Irreversible energy flow in forced Vlasov dynamics

• Published in: The European physical journal. D, Atomic, molecular, and optical physics Vol. 68; no. 10
• Main Authors: Plunk, Gabriel G., Parker, Joseph T.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.10.2014; EDP Sciences
• Subjects: Applications of Nonlinear Dynamics and Chaos Theory; Atomic; Exact sciences and technology; Fokker-plank and vlasov equations; Molecular; Optical and Plasma Physics; Physical Chemistry; Physics; Physics and Astronomy; Physics of gases, plasmas and electric discharges; Physics of plasmas and electric discharges; Plasma simulation; Quantum Information Technology; Quantum Physics; Regular Article; Spectroscopy/Spectrometry; Spintronics; Topical issue: Theory and Applications of the Vlasov Equation; Linear Vlasov Equation; Collisional Limit; Hermite Space; Vlasov Equation; Entropy Production; Conservation laws; Energy flow; Plasma simulation; Numerical solution; Energy spectra; Theoretical study; Turbulent fluctuation; Vlasov equation; Steady state
• ISSN: 1434-6060; 1434-6079
• DOI: 10.1140/epjd/e2014-50157-8

The recent paper of Plunk [G.G. Plunk, Phys. Plasmas 20 , 032304 (2013)] considered the forced linear Vlasov equation as a model for the quasi-steady state of a single stable plasma wavenumber interacting with a bath of turbulent fluctuations. This approach gives some insight into possible energy flows without solving for nonlinear dynamics. The central result of the present work is that the forced linear Vlasov equation exhibits asymptotically zero (irreversible) dissipation to all orders under a detuning of the forcing frequency and the characteristic frequency associated with particle streaming. We first prove this by direct calculation, tracking energy flow in terms of certain exact conservation laws of the linear (collisionless) Vlasov equation. Then we analyze the steady-state solutions in detail using a weakly collisional Hermite-moment formulation, and compare with numerical solution. This leads to a detailed description of the Hermite energy spectrum, and a proof of no dissipation at all orders, complementing the collisionless Vlasov result.