Particle kinetic equation including weakly turbulent mode coupling

In this article, particle kinetic equations which incorporate the nonlinear wave-particle interaction, as derived in P. H. Yoon [Phys. Plasmas 7, 4858 (2000)] and V. N. Tsytovich [Theory of Turbulent Plasma (Consultants Bureau, New York, 1977), pp. 103-110] are re-examined. A unified formalism is obtained after discrepancies in both references are resolved. The present particle kinetic equation is valid for the velocity space which does not satisfy the linear wave-particle resonance condition, ω-k·v≠0, but when the particle velocity of interest primarily satisfies the nonlinear wave-particle resonance, ω-ω'-(k-k')·v=0