Search NASA⌕ Search

SEARCH · Search NASA

Results for “ANGULAR MOTION”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Effects of low-frequency voltage on nonlinear standing wave excitation, plasma uniformity, and ion dynamics in dual-frequency asymmetric capacitive discharges

Abstract It is known that in very-high-frequency (VHF) capacitively coupled plasmas, the higher harmonics generated by nonlinear sheath motion can enhance the standing wave effect (SWE), which can lead to center-peaked plasma density profiles. In this work, an improved nonlinear electromagnetic model incorporating a transmission line model, an electron momentum balance model, a bulk plasma model, a collisionless nonlinear numerical sheath model, and an ion Monte-Carlo collision (MCC) model is developed to study the effects of low-frequency (LF) voltage V L on the nonlinear standing wave excitation, plasma uniformity, and ion energy and angular distribution functions (IEDFs and IADFs) in dual-frequency (DF) asymmetric capacitive argon discharges at relatively low pressure of 3 Pa. The plasma diffusion in the radial direction and ion dynamics within the LF oscillating sheath are self-consistently considered. The LF voltage V L at 2 MHz varies from 0 to 700 V while the HF voltage V H at 60 MHz is fixed at 100 V. Simulation results indicate that without the addition of an LF source (i.e. V L = 0 V), there are a considerable number of high-order harmonics with short wavelengths, leading to significant SWE and central peak in the radial plasma density profile. Nevertheless, the high-order harmonic excitations tend to be weakened and merely occur around the phase of the full LF sheath collapse due to a shorter characteristic damping time of the surface waves as V L increases. This, combined with increased surface wavelengths of both the driving frequency and the higher harmonics at a higher V L , leads to suppressed standing waves and improved plasma uniformity. Meanwhile, the simulations show that both the low and the high energy peaks of IEDF move towards higher energies, and the energy peak separation width ΔEbecomes wider with the increase of V L . The IEDF at the radial center of the powered electrode exhibits a broader ΔEthan that at the edge. For the IADF, an increased V L results in more ions incident on the electrode with a smaller deflection angle. Because of a thinner sheath and a higher sheath voltage at the electrode center, the peak value of IADF at the electrode center is greater than that at the edge.

Physics↗
DOE OSTI2021

Ring Formation in Protoplanetary Disks Driven by an Eccentric Instability

We find that, under certain conditions, protoplanetary disks may spontaneously generate multiple, concentric gas rings without an embedded planet through an eccentric cooling instability. Using both linear theory and nonlinear hydrodynamics simulations, we show that a variety of background states may trap a slowly processing, one-armed spiral mode that becomes unstable when a gravitationally stable disk rapidly cools. The angular momentum required to excite this spiral comes at the expense of nonuniform mass transport that generically results in multiple rings. For example, one long-term hydrodynamics simulation exhibits four long-lived, axisymmetric gas rings. We verify the instability evolution and ring-formation mechanism from first principles with our linear theory, which shows remarkable agreement with the simulation results. Dust trapped in these rings may produce observable features consistent with observed disks. Additionally, direct detection of the eccentric gas motions may be possible when the instability saturates, and any residual eccentricity left over in the rings at later times may also provide direct observational evidence of this mechanism.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Spin-mediated shear oscillators in a van der Waals antiferromagnet

Understanding how microscopic spin configuration gives rise to exotic properties at the macroscopic length scale has long been pursued in magnetic materials. One seminal example is the Einstein-de Haas effect in ferromagnets, in which angular momentum of spins can be converted into mechanical rotation of an entire object. However, for antiferromagnets without net magnetic moment, how spin ordering couples to macroscopic movement remains elusive. Here we observed a seesaw-like rotation of reciprocal lattice peaks of an antiferromagnetic nanolayer film, whose gigahertz structural resonance exhibits more than an order-of-magnitude amplification after cooling below the Neel temperature. Using a suite of ultrafast diffraction and microscopy techniques, we directly visualize this spin-driven rotation in reciprocal space at the nanoscale. This motion corresponds to interlayer shear in real space, in which individual micro-patches of the film behave as coherent oscillators that are phase-locked and shear along the same in-plane axis. Using time-resolved optical polarimetry, we further show that the enhanced mechanical response strongly correlates with ultrafast demagnetization, which releases elastic energy stored in local strain gradients to drive the oscillators. Finally, our work not only offers the first microscopic view of spin-mediated mechanical motion of an antiferromagnet but it also identifies a new route towards realizing high-frequency resonators up to the millimetre band, so the capability of controlling magnetic states on the ultrafast timescale can be readily transferred to engineering the mechanical properties of nanodevices.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Direct Monitoring of Conical Intersection Passage via Electronic Coherences in Twisted X-Ray Diffraction

