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At least 721 records · Page 40

Physics-Informed Deep Neural Network Method for Limited Observability State Estimation

The precise knowledge regarding the state of the power grid is important in order to ensure optimal and reliable grid operation. Specifically, knowing the state of the distribution grid becomes increasingly important as more renewable energy sources are connected directly into the distribution network, increasing the fluctuations of the injected power. In this paper, we consider the case when the distribution grid becomes partially observable, due to for example cyber attacks, and the state estimation problem is under-determined. We present a new methodology that leverages a deep neural network (DNN) to estimate the grid state. The standard DNN training method is modified to explicitly incorporate the physical information of the grid topology and line/shunt admittance. We show that our method leads to a superior accuracy of the estimation when compared to the case when no physical information is provided. Finally, we compare the performance of our method to the standard state estimation approach, which is based on the weighted least squares with pseudo-measurements, and show that our method performs significantly better with respect to the estimation accuracy.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Revisiting the contributions of supernova and hypernova remnants to the diffuse high-energy backgrounds: constraints on very high redshift injection

Star-forming and starburst galaxies are considered one of the viable candidate sources of the high-energy cosmic neutrino background detected in IceCube. We revisit contributions of supernova remnants (SNRs) and hypernova remnants (HNRs) in such galaxies to the diffuse high-energy neutrino and gamma-ray backgrounds, in light of the latest Fermi data above 50 GeV. We also take into account possible time-dependent effects of the cosmic-ray (CR) acceleration during the SNR evolution. CRs accelerated by the SNR shocks can produce high-energy neutrinos up to ∼100 TeV energies, but CRs from HNRs can extend the spectrum up to PeV energies. We show that, only if HNRs are dominant over SNRs, the diffuse neutrino background above 100 TeV can be explained without contradicting the gamma-ray data. However, the neutrino data around 30 TeV remain unexplained, which might suggest a different population of gamma-ray dark CR sources. We also consider possible contributions of Pop-III HNRs up to z ≲ 10 and show that they are not constrained by the gamma-ray data and thus could contribute to the diffuse high-energy backgrounds if their explosion energy reaches E{sub POP-III}∼a few×10{sup 53} erg. More conservatively, our results suggest that the explosion energy of Pop-III HNRs is E{sub POP-III}≲7×10{sup 53} erg.

79 ASTRONOMY AND ASTROPHYSICS↗

Optical source and apparatus for remote sensing

An optical amplifier is configured to amplify an injected seed optical pulse. The optical amplifier may include two or more gain sections coupled to form a continuous solid waveguide along a primary optical path. Each gain section may include: (i) an optical isolator forming an input to that gain section; (ii) a doped optical fiber having a first end coupled to the optical isolator and having a second end; (iii) a plurality of pump laser diodes; (iv) a controller providing drive signals to each of the plurality, the controller being configured to provide at least pulsed drive signals; and (v) an optical coupler having a first input port coupled to the second end, and a second input port coupled to the plurality and an output port.

Coyle, Donald Barry↗

Preliminary results toward injection locking of an incoherent laser array

The preliminary results of phase locking an incoherent laser array to a master source in an attempt to achieve coherent operation are presented. The techniques necessary to demonstrate phase locking are described along with some topics for future consideration. As expected, the results obtained suggest that injection locking of an array, where the spacing between adjacent longitudinal modes of its elements is significantly larger than the locking bandwidth, may not be feasible.

Daher, J.↗

Measurement of beam characteristics from C{sup 6+} laser ion source

We developed a C{sup 6+} laser ion source for a heavy-ion accelerator. A carbon target was irradiated with a Q-switched Nd:YAG laser (1064 nm wavelength, 1.4 J maximum laser energy, 10 ns pulse duration) to generate a high-density plasma. The laser ion source employed a rotating carbon target for continuous operation. Ion beams were extracted from the plasma through a drift space using a direct plasma injection scheme [B. Yu. Sharkov, A. V. Shumshurov, V. P. Dubenkow, O. B. Shamaev, and A. A. Golubev, Rev. Sci. Instrum. 63, 2841 (1992)] up to a maximum voltage of 40 kV. We measured the characteristics of the ion beams from the laser ion source and present the results of experiments here.

