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

The competition of the linear and nonlinear damping mechanisms for phase-mi xed Alfven waves in the solar corona is studied. It is shown that the nonli near damping of the phase-mixed Alfven waves due to their parametric decay is stronger than both collisional and Landau damping for waves with frequen cies below a critical frequency which depends on the wave amplitude. This c ritical frequency is close to the cyclotron frequency (similar to 10(5) s(- 1) in holes) even for small wave amplitudes of the order of 1% of the backg round value for the magnetic field. This means that the dissipation of the Alfven wave flux in the corona can be significantly affected by the nonline ar wave dynamics. Nonlinear decay of the low-frequency Alfven waves transmi ts 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 direct ion of the effect can be reversed in the high-frequency domain, 10 s(-1) < omega < 10(4) s(-1) where the decay into counterstreaming waves is stronges t, because the wave energy is quickly transferred to larger scales, where t he actual dissipation is reduced. These effects are introduced by the vector nonlinearity which involves wave s propagating in the different directions across magnetic held. The effects introduced by the scalar nonlinearity may also become important in phase m ixing (Voitenko & Goossens, in preparation).