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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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At least 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
NASA NTRS1994

Adiabatic invariants in stellar dynamics, 3: Application to globular cluster evolution

The previous two companion papers demonstrate that slowly varying perturbations may not result in adiabatic cutoffs and provide a formalism for computing the long-term effects of time-dependent perturbations on stellar systems. Here, the theory is implemented in a Fokker-Planck code and a suite of runs illustrating the effects of shock heating on globular cluster evolution are described. Shock heating alone results in considerable mass loss for clusters with R(sub g) less than or approximately 8 kpc: a concentration c = 1.5 cluster with R(sub g) kpc loses up to 95% of its initial mass in 15 Gyr. Only those with concentration c greater than or approximately 1.3 survive disk shocks inside of this radius. Other effects, such as mass loss by stellar evolution, will decrease this survival bound. Loss of the initial halo together with mass segregation leads to mass spectral indices, x, which may be considerably larger than their initial values.

Weinberg, Martin D.↗
NASA NTRS1994

Adiabatic invariants in stellar dynamics. 2: Gravitational shocking

A new theory of gravitational shocking based on time-dependent perturbation theory shows that the changes in energy and angular momentum due to a slowly varying disturbance are not exponentially small for stellar dynamical systems in general. It predicts significant shock heating by slowly varying perturbations previously thought to be negligible according to the adiabatic criterion. The theory extends the scenarios traditionally computed only with the impulse approximation and is applicable to a wide class of disturbances. The approach is applied specifically to the problem of disk shocking of star clusters.

Weinberg, Martin D.↗
DOE OSTI2022

Electron Drift Kinetics in Space and in the Lab [Slides]

In a magnetized plasma, dynamics are fundamentally split between the directions parallel and perpendicular to the magnetic field. Generally, gyration about the magnetic field will occur on smaller spatial and time scales than the bulk dynamics of the system. From Hamiltonian mechanics, a periodic motion on a time scale much shorter than the other system dynamics leads to an adiabatic invariant. The adiabatic invariant for this motion is the magnetic moment $\mu=\frac{mv⟂^2}{2B}$, which will be approximately conserved.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Energizing charged particles by an orbit instability in a slowly rotating magnetic field

In this work, the stability of charged particle motion in a uniform magnetic field with an added spatially uniform transverse rotating magnetic field (RMF) is studied analytically. It is found that the stability diagram of a single particle's orbit depends critically on the chosen boundary conditions. We show that for many boundary conditions and wide regions in the parameter space, RMFs oscillating far below the cyclotron frequency can cause linear instabilities in the motion which break μ invariance and energize particles. Such energization may appear at odds with the adiabatic invariance of μ; however, adiabatic invariance is an asymptotic result and does not preclude such heating by magnetic fields oscillating at slow frequencies. This mechanism may contribute to heating in the edge plasma of field-reversed configurations (FRCs) in rotamak-FRC experiments. Furthermore, these RMF-driven instabilities may significantly enhance azimuthal current drive during the formation of FRCs in such devices.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
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↗
NASA NTRS1984

Magnetopause structure and the question of particle accessibility

A simple plane model of the magnetopause is used to address the question of particle accessibility. Particle motion in the current sheet region is analyzed, showing that the concept of gyromotion is useful even when the electric and magnetic fields vary significantly over the gyroradius, as long as the variation is perpendicular to the drift direction. The first adiabatic invariant for particle motion is defined in such a way that it is preserved in regions of large field gradients, provided that the gradients are in a direction primarily perpendicular to the particle drifts. This generalized invariant provides an adiabatically conserved quantity that can be used to characterize particles as they move from a source region through the drift region and into the magnetopause itself, helping to resolve the accessibility question. Some preliminary results are given for the magnetopause structure based on the location of particle guiding points.

Whipple, E. C.↗
DOE OSTI2024

Derivations of the Total Radiation Belt Electron Content

Abstract We present multiple derivations of the Total Radiation Belt Electron Content (TRBEC), an indicator of the global number of electrons that instantaneously occupy the radiation belts. Derived from electron flux measurements, the TRBEC reduces the spatial information into a scalar quantity that concisely describes global aspects of the system. This index provides a simple, global, and long‐term assessment of the radiation belts that enables systematic analysis. In this work, we examine the TRBEC using the adiabatic invariants of which has been used in previous articles as this coordinate system removes reversible adiabatic effects. We then introduce a new expression to compute the TRBEC using the non‐adiabatic coordinates of , relevant in the contexts of energetic electron precipitation, chorus, and hiss scattering where adiabatic invariant quantities are no longer conserved. From both expressions of the TRBEC we demonstrate that an erroneous factor of that appeared in previous works using the adiabatic derivation led to an overestimate of the reported electron populations. In addition, we quantify electron loss in the outer radiation belt via a case study using the Van Allen Probes data over a 20‐day period from March 2013 specifying particle populations both in terms of the aforementioned adiabatic and non‐adiabatic variables. The total number of electrons in the outer radiation belt reached upwards of electrons at the peak of the storm, a rest mass of roughly 10 g.