43 PARTICLE ACCELERATORS↗

Geophysical Monitoring Methods Evaluation for the FutureGen 2.0 Project

A comprehensive monitoring program will be needed in order to assess the effectiveness of carbon sequestration at the FutureGen 2.0 carbon capture and storage (CCS) field-site. Geophysical monitoring methods are sensitive to subsurface changes that result from injection of CO 2 and will be used for: (1) tracking the spatial extent of the free phase CO 2 plume, (2) monitoring advancement of the pressure front, (3) identifying or mapping areas where induced seismicity occurs, and (4) identifying and mapping regions of increased risk for brine or CO 2 leakage from the reservoir. Site-specific suitability and cost effectiveness were evaluated for a number of geophysical monitoring methods including: passive seismic monitoring, reflection seismic imaging, integrated surface deformation, time-lapse gravity, pulsed neutron capture logging, cross-borehole seismic, electrical resistivity tomography, magnetotellurics and controlled source electromagnetics. The results of this evaluation indicate that CO 2 injection monitoring using reflection seismic methods would likely be difficult at the FutureGen 2.0 site. Electrical methods also exhibited low sensitivity to the expected CO 2 saturation changes and would be affected by metallic infrastructure at the field site. Passive seismic, integrated surface deformation, time-lapse gravity, and pulsed neutron capture monitoring were selected for implementation as part of the FutureGen 2.0 storage site monitoring program.

54 ENVIRONMENTAL SCIENCES↗

Injection Locking of Gigahertz‐Frequency Surface Acoustic Wave Phononic Crystal Oscillator

Low-noise gigahertz (GHz) frequency sources are essential for applications in signal processing, sensing, and telecommunications. Surface acoustic wave (SAW) resonator-based oscillators offer compact form factors and low-phase noise due to their short mechanical wavelengths and high-quality (Q) factors. However, their small footprint makes them vulnerable to environmental variation, resulting in their poor long-term frequency stability. Injection locking is widely used to suppress frequency drift of lasers and oscillators by synchronizing to an ultra-stable reference. Here, injection locking of a 1-GHz SAW phononic-crystal oscillator is demonstrated, achieving 40-dB phase noise reduction at low offset frequencies and unperturbed low noise at large offset frequencies. Compared to a free-running SAW oscillator, which typically exhibits frequency drifts of several hundred hertz over minutes, the injection-locked oscillator reduces the frequency deviation to below 0.35 Hz. The locking range and oscillator dynamics is also investigated in the injection pulling region. The demonstrated injection-locked SAW oscillator could find applications in high-performance portable telecommunications and sensing systems.

injection locking↗

Circumstellar dust

The presence of dust in the general interstellar medium is inferred from the extinction, polarization, and scattering of starlight; the presence of dark nebulae; interstellar depletions; the observed infrared emission around certain stars and various types of interstellar clouds. Interstellar grains are subject to various destruction mechanisms that reduce their size or even completely destroy them. A continuous source of newly formed dust must therefore be present for dust to exist in the various phases of the interstellar medium (ISM). The working group has the following goals: (1) review the evidences for the formation of dust in the various sources; (2) examine the clues to the nature and composition of the dust; (3) review the status of grain formation theories; (4) examine any evidence for the processing of the dust prior to its injection into the interstellar medium; and (5) estimate the relative contribution of the various sources to the interstellar dust population.

Dwek, E.↗

High power operation of an X-band coaxial multi-beam relativistic klystron amplifier

An X-band coaxial multi-beam relativistic klystron amplifier is designed in order to increase output microwave power and operating frequency of the amplifier tube. The experiment is performed on a Tesla-type accelerator. The amplifier is driven by an electron beam of 2.8 kA at 720 kV, and a microwave power of 30 kW and frequency of 9.384 GHz is injected into an input cavity by means of an external source, then a microwave power of over 800 MW is extracted, the amplifier gain is about 44 dB, and conversion efficiency is 40%. The experiment proves that output power of nearly GWs can be generated with the X-band coaxial multi-beam relativistic klystron amplifier driven by a kW-level input power.

