Vertical Motions in an Intense Magnetic Flux Tube - Part Three - on the Slender Flux Tube Approximation
In a recent discussion of intense photospheric magnetic fields we gave an expansion procedure that lead to a tractible system of differential equations governing vertical motions in a slender flux tube embedded in a quiescent environment. Transverse variations were taken into account in our discussion. In support of this expansion scheme we considered the special case of a straight flux tube in a uniform atmosphere. Wilson (1978, 1979b) has now criticised our treatment of this special case. We discuss his objections here, and show them to be without foundation. The cause of the disparity between our results and his lies not in a breakdown of the slender flux tube approximation but rather in the differing assumptions as to the nature of pressure variations in the tube's exterior. We generalize the slender flux tube approximation in a uniform tube, and obtain the governing dispersion relation. This dispersion relation contains, as special cases, both the results of Roberts and Webb (1978) and those of Wilson (1979a).