Low-Frequency Waves and Instabilities on the Positive Column in a Magnetic Field. IV. Comparison of Various Theories for Helical Modes Illustrated for He at Low Pressures

The relations between three theories for helical modes of a positive column in a magnetic field, namely, those of Kadomtsev and Nedospasov, of Johnson and Jerde, and Ewald, Crawford, and Self are examined, and are shown to be different approximations, valid for different orderings of $\omega$ , ${\omega }_{\mathrm{ci}}$ , ${\nu }_i$ , to a general theory which includes both ion inertia and the effect of the magnetic field on the ions. A discussion is also given of the relation of these theories to the gradient‐driven ion acoustic and drift instabilities of an inhomogeneous magnetoplasma in a simple planar model. An experimental study of the positive column in He at low pressures supports the conclusion that there are two distinct instabilities. The first, setting in for low magnetic field and high frequency, corresponds to the ion acoustic instability and is described by the Ewald‐Crawford‐Self theory. The second, setting in for high magnetic field and low frequency, corresponds to the drift instability, and is reasonably described by the Johnson‐Jerde theory except at very low pressures. Their common asymptote is the Kadomtsev‐Nedospasov theory, valid only for high pressures.