arXiv subjects

Stefan Possanner

Publications and source records attributed to Stefan Possanner.

9 recordsLinked to original sources

arXiv2025

The Linearized Vlasov-Maxwell System as a Hamiltonian System

We present a Hamiltonian formulation for the linearized Vlasov-Maxwell system with a Maxwellian background distribution function. We discuss the geometric properties of the model at the continuous level, and how to discretize the model in the GEMPIC framework [1]. This method allows us to preserve the structure of the system at the semi-discrete level. To integrate the model in time, we employ a Poisson splitting and discuss how to integrate each subsystem separately. We test the model against the direct delta-f method, which is the non-geometric pendant of our model. The first test case is the weak Landau damping, where our model exhibits the same physical properties for short simulations, but enjoys better long-time stability and energy conservation due to its geometric construction. These advantages becomes even more pronounced for the simulation of Bernstein waves, our second test case, where the noise in the direct delta-f method washes out all features of the dispersion relation whereas our model is able to reproduce the full spectrum correctly. The model is implemented in the open-source Python library STRUPHY [2], [3].

math.NA↗

arXiv2025

Structure-Preserving MHD-Driftkinetic Discretization for Wave-Particle Interactions

We present a structure-preserving discretization of the hybrid magnetohydrodynamics (MHD)-driftkinetic system for simulations of low-frequency wave-particle interactions. The model equations are derived from a variational principle, assuring energetically consistent couplings between MHD fluids and driftkinetic particles. The spatial discretization is based on a finite-element-exterior-calculus (FEEC) framework for the MHD and a particle-in-cell (PIC) method for the driftkinetic. A key feature of the scheme is the inclusion of the non-quadratic particle magnetic moment energy term in the Hamiltonian, which is introduced by the guiding-center approximation. The resulting discrete Hamiltonian structure naturally organizes the dynamics into skew-symmetric subsystems, enabling balanced energy exchange. To handle the non-quadratic energy term, we develop energy-preserving time integrators based on discrete gradient methods. The algorithm is implemented in the open-source Python package $\texttt{STRUPHY}$. Numerical experiments confirm the energy-conserving property of the scheme and demonstrate the capability to simulate energetic particles (EP) induced excitation of toroidal Alfvén eigenmodes (TAE) without artificial dissipation or mode filtering. This capability highlights the potential of structure-preserving schemes for high-fidelity simulations of hybrid systems.

physics.comp-ph↗

arXiv2025

On the Poisson brackets of hybrid plasma models with kinetic ions and massless electrons

We investigate the conditions under which the Jacobi identity holds for a class of recently introduced anti-symmetric brackets for the hybrid plasma models with kinetic ions and massless electrons. In particular, we establish the precise conditions under which the brackets for the vector-potential-based formulations satisfy the Jacobi identity, and demonstrate that these conditions are fulfilled by all physically relevant functionals. Moreover, for the magnetic-field-based formulation, we show that the corresponding anti-symmetric bracket constitutes a Poisson bracket under the divergence-free condition of the magnetic field, and we provide a direct proof of the Jacobi identity. These results are further extended to models incorporating electron entropy as well as more general hybrid kinetic-fluid models.

physics.plasm-ph↗

arXiv2024

Canonical variables based numerical schemes for hybrid plasma models with kinetic ions and massless electrons

We study the canonical variables based numerical schemes of a hybrid model with kinetic ions and mass-less electrons. Two equivalent formulations of the hybrid model are presented with the vector potentials in different gauges and the distribution functions depending on canonical momentum (not velocity), which constitutes a pair of canonical variables with the position variable. Particle-in-cell methods are used for the distribution functions, and the vector potentials are discretized by the finite element methods in the framework of finite element exterior calculus. Splitting methods are used for the time discretizations. It is illustrated that the second formulation is numerically superior and the schemes constructed based on the anti-symmetric bracket proposed have better conservation properties and lower noise, although the filters can be used to improve the schemes of the first formulation.

math.NA↗

arXiv2023

Geometric Particle-In-Cell discretizations of a plasma hybrid model with kinetic ions and mass-less fluid electrons

