Scattering Theory in Noncanonical Phase Space: A Drift-Kinetic Collision Operator for Weakly Collisional Plasmas

TL;DR

This paper develops a new collision operator for weakly collisional plasmas in noncanonical phase space, capturing guiding center dynamics and conserving key physical quantities, with potential applications in plasma turbulence and transport.

Contribution

It introduces a guiding center collision operator based on noncanonical Hamiltonian structure, ensuring conservation laws and satisfying an H-theorem in plasma physics.

Findings

The collision operator conserves particle number, momentum, and energy.

It satisfies an H-theorem, allowing for non-Maxwellian equilibrium states.

The operator is applicable to turbulence and transport studies in plasmas.

Abstract

After developing a scattering theory for grazing collisions in general noncanonical phase spaces, we introduce a guiding center collision operator in five-dimensional phase space designed for plasma regimes characterized by long wavelengths (relative to the Larmor radius), low frequencies (relative to the cyclotron frequency), and weak collisionality (where repeated Coulomb collisions induce cumulatively small changes in particle magnetic moment). The collision operator is fully determined by the noncanonical Hamiltonian structure of guiding center dynamics and exhibits a metriplectic structure, ensuring the conservation of particle number, momentum, energy, and interior Casimir invariants. It also satisfies an H-theorem, allowing for deviations from Maxwell-Boltzmann statistics due to the nontrivial kernel of the noncanonical guiding center Poisson tensor, spanned by the magnetic moment. We propose that this collision operator and its underlying mathematical structure may offer valuable insights into the study of turbulence, transport, and self-organizing phenomena in both laboratory and astrophysical plasmas.