43 PARTICLE ACCELERATORS↗

Injection locking of a high power ultraviolet laser diode for laser cooling of ytterbium atoms

We developed a high-power laser system at a wavelength of 399 nm for laser cooling of ytterbium atoms with ultraviolet laser diodes. The system is composed of an external cavity laser diode providing frequency stabilized output at a power of 40 mW and another laser diode for amplifying the laser power up to 220 mW by injection locking. The systematic method for optimization of our injection locking can also be applied to high power light sources at any other wavelengths. Our system does not depend on complex nonlinear frequency-doubling and can be made compact, which will be useful for providing light sources for laser cooling experiments including transportable optical lattice clocks.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Direct electron acceleration in multi-kilojoule, multi-picosecond laser pulses

The physics mechanism behind the acceleration of electrons to energies much higher than the laser ponderomotive potential is reported. While electrons with these energies have been observed for the last twenty years at the one percent level, it is only with the recent advent of high power lasers with extended pulse durations, large focal spots, and high intensities that significant numbers (>10%) of the so-called “superponderomotive” electrons have been observed. Evidence is provided that the dominant acceleration mechanism of superponderomotive electrons is direct acceleration by the electromagnetic (EM) wave of the laser as they co-propagate in an under-dense plasma; one-dimensional particle-in-cell simulations yield electron spectra with typically ten times the ponderomotive temperature. Direct acceleration requires tens of plasma wavelengths of under-dense plasma, as well as pulse durations of tens of plasma periods, conditions that can be found in large focal spot multi-picosecond laser pulses. It is shown that the plasma simply provides the source of accelerated electrons and a variety of methods to inject a significant population of electrons into the EM waves at relativistic energy.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

First use of an InSb crystal for x-ray imaging spectroscopy of highly ionized tungsten in the Wendelstein 7-X stellarator

Advances in time and space resolved measurements of highly charged states of tungsten (W) through x-ray imaging spectroscopy have enabled investigation of impurity transport in the Wendelstein 7-X (W7-X) stellarator. The high-resolution x-ray imaging spectrometer (HR-XIS) system on W7-X utilizes the Bragg diffraction properties of a set of multiple crystals to measure a range of impurity emission lines within sections of the 1–7 Å wavelength range, including transitions of W. A new indium–antimonide crystal has been installed on the HR-XIS system to allow viewing of the 5.5–6.2 Å region focusing on emissions of W. Consequently, many bright W emission lines from W 40+ to W 47+ were observed in this wavelength range, both in plasmas with injected W and in those with only intrinsic W impurity sources, showing the high sensitivity of the diagnostic. Three W 46+ emissions correspond in wavelength and intensity with calculated photon emissivity coefficients and can be exploited for W transport and concentration applications in plasmas with T e ≳ 2.1 keV. Here, an estimate of the core W density behavior in two separate turbulence-reduced ‘high-performance’ (HP) discharges on W7-X is done using the 5.6893 Å W 46+ line. The n W behavior in HP scenarios can be explained by previous experimental results and neoclassical predictions.

XICS↗

Detectability of subsolar mass neutron stars through a template bank search

Here, we study the detectability of gravitational-wave signals from subsolar-mass binary neutron star systems by the current generation of ground-based gravitational-wave detectors. We find that finite size effects from large tidal deformabilities of the neutron stars and lower merger frequencies can significantly impact the sensitivity of the detectors to these sources. By simulating a matched-filter based search using injected binary neutron star signals with tidal deformabilities derived from physically motivated equations of state, we calculate the reduction in sensitivity of the detectors. We conclude that the loss in sensitive volume can be as high as 78.4% for an equal mass binary system of chirp mass 0.17M ⊙ , in a search conducted using binary black hole template banks. We use this loss in sensitive volume, in combination with the results from the search for subsolar-mass binaries conducted on data collected by the LIGO-Virgo observatories during their first three observing runs, to obtain a conservative upper limit on the merger rate of subsolar-mass binary neutron stars. Since the discovery of a low-mass neutron star would provide new insight into formation mechanisms of neutron stars and further constrain the equation of state of dense nuclear matter, our result merits a dedicated search for subsolar-mass binary neutron star signals.

