# Mean Force Kinetic Theory: a Convergent Kinetic Theory for Weakly and Strongly Coupled Plasmas

## TL;DR

This paper introduces a convergent kinetic theory for plasmas that remains valid from weak to strong Coulomb coupling, avoiding divergences of standard theories by using a novel closure based on the potential of mean force.

## Contribution

A new closure of the BBGKY hierarchy is developed, providing a convergent kinetic equation applicable to strongly coupled plasmas, extending traditional plasma kinetic theory.

## Key findings

- The kinetic theory remains valid at strong Coulomb coupling.
- Particles interact via the potential of mean force, defining the collision volume.
- The collision operator relates to the effective potential theory.

## Abstract

A new closure of the BBGKY hierarchy is developed, which results in a convergent kinetic equation that provides a rigorous extension of plasma kinetic theory into the regime of strong Coulomb coupling. The approach is based on a single expansion parameter which enforces that the exact equilibrium limit is maintained at all orders. Because the expansion parameter does not explicitly depend on the range or the strength of the interaction potential, the resulting kinetic theory does not suffer from the typical divergences at short and long length scales encountered when applying the standard kinetic equations to Coulomb interactions. The approach demonstrates that particles effectively interact via the potential of mean force and that the range of this force determines the size of the collision volume. When applied to a plasma, the collision operator is shown to be related to the effective potential theory [Baalrud and Daligault, Phys. Rev. Lett 110, 235001 (2013)]. The relationship between this and previous kinetic theories is discussed.