We explore the possibilities of applying structure-preserving numerical methods to a plasma hybrid model with kinetic ions and mass-less fluid electrons satisfying the quasi-neutrality relation. The numerical schemes are derived by finite element methods in the framework of finite element exterior calculus (FEEC) for field variables, particle-in-cell (PIC) methods for the Vlasov equation, and splitting methods in time based on an anti-symmetric bracket proposed. Conservation properties of energy, quasi-neutrality relation, positivity of density, and divergence-free property of the magnetic field are given irrespective of the used resolution and metric. Local quasi-interpolation is used for dealing with the current terms in order to make the proposed methods more efficient. The implementation has been done in the framework of the Python package STRUPHY [1], and has been verified by extensive numerical experiments.

math.NA↗

arXiv2019

Gyrokinetic theory with polynomial transforms: a model for ions and electrons in maximal ordering

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, where the guiding-center coordinate transformation is followed by the gyrocenter coordinate transformation in the single-particle phase space. For the first time both steps are addressed within a unique methodology, based on near-identity coordinate transformations constructed as polynomial transforms. These are well-defined transformations composed of a finite number of terms that are linear and algebraic with respect to the generating functions. The derivation is carried out in a fully non-dimensional framework, based on parameters governing the magnetic fusion experiments ASDEX Upgrade and ITER. Our method leads to a gyrokinetic Vlasov-Maxwell model for ions and electrons, derived without the use of Lie perturbation methods. It is found that, based on the employed ordering, curvature terms such as the gyro-gauge term and the Baños drift appear at first order in the ion Hamiltonian, whereas ion polarization terms appear only at second order. By contrast, curvature terms are absent from the first-order electron Hamiltonian, where instead magnetic flutter plays a role.

physics.plasm-ph↗

arXiv2018

Asymptotic-Preserving scheme for the resolution of evolution equations with stiff transport terms

We develop an asymptotic-preserving scheme to solve evolution problems containing stiff transport terms. This scheme is based to a micro-macro decomposition of the unknown, coupled with a stabilization procedure. The numerical method is applied to the Vlasov equation in the gyrokinetic regime and to the Vlasov-Poisson 1D1V equation, which occur in plasma physics. The asymptotic-preserving properties of our procedure permit to study the long-time behavior of these models. In particular, we limit drastically by this method the numerical pollution, appearing in such time asymptotics when using classical numerical schemes.

math.NA↗

arXiv2017

Gyrokinetics from variational averaging: existence and error bounds

The gyrokinetic paradigm in the long wavelength regime is reviewed from the perspective of variational averaging (VA). The VA-method represents a third pillar for averaging kinetic equations with highly-oscillatory characteristics, besides classical averaging or Chapman-Enskog expansions. VA operates on the level of the Lagrangian function and preserves the Hamiltonian structure of the characteristics at all orders. We discuss the methodology of VA in detail by means of charged-particle motion in a strong magnetic field. The application of VA to a broader class of highly-oscillatory problems can be envisioned. For the charged particle, we prove the existence of a coordinate map in phase space that leads to a gyrokinetic Lagrangian at any order of the expansion, for general external fields. We compute this map up to third order, independent of the electromagnetic gauge. Moreover, an error bound for the solution of the derived gyrokinetic equation with respect to the solution of the Vlasov equation is provided, allowing to estimate the quality of the VA-approximation in this particular case.

math-ph↗

arXiv2013

Derivation of a linear collision operator for the spinorial Wigner equation and its semiclassical limit

We systematically derive a linear quantum collision operator for the spinorial Wigner transport equation from the dynamics of a composite quantum system. For suitable two particle interaction potentials, the particular matrix form of the collision operator describes spin decoherence or even spin depolarization as well as relaxation towards a certain momentum distribution in the long time limit. It is demonstrated that in the semiclassical limit the spinorial Wigner equation gives rise to several semiclassical spin-transport models. As an example, we derive the Bloch equations as well as the spinorial Boltzmann equation, which in turn gives rise to spin drift-diffusion models which are increasingly used to describe spin-polarized transport in spintronic devices. The presented derivation allows to systematically incorporate Born-Markov as well as quantum corrections into these models.

quant-ph↗