By W. B. Thompson (Auth.)

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Similarly a cylindrical flux tube could be held in equilibrium by a conducting fluid. We have already displayed an example of a gas confined by a uniform axial current, and it is clear that arbitrary axial currents can maintain systems in equilibrium. An interesting relation holds for any such system. 2) 54 AN INTRODUCTION TO PLASMA PHYSICS There is an important class of cylindrical equilibria in which the gas pressure is balanced by helical field lines. In these, the pressure due to the axial magnetic field is simply added to the gas pressure and relationships similar to eq.

6, 218, 1942). in the ionization potential increases the effective cross section exponentially, while at the same time the intrinsic cross sections are much higher for ionization from excited states. In spite of these difficulties attempts have been made to calculate the approximate characteristics of the positive column, noticeably by KARFELD 36 AN I N T R O D U C T I O N TO PLASMA PHYSICS (1941) and KARELINA (1942). From the plasma balance equation, the electron temperature T_ can be obtained as a function of apo, the product of the tube radius and gas pressure, and here the difficulty already observed in Langmuir's calculation of λ appears, measured temperatures being ~20 per cent below calculated ones.

Phys. S oc. B . 64, 345, 1951). This has been an exceedingly simplified discussion of the pinch effect, but it has displayed some aspects of the phenomenon. To proceed with the study of such systems, which are of great interest in plasma physics, it is necessary to use even cruder models of the plasma, but much more powerful methods of study. An early experiment on the constriction of an arc was performed by THONEMANN and COWIIIG (1951). These authors assumed that the electron 4 42 AN I N T R O D U C T I O N TO PLASMA PHYSICS axial drift velocity rather than the current density was uniform across the tube, supporting this by experimental evidence, and obtained a density distribution in the form n — = (l + 6r2)-2 n0 where b = (nnoe2w2/2kTc2) was a constant that could be expressed in terms of the measurable electron temperature, current and drift velocity.