Distribution function and potential in the cathode region of a glow discharge
In view of the minor role played by ionization in the cathode dark space of a glow discharge, the ion distribution function and the potential profile must be determined by simultaneous solution of the Boltzmann equation and the Poisson equation. Knowing the distribution function enables us to find the ion density profile, the average energy and energy spectrum of the ions incident on the wall, etc. The calculation of these properties is essential in analyzing the cathode sheath of any discharge. The numerical solution of the problem is quite involved and provides a rather obscure picture of the role played by the various physical parameters. In the present work we consider a form of analytical solution of the problem of determining the ion distribution function and the potential in the cathode dark space, which with some modification yields a nearly exact description of all the practically important situations and the basic ion properties in the cathode dark space. For this purpose we assume cylindrical geometry for the cathode and assume that the charge-exchange cross section depends on the ion velocity. This situation is close to the problem formulated elsewhere, but here we manage to obtain simpler analytical expressions over a wide range of the parameters of the problem. 2 refs., 2 figs.
- OSTI ID:
- 136386
- Journal Information:
- Soviet Journal of Plasma Physics, Journal Name: Soviet Journal of Plasma Physics Journal Issue: 1 Vol. 18; ISSN SJPPDC; ISSN 0360-0343
- Country of Publication:
- United States
- Language:
- English
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