical modeling of transfer processes near charged bodies in turbulent plasma stream), Doctor’s thesis, Moscow, MAI, 2001, 102 p.
  5. Kotel’nikov V.A., Ul’danov S.V., Kotel’nikov M.V. Protsessy perenosa v pristenochnykh sloyakh plazmy (Transfer processes near the wall layers of plasma), Moscow, Nauka, 2004, 422 p.
  6. Kotel’nikov V.A., Gidaspov V.Yu., Kotel’nikov M.V. Matematicheskoe modelirovanie obtekaniya tel potokami besstolknovitel’noi i stolknovitel’noi plazmy (Mathematical modeling of flow past a bodies with collisionless and collisional plasma stream), Moscow, Fizmatlit, 2010, 288 p.


mai.ru — informational site MAI

Copyright © 2000-2024 by MAI