PROTON HEATING BY NONLINEAR FIELD-ALIGNED ALFVEN WAVES IN SOLAR CORONAL HOLES

Field-aligned Alfven waves are often viewed as a source of the proton heating that accelerates the fast solar wind. However, the energy that they can inject into the protons in the limit of cyclotron-resonant quasi-linear diffusion is insufficient to account for the observed acceleration. To test the validity of this limit in coronal holes, nonlinear Alfven waves are modeled using a hybrid code. It is found that the nonlinearity is particularly strong when the intensity of antisunward-propagating waves is comparable to that of sunward waves. The sunward waves can be generated by the proton distribution as it evolves with the heliocentric distance. The ponderomotive force and beat interaction are identified as the most important nonlinear effects. The nonlinearity of the field-aligned Alfven waves produces density fluctuations. In the simulations, the amplitude of the density fluctuations was kept within the observed constraints from the interplanetary scintillation measurements in the corona. In this case, the characteristic time of the proton heating is almost 2 orders of magnitude smaller than the solar wind expansion time. Therefore, it can contribute to the energization of the solar wind on the global scale. The nonlinear wave damping operating alone cannot be responsible for the energization because it only causes particle diffusion parallel to the magnetic field. However, it can relax the limitation on the perpendicular diffusion imposed by the cyclotron resonance condition. The nonlinear damping combined with the linear one can then inject the additional thermal energy needed to accelerate the solar wind.