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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 1,693 records · Page 94
All sourcesNASA NTRSDOE OSTI
NASA NTRS1993

Evolution of large-scale plasma structures in comets: Kinematics and physics

Cometary and solar wind data from December 1985 through April 1986 are presented for the purpose of determining the solar wind conditions associated with comet plasma tail disconnection events (DE's). The cometary data are from The International Halley Watch Atlas of Large-Scale Phenomena (Brandt, Niedner, and Rahe, 1992). In addition, we present the kinematic analysis of 4 DE's, those of Dec. 13.5 and 31.2, 1985, and Feb. 21.7 and 28.7, 1986. The circumstances of these DE's clearly illustrate the need to analyze DE's in groups. In situ solar wind measurements from IMP-8, ICE, and PVO were used to construct the variation of solar wind speed, density, and dynamic pressure during this interval. Data from these same spacecraft plus Vega-1 were used to determine the time of 48 current sheet crossings. These data were fitted to heliospheric current sheet curves extrapolated from the corona into the heliosphere in order to determine the best-fit source surface radius for each Carrington rotation. Comparison of the solar wind conditions and 16 DE's in Halley's comet (the four DE's discussed in this paper and 12 DE's in the literature) leaves little doubt that DE's are associated primarily with crossings of the heliospheric current sheet and apparently not with any other property of the solar wind. If we assume that there is a single or primary physical mechanism and that Halley's DE's are representative, efforts at simulation should concentrate on conditions at current sheet crossings. The mechanisms consistent with this result are sunward magnetic reconnection and tailward magnetic reconnection, if tailward reconnection can be triggered by the sector boundary crossing.

Brandt, John C.↗
NASA NTRS1982

Highlights of theoretical progress related to the International Magnetospheric Study

U.S. theoretical research efforts have addressed three areas within the International Magnetospheric Study. The first, solar wind/magnetosphere interaction, is presently concerned with the suggestion that magnetic merging may predominantly occur near the polar cusps rather than near the subsolar point. Mechanisms have been proposed for noncollisional diffusion of solar wind plasma across the closed magnetopause entailed by such a phenomenon. The second area considers the importance to magnetotail dynamics of a continuous source of solar wind plasma, and of sporadic plasma loss associated with an unsteady convection cycle. In the third area, the electrodynamic magnetosphere/ionosphere interaction, an advanced state has been reached in the understanding of the relevant physics, with respect both to coupling in the subauroral region and the large scale structure of auroral zone electric fields parallel, and perpendicular to, the magnetic field.

Hill, T. W.↗
DOE OSTI2022

Can we have clean energy and grow our crops too? Solar siting on agricultural land in the United States

We report a record amount of large-scale solar development is proposed and under construction in the US Midwest, much of it on agricultural land. This article contributes to the social science literature on renewable energy and public acceptance by addressing stakeholder perspectives on developing utility-scale solar power on agricultural land and complex institutional dynamics that shape these siting decisions. How do stakeholders’ interactions coproduce solar siting decisions? How are the existing complex contexts of energy and agricultural systems affecting solar siting? Who are the stakeholders involved in agricultural solar siting, and how do their epistemic paradigms about using agricultural land, especially prime farmland, differ? To answer these questions, interviews were conducted and analyzed across energy, agriculture, government, and expert stakeholder groups, focusing on Michigan, with comparison to other states. The results provide a conceptual map of stakeholder interaction related to solar development on farmland and characterize the main epistemic paradigms shaping stakeholder conflict. Issues shaping agricultural community perceptions include identity and farmland, the decisions of local farmland renters and non-operating landlords, prime versus lower quality farmland, farm financial viability, and farmland as private property or a public good. Some scientists and engineers seek to alleviate conflicts and drawbacks of agricultural land conversion for solar use by combining farming and solar energy generation: a practice called agrivoltaics. We argue that agrivoltaics are currently treated as a technological fix by not accounting for stakeholder interaction in complex policy, community, and scientific institutions. We conclude by identifying interdisciplinary research priorities to develop socially robust designs.

