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DOE OSTI2024

Shapiro steps and stability of skyrmions interacting with alternating anisotropy under the influence of ac and dc drives

Here we use atomistic simulations to examine the sliding dynamics of a skyrmion in a two-dimensional system containing a periodic one-dimensional stripe pattern of variations between low and high values of the perpendicular magnetic anisotropy. The skyrmion changes in size as it crosses the interface between two anisotropy regions. On applying combined dc and ac driving in either parallel or perpendicular directions, we observe a wide variety of Shapiro steps, Shapiro spikes, and phase-locking phenomena. The phase-locked orbits have two-dimensional dynamics due to the gyrotropic or Magnus dynamics of the skyrmions and are distinct from the phase-locked orbits found for strictly overdamped systems. Along a given Shapiro step when the ac drive is perpendicular to the dc drive, the velocity parallel to the ac drive is locked while the velocity in the perpendicular direction increases with increasing drive to form Shapiro spikes. At the transition between adjacent Shapiro steps, the parallel velocity jumps up to the next step value, and the perpendicular velocity drops. The skyrmion Hall angle shows a series of spikes as a function of increasing dc drive, where the jumps correspond to the transition between different phase-locked steps. At high drives, the Shapiro steps and Shapiro spikes are lost. When both the ac and dc drives are parallel to the stripe periodicity direction, Shapiro steps appear, while if the dc drive is parallel to the stripe periodicity direction and the ac drive is perpendicular to the stripe periodicity, then there are only two locked phases, and the skyrmion motion consists of a combination of sliding along the interfaces between the two anisotropy values and jumping across the interfaces.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2025

Orientation-dependent enhanced ionization in acetylene revealed by ultrafast cross-polarized pulse pairs

We investigate the orientation dependence of enhanced ionization (EI) during strong-field-driven nuclear motion in acetylene (C 2 ⁢H 2 ). Here, we both initiate and probe molecular dynamics in acetylene with intense 6-fs cross-polarized pulse pairs, separated by a variable delay. Following multiple ionization by the first pulse, acetylene undergoes simultaneous elongation of the carbon-carbon and carbon-hydrogen bonds, enabling further ionization by the second pulse and the formation of a very highly charged state, [C 2 ⁢H 2 ] 6+ . At small interpulse delays (< 20 fs), this enhancement occurs when the molecule is aligned to the probe pulse. Conversely, at large delays (> 40 fs), formation of [C 2 ⁢H 2 ] 6+ occurs when the molecule is aligned to the pump pulse. By analyzing the polarization and time dependence of sequentially ionized [C 2 ⁢H 2 ] 6+ , we resolve two transient alignments that both contribute to a large increase in the multiple ionization yield. In conclusion, this cross-polarized pulse pair scheme uniquely enables selective probing of deeply bound orbitals, providing new insights on orientation-dependent EI in highly charged hydrocarbons.

Atomic & molecular clusters↗

DOE OSTI2026

Degenerate coupled-cluster theory

A size-extensive, converging, black-box, ab initio coupled-cluster (ΔCC) ansatz is introduced that computes the energies and wave functions of states from any degenerate or nondegenerate Slater-determinant references with any numbers of α- and β-spin electrons, any patterns of orbital occupancy, any spin multiplicities, and any spatial symmetries. For a nondegenerate reference, it reduces to the single-reference coupled-cluster ansatz. For a degenerate multireference, it is a natural coupled-cluster extension of degenerate Møller–Plesset perturbation (ΔMP) theory. For ionized and electron-attached references, it is a coupled-cluster Green’s function, although the present theory is convergent toward the full-configuration-interaction limits, while the Feynman–Dyson many-body Green’s function (MBGF) theory generally is not. Its single-excitation instance is a projection Hartree–Fock theory as per the Thouless theorem, which may be useful for core ionizations, high-spin states, and possibly electron affinities. Additionally, a new multireference coupled-cluster theory for a general model space is developed. This quasidegenerate coupled-cluster (QCC) theory is exactly converging, but not black-box, and intended for strong correlation. Determinant-based, general-order algorithms of ΔCC and QCC theories are implemented and compared with configuration-interaction (CI) and equation-of-motion coupled-cluster (EOM-CC) theories through octuple excitations and with ΔMP and MBGF theories up to the nineteenth order. An algebraic, optimal-scaling algorithm of the ΔCC theory is computer-synthesized at the levels of single excitations (ΔCCS) and of single and double excitations (ΔCCSD). As a result, the order of performance is QCC ≈ ΔCC > EOM-CC > CI at the same order or QCC ≈ ΔCC > ΔMP > MBGF at the same cost scaling.

