Mechanical analogy of the nonlinear dynamics of a driven unstable mode near marginal stability

Journal article, 2009

The universal integrodifferential model equation derived by Berk [Phys. Rev. Lett. 76, 1256 (1996)] for studying the nonlinear evolution of unstable modes driven by kinetic wave particle resonances near the instability threshold is reduced to a differential equation and next as a further simplification to a nonlinear oscillator equation. This mechanical analogy properly reproduces most of the essential physics of the system and allows an understanding of the qualitative features of the theory of Berk.