Resonant Damping of Propagating Kink Waves in Time-Dependent Magnetic Flux Tube
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We explore the notion of resonant absorption in a dynamic time-dependent magnetised plasma background. Very many works have investigated resonance in the Alfvén and slow MHD continua under both ideal and dissipative MHD regimes. Jump conditions in static and steady systems have been found in previous works, connecting solutions at both sides of the resonant layer. Here, we derive the jump conditions in a temporally dependent, magnetised, inhomogeneous plasma background to leading order in the Wentzel–Kramers–Billouin (WKB) approximation. Next, we exploit the results found in Williamson and Erdélyi (Solar Phys. 289, 899, 2014) to describe the evolution of the jump condition in the dynamic model considered. The jump across the resonant point is shown to increase exponentially in time. We determined the damping as a result of the resonance over the same time period and investigated the temporal evolution of the damping itself. We found that the damping coefficient, as a result of the evolution of the resonance, decreases as the density gradient across the transitional layer decreases. This has the consequence that in such time-dependent systems resonant absorption may not be as efficient as time progresses.
KeywordsMHD waves Resonant damping Time-dependent medium
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