79 ASTRONOMY AND ASTROPHYSICS↗

Theoretical and Experimental Studies in Accelerator Physics

This report describes research supported by the US Dept. of Energy Office of High Energy Physics (OHEP), performed by the UCLA Particle Beam Physics Laboratory (PBPL). The UCLA PBPL has, over the last two decades-plus, played a critical role in the development of advanced accelerators, fundamental beam physics, and new applications enabled by these thrusts, such as new types of accelerator-based light sources. As the PBPL mission is broad it is natural that it has been grown within the context of the accelerator science and technology stewardship of the OHEP. Indeed, steady OHEP support for the program has always been central to the success of the PBPL; it has provided stability, and above all has set the over-arching themes for our research directions, which have producing over 500 publications (>120 in high level journals). While other agency support has grown notably in recent years, permitting more vigorous pursuit of the program, it is transient by comparison. Beyond permitting program growth in a time of flat OHEP budgets, the influence of other agency missions is found in push to adapt advanced accelerator methods to applications, in light of the success the field has had in proof-of-principle experiments supported first by the DoE OHEP. This three-pronged PBPL program — advanced accelerators, fundamental beam physics and technology, and revolutionary applications — has produced a generation of students that have had a profound affect on the US accelerator physics community. PBPL graduates, numbering 28 in total, form a significant population group in the accelerator community, playing key roles as university faculty, scientific leaders in national labs (two have been named Panofsky Fellows at SLAC), and vigorous proponents of industrial application of accelerators. Indeed, the development of advanced RF, optical and magnet technology at the PBPL has led directly to the spin-off company, RadiaBeam Technologies, now a leading industrial accelerator firm. We note also that PBPL graduates remain as close elaborators for the program after leaving UCLA. The UCLA PBPL program is a foremost developer of on-campus facilities, such as the Neptune and Pegasus Laboratories, providing a uniquely strong environment for student-based research. In addition, the PBPL is a strong user of off-campus national lab facilities, such as SLAC FACET and NLCTA, and the BNL ATF. UCLA has also vigorously participated in the development of these facilities. The dual emphases on off- and on-campus opportunities permit the PBPL to address in an agile way a wide selection of cutting-edge research topics. The topics embraced by this proposal illustrate this program aspect well. These include: GV/m dielectric wakefield acceleration/coherent Cerenkov radiation experiments at FACET (E-201) and the ATF; synergistic laser-excited dielectric accelerator and light source development; plasma wakefield (PWFA) experiments on “Trojan horse” ionization injection (FACET E-210), quasi-nonlinear PWFA at BNL and the production at Neptune high transformer ratio plasma wakes; the inauguration of a new type of RF photoinjector termed “hybrid” at UCLA, and application to PWFA; space-charge dominated beam and cathode/near cathode physics; the study of advanced IFEL systems, for very high energy gain and utilization of novel OAM modes; the physcis of inverse Compton scattering (ICS), with applications to e+ production and γγ colliders; electron diffraction; and advanced beam diagnostics using coherent imaging techniques. These subjects are addressed under the leadership of PBPL director Prof. James Rosenzweig in Task A, and Prof. Pietro Musumeci in Task J, which was initiated following his OHEP Outstanding Junior Investigator award.

43 PARTICLE ACCELERATORS↗

Mid-Atlantic U.S. Offshore Carbon Storage Resource Assessment Project (Final Technical Report)

