arXiv subjects

E. Hirvijoki

Publications and source records attributed to E. Hirvijoki.

6 recordsLinked to original sources

arXiv2021

Nearly-periodic maps and geometric integration of noncanonical Hamiltonian systems

M. Kruskal showed that each continuous-time nearly-periodic dynamical system admits a formal $U(1)$ symmetry, generated by the so-called roto-rate. When the nearly-periodic system is also Hamiltonian, Noether's theorem implies the existence of a corresponding adiabatic invariant. We develop a discrete-time analoue of Kruskal's theory. Nearly-periodic maps are defined as parameter-dependent diffeomorphisms that limit to rotations along a $U(1)$-action. When the limiting rotation is non-resonant, these maps admit formal $U(1)$ symmetries to all orders in perturbation theory. For Hamiltonian nearly-periodic maps on exact presymplectic manifolds, we prove that the formal $U(1)$ symmetry gives rise to a discrete-time adiabatic invariant using a discrete-time extension of Noether's theorem. When the unperturbed $U(1)$-orbits are contractible, we also find a discrete-time adiabatic invariant for mappings that are merely presymplectic, rather than Hamiltonian. As an application of the theory, we use it to develop a novel technique for geometric integration of non-canonical Hamiltonian systems on exact symplectic manifolds.

math.DS↗

arXiv2021

Normal stability of slow manifolds in nearly-periodic Hamiltonian systems

M. Kruskal 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. We prove that one previous embedding, and two new embeddings enjoy long-term normal stability, and thereby strengthen the theoretical justification for these models.

math.DS↗

arXiv2018

Magnetohydrodynamic Turbulence in the Plasmoid-Mediated Regime

Magnetohydrodynamic turbulence and magnetic reconnection are ubiquitous in astrophysical environments. In most situations, these processes do not occur in isolation, but interact with each other. This renders a comprehensive theory of these processes highly challenging. Here, we propose a theory of magnetohydrodynamic turbulence driven at large scale that self-consistently accounts for the mutual interplay with magnetic reconnection occurring at smaller scales. Magnetic reconnection produces plasmoids that grow from turbulence-generated noise and eventually disrupt the sheet-like structures in which they are born. The disruption of these structures leads to a modification of the turbulent energy cascade, which, in turn, exerts a feedback effect on the plasmoid formation via the turbulence-generated noise. The energy spectrum in this plasmoid-mediated range steepens relative to the standard inertial range and does not follow a simple power law. As a result of the complex interplay between turbulence and reconnection, we also find that the length scale which marks the beginning of the plasmoid-mediated range and the dissipation length scale do not obey true power laws. The transitional magnetic Reynolds number above which the plasmoid formation becomes statistically significant enough to affect the turbulent cascade is fairly modest, implying that plasmoids are expected to modify the turbulent path to dissipation in many astrophysical systems.

physics.plasm-ph↗

arXiv2017

Landau Collision Integral Solver with Adaptive Mesh Refinement on Emerging Architectures

The Landau collision integral is an accurate model for the small-angle dominated Coulomb collisions in fusion plasmas. We investigate a high order accurate, fully conservative, finite element discretization of the nonlinear multi-species Landau integral with adaptive mesh refinement using the PETSc library (www.mcs.anl.gov/petsc). We develop algorithms and techniques to efficiently utilize emerging architectures with an approach that minimizes memory usage and movement and is suitable for vector processing. The Landau collision integral is vectorized with Intel AVX-512 intrinsics and the solver sustains as much as 22% of the theoretical peak flop rate of the Second Generation Intel Xeon Phi, Knights Landing, processor.

cs.CE↗

arXiv2015

Radiation reaction induced non-monotonic features in runaway electron distributions

Runaway electrons, which are generated in a plasma where the induced electric field exceeds a certain critical value, can reach very high energies in the MeV range. For such energetic electrons, radiative losses will contribute significantly to the momentum space dynamics. Under certain conditions, due to radiative momentum losses, a non-monotonic feature - a "bump" - can form in the runaway electron tail, creating a potential for bump-on-tail-type instabilities to arise. Here we study the conditions for the existence of the bump. We derive an analytical threshold condition for bump appearance and give an approximate expression for the minimum energy at which the bump can appear. Numerical calculations are performed to support the analytical derivations.

physics.plasm-ph↗

arXiv2015

Bump formation in the runaway electron tail

Runaway electrons are generated in a magnetized plasma when the parallel electric field exceeds a critical value. For such electrons with energies typically reaching tens of MeV, the Abraham-Lorentz-Dirac (ALD) radiation force, in reaction to the synchrotron emission, is significant and can be the dominant process limiting the electron acceleration. The effect of the ALD-force on runaway electron dynamics in a homogeneous plasma is investigated using the relativistic finite-difference Fokker-Planck codes LUKE [Decker & Peysson, Report EUR-CEA-FC-1736, Euratom-CEA, (2004)] and CODE [Landreman et al, Comp. Phys. Comm. 185, 847 (2014)]. Under the action of the ALD force, we find that a bump is formed in the tail of the electron distribution function if the electric field is sufficiently large. We also observe that the energy of runaway electrons in the bump increases with the electric field amplitude, while the population increases with the bulk electron temperature. The presence of the bump divides the electron distribution into a runaway beam and a bulk population. This mechanism may give rise to beam-plasma types of instabilities that could in turn pump energy from runaway electrons and alter their confinement.

physics.plasm-ph↗