ABSTRACT
This chapter describes the passive evolution problem in some detail, using it to make several main points. It shows that the random fluctuation of the frequency of an oscillator interacting with a turbulent bath causes damping of the oscillation, and an associated broadening of the oscillator resonance. The chapter also describes the role of the ratio between the correlation time and the "eddy-turnover time," or the time required for the turbulent field to affect a test field. It discusses how approximate solutions can be found in the limit of short autocorrelation time, thereby motivating the more detailed development of quasilinear theory. The resonant nature of the diffusion coefficient in the limit of short correlation time is due to the fact that approximation method treats the particle motion as unperturbed. The chapter concludes with the quasilinear theory for the relaxation of a gentle bump on the tail of a distribution function.
