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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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35 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Gromov ground state in phase space engineering for fusion energy

Phase space engineering by rf waves plays important roles in both thermal D-T fusion and nonthermal advanced fuel fusion, but not all phase space manipulation is allowed; certain fundamental limits exist. In addition to Liouville's theorem, which requires the manipulation to be volume preserving, Gromov's nonsqueezing theorem imposes another constraint. Here, the Gardner ground state is defined as the ground state accessible by smooth volume-preserving maps. However, the extra Gromov constraint should produce a higher-energy ground state. An example of a Gardner ground state forbidden by Gromov's nonsqueezing theorem is given. The challenge question is “What is the Gromov ground state, i.e., the lowest energy state accessible by smooth symplectic maps?” This is a difficult problem. As a simplification, we conjecture that the linear Gromov ground state problem is solvable.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1999

Dynamical Chaos in the Wisdom-Holman Integrator: Origins and Solutions

We examine the nonlinear stability of the Wisdom-Holman (WH) symplectic mapping applied to the integration of perturbed, highly eccentric (e-0.9) two-body orbits. We find that the method is unstable and introduces artificial chaos into the computed trajectories for this class of problems, unless the step size chosen 1s small enough that PeriaPse is always resolved, in which case the method is generically stable. This 'radial orbit instability' persists even for weakly perturbed systems. Using the Stark problem as a fiducial test case, we investigate the dynamical origin of this instability and argue that the numerical chaos results from the overlap of step-size resonances; interestingly, for the Stark-problem many of these resonances appear to be absolutely stable. We similarly examine the robustness of several alternative integration methods: a time-regularized version of the WH mapping suggested by Mikkola; the potential-splitting (PS) method of Duncan, Levison, Lee; and two original methods incorporating approximations based on Stark motion instead of Keplerian motion. The two fixed point problem and a related, more general problem are used to conduct a comparative test of the various methods for several types of motion. Among the algorithms tested, the time-transformed WH mapping is clearly the most efficient and stable method of integrating eccentric, nearly Keplerian orbits in the absence of close encounters. For test particles subject to both high eccentricities and very close encounters, we find an enhanced version of the PS method-incorporating time regularization, force-center switching, and an improved kernel function-to be both economical and highly versatile. We conclude that Stark-based methods are of marginal utility in N-body type integrations. Additional implications for the symplectic integration of N-body systems are discussed.

Rauch, Kevin P.↗
DOE OSTI2025

Minimizing phase-space energies

A primary technical challenge for harnessing fusion energy is to control and extract energy from a nonthermal distribution of charged particles. The fact that phase space evolves by symplectomorphisms fundamentally limits how a distribution may be manipulated. While the constraint of phase-space volume preservation is well understood, other constraints remain to be fully appreciated. To better understand these constraints, we study the problem of extracting energy from a distribution of particles using area-preserving and symplectic linear maps. When a quadratic potential is imposed, we find that the maximal extractable energy can be computed as trace minimization problems. We solve these problems and show that the extractable energy under linear symplectomorphisms may be much smaller than the extractable energy under special linear maps. As a result, the method introduced in the present study enables an energy-based proof of the linear Gromov nonsqueezing theorem.

First-principles calculations in plasma physics↗
NASA NTRS1992

Polynomial approximation of Poincare maps for Hamiltonian system

Different methods are proposed and tested for transforming a non-linear differential system, and more particularly a Hamiltonian one, into a map without integrating the whole orbit as in the well-known Poincare return map technique. We construct piecewise polynomial maps by coarse-graining the phase-space surface of section into parallelograms and using either only values of the Poincare maps at the vertices or also the gradient information at the nearest neighbors to define a polynomial approximation within each cell. The numerical experiments are in good agreement with both the real symplectic and Poincare maps.

