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At least 109 records · Page 6

Fabrication of Silicon Backshort Assembly for Waveguide-Coupled Superconducting Detectors

The Cosmology Large Angular Scale Surveyor (CLASS) is a ground-based instrument that will measure the polarization of the cosmic microwave background to search for gravitational waves from a posited epoch of inflation early in the universe s history. We are currently developing detectors that address the challenges of this measurement by combining the excellent beam-forming attributes of feedhorns with the low-noise performance of Transition-Edge sensors. These detectors utilize a planar orthomode transducer that maps the horizontal and vertical linear polarized components in a dual-mode waveguide to separate microstrip lines. On-chip filters define the bandpass in each channel, and the signals are terminated in resistors that are thermally coupled to the transition-edge sensors operating at 150 mK.

Crowe, E.↗

Advanced Measurement Technology at NASA Langley Research Center

Instrumentation systems have always been essential components of world class wind tunnels and laboratories. Langley continues to be on the forefront of the development of advanced systems for aerospace applications. This paper will describe recent advances in selected measurement systems which have had significant impact on aerospace testing. To fully understand the aerodynamics and aerothermodynamics influencing aerospace vehicles, highly accurate and repeatable measurements need to be made of critical phenomena. However, to maintain leadership in a highly competitive world market, productivity enhancement and the development of new capabilities must also be addressed aggressively. The accomplishment of these sometimes conflicting requirements has been the challenge of advanced measurement developers. However, several new technologies have recently matured to the point where they have enabled the achievement of these goals. One of the critical areas where advanced measurement systems are required is flow field velocity measurements. These measurements are required to correctly characterize the flowfield under study, to quantify the aerodynamic performance of test articles and to assess the effect of aerodynamic vehicles on their environment. Advanced measurement systems are also making great strides in obtaining planar measurements of other important thermodynamic quantities, including species concentration, temperature, pressure and the speed of sound. Langley has been on the forefront of applying these technologies to practical wind tunnel environments. New capabilities in Projection Moire Interferometry and Acoustics Array Measurement systems have extended our capabilities into the model deformation, vibration and noise measurement arenas. An overview of the status of these techniques and recent applications in practical environments will be presented in this paper.

Antcliff, Richard R.↗

Lidar Observations of Atmospheric CO2 Column During 2014 Summer Flight Campaigns

Advanced knowledge in atmospheric CO2 is critical in reducing large uncertainties in predictions of the Earth' future climate. Thus, Active Sensing of CO2 Emissions over Nights, Days, and Seasons (ASCENDS) from space was recommended by the U.S. National Research Council to NASA. As part of the preparation for the ASCENDS mission, NASA Langley Research Center (LaRC) and Exelis, Inc. have been collaborating in development and demonstration of the Intensity-Modulated Continuous-Wave (IM-CW) lidar approach for measuring atmospheric CO2 column from space. Airborne laser absorption lidars such as the Multi-Functional Fiber Laser Lidar (MFLL) and ASCENDS CarbonHawk Experiment Simulator (ACES) operating in the 1.57 micron CO2 absorption band have been developed and tested to obtain precise atmospheric CO2 column measurements using integrated path differential absorption technique and to evaluate the potential of the space ASCENDS mission. This presentation reports the results of our lidar atmospheric CO2 column measurements from 2014 summer flight campaign. Analysis shows that for the 27 Aug OCO-2 under flight over northern California forest regions, significant variations of CO2 column approximately 2 ppm) in the lower troposphere have been observed, which may be a challenge for space measurements owing to complicated topographic condition, heterogeneity of surface reflection and difference in vegetation evapotranspiration. Compared to the observed 2011 summer CO2 drawdown (about 8 ppm) over mid-west, 2014 summer drawdown in the same region measured was much weak (approximately 3 ppm). The observed drawdown difference could be the results of the changes in both meteorological states and the phases of growing seasons. Individual lidar CO2 column measurements of 0.1-s integration were within 1-2 ppm of the CO2 estimates obtained from on-board in-situ sensors. For weak surface reflection conditions such as ocean surfaces, the 1- s integrated signal-to-noise ratio (SNR) of lidar measurements at 11 km altitude reached 376, which was equivalent to a 10-s CO2 error 0.33 ppm. For the entire processed 2014 summer flight campaign data, the mean differences between lidar remote sensed and in-situ estimated CO2 values were about -0.013 ppm. These results indicate that current laser absorption lidar approach could meet space measurement requirements for CO2 science goals.

