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Transport theory in moderately anisotropic plasmas: I, Collisionless aspects of axisymmetric velocity space

Yanpeng Wang

TL;DR

The paper develops a nonlinear transport theory for collisionless plasmas with axisymmetric velocity space by deriving a kinetic moment evolution framework (KMEE) from the Vlasov equation, using spherical harmonics in velocity space and King function expansions to implement a finite-feature closure (FDIF). Closure is achieved both in the angular-space index $(l)$ through a natural truncation (NCR) and in the velocity-moment index $(j)$ via a King mixture model (GKMM) with characteristic parameter equations (CPEs); together these yield the kinetic moment-closed model (KMCM) valid for moderately anisotropic non-equilibrium plasmas. KMCM connects to conventional fluid equations through the first few velocity moments and conservation laws, while providing a scalable, high-order kinetic description that remains computationally tractable through data-driven closures and well-posed nonlinear solvers. The framework promises improved modeling of kinetic effects in multi-scale, strongly nonlinear plasmas and offers a pathway to extending Vlasov-based simulations beyond traditional perturbative closures, with potential applications in fusion and space plasmas.

Abstract

A novel transport theory, based on the finitely distinguishable independent features (FDIF) hypothesis, is presented for scenarios when velocity space exhibits axisymmetry. In this theory, the transport equations are derived from the 1D-2V Vlasov equation, employing the spherical harmonics expansions (SHE) together with the King function expansion (KFE) in velocity space. The characteristic parameter equations (CPEs) are provided based on the general King mixture model (GKMM), serving as the constraint equations of the transport equations. It is a nature process to present the closure relations of transport equations based on SHE and KFE, successfully providing a kinetic moment-closed model (KMCM). This model is typically a nonlinear system, effective for moderately anisotropic non-equilibrium plasmas.

Transport theory in moderately anisotropic plasmas: I, Collisionless aspects of axisymmetric velocity space

TL;DR

The paper develops a nonlinear transport theory for collisionless plasmas with axisymmetric velocity space by deriving a kinetic moment evolution framework (KMEE) from the Vlasov equation, using spherical harmonics in velocity space and King function expansions to implement a finite-feature closure (FDIF). Closure is achieved both in the angular-space index through a natural truncation (NCR) and in the velocity-moment index via a King mixture model (GKMM) with characteristic parameter equations (CPEs); together these yield the kinetic moment-closed model (KMCM) valid for moderately anisotropic non-equilibrium plasmas. KMCM connects to conventional fluid equations through the first few velocity moments and conservation laws, while providing a scalable, high-order kinetic description that remains computationally tractable through data-driven closures and well-posed nonlinear solvers. The framework promises improved modeling of kinetic effects in multi-scale, strongly nonlinear plasmas and offers a pathway to extending Vlasov-based simulations beyond traditional perturbative closures, with potential applications in fusion and space plasmas.

Abstract

A novel transport theory, based on the finitely distinguishable independent features (FDIF) hypothesis, is presented for scenarios when velocity space exhibits axisymmetry. In this theory, the transport equations are derived from the 1D-2V Vlasov equation, employing the spherical harmonics expansions (SHE) together with the King function expansion (KFE) in velocity space. The characteristic parameter equations (CPEs) are provided based on the general King mixture model (GKMM), serving as the constraint equations of the transport equations. It is a nature process to present the closure relations of transport equations based on SHE and KFE, successfully providing a kinetic moment-closed model (KMCM). This model is typically a nonlinear system, effective for moderately anisotropic non-equilibrium plasmas.
Paper Structure (18 sections, 69 equations, 1 figure)

This paper contains 18 sections, 69 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Maxwell-Vlasov system
  3. Vlasov spectrum equation for axisymmetric velocity space
  4. Weak form of Vlasov spectrum equation
  5. Transport equations
  6. Kinetic moment evolution equation
  7. Velocity moments and conservation laws
  8. Velocity moments
  9. Conservation laws
  10. Kinetic moment-closed model for moderately anisotropic plasmas
  11. Closure in $(l)$ space
  12. Closure in $(j)$ space
  13. Application of KMCM
  14. Numerical solution
  15. Physical application
  16. ...and 3 more sections

Figures (1)

  • Figure 1: Convergence of SHE for drift-Maxwellian distribution: Truncated order $l_M$ as a function of $\hat{u}_a$ when tolerance $Atol_{df}=10^{-14}$.