H. Stenuit et al., EIGENFREQUENCIES AND OPTIMAL DRIVING FREQUENCIES OF 1D NONUNIFORM MAGNETIC-FLUX TUBES, Astronomy and astrophysics, 331(1), 1998, pp. 392-404
The eigenfrequencies and the optimal driving frequencies for flux tube
s embedded in uniform but wave-carrying surroundings are calculated, b
ased on matching conditions formulated in terms of the normal acoustic
impedances at the Bur tube boundary. The requirement of the equality
of the normal acoustic impedance of the transmitted wave field with th
e normal acoustic impedance of the outgoing wave field selects the eig
enmodes, while the equality of the ingoing and the transmitted normal
acoustic impedance selects the optimal driving frequencies (Keppens 19
96). Even if the flux tube is uniform, the eigenfrequencies can be com
plex due to leakage of wave energy into the surroundings. The case of
uniform flux tubes has been considered previously (e.g. Cally 1986), a
nd serves as a testcase of our formalism. We extend Cally's results by
taking a radial stratification of the flux tube into account. The non
-uniformity of the flux tube can introduce another cause for energy lo
ss, namely resonant absorption internal to the flux tube. When resonan
t absorption occurs. we must incorporate the appropriate jump conditio
ns over the dissipative layer(s). This can be done using a simple nume
rical scheme as introduced by Stenuit et al. (1995).