# Analysis Seminar

#### Kinetic, Nonlinear, Non-Stationary, Multimode, Self-Sustaining Structures in Vlasov Plasmas

**Speaker:**
Bedros Afeyan, Polymath Research Inc.

**Location:**
Warren Weaver Hall 412

**Date:**
Tuesday, November 24, 2015, 11 a.m.

**Synopsis:**

Beyond the single mode assumption of common theoretical practice, and much before any stationary state might be reached, we show that it is possible to excite and sustain nonlinear kinetic structures in Vlasov-Poisson plasmas. Beyond linear Landau Damping or its finite, yet small amplitude generalizations ala Villani, beyond echoes and when particle trapping is in full gear, we find multimode structures that essentially reconstitute themselves as coherent waves. They live atop mixed integrable and chaotic orbit particle trajectories. While trapping-unwrapping-retrapping oscillations abound, in certain critical regions of phase space, the overall generally multimode wave structure is preserved, breathing, and surviving undamped.

Not BGK modes, not Landau Damping, not single mode theory, nor stationary; not echoes, not weak turbulence, nor strong, these are large scale vortical structures that must be taken into account in any full picture of the nonlinear evolution of one or more species plasmas with energy injection. These waves have no linear limit in the sense that they are not resonances falling on dispersion curves in the infinitesimal amplitude case. In that limit, they would be strongly damped modes. They also have no fluid limit since they require severe modifications of the distribution function in a spatially inhomogeneous way, self-adjusting and not settling down in the time-independent sense of BGK modes and similar findings.

We will show the example of kinetic electrostatic electron nonlinear (KEEN) waves and their pair plasma generalization also involving positrons instead of a massive stationary ion background. We call these (KEEPN) Waves. The stratification of phase space into segregated regions with their own particle orbit statistics, thus their own phase-space-fluid dynamics, will be demonstrated. The multimode character, the particle orbit statistics in different partitions, and the nonlocal interaction between KEEN wave and linear resonant structures such as electron plasma waves (EPW) will also be shown.

An especially interesting prospect is that these hitherto unknown structures in the 2D Euler equation shear flow setting may connect this work to that of Bedrossian and Masmoudi on Couette flow, for instance. How such nonlinear non-stationary structures are created and how they sustain themselves, will be discussed.

Work supported by the AFOSR. Previously, by the DOE NNSA-FES Joint Program on HEDP.