Lin, Bing↗

Reexamination of the Edge Crack Torsion Test for Determining the Mode III Delamination Toughness of Laminated Composites

The edge crack torsion (ECT) test is reexamined to address two primary concerns with this method. The first of these relates to inconsistencies in the data reduction procedure that was originally proposed and is most commonly used to compute the mode III interlaminar fracture toughness, G(sub IIIc), from the experimental data. The second relates to the observation that plies neighboring the preimplanted insert in the standard ECT layup are unable to contain initiation and growth of intralaminar cracks, and that growth of these cracks contributes to errors in the apparent values of G(sub IIIc). To address these issues, an alternative data reduction technique, which uses a polynomial expression to represent the ECT specimen’s compliance versus crack length relation, is proposed. The accuracy and potential drawbacks of this expression are investigated using FE simulations. Next, seven groups of ECT specimens are fabricated and tested. Each of these groups contains specimens with preimplanted inserts that are bounded by plies at different +q and -q orientations. The seven groups consist of values of q that vary from 0° to 90° in 15° increments. Tests on these specimens show that intralaminar cracking occurs in specimens from all batches except those for which q equals 15° or 30°. However, values of G(sub IIIc) measured using specimens with these two ply orientations were not equal and, for q = 30°, the values of G(sub IIIc) that were obtained were not completely independent of initial starter crack length. Potential issues accounting for these observations and other challenges associated with measuring G(sub IIIc) using the ECT test are discussed.

Polymer matrix composites↗

Developing a Community of Practice for Applied Uses of Future PACE Data to Address Food Security Challenges

Ocean color satellite measurements have yielded valuable information about the base of the marine food web for over 20 years. The Plankton, Aerosol, Cloud, ocean Ecosystem (PACE) mission is building an advanced spectrometer to further refine ecosystem monitoring. Higher spectral resolution data from PACE will enable identification of additional marine biological indicators and their response to multiple stressors to guide sustainable management. Seafood is an important source of protein for a significant number of people. Wild catches cannot match increasing demand and their sustainability is in question. Aquaculture is an ever more important industry to feed the world's population. We share early efforts to engage a community of practice around food security to increase satellite data product use in support of resource management, business decisions, and policy analysis. Understanding the needs of applied scientists as well as non-traditional users of satellite data early in the PACE mission process will improve planning and preparation for a broader user base and hopefully help to mitigate food insecurity.

Schollaert Uz, Stephanie↗

Neutral Atmosphere Properties Determining D-region Electron Densities

The increasing discoveries of various manifestations of meteorological control of the D region ionization and the growth of techniques for its measurement provide a challenge to meteorologists to test their insight into middle atmosphere processes with the physical interpretation of D layer phenomena. Models for ion production due to photoionization of minor atmospheric nitric oxide by quasi-monochromatic solar Lyman-alpha radiation are presented. A ground based measuring technique using low frequency radio reflection heights is briefly described and an approach to the interpretation of data acquired by this method is discussed. It is shown that D region electron density variations can provide an efficient diagnostic tool for the detection of perturbations of the circulation state of the middle atmosphere.

Taubenheim, J.↗

Advanced Concepts, Technologies and Flight Experiments for NASA's Earth Science Enterprise

Over the last 25 years, NASA Langley Research Center (LaRC) has established a tradition of excellence in scientific research and leading-edge system developments, which have contributed to improved scientific understanding of our Earth system. Specifically, LaRC advances knowledge of atmospheric processes to enable proactive climate prediction and, in that role, develops first-of-a-kind atmospheric sensing capabilities that permit a variety of new measurements to be made within a constrained enterprise budget. These advances are enabled by the timely development and infusion of new, state-of-the-art (SOA), active and passive instrument and sensor technologies. In addition, LaRC's center-of-excellence in structures and materials is being applied to the technological challenges of reducing measurement system size, mass, and cost through the development and use of space-durable materials; lightweight, multi-functional structures; and large deployable/inflatable structures. NASA Langley is engaged in advancing these technologies across the full range of readiness levels from concept, to components, to prototypes, to flight experiments, and on to actual science mission infusion. The purpose of this paper is to describe current activities and capabilities, recent achievements, and future plans of the integrated science, engineering, and technology team at Langley Research Center who are working to enable the future of NASA's Earth Science Enterprise.

