Equilibrium Characteristics of a Pinched Gas Discharge Cooled by Bremsstrahlung Radiation

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Abstract
Standard formulae for the electrical resistance and for the radiating properties of a fully ionized gas have been combined with pinch-effect relations to obtain the stationary state radial distribution functions and current-voltage characteristics of a radiation-cooled discharge, using a simplified model in which a stationary, axially symmetrical discharge is generated in a long straight tube. The validity of the diffusion conditions implied in the initial equations, the transport properties of the plasma, and the cyclotron radiation arising from thermal motion in the self-magnetic field, are considered. The calculations are applied to the requirements of a power-producing thermonuclear reactor. The chief results are that in a stationary state a pinched discharge will exist with radiation cooling, that the magnitudes of the voltages, tube diameters and initial gas pressure are within reasonable engineering limits, and that a maximum current of one to two million amperes will be encountered. This maximum is a characteristic current of an ionized gas and, slowly varying numerical factors apart, depends directly only on the fundamental constants e, m, h and c. While it is possible to present grounds for supposing these results to be independent of some of the assumptions, the work gives no guidance on the extent to which they will be invalidated by the instabilities of the current channel.

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