Quantum coherences in electronic motions play a critical role in determining the pathways and outcomes of virtually all photophysical and photochemical molecular processes. However, the direct observation of electronic coherences in the vicinity of conical intersections remains a formidable challenge. Here we propose a novel time-resolved twisted x-ray diffraction technique that can directly monitor the electronic coherences created as the molecule passes through a conical intersection. We show that the contribution of electronic populations to this signal is canceled out when using twisted x-ray beams that carry a light orbital angular momentum, providing a direct measurement of transient electronic coherences in gas-phase molecules.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

MD Simulation of Water Using a Rigid Body Description Requires a Small Time Step to Ensure Equipartition

In simulations of aqueous systems, it is common to freeze the bond vibration and angle bending modes in water to allow for a longer time step δt for integrating the equations of motion. Thus, δt = 2 fs is often used in simulating rigid models of water. We simulate the SPC/E model of water using δt from 0.5 to 3.0 fs and up to 4 fs using hydrogen mass repartitioning. In these simulations, we find that for all but δt = 0.5 fs, equipartition is not obtained between translational and rotational modes, with the rotational modes exhibiting a lower temperature than the translation modes. To probe the reasons for the lack of equipartition, we study the autocorrelation of the translational velocity of the center of mass and the angular velocity of the rigid water molecule, respectively. Here, we find that the rotational relaxation occurs on a timescale comparable to vibrational periods, calling into question the original motivations for freezing the vibrations. Furthermore, a time step with δt ≥ 1 fs is not able to capture accurately the fast rotational relaxation, which reveals its impact as an effective slowing-down of rotational relaxation. The fluctuation–dissipation relation then leads to the conclusion that the rotational temperature should be cooler for δt greater than the reference value of 0.5 fs. Consideration of fluctuation–dissipation in equilibrium molecular dynamics simulations also emphasizes the need to capture the temporal evolution of fluctuations with fidelity and the role of δt in this regard. The time step also influences the solution thermodynamic properties: both the mean system potential energies and the excess entropy of hydration of a soft repulsive cavity are sensitive to δt.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Structure preserving and energy dissipative contact approaches for implicit dynamics

In this work, several structure preserving and energy dissipative contact approaches are proposed and evaluated. The time integration schemes considered are general with regard to the version of constraint type, but here the emphasis was on mortar contact. The proposed mortar contact approach conserves both linear and angular momentum for mortar contact in a novel way. The proposed time integration scheme can conserve energy or provide strict contact dissipation. In addition, the proposed scheme enforces both gap constraints and gap velocity constraints (i.e., persistency). Using a midstep time integrator often causes energy dissipation during initial impact, here this energy can be recovered in a novel way. Enforcing the gap velocity constraint mitigates the contact chatter of the contact pressure and nodes in many problems. Whereas some approaches enforce the persistency condition and gap constraints simultaneously during the solution of the equations of motion (EOM) requiring multipliers for both constraints included in the equation set, here the gap constraint is solved through the equations of motion and the persistency condition is satisfied in the time integration scheme by the velocity update after the equations of motion. It is shown that this approach is strictly dissipative in that a plastic contact condition can be achieved. Analogous to a coefficient of restitution for rigid bodies, any dissipated energy can then be returned upon release if energy conservation is desired. Structure preserving methods are good for long-time dynamics simulations and energy conserving and strictly dissipative methods can overcome stability issues associated with standard time integration algorithms such as the Newmark method.

