Linear MHD Wave Propagation in Time-Dependent Flux Tube

MHD waves and oscillations in sharply structured magnetic plasmas have been studied for static and steady systems in the thin tube approximation over many years. This work will generalize these studies by introducing a slowly varying background density in time, in order to determine the changes to the wave parameters introduced by this temporally varying equilibrium, i.e. to investigate the amplitude, frequency, and wavenumber for the kink and higher order propagating fast magnetohydrodynamic wave in the leading order approximation to the WKB approach in a zero-β plasma representing the upper solar atmosphere. To progress, the thin tube and over-dense loop approximations are used, restricting the results found here to the duration of a number of multiples of the characteristic density change timescale. Using such approximations it is shown that the amplitude of the kink wave is enhanced in a manner proportional to the square of the Alfvén speed, $V_{\mathrm{A}}^{2}$ . The frequency of the wave solution tends to the driving frequency of the system as time progresses; however, the wavenumber approaches zero after a large multiple of the characteristic density change timescale, indicating an ever increasing wavelength. For the higher order fluting modes the changes in amplitude are dependent upon the wave mode; for the m=2 mode the wave is amplified to a constant level; however, for all m≥3 the fast MHD wave is damped within a relatively small multiple of the characteristic density change timescale. Understanding MHD wave behavior in time-dependent plasmas is an important step towards a more complete model of the solar atmosphere and has a key role to play in solar magneto-seismological applications.