14 SOLAR ENERGY↗
NASA NTRS1999

Remote Thermal IR Spectroscopy of our Solar System

Indirect methods to detect extrasolar planets have been successful in identifying a number of stars with companion planets. No direct detection of an extrasolar planet has yet been reported. Spectroscopy in the thermal infrared region provides a potentially powerful approach to detection and characterization of planets and planetary systems. We can use knowledge of our own solar system, its planets and their atmospheres to model spectral characteristics of planets around other stars. Spectra derived from modeling our own solar system seen from an extrasolar perspective can be used to constrain detection strategies, identification of planetary class (terrestrial vs. gaseous) and retrieval of chemical, thermal and dynamical information. Emission from planets in our solar system peaks in the thermal infrared region, approximately 10 - 30 microns, substantially displaced from the maximum of the much brighter solar emission in the visible near 0.5 microns. This fact provides a relatively good contrast ratio to discriminate between stellar (solar) and planetary emission and optimize the delectability of planetary spectra. Important molecular constituents in planetary atmospheres have rotational-vibrational spectra in the thermal infrared region. Spectra from these molecules have been well characterized in the laboratory and studied in the atmospheres of solar system planets from ground-based and space platforms. The best example of such measurements are the studies with Fourier transform spectrometers, the Infrared Interferometer Spectrometers (IRIS), from spacecraft: Earth observed from NIMBUS 8, Mars observed from Mariner 9, and the outer planets observed from Voyager spacecraft. An Earth-like planet is characterized by atmospheric spectra of ozone, carbon dioxide, and water. Terrestrial planets have oxidizing atmospheres which are easily distinguished from reducing atmospheres of gaseous giant planets which lack oxygen-bearing species and are characterized by spectra containing hydrocarbons such as methane and ethane. Spectroscopic information on extrasolar planets thus can permit their classification. Spectra and spectral lines contain information on the temperature structure of the atmosphere. Line and band spectra can be used to identify the molecular constituents and retrieve species abundances, thereby classifying and characterizing the planet. At high enough spectral resolution characteristic planetary atmospheric dynamics and unique phenomena such as failure of local thermodynamic equilibrium can be identified. Dynamically induced effects such as planetary rotation and orbital velocity shift and change the shape of spectral features and must be modeled in detailed spectral studies. We will use our knowledge of the compositional, thermal and dynamical characteristics of planetary atmospheres in our own solar system to model spectra observed remotely on similar planets in extrasolar planetary systems. We will use a detailed radiative transfer and beam integration program developed for the modeling and interpretation of thermal infrared spectra measured from nearby planet planets to generate models of an extra-solar "Earth" and "Jupiter". From these models we will show how key spectral features distinguish between terrestrial and gaseous planets, what information can be obtained with different spectral resolution, what spectral features can be used to search for conditions for biogenic activity, and how dynamics and distance modify the observed spectra. We also will look at unique planetary phenomena such as atmospheric lasing and discuss their utility as probes for detection and identification of planets. Results of such studies will provide information to constrain design for instrumentation needed to directly detect extrasolar planets.

