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

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 $(q, p)$ 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

Generalized Courant-Snyder Theory for Charged-Particle Dynamics in General Focusing Lattices

The Courant-Snyder (CS) theory for one degree of freedom is generalized to the case of coupled transverse dynamics in general linear focusing lattices with quadrupole, skew-quadrupole, dipole, and solenoidal components, as well as torsion of the fiducial orbit and variation of beam energy. The envelope function is generalized into an envelope matrix, and the phase advance is generalized into a 4D sympletic rotation. The envelope equation, the transfer matrix, and the CS invariant of the original CS theory all have their counterparts, with remarkably similar expressions, in the generalized theory.open7