Hirata, So [University of Illinois at Urbana-Champ↗

DOE OSTI2021

The Rarity of Very Red Trans-Neptunian Objects in the Scattered Disk

We investigate the origins of the photometrically very red (VR) and less red (LR) trans-Neptunian objects (TNOs). We first reanalyze the data set of Marsset et al. and find that in addition to the known color–inclination correlation in hot TNOs, a similar trend exists for color–eccentricity. We show that VR TNOs are sharply constrained to eccentricities <0.42 and inclinations <21°, leading to a paucity of VR scattered disk and distant mean motion resonance objects. We then interpret these findings using N-body simulations accounting for Neptune’s outward migration into a massless particles disk and find that these observations are best reproduced with an LR-to-VR color transition line between ∼38 and 42 au in the primordial disk, separating the objects’ formation locations. For an initial surface density profile (Σ ∝ 1/r {sup 2}), a color transition around 38 au is needed to explain the high abundance of VR plutinos, but it creates too many VR scattered disk objects, while a transition line around 42 au seems to better reproduce the scattered disk colors but creates virtually no VR plutinos. Our simulations furthermore show that the rarity of VR particles at high eccentricity is possibly due to the absence of sweeping higher-order MMRs, and secular resonances, beyond 42 au. Inspecting individual populations, we show that the majority of VR SDOs originate as objects trapped in Neptune’s second- and third-order MMRs. These then evolve due to diffusion, scattering, Kozai–Lidov cycles, and secular resonances into their current orbits. Future unbiased color surveys are crucial to better constrain the TNOs dynamical origins.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2025

Study of Quadrupole Fringe Fields in the Interaction Region of the Hadron Storage Ring of the Electron Ion Collider

Fringe fields in quadrupole magnets are usually neglected in studies of beam dynamics at accelerators. However, the extreme optical parameters present in the final focus of a collider such as the Electron–Ion Collider (EIC) may give rise to effects that should not be overlooked. The calculation of quadrupole fringe fields presented in this study follows the procedure outlined in Ref. [1], specialized to the case of a straight reference orbit (i.e., with no dipole field component). A right-handed Cartesian coordinate system is employed, with the $z$-axis aligned with the quadrupole axis and $x$ and $y$ denoting the horizontal and vertical transverse coordinates, respectively. The magnetic quadrupole field gradient, $G = \partial B_y / \partial x$, transitions from its peak value inside the quadrupole—where it is nearly independent of the longitudinal coordinate $z$—to zero at some distance beyond the magnet edge. Consequently, $G$ is treated as a function of $z$. The region over which this variation occurs is defined as the quadrupole fringe field region. The study begins with the development of a description of the magnetic field in the fringe region using a power-series expansion in the transverse coordinates $x$and $y$, consistent with the longitudinally varying gradient. A model for the $z$-dependence of the gradient is then proposed and adjusted to reproduce magnetic field data obtained from three-dimensional field calculations. To evaluate the impact of the fringe fields on beam dynamics, the corresponding vector potential is derived and incorporated into a Hamiltonian formulation of particle motion. The significance of the fringe fields is quantified by calculating the amplitude-dependent tune shift from the Hamiltonian. Using linear beam optics parameters of the Hadron Storage Ring (HSR) of the EIC, the tune shift due to the fringe fields of all quadrupole magnets in the IR-6 interaction region is evaluated. Finally, the resulting tune shifts are compared with those arising from other nonlinear field components present in the HSR.