Meredith, Barry D.↗

Temperature coefficients of multijunction solar cells

Temperature coefficients measured in solar simulators with those measured under AM0 solar illumination are compared to illustrate the challenges in making these measurements. It is shown that simulator measurements of the short-circuit current (delta Jsc/delta T) are inaccurate due to the mismatch between the solar spectrum and the simulators at the bandgaps of the solar cells. Especially susceptible to error is the delta Jsc/delta T of cells which are components in monolithic multijunction solar cells, such as GaAs filtered by 1.93-eV AlGaAs, which has an AM0 coefficient of 6.82 micro-A/sq cm/deg C, compared to a Xenon simulator coefficient of 22.2 micro-A/sq cm/deg C.

Virshup, G. F.↗

Improvements to GNSS Positioning in Challenging Environments by 3DMA Lidar Informed Selective Satellites Usage

The use of global navigation satellite systems (GNSS) for position estimation tends to yield poor results when operating inside of an urban canyon due to large obstructions (e.g., buildings) that disrupt signals as they travel from a satellite to a receiver resulting in a position estimate that may significantly fluctuate in magnitude and direction. Identifying and removing signals that are non-line-of-sight (NLOS) to the receiver and only using signals that are line-of-sight (LOS) can improve the estimated position. However, quickly and accurately determining the LOS status of each measurement can be challenging without additional information about the operating environment. Use of publicly available lidar data can be used to incorporate techniques, such as 3D-mapping-aided (3DMA), to estimate the LOS status of satellites and augment the position solution accordingly. To complicate the issue, the error on the GNSS position estimate in an urban canyon is often so large that is it not sufficient to use as an approximate location for LOS prediction. That is, at times the calculated GNSS solution is not representative of the true location and cannot be used to accurately predict which satellites are within LOS due to the difference in the physical geometry associated with the two locations. This paper explores the use of a GNSS/inertial fused position solution as the initial position estimate for predicting which satellites are within LOS in an urban environment and the impact that removal of predicted NLOS satellites has on the GNSS position solution.

GPS↗

Development of the Potassium-Argon Laser Experiment (KArLE) Instrument for In Situ Geochronology

Absolute dating of planetary samples is an essential tool to establish the chronology of geological events, including crystallization history, magmatic evolution, and alteration. Traditionally, geochronology has only been accomplishable on samples from dedicated sample return missions or meteorites. The capability for in situ geochronology is highly desired, because it will allow one-way planetary missions to perform dating of large numbers of samples. The success of an in situ geochronology package will not only yield data on absolute ages, but can also complement sample return missions by identifying the most interesting rocks to cache and/or return to Earth. In situ dating instruments have been proposed, but none have yet reached TRL 6 because the required high-resolution isotopic measurements are very challenging. Our team is now addressing this challenge by developing the Potassium (K) - Argon Laser Experiment (KArLE) under the NASA Planetary Instrument Definition and Development Program (PIDDP), building on previous work to develop a K-Ar in situ instrument [1]. KArLE uses a combination of several flight-proven components that enable accurate K-Ar isochron dating of planetary rocks. KArLE will ablate a rock sample, determine the K in the plasma state using laser-induced breakdown spectroscopy (LIBS), measure the liberated Ar using quadrupole mass spectrometry (QMS), and relate the two by the volume of the ablated pit using an optical method such as a vertical scanning interferometer (VSI). Our preliminary work indicates that the KArLE instrument will be capable of determining the age of several kinds of planetary samples to +/-100 Myr, sufficient to address a wide range of geochronology problems in planetary science.

Cohen, Barbara A.↗

A Comprehensive Forward Model for Spaceborne Radar Instruments

We present the development and validation of a comprehensive forward model designed to enhance remote sensing capabilities of spaceborne radar instruments. To overcome limitations in existing models, we integrated a Discrete Dipole Approximation (DDA) cloud scattering database into our Radiative Transfer Model (RTM), focusing on microwave frequencies. By simulating the optical properties of non-spherical frozen hydrometeors, the DDA technique effectively reduced discrepancies between simulated and observed values, surpassing traditional Mie tables. The evaluation of DDA lookup tables involved comparisons with a collocated dataset comprising short-term forecasts and satellite microwave data, providing evidence of their superiority. Additionally, we address the challenges of assimilating active radar measurements, which offer vertically resolved insights into clouds and precipitation. We explored the assimilation of spaceborne radar measurements in Numerical Weather Prediction (NWP) models by integrating a forward radar model, along with its adjoint and tangent linear, into the data assimilation system. Evaluation using CloudSat measurements demonstrated promising agreement between simulations and observations, particularly when the input hydrometeor profiles aligned with the measured reflectivity profiles, showcasing the potential of the developed forward radar model. Moreover, we discuss other challenges in radar measurement assimilation within NWP models, including potential observation errors and biases.

