82 citations · 876 across the 71 of their papers we have counts for
72 papers
All field strengths are possible locally in Boozer coordinates
Taylor J. Klotz, Nathan Duignan, Joshua W. Burby +1
The magnetic field strength is a central design object in the theory of magnetic confinement of plasma. Desirable confinement properties such as quasi-symmetry and omnigenity are c…
A Structure-Preserving Decorated Particle Method for the Vlasov-Poisson System
Mandela B. Quashie, J. W. Burby, Andrew J. Christlieb +1
We revisit the Scovel-Weinstein framework (Scovel & Weinstein, CPAM 1994) for reducing the Vlasov-Poisson system while preserving its Hamiltonian structure. Standard particle-in-ce…
Statistical equilibrium model for stellarators
Maximilian Ruth, Joshua W. Burby, Wrick Sengupta +1
In three dimensional toroidal domains without symmetry, the standard magnetohydrodynamic (MHD) equilibrium model used for magnetic confinement fusion does not generally support smo…
Diagnosing symplecticity in simulations of high-dimensional Hamiltonian systems
William Barham, J. W. Burby
Integrals of the Liouville -form, known as the first Poincar{é} integral invariant, provide a computable figure of merit for monitoring the conservation of symplecticity in the…
Is There an Exact Magnetic-Moment for Charged Particle Motion in a Homogeneous, Time-Dependent Magnetic Field?
Michael Updike, Joshua Burby
The nonperturbative guiding-center model provides an exact alternative to full-orbit simulations of charged particle dynamics in situations where traditional guiding-center theory…
Exact expressions for nonperturbative guiding center theory in symmetric fields
I. Hollas, R. Agarwal, J. W. Burby +1
We apply a recently-developed nonperturbative guiding center formalism to charged particle dynamics in fields with two-parameter continuous symmetry groups. This entails finding ex…
Imposing quasineutrality on electrostatic plasmas via the Dirac theory of constraints
D. A. Kaltsas, J. W. Burby, P. J. Morrison +2
We present a method for imposing quasineutrality and, more generally, charge density conservation in the Vlasov-Poisson (VP) and Vlasov-Ampère (VA) systems, which describe electros…
Poisson-Dirac Submanifolds as a Paradigm for Imposing Constraints in Non-dissipative Plasma Models
F. W. Pinto, J. W. Burby
We present a generalization of Dirac constraint theory based on the theory of Poisson-Dirac submanifolds. The theory is formulated in a coordinate-free manner while simultaneously…
Hamiltonian formulation of the quasineutral Vlasov-Poisson system
J. W. Burby, D. A. Kaltsas, P. J. Morrison +2
Slow manifold reduction and the theory of Poisson-Dirac submanifolds are used to deduce a Hamiltonian formulation for a quasineutral limit of the planar, collisionless, magnetized…
Robust computation of higher-dimensional invariant tori from individual trajectories
Maximilian Ruth, Jackson Kulik, Joshua Burby
We present a method for computing invariant tori of dimension greater than one. The method uses a single short trajectory of a dynamical system without any continuation or initial…
A conditional formulation of the Vlasov-Ampere Equations: A conservative, positivity, asymptotic, and Gauss law preserving scheme
William T Taitano, Joshua W Burby, Alex Alekseenko
We propose a novel reformulation of the Vlasov-Amp{è}re equations for plasmas. This reformulation exposes discrete symmetries to achieve simultaneous conservation of mass, momentum…
Neural Network Representations of Multiphase Equations of State
George A. Kevrekidis, Daniel A. Serino, Alexander Kaltenborn +3
Equations of State model relations between thermodynamic variables and are ubiquitous in scientific modelling, appearing in modern day applications ranging from Astrophysics to Cli…
Characterization of admissible quasisymmetries
J. W. Burby, N. Kallinikos, R. S. MacKay +2
We solve "half" the problem of finding three-dimensional quasisymmetric magnetic fields that do not necessarily satisfy force balance. This involves determining which hidden symmet…
Fast-Slow Neural Networks for Learning Singularly Perturbed Dynamical Systems
Daniel A. Serino, Allen Alvarez Loya, Joshua W. Burby +2
Singularly perturbed dynamical systems play a crucial role in climate dynamics and plasma physics. A powerful and well-known tool to address these systems is the Fenichel normal fo…
Coarse-Graining Hamiltonian Systems Using WSINDy
Daniel A. Messenger, Joshua W. Burby, David M. Bortz
The Weak-form Sparse Identification of Nonlinear Dynamics algorithm (WSINDy) has been demonstrated to offer coarse-graining capabilities in the context of interacting particle syst…
Spatial dynamics formulation of magnetohydrostatics
J. W. Burby, M. H. Updike
We present a formalism for importing techniques from dynamical systems theory in the study of three-dimensional magnetohydrodynamic (MHD) equilibria. By treating toroidal angle as…
A BBGKY-like Hierarchy for Quantum Field Theories
Michael Updike, Joshua Burby
We present a Hamiltonian method of constructing BBGKY-like hierarchies for quantum field theories. With suitable choices, our method creates a hierarchical system of evolution equa…
Variable-moment fluid closures with Hamiltonian structure
J. W. Burby
Based on ideas due to Scovel-Weinstein, I present a general framework for constructing fluid moment closures of the Vlasov-Poisson system that exactly preserve that system's Hamilt…
Mean field theory for intense light-matter interactions in high energy density plasmas
J. W. Burby, P. J. Morrison
We present a generalization of Vlasov-Maxwell kinetic theory that accounts for intense electromagnetic fields. A strongly-radiating, possibly optically-thick plasma is decomposed i…
Isodrastic Magnetic fields for suppressing transitions in guiding-centre motion
J. W. Burby, R. S. MacKay, S. Naik
In a magnetic field, transitions between classes of guiding-centre motion can lead to cross-field diffusion and escape. We say a magnetic field is isodrastic if guiding centres mak…
Minimizing Separatrix Crossings through Isoprominence
Joshua W. Burby, Nathan Duignan, James D. Meiss
A simple property of magnetic fields that minimizes bouncing to passing type transitions of guiding center orbits is defined and discussed. This property, called isoprominence, is…
Approximation of nearly-periodic symplectic maps via structure-preserving neural networks
Valentin Duruisseaux, Joshua W. Burby, Qi Tang
A continuous-time dynamical system with parameter is nearly-periodic if all its trajectories are periodic with nowhere-vanishing angular frequency as ap…
Metriplectic foundations of gyrokinetic Vlasov-Maxwell-Landau theory
Eero Hirvijoki, Joshua W. Burby, Alain J. Brizard
This letter reports on a metriplectic formulation of collisional, nonlinear full- electromagnetic gyrokinetic theory compliant with energy conservation and monotonic entropy pro…
Stabilized Neural Ordinary Differential Equations for Long-Time Forecasting of Dynamical Systems
Alec J. Linot, Joshua W. Burby, Qi Tang +3
In data-driven modeling of spatiotemporal phenomena careful consideration often needs to be made in capturing the dynamics of the high wavenumbers. This problem becomes especially…