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!
Interesting thesis. One might find this book of interest. http://www.physics.ucsd.edu/~tmurphy/phys239/BookFINAL.pdf With respect to: I believe that CMEs (and flares and prominences) and solar helioseismology (turbulence) involved investigation of nonlinear effects of phase-space structures.
Thank you! Actually it is this very book that inspired my current work. Very insightful indeed. On the theory side at least. The first author of this book is also a co-author of a paper I'm writing on a related topic. I'll post the paper here when it's published. However, in this book I didn't find any example of experimental study of the effect of phase-space structures (granulations) on turbulent astrophysical systems. One example, which shows striking similarities with phase-space structures in turbulent plasmas, is zonal flow in quasi-geostrophic systems, such as Jupiter. However, the structures live in real space, not in phase-space. The equations of conservation of potential vorticity and phase-space density (the QG equation and the Vlasov equation) are similar, but there's an important qualitative difference in the Hamiltonian, which makes me doubt we can expect similar physics.