Date of Award
Doctor of Engineering Science in Electrical Engineering
Raj Pratap Misra
Paul O. Hoffmann
The energy relaxation and electrical conductivity of an electron gas in one atmosphere argon arc discharge has been examined theoretically and observed quantitatively in an experimental arrangement. The plasma column utilized for study is the type generated in a fluid transpiration arc equipment in which the argon working fluid is injected through a porous graphite anode. The rate of forced convection is such as to insure significant electron-heavy particle nonequilibrium in the sample volume of interest. A simple model of a developing arc column with internal heat generation indicates that, with typical rates of argon injection realized in practice, the development of the column in the axial direction from a constant radial profile to a nearly fully-developed profile requires several cm, of which the first cm or so may be characterized as quasi one-dimensional in z. This region is large enough to allow transient probings and spectrometric observations the results of which can then be compared in a straight forward manner with a theoretical one-dimensional model. An examination of the various relaxation times in a three-component fluid (electron-ion-neutral) reveals that the self-relaxation times are short and the electron-heavy particle relaxation times are not negligible compared with the transit times through the nonequilibrium volume. It is therefore proper to employ the usual two-temperature macroscopic model equations obtained from the Boltzmann equation. Accordingly, the electrical conductivity and the two-temperature volume rates of energy transfer have been obtained. The diagnostic techniques utilized include (1) Hall-effect magnetic field probe for current density, (2) floating electrostatic probe for electric field, (3) spherical thermocouple heat transfer probe for heavy particle temperature, and, (4) continuum intensity measurement for electron density and temperature. High-speed motion pictures give qualitative measure of the plasma volume and its reaction to a material probe.
The results indicate that while somewhat higher electrical conductivities are observed the volume rates of energy transfer show fairly wide discrepancy between theory and experiment. Thus, although electron energy loss is observed to be due to volume transfer to the heavy particles the familiar current density compatibility relation, J = nee√3k(Ts- Ts)/ms appears not to hold. This is ascribed to the possibility that the collision frequency for momentum transfer and the collision frequency for energy transfer may not be the same. In particular, the observed collision frequency for energy transfer between electron and ion appears to be one fifth of that magnitude predicted by current theories. It is suggested that a modified theory is needed for the particular condition of low nD (the number of electrons within a Debye sphere) for ne≈2x1016 cm-3 and Te≈ 104 °K.
Tschang, Pin-Seng, "Energy transfer and electron conduction in the fluid transpiration arc column" (1967). Dissertations. 1332.