Emergence of persistent advection-diffusion transport structure and nonlinear amplitude evolution of strongly-driven instabilities

We develop a transparent analytic formulation to describe the transport structure and nonlinear amplitude evolution of a strongly driven kinetic instability in the presence of a Fokker-Planck scattering operator at a single resonance. In this regime, the initial system gradient is steep enough that the wave grows to a large amplitude via nearly collisionless Landau damping before the system’s sources and sinks start to play a role in the dynamics. This gives rise to a strong separation of timescales which can be used to split the dynamics into two phases which can be analyzed separately. In the second phase of evolution, the leading order distribution function is found to satisfy an advection-diffusion equation in time and energy variables. Under realistic conditions, collisions and dissipation control the dynamics in this phase and the distribution evolves time locally. We exploit this time locality and construct a piecewise-continuous solution for the nonlinear evolution of the mode amplitude. This result agrees closely with nonlinear kinetic simulations performed using the BOT code [1] and is in some cases robust beyond the strongly driven limit.



[1] M. K. Lilley, et al., Physics of Plasmas 17, 092305 (2010).