Here is a glimpse of my current research. This is a kinetic simulation of electrostatic waves in a bump-on-tail plasma, with multiple resonances and some dissipation. Quasi-linear theory predicts a flattening of the velocity distribution over the range of resonant velocities of linearly unstable modes. However, self-coherent phase-spaces structures known as holes and clumps change this picture significantly. This physics is relevant to tokamaks (magnetically confined fusion devices), where the frequencies of several co-existing Alfvén eigenmodes, which are driven by energetic ions, have been observed to sweep in time (chirping). Chirping is a signature of evolving holes and clumps. What I am wondering is whether there are implications in space plasma. Do you know of any experimental observation or theoretical work on the nonlinear effect of phase-space structures on turbulence? More on this simulation: Nonlinear growth, evolution and interaction of self-coherent phase-space structures in a dissipative bump-on-tail plasma simulation with multiple resonances, using the kinetic code COBBLES. Up: perturbed distribution function. Down: spatially-averaged velocity distribution. Dashed vertical lines at the beginning of the video show the resonances that are linearly unstable. Holes are in blue and clumps are in yellow. Quasi-linear theory predicts a flattening of the velocity distribution over the range of resonant velocities of linearly unstable modes. However, self-coherent phase-spaces structures known as holes and clumps change this picture significantly. During this simulation, several hole/clump pairs spontaneously emerge at different resonance velocities and subsequently merge with each others, until there remains mainly one single hole. Note that phase-space structures survive for a collisional diffusion time, which is much longer than the quasi-linear diffusion time. Final time in this video, normalized to the plasma frequency: 2400. More on the code: M. Lesur, Y. Idomura, and X. Garbet, Fully nonlinear features of the energy beam-driven instability, Phys. Plasmas 16, 092305 (2009). More on the model: M. Lesur, The Berk-Breizman model as a paradigm for energetic particle-driven Alfvén eigenmodes, PhD Thesis (2011). Thanks!