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## Decayless Kink Oscillations Excited by Random Driving: Motion in Transitional Layer

In this article we study the plasma motion in the transitional layer of a coronal loop randomly

driven at one of its footpoints in the thin-tube and thin-boundary-layer (TTTB) approximation. We introduce the average of the square of a random function with respect to time. This

average can be considered as the square of the oscillation amplitude of this quantity. Then

we calculate the oscillation amplitudes of the radial and azimuthal plasma displacement as

well as the perturbation of the magnetic pressure. We find that the amplitudes of the plasma

radial displacement and the magnetic-pressure perturbation do not change across the transitional layer. The amplitude of the plasma radial displacement is of the same order as the

driver amplitude. The amplitude of the magnetic-pressure perturbation is of the order of

the driver amplitude times the ratio of the loop radius to the loop length squared. The amplitude of the plasma azimuthal displacement is of the order of the driver amplitude times

Re1/6, where Re is the Reynolds number. It has a peak at the position in the transitional layer

where the local Alfvén frequency coincides with the fundamental frequency of the loop kink

oscillation. The ratio of the amplitude near this position and far from it is of the order of ,

where is the ratio of thickness of the transitional layer to the loop radius. We calculate the

dependence of the plasma azimuthal displacement on the radial distance in the transitional

layer in a particular case where the density profile in this layer is linear