42 ENGINEERING↗
DOE OSTI2025

Many-body interference in kagome crystals

When electrons in metals act collectively, they enable emergent phenomena and electronic functionalities that transcend the behaviour of individual particles. Coherent collective charge motion has so far been observed primarily in superconductors, in which it arises with the formation of Cooper pairs. Here we report experimental evidence for coherent charge transport in the normal state of the kagome metal CsV 3 Sb 5 , indicative of a distinct collective electronic state. The signature is a set of magnetoresistance oscillations in mesoscopic crystalline pillars under in-plane magnetic fields, with a periodicity determined by the number of magnetic flux quanta h/e threading between adjacent kagome layers—effectively forming an interlayer Aharonov–Bohm interferometer. The cooperative nature of this phenomenon is evidenced by a non-analytic angular dependence characterized by abrupt transitions between discrete oscillation frequencies and its persistence over length scales that exceed the single-particle mean free path. Notably, the oscillation amplitude matches other anomalous electronic responses reported in CsV 3 Sb 5 , pointing to an underlying mechanism that establishes intrinsic coherence. These findings shed new light on the debated nature of correlated order in kagome metals and establish CsV 3 Sb 5 as a platform for realizing long-range coherent charge transport in the absence of superconductivity—opening new directions for coherence in correlated electron systems beyond conventional models.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Signatures of chiral superconductivity in rhombohedral graphene

Chiral superconductors are unconventional superconducting states that break time-reversal symmetry spontaneously and typically feature Cooper pairing at non-zero angular momentum. Such states may host Majorana fermions and provide an important platform for topological physics research and fault-tolerant quantum computing. Despite intensive search and prolonged studies of several candidate systems, chiral superconductivity has remained elusive so far. Here we report the discovery of robust unconventional superconductivity in rhombohedral tetralayer and pentalayer graphene without moiré superlattice effects. We observed two superconducting states in the gate-induced flat conduction bands with T c up to 300 mK and charge density n e down to 2.4 ×10 11 cm −2 in five devices. Spontaneous time-reversal-symmetry breaking (TRSB) owing to orbital motion of the electron is found and several observations indicate the chiral nature of these superconducting states, including: (1) in the superconducting state, R xx shows magnetic hysteresis in varying out-of-plane magnetic field B ⊥ —absent from all other superconductors; (2) the superconducting states are robust against in-plane magnetic field and are developed within a spin-polarized and valley-polarized quarter-metal (QM) phase; (3) the normal states show anomalous Hall signals at zero magnetic field and magnetic hysteresis. Here, we also observed a critical B ⊥ of 1.4 T, higher than any graphene superconductivity, which indicates a strong-coupling superconductivity close to the Bardeen–Cooper–Schrieffer (BCS)–Bose–Einstein condensate (BEC) crossover. Our observations establish a pure carbon material for the study of topological superconductivity, with the promise to explore Majorana modes and topological quantum computing.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Existence of tidal tails for the globular cluster NGC 5824

Context: Several dynamically cold streams have been associated with certain globular clusters (GCs) based on orbital energies and angular momenta. Some of these streams are surprisingly far apart from their progenitors and one such pair is Triangulum and NGC 5824. Triangulum can be considered as a piece of the leading tail of NGC 5824 since the cluster’s future orbit matches well with the stream’s track. The existence of the leading tail of NGC 5824 is the motivation behind the search for its trailing tail. Aims: Our goal is to confirm the connection between Triangulum and NGC 5824. We also search for the trailing tail of the cluster. Methods: The selection of member stars of Triangulum is made through various cuts in metallicity, proper motions (PMs), radial velocity and a color–magnitude diagram (CMD). The selected members are compared in phase space to a mock stream that models the disruption of NGC 5824. We then try to detect the trailing tail of the cluster based on a modified matched-filter technique. Stars are assigned weights using their color differences from the cluster’s locus in the CMD. These weights are further scaled, based on the stars’ departures from expected PMs of the model stream. Results: A total of 26 member stars for Triangulum are obtained, 16 of which are newly identified. These members are consistent with the mock stream in the phase space, and their metalicity and position on the CMD are in good agreement with NGC 5824. By applying the matched filter, a tenuous trailing tail of the cluster is detected, spanning ~50° long on sky. The signature matches well with the mock stream’s trajectory. Conclusions: Our results support that the Triangulum stream acts as a part of the leading tail for NGC 5824. On the trailing side, we detected a 50° tail extending from the cluster. The existence of both leading and trailing tails for the GC NGC 5824 is verified.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Two-electron interference in two-photon attosecond double ionization of neon