Isaac Moradi↗

Ground Based, Millimeter Wave Measurement of Ozone in the Middle Atmosphere

There is a need for highly reliable measurements of stratospheric ozone. Policy makers worldwide concerned with public health rely oil a clear consensus from the scientific community as a basis for ozone-related environmental policy that has a significant impact oil national economies. Tile latest Such consensus was presented in WMO, and used in a 1999 meeting of the parties considering amendments to the Montreal Protocol oil Substances that Deplete the Ozone Layer. Tile scientific community, in turn, needs highly precise and accurate measurements of ozone levels, and small time derivatives of these levels, both in continued - development of its understanding of the physical and chemical processes involved and as clear evidence that these processes are occurring as stated. Over most of the world, changes in ozone levels are small. For example, over the heavily populated northern midlatitudes, the linearized rate of ozone decline is between 0.2% per year and 0.7% per year, depending on altitude. These values are small enough to make measurement requirements technically challenging. Data quality may suffer from imperfections in individual instruments. In one instance, early results from a satellite-borne ozone sensor were later found to be invalid because of calibration drift. Even in the absence of drift, tile absolute calibration of a new sensor may differ slightly from that of its predecessor in service. Most ozone remote sensing instruments operate at ultraviolet or infrared wavelengths where scattering from dust and aerosols must be taken into account; results from these systems may be or are affected following a major volcanic eruption, such as tile one at Mt. Pinatubo in 1991. Given these difficulties, a consensus of measurements from several independent systems is required to insure a reliable understanding of stratospheric ozone levels. Because of the above-described need for highly precise and accurate ozone measurements using several independent techniques, there was interest in developing several techniques which were known but not highly developed in the 1980's into systems capable of being used in ail operational manner to make measurements with the level of quality needed to-detect small trends in ozone levels. A ground-based microwave instrument capable of remotely sensing stratospheric ozone had been designed by tile Principal Investigator of the present project. This instrument was built at tile Millitech Corporation in South Deerfield, Massachusetts before tile present work began. (Funding for design and construction of the instrument came from sources other than the present grant.) Tile instrument measured the spectrum of one of the many emission lines produced by purely rotational transitions of ozone, one at a frequency of 110.8 GHz. The altitude distribution of ozone can. in principle, be retrieved from the details of the pressure-broadened spectrum of the ozone transition. However, the level of contamination of the spectral measurement by instrumentally induced artifacts must be very low in order to retrieve a ozone profile of useful quality from it. The Millitech instrument demonstrated spectral purity at ail adequate level, and there were promising ideas for instrumental improvements and for further development of the technique. The initial objectives of the present project, then, were to develop techniques for calibrating the Millitech instrument, to minimize artifacts in tile spectra it produces, to optimally retrieve ozone profiles from tile spectra, to test tile quality of the microwave profiles by comparing them with profiles obtained using several other, independent techniques over both short and periods of time, and to perform research using the ozone data gathered with the instrument.

Parrish, Alan↗

Experience with advanced instrumentation in a hot section cascade

The Lewis Research Center gas turbine Hot Section Test Facility was developed to provide a real engine environment with known boundary conditions for the aerothermal performance evaluation and verification of computer design codes. This verification process requires experimental measurements in a hostile environment. The research instruments used in this facility are presented, and their characteristics and how they perform in this environment are discussed. The research instrumentation consisted of conventional pressure and temperature sensors, as well as thin-film thermocouples and heat flux gages. The hot gas temperature was measured by an aspirated temperature probe and by a dual-element, fast-response temperature probe. The data acquisition mode was both steady state and time dependent. These experiments were conducted over a wide range of gas Reynolds numbers, exit gas Mach numbers, and heat flux levels. This facility was capable of testing at temperatures up to 1600 K, and at pressures up to 18 atm. These corresponded to an airfoil exit Reynolds number range of 0.5 x 10(6) to 2.5 x 10(6) based on the airfoil chord of 5.55 cm. The results characterize the performance capability and the durability of the instrumentation. The challenge of making measurements in hostile environments is also discussed. The instruments exhibited more than adequate durability to achieve the measurement profile. About 70 percent of the thin-film thermocouples and the dual-element temperature probe survived several hundred thermal cycles and more than 35 hr at gas temperatures up to 1600 K. Within the experimental uncertainty, the steady-state and transient heat flux measurements were comparable and consistent over the range of Reynolds numbers tested.

