Hostname: page-component-586b7cd67f-t8hqh Total loading time: 0 Render date: 2024-11-26T13:26:43.814Z Has data issue: false hasContentIssue false
  • English
  • Français

On ion—electron beams emitted by a plane

Published online by Cambridge University Press:  13 March 2009

Yeshaiahu Y. Winograd
Yeshaiahu Y. Winograd
Affiliation:
Brown University, Providence, R.I.
Get access Rights & Permissions [Opens in a new window]

Abstract

The non-linear one-dimensional steady-state equations which govern the flow of an ion—electron beam emitted from a plane are solved in the phase plane, and it is shown that a perfectly neutralized beam follows for a large range of injection velocities of the electrons. When the velocity of the ions is less than the electron sound speed the transition region for the neutralization has a length of the order of a Debye length λD = (kT)½ (4πNe2)–½, which is a typical plasma sheath. The maximum velocity of injection of the electrons for which neutralization is predicted is, in this case, the sound speed of the electrons. If the electrons are injected with a supersonic speed, they cannot be decelerated continuously to the subsonic speed corresponding to the velocity of the ions. No bound is set on the electron injection velocity from below. When the velocity of the ion beam is greater than the electron sound speed, oscillations with an amplitude which depends on the velocity of injection of the electrons, and a wavelength which depends on the ratio of the ion velocity to the electron speed of sound, are found. In this case the injection speed of the electrons needed to obtain the steady-state oscillatory solution is bounded both from above and from below. Subsonic electrons cannot be accelerated continuously to the supersonic velocity required to match the velocity of the ions, and within the supersonic range there is shown to be a limit (depending on the ratio of the ion velocity to the electron speed of sound, so that faster electrons cannot be decelerated continuously to match the (supersonic) ion velocity.

Type
Research Article
Information
Journal of Plasma Physics , Volume 1 , Issue 3 , August 1967 , pp. 267 - 288
Copyright
Copyright © Cambridge University Press 1967

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCE

Abramowitz, M. & Stegun, I. A. 1964 Handbook of Mathematical Functions. National Bureau of Standards, Washington, D.C.Google Scholar
Burgers, J. M. 1960 Plasma Dynamics, p. 119. Edited by Clanser, F. H.. Reading: Addison Wesley.Google Scholar
Carslaw, H. S. & Jaeger, J. C. 1963 Operational Methods in Applied Mathematics. New York: Dover.Google Scholar
Chistova, E. A. 1959 Table of Bessel Functions of the True Arguments and of Integrals Derived from Them. Oxford: Pergamon Press.Google Scholar
Chistova, R. V. 1958 Operational Mathematics. New York: McGraw Hill.Google Scholar
Cybulski, R. J., Shellhammer, D. M., Lovell, R. R., Domino, K. J. & Kotnik, J. T. 1965 Results from Sert I ion rocket ffight test. NASA TDN-2718.Google Scholar
Derfler, H. 1964 Phys. Fluids 7, 1625.Google Scholar
Fröberg, C. F. & Wllhelmsson, H. 1957 Kungl. Fysiograflska Sällskapets i Lund Förhandlingar, Bd. 27, no. 16.Google Scholar
Gold, H., Julis, R. J., Murana, F. A. & Hawersaat, W. H. 1965 Description and operation of spacecraft in Sert I ion thruster ifight test. NASA TMX-1077.Google Scholar
Halverson, W. D., Degroff, H. M. & Holmes, R. A. 1961 Electrostatic Propulsion, p. 251. Edited by Langmuir, D. B., Stuhlinger, E. and Sellen, J. M.. New York: Academic Press.CrossRefGoogle Scholar
Ignatenko, V. P. & Myasinkov, A. S. 1961 Radio Engnq Electron. Phys. 6, 1868.Google Scholar
Kemp, R. F. & Sellen, J. M. 1963 Neutralizer tests on a flight-model electron-bombardment ion thrustor. NASA TND-1733.Google Scholar
Mirels, H. 1961 Electrostatic Propulsion, p. 373. Edited by Langmuir, D. B., Stuhlinger, E. and Sellen, J. M.. New York: Academic Press.CrossRefGoogle Scholar
Mirels, H. & Rosenbaum, B. M. 1960 Analysis of one-dimensional ion rocket with grid neutralization. NASA TND-266.Google Scholar
Smirnov, V. M. 1963 Radio Engng Electron. Phys. 8, 1632.Google Scholar
Stuhlinger, E. 1954 Proc. Fifth Int. Astro. Cong. p. 109.Google Scholar
Stuhlinger, E. 1964 Ion Propulsion for Space Flight, Ch. 5. New York: McGraw Hill.Google Scholar
Watson, G. N. 1944 A Treatise on the Theory of Bessel Function. Cambridge University Press.Google Scholar
Winograd, Y. Y. 1966 Ph.D. Thesis. Brown University, Providence, R.I.Google Scholar
Langmuir, et al. 1961 Electrostatic Propulsion, pp. 217–422. Edited by Langnuur, D. B., Stuhlinger, E. and Sellen, J. M.. New York: Academic Press.CrossRefGoogle Scholar
Staff of Ramo-Wooldridge Research Laboratories 1960 Proc. IRE 48, 477.Google Scholar