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We present results from a kinetic model of collisionless gyrotropic coronal hole protons heated by cyclotron and Landau resonant dissipation of critically balanced kinetic Alfv\'en waves. The model incorporates the kinetic effects of gravity, ambipolar electric field, ponderomotive force of the large-scale Alfv\'en waves and the mirror force in a super-radially expanding flux tube. The flow speed is self- consistently obtained as the bulk flow of the proton distribution. Two cases, taking the intensities of the turbulent spectra to be balanced in the parallel propagation direction or imbalanced at a ratio of 9:1 show almost no difference. The distributions develop parallel extensions outward due to the Landau resonance, but exhibit very little perpendicular heating under the parameter choices used here. The speeds and temperatures fall well short of the requirements for a fast solar wind. Rather than continuing to explore the parameter space of this system, we propose that a modified model using turbulent spectra based on the recent helicity barrier scenario would be an appropriate next step.
Isenberg et al. (Sat,) studied this question.