The greatest potential for carbon storage in the northeastern United States lies in the offshore geologic formations comprising the outer continental shelf (Monteverde et al., 2011). Offshore storage can be linked to large point-sources of carbon dioxide (CO 2 ) while avoiding many of the logistical difficulties and potential risks encountered when siting onshore projects, especially in densely populated areas of the East Coast. Offshore CO 2 storage assessment and research in the United States is underway to address uncertainty in potential storage resources, particularly in the mid- and north-Atlantic offshore area. Given the current knowledge base and access to publicly available data, the objectives of the Mid-Atlantic U.S. Offshore Carbon Storage Resource Assessment Project (MAOCSRAP) were fourfold: (1) complete a systematic carbon storage resource assessment of the mid-Atlantic offshore coastal region from the Georges Bank Basin (GBB) through the Long Island Platform (LIP) to the southern Baltimore Canyon Trough (BCT); (2) define key input parameters to reduce uncertainty for offshore storage resource and efficiency estimates; (3) perform a preliminary assessment of risk factors, uncertainties, and data gaps; and (4) engage industry and regulatory stakeholders through development of a Road Map to assist future project planning and implementation. The MAOCSRAP project has compiled, inventoried, and assimilated various publicly available data sets to provide a strong technical basis on which future carbon storage studies and applications can be built. The knowledge infrastructure necessary to support the development of full-scale offshore carbon storage include: Defining the geologic characteristics of candidate storage sites (Chapter 2). Using existing seismic data to better define the continuity of the storage zones and seals (Chapter 3). Cataloguing the hydrogeologic properties of mid-Atlantic offshore storage sites (Chapter 4). Calculating prospective CO 2 storage resources using net effective pore volumes and fluid displacement properties specific to offshore lithologies (Chapter 5). Examining risk factors related to offshore storage (Chapter 6). Communicating with industry and other stakeholders about the future prospects for offshore storage (Chapter 7). Ensuring technology transfer to industry and other stakeholders (Chapter 8). Led by Battelle, this project was conducted by public and private entities with expertise in offshore geology and resources for the study region, including state geological surveys of Delaware, Maryland, and Pennsylvania; United States Geological Survey-Woods Hole Coastal and Marine Science Center and Haifa University; Rutgers University; Harvard University; and Lamont-Doherty Earth Observatory (LDEO) at Columbia University. The storage resource assessment was completed for a broad region offshore of the U.S. East Coast, from Massachusetts to Virginia. The results include high-level storage resource estimates for areas not previously characterized and improved storage resource estimates for geographically expansive portions of offshore geologic units. Results of the project provide a foundation for developing CO 2 storage along offshore areas of the mid-Atlantic United States. A combination of information was used to provide confidence in project results. Key findings of the major project tasks are summarized as follows. Subsurface Data Analysis: Legacy seismic, well-log, core, and biostratigraphic data were digitized, reprocessed, and analyzed using modern techniques, augmenting previous characterization efforts. The sequence stratigraphic framework for the Cretaceous and Jurassic strata was developed by correlating well-log depositional sequences to seismic reflectors identified in the BCT, LIP, and GBB. The integration of well-log stratigraphy with seismic stratigraphy and petrophysical analysis helped to identify and map potential storage zones within sequences of the Logan Canyon (LC), Missisauga, and Mohawk formations, as well as the regionally extensive caprock comprised of the Dawson Canyon shale. Approximately 4,000 kilometers (km) of seismic data was reprocessed to create a structural framework that was used to tie together all available well data, constrain sequence stratigraphic interpretations, and make regional assessments of offshore carbon storage resources. Prospective storage resource estimates were 150 to 1136 megatons (Mt) for the combined storage zones. This suggests mid-Atlantic U.S. offshore formations can store decades of CO 2 from industrial sources in the region. Preliminary local reservoir simulations suggest that injection rates of 1 Mt CO 2 /year may be sustained for 30 years in single injection wells in the BCT. Advanced geologic modeling and new data acquisition are needed to address data gaps and advance carbon capture and storage (CCS) in key offshore areas selected for further investigation. Offshore Risk Factors: Offshore geologic risk factors include soft sediment deformation, unit continuity, sedimentological and structural features, seismicity and hydrates. CO 2 storage risks include inadequate seals, migration/leakage, and chemical interactions leading to decreased storage. Sensitive habitats, environmental impacts, disturbance to seafloor, and other risks need to be identified in advance of project activities and integrated into detailed mitigation plans for all project phases. Stakeholder Engagement: Input and participation from government, industry, and environmental groups provided input into the Road Map and address next steps needed for project deployment. Early engagement and ongoing communication, as well as policy framework development, is key to large-scale deployment of CCS. Next Steps: This project represents an important first step by completing a high-level CO 2 storage resource assessment and building the knowledge infrastructure necessary to improve quantitative storage resource estimates. The data sets that have been curated under this project provide an opportunity to conduct research and development (R&D) needed to address data gaps and reduce risk and uncertainty. Offshore characterization and validation strategies that are systematically designed to provide data and infrastructure that can be upscaled to meet commercial requirements could be developed off of this foundation.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

Final Report DE-FE0031785 Mohsen Ahmadian, Ph.D. Demonstration of Proof of Concept of a Multiphysics Approach for Real-Time Remote Monitoring of Dynamic Changes in Pressure and Salinity in Hydraulically Fractured Networks

