The presence of finite current sheets at the boundaries of a magnetic flux sheath will lead to a somewhat reduced transmission of the energy of an incident acoustic wave.
In order to study the role played by magnetic structures in the energy transport in the solar atmosphere, Cram and Wilson (1975) considered the transmission of the energy of an acoustic wave incident on a magnetic flux sheath embedded in a homogeneous non-magnetic plasma. It is clear from their results that the transmission is affected substantially whenever the wavelength of the incident wave becomes comparable to the thickness of the flux sheath. This fact becomes very significant because the small scale magnetic structures in the chromosphere (e.g. Foukal, 1971) have their cross-sections comparable to the wavelengths of some of the more prominent waves (e.g. those corresponding to the five minutes oscillations) which may be incident on them*.
Cram and Wilson assumed a rectangular profile for the magnetic field intensity in the structure. Such a structure obviously implies infinite current densities at the boundaries. In this note, we consider a similar structure but with finite current sheets between the flux sheath and the non-magnetic region outside. The geometrical configuration is given in Figure 1. The magnetic field in the current sheet (of thickness 'a') has a constant spatial gradient along the x-direction.
It levels off at a constant value Hm in the flux sheath and continues for a length 'b' times 'a'. Thereafter it reduces symmetrically to zero at the edge of the field-free plasma.
The x-dependance of the field prevents all perturbations from being simple harmonic along that direction. We have therefore assumed perturbations of the form * We have also compared the transmission efliciencies of the two kinds of structures with equal amounts of magnetic flux and with the same value for the field intensity (M = 1.2) in the flux sheath. This sample calculation indicates that the main conclusion is valid even for such a comparison.