Froeschle, Claude↗
DOE OSTI2025

Symplectic machine learning model for fast simulation of space-charge effects

Symplectic simulation of space-charge effects is crucial for the design and operation of high-intensity particle accelerators. Traditional methods for simulating these effects are often computationally expensive, resulting in significant overhead. In this work, we introduce a generative model based on a U-Net architecture within a generative adversarial network framework to efficiently simulate space-charge effects. The model is trained to predict the transverse multiparticle space-charge Hamiltonian, which can be physically computed using a gridless spectral method. The one-step symplectic transverse transfer map for the particles is then obtained by differentiating the predicted Hamiltonian. Benchmarking results demonstrate that this generative model achieves an order of magnitude higher computational efficiency compared to the spectral method, providing a highly efficient alternative for simulating space-charge effects with a large number of particles. By maintaining symplecticity, the model effectively preserves the phase-space structure and mitigates nonphysical errors in long-term simulations. This model has been integrated into jutrack, a novel autodifferentiable accelerator modeling code developed in the julia programming language.

Beam code development & simulation techniques↗
DOE OSTI2020

Fast neural Poincare maps for toroidal magnetic fields

We demonstrate how to build symplectic neural networks to approximate Hamiltonian and Poincare maps in this notebook. Two examples are given: a simple pendulum and a pertubed pendulum.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

The geometric theory of charge conservation in particle-in-cell simulations

In recent years, several gauge-symmetric particle-in-cell (PIC) methods have been developed whose simulations of particles and electromagnetic fields exactly conserve charge. While it is rightly observed that these methods’ gauge symmetry gives rise to their charge conservation, this causal relationship has generally been asserted via ad hoc derivations of the associated conservation laws. In this work, we develop a comprehensive theoretical grounding for charge conservation in gauge-symmetric Lagrangian and Hamiltonian PIC algorithms. For Lagrangian variational PIC methods, we apply Noether’s second theorem to demonstrate that gauge symmetry gives rise to a local charge conservation law as an off-shell identity. For Hamiltonian splitting methods, we show that the momentum map establishes their charge conservation laws. We define a new class of algorithms – gauge-compatible splitting methods – that exactly preserve the momentum map associated with a Hamiltonian system’s gauge symmetry – even after time discretization. This class of algorithms affords splitting schemes a decided advantage over alternative Hamiltonian integrators. We apply this general technique to design a novel, explicit, symplectic, gauge-compatible splitting PIC method, whose momentum map yields an exact local charge conservation law. Finally, our study clarifies the appropriate initial conditions for such schemes and examines their symplectic reduction.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

SDA: a symbolic differential algebra package in C++

Truncated Power Series Algebra (TPSA), or Differential Algebra (DA), is a well-established tool in accelerator physics, commonly used for generating high-order maps of dynamic systems, as well as in symplectic tracking, normal form analysis, verified integration, optimization, and fast multipole methods. This package is the first to perform symbolic DA computations, enabling traceability of initial condition contributions and runtime reduction for repeated DA calculations, potentially expanding DA’s applications.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1994

A mapping method for the gravitational few-body problem with dissipation

Recently a new class of numerical integration methods - 'mixed variable symplectic integrators' - has been introduced for studying long-term evolution in the conservative gravitational few-body problem. These integrators are an order of magnitude faster than conventional ordinary differential equations (ODE) integration methods. Here we present a simple modification of this method to include small non-gravitational forces. The new scheme provides a similar advantage of computational speed for a larger class of problems in Solar System dynamics.

Malhotra, Renu↗
DOE OSTI2022

Clebsch canonization of Lie–Poisson systems

We propose a systematic procedure called the Clebsch canonization for obtaining a canonical Hamiltonian system that is related to a given Lie–Poisson equation via a momentum map. We describe both coordinate and geometric versions of the procedure, the latter apparently for the first time. We also find another momentum map so that the pair of momentum maps constitute a dual pair under a certain condition. The dual pair gives a concrete realization of what is commonly referred to as collectivization of Lie–Poisson systems. It also implies that solving the canonized system by symplectic Runge–Kutta methods yields so-called collective Lie–Poisson integrators that preserve the coadjoint orbits and hence the Casimirs exactly. We give a couple of examples, including the Kida vortex and the heavy top on a movable base with controls, which are Lie–Poisson systems on $\mathfrak{so}$ (2,1)* and ($\mathfrak{se}$ (3) ⋉ $\mathbb{R}^3$)* and, respectively.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Gate-Based Quantum Simulation of Gaussian Bosonic Circuits on Exponentially Many Modes

