Engineering topics

Hirvijoki, Eero

Publications and source records attributed to Hirvijoki, Eero.

4 records

DOE OSTI2022

Metriplectic foundations of gyrokinetic Vlasov–Maxwell–Landau theory

Here, this Letter reports on a metriplectic formulation of a collisional, nonlinear full-f electromagnetic gyrokinetic theory compliant with energy conservation and monotonic entropy production. In an axisymmetric background magnetic field, the toroidal angular momentum is also conserved. Notably, a new collisional current, contributing to the gyrokinetic Maxwell–Ampère equation and the gyrokinetic charge conservation law, is discovered.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

Normal stability of slow manifolds in nearly periodic Hamiltonian systems

Kruskal [J. Math. Phys. 3, 806 (1962)] showed that each nearly periodic dynamical system admits a formal U(1) symmetry, generated by the so-called roto-rate. We prove that such systems also admit nearly invariant manifolds of each order, near which rapid oscillations are suppressed. We study the nonlinear normal stability of these slow manifolds for nearly periodic Hamiltonian systems on barely symplectic manifolds—manifolds equipped with closed, non-degenerate 2-forms that may be degenerate to leading order. In particular, we establish a sufficient condition for long-term normal stability based on second derivatives of the well-known adiabatic invariant. We use these results to investigate the problem of embedding guiding center dynamics of a magnetized charged particle as a slow manifold in a nearly periodic system. Here, we prove that one previous embedding and two new embeddings enjoy long-term normal stability and thereby strengthen the theoretical justification for these models.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Dispersion relation for gauge-free electromagnetic drift kinetics

Recently, a new approach to gyrokinetics, invariant under electromagnetic gauge transformations, was developed. The gyrocenter equations of motion are now expressed in terms of the perturbed fields instead of the potentials, in a form suitable for numerical simulations and analytic studies. In this paper, we verify that the long-wavelength limit, i.e., the drift-kinetic limit of the new gyrokinetic theory, is in line with existing work, providing a solid foundation for simulations. Here, we compute the dispersion relation of the new drift-kinetic theory in slab geometry and find agreement with a long-wavelength limit of the full Vlasov–Maxwell model.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2020

Energy and momentum conservation in the Euler–Poincaré formulation of local Vlasov–Maxwell-type systems

The action principle by Low for the classic Vlasov–Maxwell system contains a mix of Eulerian and Lagrangian variables. This renders the Noether analysis of reparametrization symmetries inconvenient, especially since the well-known energy- and momentum-conservation laws for the system are expressed in terms of Eulerian variables only. While an Euler–Poincaré formulation of Vlasov–Maxwell-type systems, effectively starting with Low's action and using constrained variations for the Eulerian description of particle motion, has been known for a while Cendra et al, it is hard to come by a documented derivation of the related energy- and momentum-conservation laws in the spirit of the Euler–Poincaré machinery. To our knowledge only one such derivation exists in the literature so far, dealing with the so-called guiding-center Vlasov–Darwin system Sugama et al. The present exposition discusses a generic class of local Vlasov–Maxwell-type systems, with a conscious choice of adopting the language of differential geometry to exploit the Euler–Poincaré framework to its full extent. After reviewing the transition from a Lagrangian picture to an Eulerian one, we demonstrate how symmetries generated by isometries in space lead to conservation laws for linear- and angular-momentum density and how symmetry by time translation produces a conservation law for energy density. Here, we also discuss what happens if no symmetries exist. Finally, two explicit examples will be given—the classic Vlasov–Maxwell and the drift-kinetic Vlasov–Maxwell—and the results expressed in the language of regular vector calculus for familiarity.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