Kostiuk, Theodor↗
NASA NTRS2012

The Effects of Solar Variability on Earth's Climate: A Workshop Report

Solar irradiance, the flux of the Sun s output directed toward Earth, is Earth s main energy source.1 The Sun itself varies on several timescales over billions of years its luminosity increases as it evolves on the main sequence toward becoming a red giant; about every 11 years its sunspot activity cycles; and within just minutes flares can erupt and release massive amounts of energy. Most of the fluctuations from tens to thousands of years are associated with changes in the solar magnetic field. The focus of the National Research Council's September 2011 workshop on solar variability and Earth's climate, and of this summary report, is mainly magnetically driven variability and its possible connection with Earth's climate variations in the past 10,000 years. Even small variations in the amount or distribution of energy received at Earth can have a major influence on Earth's climate when they persist for decades. However, no satellite measurements have indicated that solar output and variability have contributed in a significant way to the increase in global mean temperature in the last 50 years. Locally, however, correlations between solar activity and variations in average weather may stand out beyond the global trend; such has been argued to be the case for the El Nino-Southern Oscillation, even in the present day. A key area of inquiry deals with establishing a unified record of the solar output and solar-modified particles that extends from the present to the prescientific past. The workshop focused attention on the need for a better understanding of the links between indices of solar activity such as cosmogenic isotopes and solar irradiance. A number of presentations focused on the timescale of the solar cycle and of the satellite record, and on the problem of extending this record back in time. Highlights included a report of progress on pyroheliometer calibration, leading to greater confidence in the time history and future stability of total solar irradiance (TSI), and surprising results on changes in spectral irradiance over the last solar cycle, which elicited spirited discussion. New perspectives on connections between features of the quiet and active areas of the photosphere and variations in TSI were also presented, emphasizing the importance of developing better understanding in order to extrapolate back in time using activity indices. Workshop participants reviews highlighted difficulties as well as causes for optimism in current understanding of the cosmogenic isotope record and the use of observed variability in Sun-like stars in reconstructing variations in TSI occurring on lower frequencies than the sunspot cycle. The workshop succeeded in bringing together informed, focused presentations on major drivers of the Sun-climate connection. The importance of the solar cycle as a unique quasi-periodic probe of climate responses on a timescale between the seasonal and Milankovitch cycles was recognized in several presentations. The signal need only be detectable, not dominant, for it to play this role of a useful probe. Some workshop participants also found encouraging progress in the top-down perspective, according to which solar variability affects surface climate by first perturbing the stratosphere, which then forces the troposphere and surface. This work is now informing and being informed by research on tropospheric responses to the Antarctic ozone hole and volcanic aerosols. In contrast to the top-down perspective is the bottom-up view that the interaction of solar energy with the ocean and surface leads to changes in dynamics and temperature. During the discussion of how dynamical air-sea coupling in the tropical Pacific and solar variability interact from a bottom-up perspective, several participants remarked on the wealth of open research questions in the dynamics of the climatic response to TSI and spectral variability. The discussion of the paleoclimate record emphasized that the link between solar varbility and Earth s climate is multifaceted and that some components are understood better than others. According to two presenters on paleoclimate, there is a need to study the idiosyncrasies of each key proxy record. Yet they also emphasized that there may be an emerging pattern of paleoclimate change coincident with periods of solar activity and inactivity, but only on long timescales of multiple decades to millennia. Several speakers discussed the effects of particle events and cosmic-ray variability. These are all areas of exciting fundamental research; however, they have not yet led to conclusive evidence for significant related climate effects. The key problem of attribution of climate variability on the timescales of the Little Ice Age and the Maunder Minimum were directly addressed in several presentations. Several workshop participants remarked that the combination of solar, paleoclimatic, and climate modeling research has the potential to dramatically improve the credibility of these attribution studies.

Source record↗
NASA NTRS1980

Modeling of a solar-pumped iodine laser

The direct conversion in space of solar radiation into laser radiation for power transmission to earth, satellites, or deep space probes shows promise as a reasonably simple technology and may have cost advantage in deployment and greater reliability compared to other methods of space power generation and transmission. The main candidates for solar pumping are the gas dynamic, photochemical, and direct photoexcited lasers. Here consideration is given to the photochemical reaction of alkyliodides which predominantly excite the I(2P1/2) state which then lases at 1.315 microns. The iodine ground state is eventually lost to reconstituting the gas or in the formation of molecular iodine. The rates at which the gas is required to be recycled through the laser system are modest. The side exposure at 100-fold solar concentration of a 100-m long tube with a 1 sq m cross section is estimated to provide 20 kW of continuous laser output. Scaling laws and optimum operating conditions of this system are discussed.

Wilson, J. W.↗
NASA NTRS2004

Superposed Epoch Analysis of Ring Current Geoeffectiveness Related to Solar Wind and Plasma Sheet Drivers

The goal of that proposal was to examine the relationship between solar wind drivers and ring current dynamics through data analysis and numerical simulations. The data analysis study was a statistical examination (via superposed epoch analyses) of a solar cycle's worth of storm data. Solar wind data, geophysical indices, and geosynchronous plasma data were collected for every time period with Dst< -50 nT from 1989 through 2002, and the storm list now exceeds 400 entries. This work was first conducted by a summer undergraduate student, Mr. John Vann (University of Kansas), with funding from the NSF Research Experience for Undergraduates program. It was then continued by a University of Michigan graduate student, Mr. Jichun Zhang. Mr. Zhang is now in his fourth year at U-M and is progressing very well toward a PhD in space science. His dissertation will be based on his data analysis and modeling efforts using this geomagnetic storm database. The results of the data analysis study have been the focus of several conference presentations, and the first manuscript has just been published. Two additional papers are presently being prepared, one on average (superposed) solar wind features for various storm subsets (e.g., intense storms at solar maximum), and another on geosynchronous plasma features for these same storm subsets. The latter result was highlighted by the TR&T program director in his presentation at the COSPAR meeting this summer.

