28 research outputs found
Variational approach to low-frequency kinetic-MHD in the current coupling scheme
Hybrid kinetic-MHD models describe the interaction of an MHD bulk fluid with
an ensemble of hot particles, which is described by a kinetic equation. When
the Vlasov description is adopted for the energetic particles, different
Vlasov-MHD models have been shown to lack an exact energy balance, which was
recently recovered by the introduction of non-inertial force terms in the
kinetic equation. These force terms arise from fundamental approaches based on
Hamiltonian and variational methods. In this work we apply Hamilton's
variational principle to formulate new current-coupling kinetic-MHD models in
the low-frequency approximation (i.e. large Larmor frequency limit). More
particularly, we formulate current-coupling hybrid schemes, in which energetic
particle dynamics are expressed in either guiding-center or gyrocenter
coordinates.Comment: v3.0. 30 page
Coarse-Graining Hamiltonian Systems Using WSINDy
The Weak-form Sparse Identification of Nonlinear Dynamics algorithm (WSINDy)
has been demonstrated to offer coarse-graining capabilities in the context of
interacting particle systems (https://doi.org/10.1016/j.physd.2022.133406). In
this work we extend this capability to the problem of coarse-graining
Hamiltonian dynamics which possess approximate symmetries associated with
timescale separation. Such approximate symmetries often lead to the existence
of a Hamiltonian system of reduced dimension that may be used to efficiently
capture the dynamics of the symmetry-invariant dependent variables. Deriving
such reduced systems, or approximating them numerically, is an ongoing
challenge. We demonstrate that WSINDy can successfully identify this reduced
Hamiltonian system in the presence of large intrinsic perturbations while
remaining robust to extrinsic noise. This is significant in part due to the
nontrivial means by which such systems are derived analytically. WSINDy also
naturally preserves the Hamiltonian structure by restricting to a trial basis
of Hamiltonian vector fields. The methodology is computational efficient, often
requiring only a single trajectory to learn the global reduced Hamiltonian, and
avoiding forward solves in the learning process. Using nearly-periodic
Hamiltonian systems as a prototypical class of systems with approximate
symmetries, we show that WSINDy robustly identifies the correct leading-order
system, with dimension reduced by at least two, upon observation of the
relevant degrees of freedom. We also provide a contribution to averaging theory
by proving that first-order averaging at the level of vector fields preserves
Hamiltonian structure in nearly-periodic Hamiltonian systems. We provide
physically relevant examples, namely coupled oscillator dynamics, the
H\'enon-Heiles system for stellar motion within a galaxy, and the dynamics of
charged particles
Degenerate Variational Integrators for Magnetic Field Line Flow and Guiding Center Trajectories
Symplectic integrators offer many advantages for the numerical solution of
Hamiltonian differential equations, including bounded energy error and the
preservation of invariant sets. Two of the central Hamiltonian systems
encountered in plasma physics --- the flow of magnetic field lines and the
guiding center motion of magnetized charged particles --- resist symplectic
integration by conventional means because the dynamics are most naturally
formulated in non-canonical coordinates, i.e., coordinates lacking the familiar
partitioning. Recent efforts made progress toward non-canonical
symplectic integration of these systems by appealing to the variational
integration framework; however, those integrators were multistep methods and
later found to be numerically unstable due to parasitic mode instabilities.
This work eliminates the multistep character and, therefore, the parasitic mode
instabilities via an adaptation of the variational integration formalism that
we deem ``degenerate variational integration''. Both the magnetic field line
and guiding center Lagrangians are degenerate in the sense that their resultant
Euler-Lagrange equations are systems of first-order ODEs. We show that
retaining the same degree of degeneracy when constructing a discrete Lagrangian
yields one-step variational integrators preserving a non-canonical symplectic
structure on the original Hamiltonian phase space. The advantages of the new
algorithms are demonstrated via numerical examples, demonstrating superior
stability compared to existing variational integrators for these systems and
superior qualitative behavior compared to non-conservative algorithms
Spectral and structural stability properties of charged particle dynamics in coupled lattices
It has been realized in recent years that coupled focusing lattices in accelerators and storage rings have significant advantages over conventional uncoupled focusing lattices, especially for high-intensity charged particle beams. A theoretical framework and associated tools for analyzing the spectral and structural stability properties of coupled lattices are formulated in this paper, based on the recently developed generalized Courant-Snyder theory for coupled lattices. It is shown that for periodic coupled lattices that are spectrally and structurally stable, the matrix envelope equation must admit matched solutions. Using the technique of normal form and pre-Iwasawa decomposition, a new method is developed to replace the (inefficient) shooting method for finding matched solutions for the matrix envelope equation. Stability properties of a continuously rotating quadrupole lattice are investigated. The Krein collision process for destabilization of the lattice is demonstrated. © 2015 AIP Publishing LLC.close0
High-Precision Inversion of Dynamic Radiography Using Hydrodynamic Features
Radiography is often used to probe complex, evolving density fields in
dynamic systems and in so doing gain insight into the underlying physics. This
technique has been used in numerous fields including materials science, shock
physics, inertial confinement fusion, and other national security applications.
In many of these applications, however, complications resulting from noise,
scatter, complex beam dynamics, etc. prevent the reconstruction of density from
being accurate enough to identify the underlying physics with sufficient
confidence. As such, density reconstruction from static/dynamic radiography has
typically been limited to identifying discontinuous features such as cracks and
voids in a number of these applications.
In this work, we propose a fundamentally new approach to reconstructing
density from a temporal sequence of radiographic images. Using only the robust
features identifiable in radiographs, we combine them with the underlying
hydrodynamic equations of motion using a machine learning approach, namely,
conditional generative adversarial networks (cGAN), to determine the density
fields from a dynamic sequence of radiographs. Next, we seek to further enhance
the hydrodynamic consistency of the ML-based density reconstruction through a
process of parameter estimation and projection onto a hydrodynamic manifold. In
this context, we note that the distance from the hydrodynamic manifold given by
the training data to the test data in the parameter space considered both
serves as a diagnostic of the robustness of the predictions and serves to
augment the training database, with the expectation that the latter will
further reduce future density reconstruction errors. Finally, we demonstrate
the ability of this method to outperform a traditional radiographic
reconstruction in capturing allowable hydrodynamic paths even when relatively
small amounts of scatter are present.Comment: Submitted to Optics Expres