Density fluctuations induced by modulational instability of parallel propagating Alfvén waves with β _f ∼ 1

Density fluctuations generated by envelope modulation of Alfvén waves are studied when the sound to Alfvén velocity ratio C _s/C _A (≡ √β _f) ∼ 1, using a kinetic version of the triple-degenerate derivative nonlinear Schrödinger (TDNLS) equation set, in which both right- and left-hand polarized quasi-parallel Alfvén waves as well as sound waves, all propagating in the same direction, are included. In the model, kinetic effects along the longitudinal direction are introduced phenomenologically. Long time evolution of the Alfvén waves are discussed by numerically time integrating the obtained TDNLS model. The TDNLS model reproduces not only features of the well-known derivative nonlinear Schrödinger (DNLS) model, but also results obtained from more general frameworks. Numerical results suggest that the nonlinearly-driven modulational instability can play important roles in the dissipation of both right- and left-hand polarized Alfvén waves in the solar wind.