Competition of damping mechanisms for the phase-mixed Alfvén waves in the solar corona

The competition of the linear and nonlinear damping mechanisms for phase-mixed Alfvén waves in the solar corona is studied. It is shown that the nonlinear damping of the phasemixed Alfvén waves due to their parametric decay is stronger than both collisional and Landau damping for waves with frequencies below a critical frequency which depends on the wave amplitude. This critical frequency is close to the cyclotron frequency (∼ 105 s−1 in holes) even for small wave amplitudes of the order of 1% of the background value for the magnetic field. This means that the dissipation of the Alfvén wave flux in the corona can be significantly affected by the nonlinear wave dynamics. Nonlinear decay of the low-frequency Alfvén waves transmits a part of the wave energy from the length-scales created by phase mixing to smaller scales, where the waves damp more strongly. However, the direction of the effect can be reversed in the high-frequency domain, 10 s−1 < ω < 104 s−1, where the decay into counterstreaming waves is strongest, because the wave energy is quickly transferred to larger scales, where the actual dissipation is reduced. These effects are introduced by the vector nonlinearity which involves waves propagating in the different directions across magnetic field. The effects introduced by the scalar nonlinearity may also become important in phase mixing (Voitenko & Goossens, in preparation).