The pump-probe experiments enabled by x-ray free-electron lasers (XFEL) will allow us to directly observe correlated electronic motion with attosecond time resolution by detecting photoelectron pairs in coincidence. In helium, the transition between the nonsequential and sequential regime in two-photon double ionization (TPDI) is well explained by a virtual-sequential model. Much less is known, however, about the TPDI process in more complex atoms. Recently, we extended the virtual-sequential model to arbitrary light pulses [Chattopadhyay Phys. Rev. A 108, 013114 (2023)]. This extension employs multichannel scattering states for the single ionization of both the neutral and the ionized target, which we initially applied to helium. In the present study, we show that our extended virtual-sequential model reproduces the qualitative features of the angularly integrated observables with available experimental results for neon, a considerably more complex target. We observe an intriguing feature of inverted two-particle interference in the joint-energy distribution of Ne compared to He. Finally, this phenomenon, attributable to the presence of a final doubly ionized state with triplet symmetry coupled to the two photoelectrons, should be observable with current experimental technologies.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2022

Orbital-induced crossover of the Fulde-Ferrell-Larkin-Ovchinnikov phase into Abrikosov-like states.

The Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state can emerge in superconductors for which the orbital critical field exceeds the Pauli limit. Here, we present angular-resolved specific-heat data of the quasi-two-dimensional organic superconductor ??-(ET)2Cu(NCS )2 , with a focus on high fields in the regime of the FFLO transition. For an increasing out-of-plane tilt of the applied magnetic field, which leads to an increase of orbital contributions, we found that the nature of the superconducting transition changes from second to first order and that a further transition appears within the high-field superconducting phase. However, the superconducting state above the Pauli limit is stable for field tilt of several degrees. Since any finite perpendicular component of the magnetic field necessarily leads to quantization of the orbital motion, the resulting vortex lattice states compete with the modulated order parameter of the FFLO state leading to complex high-field superconducting phases. By solving the linearized self-consistency equation within weak-coupling BCS theory, we show that our results are clear experimental evidence of an orbital-induced transformation of the FFLO order parameter into Abrikosov-like states of higher Landau levels.

Kotte, Tommy↗
DOE OSTI2020

A Chip-Scale Oscillation-Mode Optomechanical Inertial Sensor Near the Thermodynamical Limits

Modern navigation systems integrate the global positioning system (GPS) with an inertial navigation system (INS), which complement each other for correct attitude and velocity determination. Here, the core of the INS integrates accelerometers and gyroscopes used to measure forces and angular rate in the vehicular inertial reference frame. With the help of gyroscopes and by integrating the acceleration to compute velocity and distance, precision and compact accelerometers with sufficient accuracy can provide small–error location determination. Solid–state implementations, through coherent readout, can provide a platform for high performance acceleration detection. In contrast to prior accelerometers using piezoelectric or capacitive readout techniques, optical readout provides narrow–linewidth high–sensitivity laser detection along with low–noise resonant optomechanical transduction near the thermodynamical limits. Here an optomechanical inertial sensor with an 8.2 µg Hz –1/2 velocity random walk (VRW) at an acquisition rate of 100 Hz and 50.9 µg bias instability is demonstrated, suitable for applications, such as, inertial navigation, inclination sensing, platform stabilization, and/or wearable device motion detection. Driven into optomechanical sustained–oscillation, the slot photonic crystal cavity provides radio–frequency readout of the optically–driven transduction with an enhanced 625 µg Hz –1 sensitivity. Measuring the optomechanically–stiffened oscillation shift, instead of the optical transmission shift, provides a 220× VRW enhancement over pre–oscillation mode detection.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2020

Energy and momentum conservation in the Euler–Poincaré formulation of local Vlasov–Maxwell-type systems