Astronomy & Astrophysics↗
NASA NTRS1990

Ion precipitation from the inner plasma sheet due to stochastic diffusion

Plasma sheet ions do not conserve their first adiabatic invariant when the magnetic field is appreciably tail-like. They do conserve a different adiabatic invariant but only to linear, rather than exponential, accuracy in the appropriate small parameter. Thus significant stochastic diffusion can occur for particles crossing the separatrix dividing the segments of orbits on which the particles cross and do not cross the tail midplane. Such ions can escape the plasma sheet and precipitate into the atmosphere. Stochastic scattering is strongest from those field lines where the ion's Larmor period in the normal component of the neutral sheet magnetic field approximately equals its bounce period. By comparing the rates of stochastic ion loss and convection in the tail, it is possible to estimate the location and thickness of the inner edge of the ion plasma sheet created by stochastic ion loss. Ions of different masses precipitate into the atmosphere at slightly different locations. Since wave particle interactions are not needed, this precipitation will always occur and should be particularly evident during quiet geomagnetic conditions, when it is less likely to be masked by other precipitation mechanisms.

Zelenyi, L.↗
NASA NTRS1990

The magnetic pumping of plasmas with sawtooth waveforms

The pumping of plasmas by sawtooth-waveform magnetic induction variations is studied theoretically and by means of computer simulations. A sawtooth is a cycle waveform that is characterized by a slow increase in the magnetic induction followed by a rapid drop in the induction. Two types of sawtooth pumping are analyzed, and the types classified as to whether or not the first adiabatic invariants of the plasma particles are conserved during the rapid drops in the magnetic induction. When the invariants are conserved, the sawtooth waveforms are found to be less efficient than square waves for pumping plasmas. When the adiabatic invariations are not conserved, the pumping efficiency is found to be a slight improvement over square waves. Both types of pumping are applied to a hypothetical tokamak plasma and it is concluded that neither type of sawtooth pumping is practical for heating magnetically confined fusion plasmas.

Borovsky, Joseph E.↗
DOE OSTI2023

Approximation of nearly-periodic symplectic maps via structure-preserving neural networks

A continuous-time dynamical system with parameter ε is nearly-periodic if all its trajectories are periodic with nowhere-vanishing angular frequency as ε approaches 0. Nearly-periodic maps are discrete-time analogues of nearly-periodic systems, defined as parameter-dependent diffeomorphisms that limit to rotations along a circle action, and they admit formal U(1) symmetries to all orders when the limiting rotation is non-resonant. For Hamiltonian nearly-periodic maps on exact presymplectic manifolds, the formal U(1) symmetry gives rise to a discrete-time adiabatic invariant. In this paper, we construct a novel structure-preserving neural network to approximate nearly-periodic symplectic maps. This neural network architecture, which we call symplectic gyroceptron, ensures that the resulting surrogate map is nearly-periodic and symplectic, and that it gives rise to a discrete-time adiabatic invariant and a long-time stability. This new structure-preserving neural network provides a promising architecture for surrogate modeling of non-dissipative dynamical systems that automatically steps over short timescales without introducing spurious instabilities.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1986

Monte Carlo simulation of charged particle impact on the satellites of Jupiter and Saturn

Ensemble-averaged lifetimes of Jovian and Saturnian trapped charged particles against loss by impact on natural satellites are presented. Precise values of these loss rates can be obtained from the known geometry of the satellite orbits, magnetic fields, and particle trajectory. These loss rates are needed as an ingredient of transport theory which is usually formulated in terms of the first and second adiabatic invariants and radial distance. The effects of satellite orbital inclination and eccentricity, ion charge to mass ratio and energy, equatorial pitch, and distance from the planet on the particle lifetime are discussed utilizing a tilted, but not offset, dipolar field geometry resulting in lifetime values expressed as functions of the first two adiabatic invariants and the equatorial radial distance from the planet.

Bell, E. V., II↗
DOE OSTI2022

Pitch-Angle Diffusion in the Earth’s Magnetosphere Organized by the Mozer-Transformed Coordinate System

In the Earth’s dipole magnetosphere finite-gyroradius effects produce a shift of the atmospheric loss cone away from the direction of the magnetic field. This loss-cone shift is theoretically described by the “Mozer transform”, which is based upon the curvature drift of particles crossing the equatorial plane. For positive ions the northern and southern loss cones both shift westward and for electrons the northern and southern loss cones both shift eastward. This loss-cone shift is part of a coordinate-system transform, with the transformed coordinates better organizing the behavior of particle orbits in the dipole magnetic field (e.g. first adiabatic invariants, mirror heights, and bounce times). In this report it is demonstrated that the transformed coordinate system also properly organizes pitch-angle diffusion. This improved organization of the diffusion is true whether the angular scattering is produced by plasma-wave scattering or by field-line-curvature (FLC) scattering. It is shown that FLC scattering and the loss cone shift are linked, so that if FLC scattering is occurring, there is a loss cone shifted away from the magnetic-field direction and the Mozer-transformed coordinates are needed.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1995

Bounce-averaged Hamiltonian for charged particles in an axisymmetric but nondipolar model magnetosphere

In order to facilitate bounce-averaged guiding center simulations of geomagnetically trapped particles, we express the kinetic energy of a particle with magnetic coordinates (L,phi) as an analytic function of the first two adiabatic invariants (M,J) and the L value of the field line. The magnetic field model is axisymmetric, consisting of a dipolar vector-B field plus a uniform southward magnetic field parallel to the dipole moment mu(sub E). This model magnetosphere is surrounded by a circular equatorial neutral line whose radius b is an adjustable parameter. Our formulation provides a computationally efficient method for tracing the bounce-averaged adiabatic motion (conserving all three invariants) and nonadiabatic transport (violating the third invariant while conserving the first two invariants) of geomagnetically trapped particles in the model magnetosphere.

Schulz, Michael↗