The Eulerian variational formulation of the gyrokinetic system in general spatial coordinates
arXiv:2009.00259 · doi:10.1063/5.0027905
Abstract
The Eulerian variational formulation of the gyrokinetic system with electrostatic turbulence is presented in general spatial coordinates by extending our previous work [H. Sugama, {\it et al}., Phys.\ Plasmas {\bf 25}, 102506 (2018)]. The invariance of the Lagrangian of the system under an arbitrary spatial coordinate transformation is used to derive the local momentum balance equation satisfied by the gyrocenter distribution functions and the turbulent potential which are given as solutions of the governing equations. This derivation is in contrast with the conventional method using the spatial translation in which the asymmetric canonical pressure tensor generally enters the momentum balance equation. In the present study, the variation of the Lagrangian density with respect to the metric tensor is taken to directly obtain the symmetric pressure tensor which includes the effect of turbulence on the momentum transport. In addition, it is shown in this work how the momentum balance is modified when the collision and/or external source terms are added to the gyrokinetic equation. The results obtained here are considered useful for global gyrokinetic simulations investigating both neoclassical and turbulent transport processes even in general non-axisymmetric toroidal systems.
References in corpus (17)
- Astrophysical gyrokinetics: kinetic and fluid turbulent cascades in magnetized weakly collisional plasmas
- Multiscale Gyrokinetics for Rotating Tokamak Plasmas: Fluctuations, Transport and Energy Flows
- Structure and structure-preserving algorithms for plasma physics
- Energetic Consistency and Momentum Conservation in the Gyrokinetic Description of Tokamak Plasmas
- Up-down symmetry of the turbulent transport of toroidal angular momentum in tokamaks
- Phase-space Lagrangian derivation of electrostatic gyrokinetics in general geometry
- The Maxwell-Vlasov equations in Euler-Poincare form
- Variational integration for ideal magnetohydrodynamics with built-in advection equations
- The Hamiltonian structure and Euler-Poincaré formulation of the Vlasov-Maxwell and gyrokinetic systems
- Variational principles for the guiding-center Vlasov-Maxwell equations
- Energetically-consistent collisional gyrokinetics
- Field theory and weak Euler-Lagrange equation for classical particle-field systems
- Effects of collisions on conservation laws in gyrokinetic field theory
- Energy and momentum conservation in the Euler-Poincaré formulation of local Vlasov-Maxwell-type systems
- Discovering exact, gauge-invariant, local energy-momentum conservation laws for the electromagnetic gyrokinetic system by high-order field theory on heterogeneous manifolds
- Eulerian variational formulations and momentum conservation laws for kinetic plasma systems
- General field theory and weak Euler-Lagrange equation for classical particle-field systems in plasma physics