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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 325 records · Page 18
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Digital Light Process 3D Printing of Magnetically Aligned Liquid Crystalline Elastomer Free–forms

Liquid crystalline elastomers (LCEs) are anisotropic soft materials capable of large dimensional changes when subjected to a stimulus. The magnitude and directionality of the stimuli-induced thermomechanical response is associated with the alignment of the LCE. Recent reports detail the preparation of LCEs by additive manufacturing (AM) techniques, predominately using direct ink write printing. Another AM technique, digital light process (DLP) 3D printing, has generated significant interest as it affords LCE free-forms with high fidelity and resolution. However, one challenge of printing LCEs using vat polymerization methods such as DLP is enforcing alignment. Here, we document the preparation of aligned, main-chain LCEs via DLP 3D printing using a 100 mT magnetic field. Systematic examination isolates the contribution of magnetic field strength, alignment time, and build layer thickness on the degree of orientation in 3D printed LCEs. Informed by this fundamental understanding, DLP is used to print complex LCE free-forms with through-thickness variation in both spatial orientations. Further, the hierarchical variation in spatial orientation within LCE free-forms is used to produce objects that exhibit mechanical instabilities upon heating. DLP printing of aligned LCEs opens new opportunities to fabricate stimuli-responsive materials in form factors optimized for functional use in soft robotics and energy absorption.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Classification of Orbits in Poincare Maps Using Machine Learning

Poincare plots, also called Poincare maps, are used by plasma physicists to understand the behavior of magnetically confined plasma in numerical simulations of a tokamak. These plots are created by the intersection of field lines with a two-dimensional poloidal plane that is perpendicular to the axis of the torus representing the tokamak. A plot is composed of multiple orbits, each created by a different field line as it goes around the torus. Each orbit can have one of four distinct shapes, or classes, that indicate changes in the topology of the magnetic fields confining the plasma. Given the (x, y) coordinates of the points that form an orbit, the analysis task is to assign a class to the orbit, a task that appears ideally suited for a machine learning approach. In this paper, we describe how we overcame two major challenges in solving this problem - creating a high-quality training set, with few mislabeled orbits, and converting the coordinates of the points into features that are discriminating, despite the variation within the orbits of a class and the apparent similarities between orbits of different classes. Our automated approach is not only more objective and accurate than visual classification, but is also less tedious, making it easier for plasma physicists to analyze the topology of magnetic fields from numerical simulations of the tokamak.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Low fractional volume superconductivity in single crystals of Pr{sub 4}Ni{sub 3}O{sub 10} under pressure

Magnetotransport measurements of P⁢r4⁢N⁢i3⁢O10 single crystals performed under externally applied pressures up to 73 GPa in diamond anvil cells with either KBr or Nujol oil as pressure media yield signatures of superconductivity with a maximum onset temperature of approximately 31 K. True zero resistance was not observed, consistent with a nonpercolating superconducting volume fraction. Magnetization measurements provided corroborating evidence of superconductivity, with a pressure-dependent diamagnetic signal occurring below the onset temperature, and an estimate from the absolute value of the susceptibility suggests a superconducting volume fraction on the order of 10%. We observe sample to sample variations in the magnitude and pressure dependence of 𝑇𝑐 as well as a dependence on the configuration of electrical contacts on a given sample. Possible causes of this behavior may be significant inhomogeneities in the pressure and/or damage to the samples induced by the pressure media as well as inhomogeneities in the crystals themselves. The results imply that our as-grown P⁢r4⁢N⁢i3⁢O10 single crystals are not bulk superconductors but that there is a minority structure present within the crystals that is indeed superconductin