43 PARTICLE ACCELERATORS↗

DOE OSTI2020

Two Cycling Centers in One Molecule: Communication by Through-Bond Interactions and Entanglement of the Unpaired Electrons

Many applications in quantum information science (QIS) rely on the ability to laser- cool molecules. The scope of applications can be expanded if laser-coolable molecules possess two or more cycling centers, i.e., moieties capable of scattering photons via multiple absorption-emission events. Here in this paper we employ equation-of-motion coupled-cluster method for double electron attachment (EOM-DEA-CCSD) to study the electronic structure of hypermetallic molecules with two alkaline earth metals connected by an acetylene linker. The electronic structure of the molecules is similar to that of two separated alkali metals; however, the interaction between the two electrons is weak and largely dominated by through-bond interactions. The communication between the two cycling centers is quantified by the extent of the entanglement of the two unpaired electrons associated with each center. This contribution highlights the rich electronic structure of hypermetallic molecules that may advance various applications in QIS and beyond.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

Virtual prototyping of liquid metal blanket performance in fusion pilot plant

Liquid metal blanket is a dominant design option for the next step fusion devices responsible for harvesting energy from fusion reaction, and simultaneously producing fuel for the same reaction through tritium breeding. Liquid metal blankets introduce additional complexity to the design due to fluid motion, fluid structure interaction, and magnetohydrodynamic (MHD) effects arising from the motion of the conducting fluid through the magnetic field. They are also directly affected by the plasma heat flux and neutronic fluence. PPPL is currently developing a virtual prototyping system for numerical analysis of the liquid metal blankets for future fusion devices. The system has a customized 3D computational fluid dynamics (CFD) code in its core, allowing MHD flow and conjugate heat transfer analysis in blankets fluids and solids. The code was successfully used before for dual coolant blanket analysis [A. Khodak et al., Fusion Eng. and Des. 137 (2018)]. Recently the same code was modified to allow verified simulation of MHD flows at high Hartmann numbers of several thousand typical for blanket applications. CFD code receives volumetric heat source distribution from the neutronic analysis based on MCNP code. In addition, direct tritium breeding simulation will be performed allowing optimization of the blanket performance. 2D axisymmetric version of neutronics code will be used for rapid optimization, with 3D version employed for detailed analysis. The surface heat distribution on the plasma facing wall will be defined by the software HEAT allowing 3D modeling of the heat flux based on the magnetic field distribution including gyro-orbit effects. Results of thermal analysis are imported into structural analysis code also included in the system. Finally, direct import of CAD geometry will be used for analyzing all components and as a result design option can be efficiently optimized.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2026

Reduced-Cost Four-Component Relativistic Double Ionization Potential Equation-of-Motion Coupled-Cluster Approaches with 4-Hole–2-Particle Excitations and Three-Body Clusters