The action principle by Low for the classic Vlasov–Maxwell system contains a mix of Eulerian and Lagrangian variables. This renders the Noether analysis of reparametrization symmetries inconvenient, especially since the well-known energy- and momentum-conservation laws for the system are expressed in terms of Eulerian variables only. While an Euler–Poincaré formulation of Vlasov–Maxwell-type systems, effectively starting with Low's action and using constrained variations for the Eulerian description of particle motion, has been known for a while Cendra et al, it is hard to come by a documented derivation of the related energy- and momentum-conservation laws in the spirit of the Euler–Poincaré machinery. To our knowledge only one such derivation exists in the literature so far, dealing with the so-called guiding-center Vlasov–Darwin system Sugama et al. The present exposition discusses a generic class of local Vlasov–Maxwell-type systems, with a conscious choice of adopting the language of differential geometry to exploit the Euler–Poincaré framework to its full extent. After reviewing the transition from a Lagrangian picture to an Eulerian one, we demonstrate how symmetries generated by isometries in space lead to conservation laws for linear- and angular-momentum density and how symmetry by time translation produces a conservation law for energy density. Here, we also discuss what happens if no symmetries exist. Finally, two explicit examples will be given—the classic Vlasov–Maxwell and the drift-kinetic Vlasov–Maxwell—and the results expressed in the language of regular vector calculus for familiarity.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Terahertz electric-field-driven dynamical multiferroicity in SrTiO 3

The emergence of collective order in matter is among the most fundamental and intriguing phenomena in physics. In recent years, the dynamical control and creation of novel ordered states of matter not accessible in thermodynamic equilibrium is receiving much attention. The theoretical concept of dynamical multiferroicity has been introduced to describe the emergence of magnetization due to time-dependent electric polarization in non-ferromagnetic materials. In simple terms, the coherent rotating motion of the ions in a crystal induces a magnetic moment along the axis of rotation. Here we provide experimental evidence of room-temperature magnetization in the archetypal paraelectric perovskite SrTiO 3 due to this mechanism. We resonantly drive the infrared-active soft phonon mode with an intense circularly polarized terahertz electric field and detect the time-resolved magneto-optical Kerr effect. A simple model, which includes two coupled nonlinear oscillators whose forces and couplings are derived with ab initio calculations using self-consistent phonon theory at a finite temperature, reproduces qualitatively our experimental observations. A quantitatively correct magnitude was obtained for the effect by also considering the phonon analogue of the reciprocal of the Einstein–de Haas effect, which is also called the Barnett effect, in which the total angular momentum from the phonon order is transferred to the electronic one. Our findings show a new path for the control of magnetism, for example, for ultrafast magnetic switches, by coherently controlling the lattice vibrations with light.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Department of Energy Project DE-SC0012198: Probing Electron-Molecule Scattering with HHG: Theory and Experiment (Final Report)

The study of the motion of atoms in molecules is important to understanding many areas of physical and life sciences. Such motion occurs on many different times scales, with electronic motion occurring on a sub-femtosecond time scale, and simple vibrational motion in tens to hundreds of femtoseconds. One way to follow such processes in real time is by the use of shortpulsed lasers, and in particular by studying time-resolved photoionization and the related process of high-harmonic generation (HHG). Thus there has been much effort to develop the tools necessary to probe molecular systems using short pulse lasers and understanding the sensitivity of the different possible probes to the time dependent geometric structure as well as the electronic structure of molecules. Our research has particularly focused on the connection between high-field processes and the more traditional weak field photoionization processes. Strong field and weak field processes can be connected through models that involve the same matrix elements. We have demonstrated in our study of HHG from SF 6 that the spectrum is sensitive to the interplay between the angular dependence of the ionization step and recombination step. In our study of rescattering spectroscopy, we have shown that with a combination of experiment and theory, we can use this high-field spectroscopy to determine molecular structure in molecules such as C 2 H 4 . We have also developed new computational tools based on overset grids to enable studies on larger molecular systems which use much more robust numerical approaches so that the resulting code can be a tool that non-specialists can use to study related systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Quantum dynamics of the temporary capture of light atoms by superfluid helium nanodroplets at very low collision energies (≈1–13 meV): the case of the hydrogen atom and its isotopes