Liemohm, M. W.↗
NASA NTRS2010

Heliophysics 2009 Roadmap and Global Change: Possibilities for Improved Understanding of the Connection

Heliophysics is the science that includes all aspects of the research needed to understand the Sun and its effects on the Earth and the solar system. Six science targets: 1. Origins of Near-Earth Plasma - to understand the origin and transport of terrestrial plasma from its source to the magnetosphere and solar wind. 2. Solar Energetic Particle Acceleration and Transport - to understand how and where solar eruptions accelerate energetic particles that reach Earth. 3. Ion-Neutral Coupling in the Atmosphere - to understand how neutral winds control ionospheric variability. 4. Climate Impacts of Space Radiation - to understand our atmosphere s response to auroral, radiation belt, and solar energetic particles, and the associated effects on nitric oxide (NO) and ozone. 5. Dynamic Geospace Coupling - to understand how magnetospheric dynamics provides energy into the coupled ionosphere-magnetosphere system. 6. Heliospheric Magnetics - to understand the flow and dynamics of transient magnetic structures form the solar interior to Earth.

Spann, Jim↗
NASA NTRS2017

Data Assimilation and Uncertainties in Early Solar Cycle Predictions

Stochastic nature of solar activity variations together with our limited knowledge of the dynamo mechanism and subsurface dynamics causes uncertainty in predictions of the solar cycle. For improving the physics-­‐based predictions we can take advantage of the mathematical data assimilation approach that allows us to take into account both, observational errors and model uncertainties, and provide estimates of the next solar cycle along with prediction uncertainties. In this study we use the Parker's migratory dynamo model together with the equation of magnetic helicity balance, which reproduces main properties of the sunspot cycles and allow us to minimize discrepancies between the observed global activity variations and the model solution. The test simulation runs show that a reliable prediction can be obtained for two phases of preceding solar cycle: 1) if the polar field reversals shortly after the solar maxima (strong toroidal field and weak poloidal field), and 2) during the solar minima (strongest poloidal and weak toroidal fields). The early estimate of Cycle 25 obtained by this method shows that this cycle will start in 2019 – 2020, reach the maximum in 2023 – 2024, and that the mean sunspot number at the maximum will be about 90 (for the v2.0 sunspot number series).

Data Assimilation↗
NASA NTRSDate not supplied

Solar Sail Spacecraft Development

During the spring semester, the author had the chance to support various activities in the structure dynamics branch including the testing of a solar sail and the development of deployable structures that are integrated into the solar sail membrane through 3D printing.

Danielle R DaCosta↗
NASA NTRS2022

Interplanetary Mesoscale Observatory (InterMeso): A Mission to Untangle Dynamic Mesoscale Structures Throughout the Heliosphere

Mesoscale dynamics are a fundamental process in space physics, but fall within an observational gap of current and planned missions. Particularly in the solar wind, measurements at the mesoscales (100s RE to a few degrees heliographic longitude at 1 au) are crucial for understanding the connection between the corona and an observer anywhere within the heliosphere. Mesoscale dynamics may also be key to revealing the currently unresolved physics regulating particle acceleration and transport, magnetic field topology, and the causes of variability in the composition and acceleration of solar wind plasma. Studies using single-point observations do not allow for investigations into mesoscale solar wind dynamics and plasma variability, nor do they allow for the exploration of the sub-structuring of large-scale solar wind structures like coronal mass ejections (CMEs), co-rotating/stream interaction regions (CIR/SIRs), and the heliospheric plasma sheet. To address this fundamental gap in our knowledge of the heliosphere at these scales, the Interplanetary Mesoscale Observatory (InterMeso) concept employs a multi-point approach using four identical spacecraft in Earth-trailing orbits near 1 au. Varying drift speeds of the InterMeso spacecraft enable the mission to span a range of mesoscale separations in the solar wind, achieving significant and innovative science return. Simultaneous, longitudinally-separated measurements of structures co-rotating over the spacecraft also allow for disambiguation of spatiotemporal variability, tracking of the evolution of solar wind structures, and determination of how the transport of energetic particles is impacted by these variabilities.