The double ionization potential (DIP) equation-ofmotion (EOM) coupled-cluster (CC) method with 4-hole−2- particle (4h-2p) excitations on top of the CC with singles, doubles, and triples calculation, abbreviated as DIP-EOMCCSDT(4h-2p), along with its perturbative DIP-EOMCCSD(T)(a)(4h-2p) approximation, are extended to a relativistic four-component (4c) framework. In addition, we introduce and test a new computationally practical DIP-EOMCC approach, which we call DIPEOMCCSD( T)(ã)(4h-2p), that approximates the treatment of 4h- 2p correlations within the DIP-EOMCCSD(T)(a)(4h-2p) method and reduces the $\mathcal{N}$ 8 scaling characterizing DIP-EOMCCSDT(4h- 2p) and DIP-EOMCCSD(T)(a)(4h-2p) to $\mathcal{N}$ 7 with the system size $\mathcal{N}$. Further improvements in computational efficiency are obtained using the frozen natural spinor (FNS) approximation to reduce the numbers of unoccupied spinors entering the correlated steps of the DIP-EOMCC calculations according to a well-defined occupation-number-based threshold. The resulting 4c-FNS-DIPEOMCC approaches are used to compute DIPs for the series of inert gas atoms from argon to radon as well as the vertical DIPs in Cl 2 , Br 2 , HBr, and HI, which have been experimentally examined in the past. We demonstrate that, when using complete basis set extrapolations and FNS truncation threshold of 10 −4.5 , the 4c-FNS-DIP-EOMCCSD(T)(ã)(4h-2p) calculations are capable of predicting DIPs in agreement with experimental data, improving upon their nonrelativistic and spin-free scalar-relativistic counterparts, particularly when examining DIPs characterized by stronger spin−orbit coupling effects.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

Substructure in the stellar halo near the Sun: II. Characterisation of independent structures

In an accompanying paper, we present a data-driven method for clustering in ‘integrals of motion’ space and apply it to a large sample of nearby halo stars with 6D phase-space information. The algorithm identified a large number of clusters, many of which could tentatively be merged into larger groups. The goal here is to establish the reality of the clusters and groups through a combined study of their stellar populations (average age, metallicity, and chemical and dynamical properties) to gain more insights into the accretion history of the Milky Way. To this end, we developed a procedure that quantifies the similarity of clusters based on the Kolmogorov–Smirnov test using their metallicity distribution functions, and an isochrone fitting method to determine their average age, which is also used to compare the distribution of stars in the colour–absolute magnitude diagram. Also taking into consideration how the clusters are distributed in integrals of motion space allows us to group clusters into substructures and to compare substructures with one another. We find that the 67 clusters identified by our algorithm can be merged into 12 extended substructures and 8 small clusters that remain as such. The large substructures include the previously known Gaia-Enceladus, Helmi streams, Sequoia, and Thamnos 1 and 2. We identify a few over-densities that can be associated with the hot thick disc and host a small metal-poor population. Especially notable is the largest (by number of member stars) substructure in our sample which, although peaking at the metallicity characteristic of the thick disc, has a very well populated metal-poor component, and dynamics intermediate between the hot thick disc and the halo. We also identify additional debris in the region occupied by Sequoia with clearly distinct kinematics, likely remnants of three different accretion events with progenitors of similar masses. Although only a small subset of the stars in our sample have chemical abundance information, we are able to identify different trends of [Mg/Fe] versus [Fe/H] for the various substructures, confirming our dissection of the nearby halo. We find that at least 20% of the halo near the Sun is associated to substructures. When comparing their global properties, we note that those substructures on retrograde orbits are not only more metal-poor on average but are also older. We provide a table summarising the properties of the substructures, as well as a membership list that can be used for follow-up chemical abundance studies for example.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2020

Probing ab initio emergence of nuclear rotation

Structural phenomena in nuclei, from shell structure and clustering to superfluidity and collective rotations and vibrations, reflect emergent degrees of freedom. Ab initio theory describes nuclei directly from a fully microscopic formulation. We can therefore look to ab initio theory as a means of exploring the emergence of effective degrees of freedom in nuclei. For the illustrative case of emergent rotational bands in the $Be$ isotopes, we establish an understanding of the underlying oscillator space and angular momentum (orbital and spin) structure. We consider no-core configuration interaction (NCCI) calculations for 7, 9, 11 Be with the Daejeon16 internucleon interaction. Although shell model or rotational degrees of freedom are not assumed in the ab initio theory, the NCCI results are suggestive of the emergence of effective shell model degrees of freedom (0$\hbar$ω and 2$\hbar$ω excitations) and LS-scheme rotational degrees of freedom, consistent with an Elliott–Wilsdon SU(3) description. Finally, these results provide some basic insight into the connection between emergent effective collective rotational and shell model degrees of freedom in these light nuclei and the underlying ab initio microscopic description.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2020