Yeh, Frederick C.↗

Autonomous Navigation of a Lunar Relay Using GNSS and Other Measurements

Many of the highest priority destinations at the Moon lack a continuous view of Earth, such as the lunar poles or lunar far side. Exploration of these sites will require spacecraft in cislunar space to relay communications and provide position, navigation, and timing (PNT) services. Accurate knowledge of relay position, velocity, and time is essential to these services. This paper describes a concept for a PNT Instrument being developed for the Lunar Communications Relay and Navigation Systems (LCRNS) Project. The instrument is intended as a payload that would enable autonomous, on-board, real-time navigation and timing using Global Navigation Satellite System (GNSS), optical navigation, and one-way measurements from Earth-based ground stations. Hardware-in-the-loop simulations using flight software are used to realistically characterize performance on hardware platforms with a path to flight. These results provide preliminary validation of the proposed PNT Instrument, demonstrate the benefits of augmenting GNSS with other measurements, and serve as an insightful reference for the design of future lunar missions, including those that will operate within the LunaNet framework of standards. This instrument concept relies on several technologies developed at NASA Goddard Space Flight Center (GSFC). For GNSS observables, the instrument relies on the high-altitude NavCube 3 mini (NC3m) GNSS receiver specifically designed for cislunar applications. The autoNGC system, which consists of flight software and a hardware platform, is responsible for fusing the observables using its extended Kalman filter, the Goddard Enhanced Onboard Navigation System (GEONS). Optical navigation observables are processed within autoNGC (“autonomous Navigation, Guidance, and Control”) using the Goddard Image Analysis & Navigation Tool (GIANT) which is also responsible for simulating high-fidelity images for test and analysis. In addition to describing the PNT Instrument and its components, the paper will present predicted performance based on simulation results. As a baseline, it will present GNSS-only hardware-in-the loop results using a NC3m test unit to process Spirent-simulated GPS signals in a potential lunar relay trajectory: a 12-hour elliptical frozen lunar orbit (ELFO). GEONS then processes the GPS pseudorange and time differenced carrier phase measurements to estimate and propagate the relay state (position, velocity, and time). These results extend previously published work that showed preliminary ELFO performance. Previous work has shown the importance of other measurement types, so additional simulations are performed which augment GNSS with ground station observables and several methods of optical navigation, including celestial navigation, limb-finding (e.g., observations of the lunar horizon), and terrain relative navigation (TRN). TRN involves correlating simulated predicted images of the lunar surface with actual imagery; misalignments of landmarks identified in each image are translated into relay state updates. TRN is valuable as a measurement of the relay’s state relative to the Moon, especially during GNSS outages or after maneuvers. One-way Pseudorange and Doppler measurements from Earth-based ground stations are also simulated. The full set of observables is processed using autoNGC. These simulations make use of autoNGC and NC3m test units, a lab atomic clock, and a pulse-per-second (PPS) generation and distribution system. This combination of subsystems, and the hardware platforms used in this analysis, represents a PNT Instrument that could be flown on a lunar relay. Results from the hardware-in-the-loop simulations presented in this paper provide a preliminary assessment of the achievable navigation performance of this instrument concept. PNT Instrument performance is compared to the GPS-only performance, and a discussion is provided on the apparent merits and challenges of each measurement type.

Ben Ashman↗

Shake Test Results and Dynamic Calibration Efforts for the Large Rotor Test Apparatus

A shake test of the Large Rotor Test Apparatus (LRTA) was performed in an effort to enhance NASAscapability to measure dynamic hub loads for full-scale rotor tests. This paper documents the results of theshake test as well as efforts to calibrate the LRTA balance system to measure dynamic loads.Dynamic rotor loads are the primary source of vibration in helicopters and other rotorcraft, leading topassenger discomfort and damage due to fatigue of aircraft components. There are novel methods beingdeveloped to reduce rotor vibrations, but measuring the actual vibration reductions on full-scale rotorsremains a challenge. In order to measure rotor forces on the LRTA, a balance system in the non-rotatingframe is used. The forces at the balance can then be translated to the hub reference frame to measure therotor loads. Because the LRTA has its own dynamic response, the balance system must be calibrated toinclude the natural frequencies of the test rig.

