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References in periodicals archive ?
By means of the solutions to (5) in both media, one can find the corresponding expressions for [[xi].sub.r], and after merging these solutions, together with those for [p.sub.tot], through appropriate boundary conditions at the interface r = a, one can derive the dispersion relation of the normal modes propagating in the moving magnetic flux tube.
In an untwisted magnetic flux tube, the coefficient [C.sub.1] = 0, while [C.sub.3] = [[rho].sub.0]D([[OMEGA].sup.2] - [[omega].sup.2.sub.A])--then (5) takes the form
The boundary conditions which merge the solutions of the Lagrangian displacement and total pressure perturbation inside and outside the twisted magnetic flux tube have the forms [85]
With the help of these boundary conditions we derive the dispersion relation of the normal MHD modes propagating along a twisted magnetic flux tube with axial mass flow [v.sub.0]
Firstly we shall study the dispersion characteristics of the kink (m - 1) mode in untwisted moving magnetic flux tube (in two approaches, notably (i) considering the jet and its surrounding plasma as compressible media and (ii) treating the jet as an incompressible medium while its environment is assumed to be cool plasma) and, later on, explore the same thing for the kink (m - 1) and higher (m > 1) MHD modes propagating in a twisted moving flux tube.
The speed ordering, [v.sub.A]i < [] < [v.sub.Ae] < [], according to Cally's [86] classification, tells us that in a rest magnetic flux tube the propagating wave must be a pure surface mode of type [S.sup.-.sub.+].
In this case, the speed ordering is [] < [] < [v.sub.Ai] < [v.sub.Ae] and the kink (m = 1) mode propagating in a rest magnetic flux tube is a pseudosurface (body) wave of type [B.sup.-.sub.+] (see Table I in [86]).
We note that while the wave attenuation coefficient of the m = 1 mode propagating in untwisted moving magnetic flux tube of incompressible plasma surrounded by a cool medium is not changed by the flow, in the twisted flux tube (in the same approximations) that attenuation coefficient becomes a complex number with positive imaginary part, like the attenuation coefficient in the cool environment.
We note that all the threshold Alfveen Mach numbers of higher MHD modes (m [greater than or equal to] 2) traveling on the moving twisted magnetic flux tube are larger than the predicted ones, but while for [epsilon] = 0.025 they (Alfven Mach numbers) are decreasing with increasing the mode number, at [epsilon] = 0.4 we have just the opposite ordering.
(i) The flow does not change the nature of propagating stable MHD modes being pure surface waves in a rest magnetic flux tube, but unstable ones due to high enough jet speed become partly surface and partly leaky waves.
Accessible flow velocities for instability onset in jet #11 have been derived for moving untwisted magnetic flux tube of compressible plasma (429 km [s.sup.-1]) and for the m = 4 MHD mode propagating in weakly twisted magnetic flux tube ([epsilon] = 0.025) of incompressible plasma surrounded by cool coronal medium (435.6 km [s.sup.-1]).
Numerically found threshold [M.sub.A] for initiating KH instability of the kink (m = 1) mode in moving untwisted magnetic flux tube of compressible plasma is 12.435 that yields a critical velocity of 607km [s.sup.-1].