Electrical control of spin relaxation anisotropy during drift transport in a two-dimensional electron gas

Spin relaxation was studied in a two-dimensional electron gas confined in a wide GaAs quantum well. Recently, the control of the spin relaxation anisotropy by diffusive motion was first shown in D. Iizasa et al., arXiv:2006.08253. Here, we demonstrate electrical control by drift transport in a system with two subbands occupied. The combined effect of in-plane and gate voltages was investigated using time-resolved Kerr rotation. Furthermore, the measured relaxation time presents strong anisotropy with respect to the transport direction. For an in-plane accelerating electric field along [110], the lifetime was strongly suppressed irrespective of the applied gate voltage. Remarkably, for transport along [$1\bara{1}0$], the data shows spin lifetime that was gate dependent and longer than in the [110] direction regardless of the in-plane voltage. In agreement, independent results of anisotropic spin precession frequencies are also presented. Nevertheless, the long spin lifetime, strong anisotropy and drift response seen in the data are beyond the existing models for spin drift and diffusion.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2021

Accurately simulating nine-dimensional phase space of relativistic particles in strong fields

Next-generation high-power laser systems that can be focused to ultra-high intensities exceeding 10 23 W/cm 2 are enabling new physics regimes and applications. The physics of how these lasers interact with matter is highly nonlinear, relativistic, and can involve lowest-order quantum effects. The current tool of choice for modeling these interactions is the particle-in-cell (PIC) method. In the presence of strong electromagnetic fields, the motion of charged particles and their spin is affected by radiation reaction (either the semi-classical or the quantum limit). Standard (PIC) codes usually use Boris or similar operator-splitting methods to advance the particles in standard phase space. These methods have been shown to require very small time steps in the strong-field regime in order to obtain accurate results. In addition, some problems require tracking the spin of particles, which creates a nine-dimensional (9D) particle phase space, i.e., (x, u, s). Therefore, numerical algorithms that enable high-fidelity modeling of the 9D phase space in the strong-field regime (where both the spin and momentum evolution are affected by radiation reaction) are desired. Here we present a new particle pusher that works in 9D and 6D phase space (i.e., with and without spin) based on analytical rather than leapfrog solutions to the momentum and spin advance from the Lorentz force, together with the semi-classical form of radiation reaction in the Landau-Lifshitz equation and spin evolution given by the Bargmann-Michel-Telegdi equation. Analytical solutions for the position advance are also obtained, but these are not amenable to the staggering of space and time in standard PIC codes. These analytical solutions are obtained by assuming a locally uniform and constant electromagnetic field during a time step. The solutions provide the 9D phase space advance in terms of a particle's proper time, and a mapping is used to determine the proper time step duration for each particle as a function of the lab frame time step. Due to the analytical integration of particle trajectory and spin orbit, the constraint on the time step needed to resolve trajectories in ultra-high fields can be greatly reduced. The time step required in a PIC code for accurately advancing the fields may provide additional constraints. We present single-particle simulations to show that the proposed particle pusher can greatly improve the accuracy of particle trajectories in 6D or 9D phase space for given laser fields. We have implemented the new pusher into the PIC code Osiris. Example simulations show that the proposed pusher provides improvement for a given time step. A discussion on the numerical efficiency of the proposed pusher is also provided.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2025

Relativistic core–valence-separated equation-of-motion coupled-cluster singles and doubles method: Efficient implementation and benchmark calculations

An efficient implementation for the relativistic exact two-component core–valence-separated equation-of-motion coupled-cluster singles and doubles (X2C-CVS-EOM-CCSD) method is reported. The explicit exclusion of pure valence excitations in the EOM-CCSD excited-state eigenvalue equations significantly improves the efficiency for calculations of core-excited states. Benchmark relativistic CVS-EOM-CC calculations with systematic inclusion of relativistic, correlation, and basis-set effects are shown to provide highly accurate results for core ionized and excited states involving heavy atoms.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

