We analyze nonlinear evolution of torsional Alfvén waves in a straight magnetic flux tube filled in with a low-β plasma, and surrounded with a plasma of lower density. Such magnetic tubes model, in particular, a segment of a coronal loop or a polar plume. The wavelength is taken comparable to the tube radius. We perform a numerical simulation of the wave propagation using ideal magnetohydrodynamics. We find that a torsional wave nonlinearly induces three kinds of compressive flows: the parallel flow at the Alfvén speed, which constitutes a bulk plasma motion along the magnetic field, the tube wave, and also transverse flows in the radial direction, associated with sausage fast magnetoacoustic modes. In addition, thenonlinear torsional wave steepens and its propagation speed increases. The latter effect leads to the progressive distortion of the torsional wave front, i.e., nonlinear phase mixing. Because of the intrinsic non-uniformity of the torsional wave amplitude across the tube radius, the nonlinear effects are more pronounced in regions with higher wave amplitudes. They are always absent at the axes of the flux tube. In the case of a linear radial profile of the wave amplitude, the nonlinear effects are localized in an annulus region near the tube boundary. Thus, the parallel compressive flows driven by torsional Alfvén waves in the solar and stellar coronae, are essentially non-uniform in the perpendicular direction. The presence of additional sinks for the wave energy reduces the efficiency of the nonlinear parallel cascade in torsional Alfvén waves.

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We study the coronal mass ejection (CME) with a complex acceleration profile. The event occurred on April 23, 2009. It had an impulsive acceleration phase, an impulsive deceleration phase, and a second impulsive acceleration phase. During its evolution, the CME showed signatures of different acceleration mechanisms: kink instability, prominence drainage, flare reconnection, and a CME-CME collision. The special feature of the observations is the usage of the TESIS EUV telescope. The instrument could image the solar corona in the Fe 171Å line up to a distance of 2 R ⊙ from the center of the Sun. This allows us to trace the CME up to the LASCO/C2 field of view without losing the CME from sight. The onset of the CME was caused by kink instability. The mass drainage occurred after the kink instability. The mass drainage played only an auxiliary role: it decreased the CME mass, which helped to accelerate the CME. The first impulsive acceleration phase was caused by the flare reconnection. We observed the two ribbon flare and an increase of the soft X-ray flux during the first impulsive acceleration phase. The impulsive deceleration and the second impulsive acceleration phases were caused by the CME-CME collision. The studied event shows that CMEs are complex phenomena that cannot be explained with only one acceleration mechanism. We should seek a combination of different mechanisms that accelerate CMEs at different stages of their evolution.

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