Chen, Xinglong↗
DOE OSTI2020

Negatively Charged Excitons in CdSe Nanoplatelets

The low-temperature emission spectrum of CdSe colloidal nanoplatelets (NPLs) consists of two narrow lines. The high-energy line stems from the recombination of neutral excitons. The origin of the low-energy line is currently debated. Here, we experimentally study the spectral shift, emission dynamics, and spin polarization of both lines at low temperatures down to 1.5 K and in high magnetic fields up to 60 T and show that the low-energy line originates from the recombination of negatively charged excitons (trions). This assignment is confirmed by the NPL photocharging dynamics and associated variations in the spectrum. We show that the negatively charged excitons are considerably less sensitive to the presence of surface spins than the neutral excitons. The trion binding energy in three-monolayer-thick NPLs is as large as 30 meV, which is 4 times larger than its value in the two-dimensional limit of a conventional CdSe quantum well confined between semiconductor barriers. A considerable part of this enhancement is gained by the dielectric enhancement effect, which is due to the small dielectric constant of the environment surrounding the NPLs.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2024

Composition dependence of bulk properties in the Co-intercalated transition metal dichalcogenide $\mathrm{Co_{1/3}TaS_2}$

Spontaneous Hall conductivity has recently been reported in the triangular lattice antiferromagnet Co 1/3 TaS 2 under a zero magnetic field. This phenomenon originates from the distinctive noncoplanar triple-Q magnetic ground state, possessing uniform real-space Berry curvature characterized by scalar spin chirality. We investigated the physical properties of Co 1/3 TaS 2 by judiciously controlling the composition, revealing a drastic change in its bulk properties, even by slight variations in cobalt composition, despite the same crystal structure. For 0.299≤x≤0.325, Co x TaS 2 keeps all the characteristics of the ground state consistent with the previous studies—two antiferromagnetic phase transitions at T N1 and T N2 ( N1 ), a large spontaneous Hall conductivity [σ xy (H=0)], and a weak ferromagnetic moment along the c axis. However, samples with x≥0.330 exhibit distinct bulk properties, including the absence of both σ xy (H=0) and the weak ferromagnetic moment. Our neutron diffraction data reveal that Co x TaS 2 with x≥0.330 develops coplanar helical magnetic order with q m1 =(1/3, 0, 0). This is entirely different from what has been seen in x≤0.325, explaining the observed composition dependence.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Charge Conservation beyond Uniformity: Spatially Inhomogeneous Electromagnetic Response in Periodic Solids

Nonlinear electromagnetic response functions have reemerged as a crucial tool for studying quantum materials, due to recently appreciated connections between optical response functions, quantum geometry, and band topology. Most attention has been paid to responses to spatially uniform electric fields, relevant to low-energy optical experiments in conventional solid state materials. However, magnetic and magnetoelectric phenomena are naturally connected by responses to spatially varying electric fields due to Maxwell’s equations. Furthermore, in the emerging field of moiré materials, characteristic lattice scales are much longer, allowing spatial variation of optical electric fields to potentially have a measurable effect in experiments. In order to address these issues, we develop a formalism for computing linear and nonlinear responses to spatially inhomogeneous electromagnetic fields. Starting with the continuity equation, we derive an expression for the second-quantized current operator that is manifestly conserved and model independent. Crucially, our formalism makes no assumptions on the form of the microscopic Hamiltonian and so is applicable to model Hamiltonians derived from tight-binding or calculations. We then develop a diagrammatic Kubo formalism for computing the wave vector dependence of linear and nonlinear conductivities, using Ward identities to fix the value of the diamagnetic current order by order in the vector potential. We apply our formula to compute the magnitude of the Kerr effect at oblique incidence for a model of a moiré-Chern insulator and demonstrate the experimental relevance of spatially inhomogeneous fields in these systems. We further show how our formalism allows us to compute the (orbital) magnetic multipole moments and magnetic susceptibilities in insulators. Turning to nonlinear response, we use our formalism to compute the second-order transverse response to spatially varying transverse electric fields in our moiré-Chern insulator model, with an eye toward the next generation of experiments in these systems. Published by the American Physical Society 2024

Physics↗
DOE OSTI2021

Surrogate approximation of the Grad–Shafranov free boundary problem via stochastic collocation on sparse grids