Symmetry breaking as predicted by a phase space Hamiltonian with a spin Coriolis potential

Here, we perform electronic structure calculations for a set of molecules with degenerate spin-dependent ground states ( 3 CH 2 , 2 CH$^{•}_{3}$, 3 O 2 ) going beyond the Born–Oppenheimer approximation and accounting for nuclear motion. According to a phase space approach that parameterizes electronic states (|Φ⟩) and electronic energies (E) by nuclear position and momentum [i.e., |Φ(R, P)⟩ and E(R, P)], we find that the presence of degenerate spin degrees of freedom leads to broken symmetry ground states. More precisely, rather than a single degenerate minimum at (R, P) = (R min , 0), the ground state energy has two minima at (R,P)=(R' min ,±P min ) (where R' min is close to R min ), dramatically contradicting the notion that the total energy of the system can be written in separable form as E = $\frac{P^2}{2M}$ + V el . Although we find that the broken symmetry solutions have small barriers between them for the small molecules, we hypothesize that the barriers should be macroscopically large for metallic solids, thus offering up a new phase-space potential energy surface for simulating the Einstein–de Haas effect.

Berry connection↗

DOE OSTI2023

ESR Dipole Power Supply Current Ripple and Noise Specifications

This note presents key findings for the ESR main magnet dipole power supplies (PS), where we find the current ripple specification to be close to or beyond the state-of-the-art. These specifications originate from beam-beam considerations, with the requirement to limit the ripple-induced hadron emittance growth to below 10%/hour. Beam dynamics that drive this PS ripple specification arise from the beam motions at the Interaction Point (IP). The frequency of the motions can be separated into "low", compared to the betatron frequency, and "high", i.e. around the betatron frequency and harmonics. In terms of the driving frequency, "low" implies ƒ<<ƒ 0 v x,y and "fast" means ƒ≈{ƒ 0 v x,y , ƒ 0 (1- v x,y , etc.}, where ƒ 0 =1/ T 0 =78.2 kHz is the revolution frequency, and v x,y are the fractional parts of the betatron tunes. Frequencies higher than ƒ 0 /2 will be folded back due to the particles sampling the field once per turn. To provide flexibility for future lattice adjustments and working point variations, we do not consider the tunes as fixed. Instead, we assume a certain margin and allow them to potentially fall within the range of 0.1< v x,y <0.5. In other words, the high-frequency region spans approximately from 8kHz to 40 kHz. Consequently,, we definte the dipole PS ripple in two distinct frequency ranges: the low-frequency range of [1-8000] Hz and the high-frequency range of [8-40] kHz. For the physics effects we analyzed in this note, there is no distinction between the ripple (which can be approximately reproduced in the frequency domain) and the random noise if both have some power within the frequency bandwidth of interest. Therefore, while we will use the term "ripple" for short, it should always be understood that we are referring to "ripple plus noise." Except for the lower end of the low-frequency range, the impact of the rippling PS current on the beam will be considerably reduced due to the eddy currents induced in the walls of the vacuum chamber. We will account for this effect in the PS ripple specifications to follow. The remaining sections of this note are structure as follows: Section II outlines the beam-beam physics requirements for the positional stability of the beam at the IP. Section III describes the anticipated shielding effect of the eddy currents induced in the vacuum chamber. Section IV derives the ripple requirement for the low-frequency range by propagating the closed orbit ripple resulting from the rippling dipoles to the IP (relevant lattice simulation results are summarized in the Appendix). In Section V, we present the analytical criterion for the ripple in the high-frequency range by considering resonant oscillations of the electron beam around a stable closed orbit near the betatron frequency. Finally, Section VI provides a summary of our findings and discusses related work.

43 PARTICLE ACCELERATORS↗