Hydraulic fracturing has evolved into a multistep process with varying flow rates, carrier fluids (e.g., gel or slickwater), proppant loadings, and proppant grain sizes. As a result, primary recovery from a hydraulically fractured tight-oil reservoir is often a tiny fraction of the original oil in place, ranging between 5 and 10%. As stated in the FOA1990, “part of this problem is due to the inability of current well completion processes to effectively stimulate the entire reservoir volume in contact with the wellbore. Innovative technologies are needed that can help improve the effectiveness of reservoir completion methods, maximize stimulated reservoir volumes, and optimize recovery over the entire producing life span of a well”. We first need to enhance the current fracture diagnostic techniques to improve a well-completion design. However, detecting and delineating a subsurface hydraulic fracture is extremely difficult because the induced fracture network is only fractionally propped, and these propped fractures are generally very thin. Microseismic and tiltmeter monitoring techniques can provide information on the fracture extent but provide little or no information on the movement and final distribution of proppant or production fluids. On the other hand, electromagnetic (EM) imaging has shown the capability to monitor proppant distribution throughout the fracture area, especially in the presence of Electrically Active Proppants (EAPs). A previous EM survey of hydraulic fracturing at the Devine Fracture Pilot Site (DFPS) and subsequent EM code developments demonstrated this survey as a robust technique to remotely interrogate the extent of the EAP-filled hydraulic fracture during its propagation. The objectives of the project were threefold: (1) to capitalize on the material properties of an EAP to demonstrate remote monitoring of relative changes in pressure, pressure, and flow that are commonly encountered during production from a hydraulically fractured reservoir; (2) to evaluate EM imaging tools, to achieve Objective 1 in near real-time; and (3) to develop a multi-physics joint inversion approach to precisely predict flow patterns and physiochemical changes within an EAP-filled fracture network. This research project was built upon our previous work at the Devine Test Site managed by the Bureau of Economic Geology (BEG) at The University of Texas at Austin (UT-Austin). It also leveraged a significant investment from the Advanced Energy Consortium (AEC) to address the DOE's interest in subsurface flow, containment, and characterization by multiple signals. This three-year and three-month project succeeded in demonstrating the feasibility of a real-time dynamic fluid flow mapping technique at Technology Readiness Level 5 (TRL5) by utilizing a commercially available surface-based Controlled-Source Electromagnetic (CSEM) method (Objectives 1, 2). We demonstrated that injections into an EAP-filled fracture could be successfully coupled with real-time electric field measurements on the surface, leading to remote monitoring of dynamic changes within the EAP-filled fracture. Furthermore, the observed electric field in our study is influenced by bottomhole pressure, flow rate, and salinity, which is demonstrated by comparing these parameters with the electrical field potentials. EM simulations solely based on assumptions of fracture conductivity changes during injection did not reproduce the whole measured electric field magnitudes. Preliminary estimates showed that including Streaming Potential (SP) in our geophysical model is likely needed to reduce the simulation misfit.

02 PETROLEUM↗

Carbon Storage Site Mapping Inquiry Tool (MapIT)

The Carbon Storage Site Mapping Inquiry Tool (MapIT) is an online web mapping tool designed to help users discover available public-sourced data to facilitate data exploration in support of Underground Injection Control (UIC) Program Class VI Well Site permitting for the geologic sequestration of carbon dioxide.

Pantaleone, Scott↗

Ring current proton decay by charge exchange

Explorer 45 measurements during the recovery phase of a moderate magnetic storm have confirmed that the charge exchange decay mechanism can account for the decay of the storm-time proton ring current. Data from the moderate magnetic storm of 24 February 1972 was selected for study since a symmetrical ring current had developed and effects due to asymmetric ring current losses could be eliminated. It was found that after the initial rapid decay of the proton flux, the equatorially mirroring protons in the energy range 5 to 30 keV decayed throughout the L-value range of 3.5 to 5.0 at the charge exchange decay rate calculated by Liemohn. After several days of decay, the proton fluxes reached a lower limit where an apparent equilibrium was maintained, between weak particle source mechanisms and the loss mechanisms, until fresh protons were injected into the ring current region during substorms. While other proton loss mechanisms may also be operating, the results indicate that charge exchange can entirely account for the storm-time proton ring current decay, and that this mechanism must be considered in all studies involving the loss of proton ring current particles.

Smith, P. H.↗