In magnetic confinement fusion devices, the equilibrium configuration of a plasma is determined by the balance between the hydrostatic pressure in the fluid and the magnetic forces generated by an array of external coils and the plasma itself. The location of the plasma is not known a priori and must be obtained as the solution to a free boundary problem. The partial differential equation that determines the behavior of the combined magnetic field depends on a set of physical parameters (location of the coils, intensity of the electric currents going through them, magnetic permeability, etc.) that are subject to uncertainty and variability. The confinement region is in turn a function of these stochastic parameters as well. In this work, we consider variations on the current intensities running through the external coils as the dominant source of uncertainty. This leads to a parameter space of dimension equal to the number of coils in the reactor. With the aid of a surrogate function built on a sparse grid in parameter space, a Monte Carlo strategy is used to explore the effect that stochasticity in the parameters has on important features of the plasma boundary such as the location of the x-point, the strike points, and shaping attributes such as triangularity and elongation. Furthermore, the use of the surrogate function reduces the time required for the Monte Carlo simulations by factors that range between 7 and over 30.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

The magnetic structure of long-wavelength magnetohydrodynamic modes in current-carrying stellarator plasmas

Magnetic field fluctuations are observed in current-carrying stellarator plasmas when the rotational transform is close to a rational value at the edge of the plasma. At low plasma pressure, these fluctuations are associated with perturbed currents parallel to the equilibrium magnetic field lines. A model for these magnetohydrodynamic modes in a low-β, three-dimensional stellarator equilibria has been developed. A set of helical current filaments are constrained to mimic the structure of magnetic field lines on rational surfaces derived from three-dimensional (3D) equilibrium reconstructions. Transformation to straight field line coordinates then allows fitting of the poloidal magnetic sensor data to a single harmonic function, which fixes the modeled toroidal mode structure via the field line flow geometry. The developed procedure accurately captures phase and amplitude variation for m/n = 3/2, 3/1, and 4/1 modes in the 3D equilibria of the compact toroidal hybrid experiment.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Modeling plasma toroidal flow profile control via NTV torque with n = 2 3D fields in MAST-U

Toroidal modeling utilizing the MARS-Q code shows that large (compared to electromagnetic torque) neoclassical toroidal viscous (NTV) torque can be achieved in the plasma core region in reference MAST(-U) L-mode plasmas, by applying the n=2 (n is the toroidal mode number) 3-D fields generated by the magnetic coils used for controlling the edge localized mode and/or by the error field correction coils. Large NTV torque, occurring at relatively slow plasma flow, in combination with strong variation of the torque amplitude versus the coil phasing of the 3-D coils, offers a tool to control the plasma toroidal rotation profile in spherical tokamaks. To effectively employ the toroidal NTV torque, the potentially fast initial flow needs to first be damped by 3-D fields. In conclusion, MARS-Q quasi-linear initial value simulations demonstrate that this is achievable in MAST-U, within the designed 3-D coil current capability for the device.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Experimental investigation of PDI bifurcation of lower hybrid waves during electron density ramp-up in EAST

Abstract The effect of parametric decay instability (PDI) on the current drive efficiency of 4.6 GHz lower hybrid (LH) waves in EAST is investigated experimentally, showing the PDI channel bifurcation of LH waves for the first time in EAST. First, experiments with three platforms of LH power were performed, achieving the LH power required for the PDI occurrence. Second, PDI bifurcation experiments were further carried out by ramping up the plasma electron density. The loop voltage increases with an increase in density, implying a decrease in the current driven by the LH wave. PDI bifurcation during electron density ramp-up was studied by analyzing the parallel refractive index ( n ∥ ) and the frequency spectrum broadening, which is measured with a radio frequency magnetic probe array recently installed close to the LH antenna. It is observed for the first time that they both first increase with density, then there is not much variation and a clear sideband in the frequency spectrum is also observed when the density is up to 4 × 10 19 m − 3 , suggesting a change in the PDI channel. Calculation of the mode growth rate driven by PDI shows that when the edge electron density is up to 1.9 × 10 18 m − 3 , the growth rate of the ion cyclotron quasi-mode (ICQM) will exceed that of the ion sound quasi-mode (ISQM), quantitively explaining that with an increase in density, the PDI channel partly transits from the ISQM to the ICQM channel. Studies provide a possible way to reduce the power deposition in the edge region and improve drive capability by means of mitigating PDI behavior.

