A Unified Hamiltonian Formulation for Energy Loss, Entropy Evolution, and Fusion Performance in Plasmas

TL;DR

This paper introduces a unified Hamiltonian framework for plasma dynamics that integrates collisionless and collisional processes, linking microscopic turbulence with macroscopic energy and fusion performance measures.

Contribution

It presents a novel Hamiltonian formulation that incorporates collisions directly, enabling analysis of energy loss, entropy evolution, and fusion efficiency in plasmas.

Findings

Derived quantitative relations between turbulence, entropy production, and confinement.

Unified treatment of collisionless and collisional plasma processes within Hamiltonian structure.

Connected microscopic kinetic effects with macroscopic fusion performance metrics.

Abstract

We develop a comprehensive Hamiltonian formulation for plasma dynamics that unifies collisionless gyrokinetic and collisional processes. Our framework rigorously describes the evolution of free energy and entropy during the transition from Maxwellian to non-Maxwellian distributions, explicitly coupling microscopic turbulent processes with macroscopic measures of energy confinement and fusion performance. Unlike standard gyrokinetic treatments that treat collisions as a minor perturbation, our approach incorporates a collision operator directly into the Hamiltonian structure, thereby accounting for irreversible dissipation and entropy production. We derive quantitative relations linking turbulence intensity, entropy production, energy confinement time and fusion yield. Our work builds on recent energetic bounds and optimal mode analyses by Helander and Plunk and on Zhdankin's generalised entropy-production framework, thus providing a bridge between microscopic kinetics and reactor-scale performance.