Shake Test Results↗

Analysis of Aircraft Clusters to Measure Sector-Independent Airspace Congestion

The Distributed Air/Ground Traffic Management (DAG-TM) concept of operations* permits appropriately equipped aircraft to conduct Free Maneuvering operations. These independent aircraft have the freedom to optimize their trajectories in real time according to user preferences; however, they also take on the responsibility to separate themselves from other aircraft while conforming to any local Traffic Flow Management (TFM) constraints imposed by the air traffic service provider (ATSP). Examples of local-TFM constraints include temporal constraints such as a required time of arrival (RTA), as well as spatial constraints such as regions of convective weather, special use airspace, and congested airspace. Under current operations, congested airspace typically refers to a sector(s) that cannot accept additional aircraft due to controller workload limitations; hence Dynamic Density (a metric that is indicative of controller workload) can be used to quantify airspace congestion. However, for Free Maneuvering operations under DAG-TM, an additional metric is needed to quantify the airspace congestion problem from the perspective of independent aircraft. Such a metric would enable the ATSP to prevent independent aircraft from entering any local areas of congestion in which the flight deck based systems and procedures may not be able to ensure separation. This new metric, called Gaggle Density, offers the ATSP a mode of control to regulate normal operations and to ensure safety and stability during rare-normal or off-normal situations (e.g., system failures). It may be difficult to certify Free Maneuvering systems for unrestricted operations, but it may be easier to certify systems and procedures for specified levels of Gaggle Density that could be monitored by the ATSP, and maintained through relatively minor flow-rate (RTA type) restrictions. Since flight deck based separation assurance is airspace independent, the challenge is to measure congestion independent of sector boundaries. Figure 1 , reproduced from Ref. 1, depicts an example traffic situation. When the situation is analyzed by sector boundaries (left side of figure), a Dynamic Density metric would identify excessive congestion in the central sector. When the same traffic situation is analyzed independent of sector boundaries (right side of figure), a Gaggle Density metric would identify congestion in two dynamically defined areas covering portions of several sectors. The first step towards measuring airspace-independent congestion is to identify aircraft clusters, i.e., groups of closely spaced aircraft. The objective of this work is to develop techniques to detect and classify clusters of aircraft.

Bilimoria, Karl D.↗

Performance modeling of daytime Raman lidar systems for profiling atmospheric water vapor

We describe results from a comprehensive computer model developed to guide optimization of an ultraviolet Raman lidar system for measuring daytime profiles of atmospheric water vapor. Daytime measurements present added challenges because of the difficulties inherent in detecting Raman signals against solar backgrounds. We are pursuing two concepts for optimizing the daytime performance of a Raman lidar system. The first involves operating the system in the solar blind region of the ultraviolet spectrum. The second concept involves operation of the system in a narrowband, narrow field-of-view mode. Calculations for lidar systems based on both concepts are presented.

Goldsmith, J. E. M.↗

Multiple periodicities in the solar magnetic field - Possible origin in a multiple-mode solar dynamo

The solar magnetic field is generated in an oscillatory mode with a 22 yr full period and gives rise to the 11 yr sunspot cycle. However, analyses of contemporary solar records, as well as other surrogate indicators of solar activity, suggest the presence also of longer term periodicities in the solar magnetic cycle. This paper suggests that the solar dynamo can operate in a multiply periodic state, with several periodicites being generated simultaneously at different depths in the convection zone. A simple two-layer model of the solar convection zone is used to illustrate the physical mechanism of spatially localized, multiple-periodicity-mode dynamo regeneration. The two layers are characterized by differences in their respective turbulent magnetic diffusivities. Although the magnetic modes interact with one another, each mode is produced large in one layer or the other, and has an oscillation period approximately equal to the time characteristic of magnetic diffusion across the layer. The observed complicated periodicity pattern in the solar magnetic field could be a combination of two (or more) dynamo modes generated in this manner. The calculations are carried out using a differential rotation model consistent with recent helioseismological measurements, illustrating the challenge to dynamo theory raised by those observational results.

Boyer, D. W.↗