Physics↗
DOE OSTI2021

3D Mechanical Analysis of a Compact Nb 3 Sn IR Quadrupole for EIC

Abstract-The Electron Ion Collider (EIC) will require large aperture quadrupole magnets for the Hadron beam in the insertion region. Key requirements include high field, compact size, and tight control of the fringe fields. A 120 mm aperture, 308.4 mm outer diameter actively shielded Nb 3 Sn quadrupole model is under development to support these goals. This work is being carried out by a collaboration of BNL, JLAB and LBNL. A compact shell-based structure preloaded with a bladder and key system was developed for this project. In this paper, the effect of the compact structure on the mechanical behavior was investigated. In particular, the impact of the assembly tolerances and coil size variations on the actual coil stresses and bladder pressures was computed and compared with results from larger bladder and key structures developed for the LHC IR. The longitudinal preload is provided by stainless steel rods. Differently from other bladder and key magnets, the rods are first preloaded axially before coil axial load is applied. This new design aims to increase the overall stiffness of the system and reduce the longitudinal coil displacement during powering. Based on the results of a 3D mechanical analysis, the preliminary preload targets for the EIC quadrupole assembly will be reviewed and discussed.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Magnetic and electron transport properties of Co 2 Si nanomagnets

In this study, magnetotransport and ferromagnetism in thin films of Co 2 Si nanoclusters are investigated experimentally and theoretically. The nanoclusters are fabricated by an inert-gas condensation-type cluster-deposition method and have an average size of 11.3 nm. Unlike the bulk Co 2 Si that exhibits a very weak net magnetic moment only below 10 K, the nanoclusters exhibit room-temperature ferromagnetism with a substantial saturation magnetization. Key features of the system are its closeness to the Stoner transition, magnetic moments induced by spin polarization starting from surface atoms, and nonuniaxial anisotropy associated with the orthorhombic crystal structure of Co 2 Si . A method is introduced to determine the effective anisotropy using the experimental magnetization data of this complex system and its relationship with the two lowest-order nonuniaxial anisotropy constants. On decreasing temperature from 300 K, the nanoclusters show electron-transport properties unusual for a ferromagnetic metal, including an increase of Hall resistivity and a nonmonotonic change of negative magnetoresistance with a peak at around 100 K. The underlying physics is explained on the basis of the large polarization of surface spins and variation in the degree of their misalignments due to temperature-dependent effective anisotropy.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Zr 3 Mn 3 Sn 4 Ga: A new hetero-kagome bilayer antiferromagnet

Here, we report the magnetic and electrical transport properties of single-crystalline Zr 3 Mn 3 Sn 4 Ga, featuring two distinct kagome lattices: a non-magnetic breathing Zr 3 Sn 4 lattice and a magnetic intact Mn 3 Ga lattice. The material undergoes an antiferromagnetic phase transition at T N = 87 K, with neutron diffraction confirming commensurate ordering characterized by k = (1/3,1/3,0). Transport measurements show metallic behavior, a resistivity anomaly near T N , and 12% magnetoresistance at 2 K under 9 T. Deviations from the conventional second-order power law, along with negative magnetoresistance and nonlinear Hall slope variations near T N , suggest strong magneto-electronic coupling. Resonant photoemission spectroscopy identifies Zr 4d and Mn 3d orbitals as dominant contributors to the valence band, linking the material’s unique electronic properties to its kagome layers. Zr 3 Mn 3 Sn 4 Ga offers a valuable platform to study interactions between magnetism and topological electronic bands in hetero-kagome systems using the co- existence of magnetic and non-magnetic kagome layers and its tunable electronic structure.

