Transverse oscillations of two parallel magnetic tubes with slowly changing density

We study kink oscillations of the system of two parallel magnetic tubes in the presence of plasma cooling. We assume that the characteristic cooling time is much larger than the characteristic time of kink oscillations. Using the ratio of two characteristic times as a small parameter, we derive the expression for the adiabatic invariant, which is a quantity that remains constant during the cooling process. Then, we study in detail a particular case where the plasma densities in the two tubes are the same, the plasma temperature outside of the tube does not change, and the plasma temperature inside the tubes decreases exponentially. We found that cooling causes the increase of the oscillation frequencies and amplitudes. These results are the generalization of similar results previously obtained for a single magnetic tube. We compared the efficiency of amplification of kink oscillations caused by cooling in counteracting the damping of oscillations due to resonant absorption in two models of coronal magnetic loops: monolithic and consisting of two parallel filaments.