We introduce a framework for simulating, on an ( n + 1 )-qubit quantum computer, the action of a Gaussian bosonic (GB) circuit on a state over 2 n modes. Specifically, we encode the initial bosonic state’s expectation values over quadrature operators (and their covariance matrix) as an input qubit state. This is then evolved by a quantum circuit that effectively implements the symplectic propagators induced by the GB gates. We find families of GB circuits and initial states leading to efficient quantum simulations. For this purpose, we introduce a dictionary that maps between GB and qubit gates such that particle- (non-particle-) preserving GB gates lead to real- (imaginary-) time evolutions at the qubit level. For the special case of particle-preserving circuits, we present a bounded-error-quantum-polynomial time (BQP)-complete GB decision problem, indicating that GB evolutions of Gaussian states on exponentially many modes are as powerful as universal quantum computers. We also perform numerical simulations of an interferometer on ∼ 8 × 10 9 modes, illustrating the power of our framework. Published by the American Physical Society 2025

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Nearly Periodic Maps and Geometric Integration of Noncanonical Hamiltonian Systems

Abstract 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 analog 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.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Topological symplectic Kondo effect

Multiple conduction channels interacting with a quantum impurity—a spin in the conventional “multichannel Kondo effect” or a topological mesoscopic device (“topological Kondo effect”)—has been proposed as a platform to realize anyonic quasiparticles. However, the above implementations require either perfect channel symmetry or the use of Majorana fermions. Here, in this work, we propose a Majorana-free mesoscopic setup which implements the Kondo effect of the symplectic Lie group and can harbor emergent anyons (including Majorana fermions, Fibonacci anyons, and parafermions) even in the absence of perfect channel symmetry. In addition to the detailed prescription of the implementation, we present the strong coupling solution by mapping the model to the multichannel Kondo effect associated to an internal symmetry and exploit conformal field theory to predict the nontrivial scaling of a variety of observables, including conductance, as a function of temperature. This work does not only open the door for robust Kondo-based anyon platforms, but also sheds light on the physics of strongly correlated materials with competing order parameters.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
NASA NTRS2014

Coordinated Mineralogical and Isotopic Analysis of a Cosmic Symplectite Identified in a Stardust Terminal Particle

Comet Wild-2 samples returned by the Stardust spacecraft contain a chemically diverse mixture of material, underscoring the complex nature of comets. Studies of entire Stardust aerogel tracks afford the opportunity to examine the fine-grained particle fragments distributed along the length of the track as well as the terminal particles. Previous TEM characterization of a terminal particle (TP) in track #147 revealed a symplectically intergrown iron sulfide and oxide assemblage. Mineralogically similar assemblages, known as cosmic symplectites (COS, formerly termed "new-PCP"), have only been identified in the primitive carbonaceous chondrite Acfer 094. Meteoritic COS have isotopically heavy O compositions (delta (sup 17), O-18 = 180per mille) that point to interactions with early solar system primordial water. In this study we report mineralogical and O isotopic measurements of the Wild-2 COS assemblage. Experimental: Track #147 is a "bulbous"-type track (4600 microns long) containing 7 terminal particles. The TPs were removed from the track, embedded in epoxy, and ultramicrotomed. A JEOL 2500SE 200 keV field-emission scanning-transmission electron microscope was used to obtain quantitative elemental maps and detailed mineralogical characterization. Following TEM analysis, two thin sections of TP4 (12 microns) were analyzed for O isotopes by raster ion imaging with the JSC NanoSIMS 50L. All three O isotopes were measured simultaneously using electron multipliers. San Carlos olivine grains were used as isotopic standards. Results and Discussion: The COS in the Wild-2 track #147 TP4 sample consists of symplectically intergrown pentlandite and nanocrystalline maghemite which coexists with high-Ca pyroxene with Na and Cr (kosmochlor component). This kosmochlor component could have a nebular origin and be precursors to type II chondrules in ordinary chondrites. Yet pentlandite is not a stable phase in the nebula. The COS in Acfer 094 also consists of pentlandite, but contains magnetite [4] rather than the more oxidized maghemite observed in the Wild-2 COS. The Acfer 094 COS display heavy O isotopic compositions that are the result of sulfidization and oxidation of Fe, Ni-metal grains and sulfides by O-17- and O-18-rich water in the solar nebula or possibly on the parent body. The O isotopic composition of the Wild-2 COS, however, is indistinguishable from terrestrial, indicating it was not altered by the same primordial aqueous reservoir as the Acfer 094 COS. The alteration could have occurred on the parent body by isotopically equilibrated ice. The mineralogy and petrography of Wild-2 samples suggests an incomplete or nascent hydration process. In future work we will analyze S isotopes in the track #147 TP4 COS and search for additional COS in Stardust samples.

