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The main idea of Gyrokinetic dynamical reduction consists in systematical removing of fastest scale of motion (the gyro motion) from plasma's dynamics, resulting in a considerable model simplification and gain of computing time. Gyrokinetic…

We propose a novel derivation of the gyrokinetic field-particle Lagrangian for non-collisional ion-electron plasmas in a magnetic background with strong variations (maximal ordering). Our approach follows the two-step reduction process,…

A gyrokinetic reduction is based on a specific ordering of the different small parameters characterizing the background magnetic field and the fluctuating electromagnetic fields. In this tutorial, we consider the following ordering of the…

Explicit high-order non-canonical symplectic particle-in-cell algorithms for classical particle-field systems governed by the Vlasov-Maxwell equations are developed. The algorithm conserves a discrete non-canonical symplectic structure…

The polarization and magnetization effects associated with the dynamical reduction leading to the nonlinear gyrokinetic Vlasov-Maxwell equations are shown to introduce nonlinear finite-Larmor-radius effects into a set of nonlinear…

The foundations of gyrokinetic theory are reviewed with an emphasis on the applications of Lagrangian and Hamiltonian methods used in the derivation of nonlinear gyrokinetic Vlasov-Maxwell equations. These reduced dynamical equations…

Gyrokinetic theory is based on an asymptotic expansion in the small parameter $\epsilon$, defined as the ratio of the gyroradius and the characteristic length of variation of the magnetic field. In this article, this ordering is strictly…

This paper formulates a new particle-in-cell method for the Vlasov-Maxwell system. Under the Lorenz gauge condition, Maxwell's equations for the electromagnetic fields can be written as a collection of scalar and vector wave equations. The…

In purely non-dissipative systems, Lagrangian and Hamiltonian reduction have proven to be powerful tools for deriving physical models with exact conservation laws. We have discovered a hint that an analogous reduction method exists also for…

High-resolution simulations of particle-based kinetic plasma models typically require a high number of particles and thus often become computationally intractable. This is exacerbated in multi-query simulations, where the problem depends on…

A high-order piecewise field-aligned triangular finite element method is developed and implemented for global electromagnetic gyrokinetic particle-in-cell simulations of tokamak plasmas with open field lines. The approach combines locally…

A set of key properties for an ideal dissipation scheme in gyrokinetic simulations is proposed, and implementation of a model collision operator satisfying these properties is described. This operator is based on the exact linearized…

This paper considers the reduction of the Langevin equation arising from bio-molecular models. To facilitate the construction and implementation of the reduced models, the problem is formulated as a reduced-order modeling problem. The…

Extended guiding-center Vlasov-Maxwell equations are derived under the assumption of time-dependent and inhomogeneous electric and magnetic fields that obey the standard guiding-center space-time-scale orderings. The guiding-center…

We reanalyse an arbitrary-wavelength gyrokinetic formalism [A. M. Dimits, Phys. Plasmas $\bf17$, 055901 (2010)], which orders only the vorticity to be small and allows strong, time-varying flows on medium and long wavelengths. We obtain a…

The gyrokinetics formulation of plasmas in strong magnetic fields aims at the elimination of the angle associated with the Larmor rotation of charged particles around the magnetic field lines. In a perturbative treatment or as a…

Numerical schemes that preserve the structure of the kinetic equations can provide stable simulation results over a long time. An electromagnetic particle-in-cell solver for the Vlasov-Maxwell equations that preserves at the discrete level…

Plasmas are highly nonlinear and multi-scale, motivating a hierarchy of models to understand and describe their behavior. However, there is a scarcity of plasma models of lower fidelity than magnetohydrodynamics (MHD), although these…

Hamiltonian particle-based simulations of plasma dynamics are inherently computationally intensive, primarily due to the large number of particles required to obtain accurate solutions. This challenge becomes even more acute in many-query…

A variational method is used to derive a self-consistent macro-particle model for relativistic electromagnetic kinetic plasma simulations. Extending earlier work [E. G. Evstatiev and B. A. Shadwick, J. Comput. Phys., vol. 245, pp. 376-398,…