Resonant damping of kink oscillations of thin cooling and expanding coronal magnetic loops

We have considered resonant damping of kink oscillations of cooling and expanding coronal magnetic loops. We derived an evolutionary equation describing the dependence of the oscillation amplitude on time. When there is no resonant damping, this equation reduces to the condition of conservation of a previously derived adiabatic invariant. We used the evolutionary equation describing the amplitude to study the competition between damping due to resonant absorption and amplification due to cooling. Our main aim is to investigate the effect of loop expansion on this process. We show that the loop expansion acts in favour of amplification. We found that, when there is no resonant damping, the larger the loop expansion the faster the amplitude growths. When the oscillation amplitude decays due to resonant damping, the loop expansion reduces the damping rate. For some values of parameters the loop expansion can fully counterbalance the amplitude decay and turn the amplitude evolution into amplification