Time-nonlocal kinetic equations, jerk and hyperjerk in plasmas and solar physics

The simulation and analysis of nonlocal effects in fluids and plasmas is an inherently complicated problem due to the massive breadth of physics required to describe the nonlocal dynamics. This is a multi-physics problem that draws upon various miscellaneous fields, such as electromagnetism and statistical mechanics. In this paper we strive to focus on one narrow but motivating mathematical way: the derivation of nonlocal plasma-fluid equations from a generalized nonlocal Liouville derivative operator motivated from Suykens's nonlocal arguments. The paper aims to provide a guideline toward modeling nonlocal effects occurring in plasma-fluid systems by means of a generalized nonlocal Boltzmann equation. The generalized nonlocal equations of fluid dynamics are derived and their implications in plasma-fluid systems are addressed, discussed and analyzed. Three main topics were discussed: Landau damping in plasma electrodynamics, ideal MHD and solar wind. A number of features were revealed, analyzed and confronted with recent research results and observations.