Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-25T05:52:41.870Z Has data issue: false hasContentIssue false
  • English
  • Français

The Bohm criterion in the presence of radio-frequency fields

Published online by Cambridge University Press:  13 March 2009

J. E. Allen  and
M. A. Skorik
J. E. Allen
Affiliation:
Department of Engineering Science, University of Oxford, Parks Road, Oxford OX1 3PJ, UK
M. A. Skorik
Affiliation:
Department of Engineering Science, University of Oxford, Parks Road, Oxford OX1 3PJ, UK
Get access Rights & Permissions [Opens in a new window]

Extract

In d.c. discharges the Bohm condition is the condition for sheath formation, the ion velocity at the plasma boundary having to satisfy the condition ½Mv2 = ½kB Te, if the spread of velocities is ignored. The model is a good one if the Debye distance is small compared with the relevant scale length. As there is much current interest in radio-frequency (RF) discharges, the question arises as to whether the criterion remains valid in the presence of RF fields. The question has been studied recently by Riemann, following earlier work by Allen who compared the plasma boundary to a sonic surface. Riemann considered a wider range of frequencies and obtained a dispersion relation that was a quartic equation. The present paper examines the complex roots of this equation, using a method developed by Briggs. The results substantiate Riemann's statement that the Bohm criterion is still valid in the presence of RF fields.

Type
Articles
Information
Journal of Plasma Physics , Volume 50 , Issue 2 , October 1993 , pp. 243 - 249
Copyright
Copyright © Cambridge University Press 1993

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

REFERENCES

Allen, J. E. 1976 J. Phys. D: Appl. Phys. 9, 2331.Google Scholar
Allen, J. E. & Phelps, A. D. R. 1977 Rep. Prog. Phys. 40, 1305.CrossRefGoogle Scholar
Bohm, D. 1949 The Characteristics of Electrical Discharges in Magnetic Fields (ed. Guthrie, A. & Wakerling, R. K.), chap. 3. McGraw-Hill.Google Scholar
Briggs, R. J. 1964 Electron Stream Interaction with Plasmas. MIT Press.CrossRefGoogle Scholar
Clemmow, P. C. & Dougherty, J. P. 1969 Electrodynamics of Particles and Plasmas. Addison-Wesley.Google Scholar
Fried, B. D. & Conte, S. D. 1961 The Plasma Dispersion Function. Academic.Google Scholar
Fried, B. D. & Gould, R. W. 1961 Phys. Fluids 4, 139.CrossRefGoogle Scholar
Jackson, J. D. 1960 J. Nucl. Energy C 1, 171.Google Scholar
Riemann, K.-U. 1992 Phys. Fluids B 4, 2693.Google Scholar
Stangeby, P. C. & Allen, J. E. 1970 J. Phys. A: Gen. Phys. 3, 304.CrossRefGoogle Scholar
Stringer, T. E. 1964 J. Nucl. Energy C 6, 267.CrossRefGoogle Scholar
Sturrock, P. A. 1958 Phys. Rev. 112, 1488.CrossRefGoogle Scholar
Sturrock, P. A. 1960 Phys. Rev. 117, 1426.Google Scholar
Twiss, R. Q. 1951 Proc. Phys. Soc. B 64, 654.Google Scholar
Twiss, R. Q. 1952 Phys. Rev. 88, 1392.CrossRefGoogle Scholar