The capture dynamics of a H atom and isotopic variants [D, T and Q (hypothetical isotope of mass equal to four times the mass of H)] by a superfluid helium nanodroplet (HeND) has been investigated theoretically. The HeND (T = 0.37 K) is ( 4 He) N=400 and a mean field quantum hybrid approach [TDDFT (helium) + quantum wave packet (H, D, T or Q)] at zero angular momentum, is used to explore a rather wide range of very low initial kinetic energies (E k,0 ≈ 10–150 K). The analysis of the capture mechanism shows the existence of a dynamical barrier and a dynamical minimum that play key roles to understand the time evolution of the capture, especially the former property. In general, the H atom shows a different behavior from the other isotopes, with the behavior of T and Q being very similar to each other and the D atom behaving inbetween H and T. Besides, it is worth noting that, in principle, at the very low initial kinetic energies considered only “short” and “long” lived atom⋯HeND collision complexes are formed, i.e., in the atom-helium nanodroplet collision only the temporary capture of the atom takes place. The different behaviors observed have been interpreted considering the faster motion of the H atom when colliding with ( 4 He) N=400 and the more quantum character of the H behavior both due to its significantly lower mass. As far as we know, this is the first quantum dynamics study carried out on the collision of light atoms with HeNDs at very low energies.

Sternberg, Michael [Argonne National Laboratory (A↗
DOE OSTI2021

The Spiral Galaxies Flat Rotational Velocity Curve Explained by the Constant Group Velocity of a Nonlinear Density Wave

The rotation velocity curves of stars in galaxies, the motions of pairs of galaxies, and the behavior of galaxies in clusters and super-clusters all indicate that there is a lack of mass on different scales in the universe. In this paper, we derive the expression for rotational velocity using the nonlinear density wave theory considering only stellar components and we show that such theory can support the observed flat rotational velocity curve due to the main property of the soliton wave, which is a constant group velocity of the wave. The surface mass density (SMD) function, used to derive gravitational potential gradient and rotational velocity, is not assumed but rather derived as a solution of the nonlinear Srödinger equation, on the contrary to the widely used, in the literature, exponential disk approximation. Three parameters relevant to the curve shape are the intensities of equilibrium SMD, the amplitude of the wave, and total angular velocity or differential rotation, equivalently. Since the shape of the rotational velocity is highly sensitive to the mentioned parameters, this theory eventually provides a method for a very accurate estimation of galaxy mass and angular velocity as well.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Modification of the Loss Cone for Energetic Particles in the Earth's Inner Magnetosphere

The behavior of energetic particles in the Earth's dipole and stretched magnetic-field models is explored with a focus on the shift of the atmospheric loss cone away from the magnetic-field direction and on non-adiabatic behavior occurring when the particle gyroradius becomes comparable with the gradient scale length of the local magnetic field. It is shown that the equatorial loss cone is aberrated away from the magnetic-field direction (pitch angle of 0°) by the perpendicular drift of a charged particle (which is referred to as the “Mozer transform” described in Mozer (1966, https://doi.org/10.1029/JZ071i011p02701). It is found that the Mozer coordinate transformation in pitch-angle/gyrophase-angle space better organizes the behavior of bounce times, mirror altitudes, drift speeds, and first adiabatic invariant. It also describes the loss-cone shift accurately for a certain range of values of the adiabaticity parameter ϵ, defined by the ratio of the particle gyroradius to the local radius of curvature of the magnetic field. For particles with larger ϵ, the Mozer transform (evaluated with the standard gradient-curvature drift) breaks down and the “central trajectory” theory can be used to calculate the angular shift of the loss cone, which now includes an Earthward shift. When ϵ becomes relatively large, stochastic field line curvature (FLC) scattering occurs: we show the intimate connection between the strength of FLC scattering and the loss-cone shift. Finally, by comparing ion orbits in the dipole and Tsyganenko (Ts89 and Ts04) magnetic fields, we conclude that the loss cone of ring-current ions is significantly modified during geomagnetically active times.

79 ASTRONOMY AND ASTROPHYSICS↗