Kinetic and hydrodynamic regimes in multi-particle-collision dynamics of a one-dimensional fluid with thermal walls

TL;DR

This study investigates the transition from kinetic to hydrodynamic transport regimes in a one-dimensional fluid with thermal walls, highlighting the role of system size and particle collision times in non-equilibrium steady states.

Contribution

It introduces a detailed analysis of the crossover between transport regimes in a 1D fluid with thermal walls, including effects of non-thermal particle injection.

Findings

Identification of a crossover size proportional to the cube of collision time.

Demonstration of non-Maxwellian velocity distributions in short systems with cold particles.

Analysis relevant to fusion plasma divertor physics.

Abstract

We study the non-equilibrium steady-states of a one-dimensional ($1D1V$) fluid in a finite space region of length $L$. Particles interact among themselves by multi-particle collisions and are in contact with two thermal-wall heat reservoirs, located at the boundaries of the region. After an initial ballistic regime, we find a crossover from a normal (kinetic) transport regime to an anomalous (hydrodynamic) one, above a characteristic size $L_*$. We argue that $L_*$ is proportional to the cube of the collision time among particles. Motivated by the physics of emissive divertors in fusion plasma, we consider the more general case of thermal walls injecting particles with given average (non-thermal) velocity. For fast and relatively cold particles, short systems fail to establish local equilibrium and display non-Maxwellian distributions of velocities.