Parallel cascade of Alfvén waves

A heuristic semi-classical kinetic theory of turbulence in magnetized plasmas was formulated in the 1960s, but the statistical mechanical formulation of the same problem, which is necessary for a quantitative analysis, has not been accomplished. Recently, the present authors formulated the statistical mechanical kinetic turbulence theory in a formal manner (P H Yoon 2007 Phys. Plasmas14 10230, P H Yoon and T-M Fang 2007 Phys. Plasmas14 102303). In this paper, the parallel cascade of Alfvén waves via the three-wave decay process is numerically investigated on the basis of the results outlined in the above references. It is shown that the cascade of low-frequency Alfvén waves to high-frequency ion-cyclotron and magnetosonic waves takes place mediated by ion-sound turbulence. The Alfvén wave cascade is important, for instance, in the solar wind acceleration and coronal heating problem, since the low-frequency, long-wavelength Alfvén waves must first undergo cascade to high-frequency, short-wavelength modes in order for cyclotron resonant absorption to take place. The cyclotron resonance is believed to be important for charged-particle acceleration in the aforementioned applications. The present analysis may be important in such a context.