Nguyen, A. N.↗
NASA NTRS1991

Mapping the stability field of Jupiter Trojans

Jupiter Trojans are a remnant of outer solar system planetesimals captured into stable or quasistable libration about the 1:1 resonance with the mean motion of Jupiter. The observed swarms of Trojans may provide insight into the original mass of condensed solids in the zone from which the Jovian planets accumulated, provided that the mechanisms of capture can be understood. As the first step toward this understanding, the stability field of Trojans were mapped in the coordinate proper eccentricity, e(sub p), and libration amplitude, D. To accomplish this mapping, the orbits of 100 particles with e(sub p) in the range of 0 to 0.8 and D in the range 0 to 140 deg were numerically integrated. Orbits of the Sun, the four Jovian planets, and the massless particles were integrated as a full N-body system, in a barycentric frame using fourth order symplectic scheme.

Levison, H. F.↗
DOE OSTI2020

Canonical Transformation of Potential Model Hamiltonian Mechanics to Geometrical Form I

Using the methods of symplectic geometry, we establish the existence of a canonical transformation from potential model Hamiltonians of standard form in a Euclidean space to an equivalent geometrical form on a manifold, where the corresponding motions are along geodesic curves. The advantage of this representation is that it admits the computation of geodesic deviation as a test for local stability, shown in recent previous studies to be a very effective criterion for the stability of the orbits generated by the potential model Hamiltonian. We describe here an algorithm for finding the generating function for the canonical transformation and describe some of the properties of this mapping under local diffeomorphisms. We give a convergence proof for this algorithm for the one-dimensional case, and provide a precise geometric formulation of geodesic deviation which relates the stability of the motion in the geometric form to that of the Hamiltonian standard form. We apply our methods to a simple one-dimensional harmonic oscillator and conclude with a discussion of the relation of bounded domains in the two representations for which Morse theory would be applicable.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Quantization: History and problems

In this work, I explore the concept of quantization as a mapping from classical phase space functions to quantum operators. I discuss the early history of this notion of quantization with emphasis on the works of Schrödinger and Dirac, and how quantization fit into their overall understanding of quantum theory in the 1920's. Dirac, in particular, proposed a quantization map which should satisfy certain properties, including the property that quantum commutators should be related to classical Poisson brackets in a particular way. However, in 1946, Groenewold proved that Dirac's mapping was inconsistent, making the problem of defining a rigorous quantization map more elusive than originally expected. This result, known as the Groenewold-Van Hove theorem, is not often discussed in physics texts, but here I will give an account of the theorem and what it means for potential ``corrections” to Dirac's scheme. Other proposals for quantization have arisen over the years, the first major one being that of Weyl in 1927, which was later developed by many, including Groenewold, and which has since become known as Weyl Quantization in the mathematical literature. Another, known as Geometric Quantization, formulates quantization in differential-geometric terms by appealing to the character of classical phase spaces as symplectic manifolds; this approach began with the work of Souriau, Kostant, and Kirillov in the 1960's. I will describe these proposals for quantization and comment on their relation to Dirac's original program. Along the way, the problem of operator ordering and of quantizing in curvilinear coordinates will be described, since these are natural questions that immediately present themselves when thinking about quantization.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