Crystal structure↗
DOE OSTI2023

Conceptual Design of 20 T Hybrid Accelerator Dipole Magnets

Hybrid magnets are currently under consideration as an economically viable option towards 20 T dipole magnets for next generation of particle accelerators. In these magnets, High Temperature Superconducting (HTS) materials are used in the high field part of the coil with so-called insert coils, and Low Temperature Superconductors (LTS) like Nb 3 Sn and Nb-Ti superconductors are used in the lower field region with so-called outsert coils. The attractiveness of the hybrid option lays on the fact that, on the one hand, the 20 T field level is beyond the Nb 3 Sn practical limits of 15-16 T for accelerator magnets and can be achieved only via HTS materials; on the other hand, the high cost of HTS superconductors compared to LTS superconductors makes it advantageous exploring a hybrid approach, where the HTS portion of the coil is minimized. Here we present in this paper an overview of different design options aimed at generating 20 T field in a 50 mm clear aperture. The coil layouts investigated include the Cos-theta design (CT), with its variations to reduce the conductor peak stress, namely the Canted Cos-theta design (CCT) and the Stress Management Cos-theta design (SMCT), and, in addition, the Block-type design (BL) including a form of stress management and the Common-Coil design (CC). Results from a magnetic and mechanical analysis are discussed, with particular focus on the comparison between the different options regarding quantity of superconducting material, field quality, conductor peak stress, and quench protection.

43 PARTICLE ACCELERATORS↗
DOE OSTI2024

Heterogeneous Integration Technologies for High-temperature, High-density, Low-profile Power Modules of Wide Bandgap Devices in Electric Drive Applications (Final Technical Report)

The goal of this project is to develop packaging technologies for making high-temperature, high-density, and low-profile wide-bandgap (WBG) power electronics modules for electric drives. These modules are aimed at enabling the DOE’s University Consortium to reach its 2025 inverter targets of ≥ 100 kW/L and ≤ 2.7 $/kW. The specific objectives are to: design and fabricate SiC half-bridge power modules with double-sided cooling and parasitic inductances < 5 nH, heat flux density > 400 W/cm 2 , and working junction temperature of 200 o C; design, fabricate, and deliver a gate driver with double-sided cooled modules for the construction of a 100 kW/L inverter at Oak Ridge National Lab; and design and prototype intelligent gate drivers with integrated current sensor and a low-profile DC-DC power supply with air-core transformer for testing power modules at 200 o C junction temperature. We followed an iterative technical approach of design, simulation, fabrication, and testing of various versions of modules, current sensors, and power supply. The state-of-the-art silicon carbide devices rated at 1.2 kV and 149 A were packaged by sintered-silver bonding on an aluminum nitride direct-bond-copper substrate for high thermal conductivity, high working temperature, and high joint reliability. Porous silver posts were used to interconnect the device’s source pads to the other direct-bond-copper substrate for low mechanical stresses, ease of manufacturing, and double-sided cooling. A current sensor based on package parasitic inductance was developed to measure switching current. A dynamic feedback scheme was developed to compensate the effect of parasitic resistance and temperature variation. A constant-current class-E dc-dc converter with air-core transformer was developed. Air-core transformer was used due to the unavailability of magnetic core at high temperatures. Gate driver and power supply were integrated with the double-side cooled, high temperature SiC power modules for testing the modules at 200 o C junction temperature. Double-pulse and continuous testing of the integrated technologies validated the design and fabrication of the three component technologies. Throughout the project, we overcame the challenge for design verification caused by low prototyping yield, which then helped train the graduate students, the future workforce, to learn the engineering know-how for low-cost manufacturing of reliable products. Below is a summary of the major accomplishments of this project: development of a prototyping process for fabricating double-side cooled (1200 V, 149 A) SiC phase-leg modules capable of working to 200 o C Tj; simulation and experimental verification of the improvement of thermo-mechanical reliability of the double-side cooled SiC phase-leg module by using rigid encapsulant; design and experimental validation of a current sensor based on package parasitic inductance and a compensation solution for eliminating the effect of parasitic resistance; design and experimental validation of a low-profile power supply with six-output air-core transformer for gate driver; functional demonstration of a SiC phase-leg module integrated with its gate driver, current sensor, and an air-core power supply at 200 o C Tj in a double-pulse switching test setup and Buck converter continuous test setup; successful completion of six PhD and two MS students who are or will work at Apple Inc., Tesla Inc., Wolfspeed Inc., Microchip Inc., Monolithic Power Systems Inc., and LG Magna Inc.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2021