solar wind↗
NASA NTRS2022

Interplanetary Mesoscale Observatory (InterMeso): A mission to untangle dynamic mesoscale structures throughout the heliosphere

Mesoscale dynamics are a fundamental process in space physics, but fall within an observational gap of current and planned missions. Particularly in the solar wind, measurements at the mesoscales (100s RE to a few degrees heliographic longitude at 1 au) are crucial for understanding the connection between the corona and an observer anywhere within the heliosphere. Mesoscale dynamics may also be key to revealing the currently unresolved physics regulating particle acceleration and transport, magnetic field topology, and the causes of variability in the composition and acceleration of solar wind plasma. Studies using single-point observations do not allow for investigations into mesoscale solar wind dynamics and plasma variability, nor do they allow for the exploration of the sub-structuring of large-scale solar wind structures like coronal mass ejections (CMEs), co-rotating/stream interaction regions (CIR/SIRs), and the heliospheric plasma sheet. To address this fundamental gap in our knowledge of the heliosphere at these scales, the Interplanetary Mesoscale Observatory (InterMeso) concept employs a multi-point approach using four identical spacecraft in Earth-trailing orbits near 1 au. Varying drift speeds of the InterMeso spacecraft enable the mission to span a range of mesoscale separations in the solar wind, achieving significant and innovative science return. Simultaneous, longitudinally-separated measurements of structures co-rotating over the spacecraft also allow for disambiguation of spatiotemporal variability, tracking of the evolution of solar wind structures, and determination of how the transport of energetic particles is impacted by these variabilities.

solar wind↗
NASA NTRS2021

Two-Spacecraft Orbiting in Opposition to Enable Bistatic Radar Observations Around an Asteroid

Fundamental answers about the origin and evolution of the Solar System hinge on our ability to image in detail the 3D interior structure of small bodies at highresolution. By collecting radar measurements we can ultimately create 3D maps of the interior structure. In this study we focus our attention on a specific mission scenario which consists of a carrier spacecraft and two daughter spacecraft sent to orbit the asteroid Apophis. The orbits of the spacecraft are optimized to maximize radar measurements by dynamically modeling the harmonics and solar radiation pressure. For long mission durations, orbital correction maneuvers maintain the spacecraft in formation.

Anderson, Rodney L.↗
NASA NTRS1995

Spectroscopic detection of the secondaries of the Hyades interferometric spectroscopic binary theta(sup 2) Tauri and of the interferometric spectroscopic binary alpha Andromedae

We report new high-resolution, wide-wavelength-coverage CCD observations of the visual and near-infrared spectra of the interferometric spectroscopic binaries theta(sup 2) Tau (primary spectral type A 7 III) and alpha And (primary spectral type B8 IVpMnHg), which allow the first direct spectroscopic detection of their secondaries. We have measured primary and secondary radial velocities and used them to redetermine the spectroscopic orbits of the primaries, make an improved determination of K(sub 2) for theta(sup 2) Tau, and measure K(sub 2) for alpha And for the first time. The spectroscopic orbits combined with the interferometrically measured visual orbits of theta(sup 2) Tau and alpha And provide masses and distances, M(sub 1) = 2.1 +/- 0.3 solar mass, M(sub 2) = 1.6 +/- 0.2 solar mass, and d = 44.1 +/- 2.2 pc for theta(sup 2) Tau and M(sub 1) = 5.5 +/- 0.5 solar mass, M(sub 2) = 2.3 +/- 0.2 solar mass, and d = 34.0 +/- 1.3 pc for alpha And. The distance to theta(sup 2) Tau and a foreground correction of 0.07 +/- 0.05 mag set the distance to the center of the Hyades cluster at 45.5 +/- 2.5 pc, or m - M = 3.29 +/- 0.12. Indirect estimates of the mass of theta(sup 2) Tau's primary, made via the mass-luminosity relation and via the Hyades cluster turnoff mass, are consistent with these dynamical masses for its primary and secondary. But in the case of alpha And, the mass-luminosity relation suggests that our dynamical masses for its primary and secondary may be too large. For alpha And somewhat smaller dynamical masses (4.0 and 1.9 solar mass) and the correspondingly smaller distance (31 pc), required by the corresponding larger orbital parallax, provide results consistent with the mass-luminosity relation for normal stars.