Scattering of Radio Frequency Waves by Density Filaments

The edge region and the scrape-off layer of magnetically confined fusion devices, like tokamaks and stellarators, are replete with turbulent plasma that is a mixture of coherent, blob or filament like, structures [1] and incoherent fluctuations [2]. The variation in the density due to turbulence can be comparable to or greater than the ambient density [2]. As part of an overall effort to optimize the efficiency of operation, radio frequency (RF) waves are commonly used for heating fusion plasmas and, in tokamaks, for generating plasma current needed for confinement and controlling instabilities. The RF waves are excited by antenna structures that are placed near the wall of a fusion device. In order to deliver energy and momentum to charged particles in the core of fusion plasmas, RF waves have to propagate through the turbulent plasma. In present fusion devices, the scrap-off layer and the edge plasma region is of the order of a few centimeters. In reactor type devices, like ITER, this region is expected to be of the order of tens of centimeters. Since the efficiency of operation of a fusion reactor is of prime importance, it is imperative that we understand the effect of turbulence on RF waves. The fluctuations in density lead to changes in the plasma permittivity. As in conventional electrodynamics, the propagation of RF waves through different dielectric media is subject to reflection, refraction, and diffraction. In this paper, we summarize our theoretical and computational studies on the propagation of RF waves through filamentary structures present in the scrape-off layer.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Robust cycloid crossover driven by anisotropy in the skyrmion host GaV 4 S 8

We report on the anomalous magnetization dynamics of the cycloidally modulated spin textures under the influence of uniaxial anisotropy in multiferroic GaV 4 S 8 . The temperature and field dependence of the linear ac susceptibility [$χ'_{1ω}$ (T, H)], AC magnetic loss [$χ''_{1ω}$ (T, H)], and nonlinear AC magnetic response [$M_{3ω}$ (T, H)] are examined across the magnetic phase diagram in the frequency range f = 10 - 10 000 Hz. According to recent theory, skyrmion vortices under axial crystal symmetry are confined along specific orientations, resulting in enhanced robustness against oblique magnetic fields and altered spin dynamics. We characterize the magnetic response of each spin texture and find that the dynamic rigidity of the Néel skyrmion lattice appears enhanced compared to Bloch-type skyrmions in cubic systems, even in the multidomain state. Anomalous M 3 ω and strong dissipation emerge over the same phase regime where strong variations in the cycloid pitch were observed on lowering temperature in recent small-angle neutron-scattering experiments [White et al., Phys. Rev. B 97, 020401(R) (2018)]. Here, we show that strong anisotropy also drives an extended crossover of the zero-field cycloid texture in GaV 4 S 8 . The frequency dependence of these dynamic signatures is consistent with that of a robust anharmonic spin texture exhibiting a correlated domain arrangement. The results underpin the essential role of magnetic anisotropy in enhancing the rigidity of topological spin textures for diverse applications.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Antiprotons and Elementary Particles over a Solar Cycle: Results from the Alpha Magnetic Spectrometer

We present results over an 11-year Solar cycle of cosmic antiprotons based on 1.1 × 10 6 events in the rigidity range from 1.00 to 41.9 GV. The $\bar{𝑝}$ fluxes exhibit distinct properties. The magnitude of the $\bar{𝑝}$ flux temporal variation is significantly smaller than those of 𝑝, 𝑒 − , and 𝑒 + . A hysteresis between the $\bar{𝑝}$ fluxes and the 𝑝 fluxes is observed, whereas the $\bar{𝑝}$ and 𝑒 − fluxes show a linear correlation. With a model-independent analysis, we found a universal relation between the shape of the rigidity spectrum and the magnitude of flux temporal variation over an 11-year Solar cycle for both positively and negatively charged particles. The simultaneous results on $\bar{𝑝}$ and 𝑝, 𝑒 − , and 𝑒 + provide unique information for understanding particle transport in the Solar System as a function of mass, charge, and spectral shape.

cosmic ray composition & spectra↗