Tomkin, Jocelyn↗
DOE OSTI2020

Analysis of GaAs Solar Cells Grown on 50 mm Wafers at 700 degrees C by Dynamic Hydride Vapor Phase Epitaxy

We grew and analyzed GaAs photovoltaics devices grown by dynamic hydride vapor phase epitaxy (D-HVPE) on 50 mm GaAs substrates. These were grown at 700 degrees C in a kinetically-limited growth regime. These devices exhibited nearly identical performance to our previous single-junction GaAs devices (>25% efficiency) that were grown at 650 degrees C in a transport-limited growth regime. We determined that the relatively low non-uniformity in device efficiency was not related to variations in structural characteristics, such as GaAs base thickness or Ga x In 1-x P composition or thickness, but rather uniformity of the absorber doping. These results show that growth of high quality material is possible in multiple growth regimes by D-HVPE.

14 SOLAR ENERGY↗
DOE OSTI2025

Transforming Windows from Energy Liabilities to Zero-Energy Assets: Next-Generation Solutions for Buildings

Windows have traditionally contributed to a building's HVAC load, but they can also become a source of net energy gain or even operate as zero-energy components. For heating applications, highly insulating windows can harness more solar heat than the energy lost through them, transforming windows from energy liabilities to assets. Dynamic glazings provide further benefits by regulating solar heat gain, reducing cooling loads in summer and heating demands in winter. This simulation study focuses on developing the next generation of zero-energy windows (ZEW) for residential new construction. Through annual energy simulations across climate zones 1-8, ZEW performance benchmarks were established based on current code-level buildings, and we've identified the regions where meeting ZEW standards are most achievable. This work evaluates both static and dynamic window technologies, assessing their effects on annual energy use and cost. Key findings demonstrate that ZEW performance is achievable across diverse climate zones, with specific regional requirements. Most climate zones from 3-8 can achieve ZEW with specific configurations, while some warm climates (1-2) appear challenging for ZEW implementation. Climate zones 4-6 consistently allow for zero energy window implementation, offering multiple pathways through either static or dynamic window technologies. Colder climate zones (7-8) ZEW products allow for higher SHGC values while requiring low U-values.

Yu, Lili↗
NASA NTRS2010

Mercury's Dynamic Magnetic Tail

The Mariner 10 and MESSENGER flybys of Mercury have revealed a magnetosphere that is likely the most responsive to upstream interplanetary conditions of any in the solar system. The source of the great dynamic variability observed during these brief passages is due to Mercury's proximity to the Sun and the inverse proportionality between reconnection rate and solar wind Alfven Mach number. However, this planet's lack of an ionosphere and its small physical dimensions also contribute to Mercury's very brief Dungey cycle, approx. 2 min, which governs the time scale for internal plasma circulation. Current observations and understanding of the structure and dynamics of Mercury's magnetotail are summarized and discussed. Special emphasis will be placed upon such questions as: 1) How much access does the solar wind have to this small magnetosphere as a function of upstream conditions? 2) What roles do heavy planetary ions play? 3) Do Earth-like substorms take place at Mercury? 4) How does Mercury's tail respond to extreme solar wind events such coronal mass ejections? Prospects for progress due to advances in the global magnetohydrodynamic and hybrid simulation modeling and the measurements to be taken by MESSENGER after it enters Mercury orbit on March 18, 2011 will be discussed.

Slavin, James A.↗
DOE OSTI2019

Perturbing neutrino oscillations around the solar resonance

Atmospheric neutrinos at low energies, $E \lesssim 500$ MeV, are known to be a rich source of information on lepton mixing parameters. We formulate a simple perturbative framework to elucidate the characteristic features of neutrino oscillation at around the solar-scale enhancement due to the matter effect. The clearest message that we could extract from our perturbation theory is that CP violation in the appearance oscillation probability is large, a factor of $\sim 10$ times larger than CP violation at around the atmospheric-scale oscillation maximum. The underlying mechanism for this is that one of the suppression factors on the CP phase-dependent terms due to the smallness of $\Delta m^2_{21} / \Delta m^2_{31}$ is dynamically lifted by the solar-scale enhancement. Our framework has a unique feature as a perturbation theory in which a large $\Delta m^2_{31}$ term outside the key 1-2 sector for the solar-scale resonance does not yield sizable corrections. On the contrary, the larger the $\Delta m^2_{31}$, the smaller the higher-order corrections.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