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At least 1,225 records · Page 68

0D, 1D, 2D, and 3D simulations of an idealized coaxial impedance-matched Marx generator

We have conducted 0D, 1D, 2D, and 3D simulations of an idealized coaxial impedance-matched Marx generator (IMG) []. The 0D calculations were conducted with a four-element circuit model; the 1D, 2D, and 3D calculations were conducted with highly resolved, fully electromagnetic representations. The IMG consists of 30 stages distributed axially and connected electrically in series. Each stage is powered by two bricks separated by 180° and connected electrically in parallel. Each brick comprises two opposite-polarity capacitors in series with a single switch. The bricks drive an internal impedance-matched coaxial transmission line terminated by a resistive load. The simulations neglect effects due to the switch-triggering circuit, the capacitor-charging circuit, external conducting boundaries, and reactive components of the load. We find dimensionality does not significantly affect the electrical power delivered by the IMG to its load: peak load powers estimated by the 0D, 1D, 2D, and 3D simulations agree to within 1%. The 3D calculations demonstrate that electromagnetic power radiated by the bricks, and axial gaps between stages, reduces the peak load power by less than ∼ 1 % . Each simulation assumes the load impedance is 34% above that at which the load power is maximized. Operating an IMG with such an overmatched load offers several advantages while decreasing the peak load power by only 2%. The 0D, 1D, 2D, and 3D models outlined herein could be adapted to assess computationally competing IMG designs, and conduct a variety of numerical IMG experiments, an IMG is constructed. Published by the American Physical Society 2024

43 PARTICLE ACCELERATORS↗

Modelling of photodegradation in solar cell modules of substrate and superstrate design made with ethylene-vinyl acetate as pottant material

A computer model which simulates, in principle, the chemical changes in the photooxidation of hydrocarbons using as input data a set of elementary reactions, corresponding kinetic rate data and appropriate initial conditions was developed. The Model was refined and exploited to examine more closely the photooxidation and photostabilization of a hydrocarbon polymer. The results lead to the following observations. (1) The time to failure, tau sub f (chosen as the level of 5% C-H bond oxidation which is within the range anticipated for marked change in mechanical properties) varies as the inverse square root of the light intensity. However, tau sub f is almost unaffected by both the photoinitiator type and concentration. (2) The time to failure decreases with the rate of abstraction of C-H by peroxy radicals but increases with the rate of bimolecular radical termination controlled by diffusion. (3) Of the various stabilization mechanisms considered, the trapping of peroxy radicals is distinctly the most effective, although the concommitant decomposition of hydroperoxide is also desirable.

Somersall, A. C.↗

Optimal design of high-efficiency tandem cells

Computer analysis indicates that a substantial increase in solar cell conversion efficiencies can be achieved by using two-cell, multi-bandgap tandem structures instead of single-junction cells. Practical AM1 efficiencies of about 30 percent at one sun and over 30 percent at multiple suns are to be expected. The further increases in efficiency calculated for a three-cell tandem structure are much smaller and may not justify the added complexity. For inexpensive two-cell tandem modules, Si is preferred for the bottom cell, and the top-cell material should have a bandgap of 1.75 to 1.80 eV. The GaAs-AlAs and GaAs-GaP systems are very attractive candidates for the top cell. Significant advances have been achieved in growing GaAs on Ge-coated Si substrates (for the two-terminal, two-cell structure) and in growing free-standing ultrathin GaAs layers (for the two-terminal or four-terminal structures). These advances should be transferable to the GaAs-AlAs and GaAs-GaP systems.

Fan, J. C. C.↗

Acceptance Testing of a Satellite SCADA Photovoltaic-Diesel Hybrid System

Satellite Supervisory Control and Data Acquisition (SCADA) of a Photovoltaic (PV)/diesel hybrid system was tested using NASA's Advanced Communication Technology Satellite (ACTS) and Ultra Small Aperture Terminal (USAT) ground stations. The setup consisted of a custom-designed PV/diesel hybrid system, located at the Florida Solar Energy Center (FSEC), which was controlled and monitored at a "remote" hub via Ka-band satellite link connecting two 1/4 Watt USATs in a SCADA arrangement. The robustness of the communications link was tested for remote monitoring of the health and performance of a PV/diesel hybrid system, and for investigating load control and battery charging strategies to maximize battery capacity and lifetime, and minimize loss of critical load probability. Baseline hardware performance test results demonstrated that continuous two-second data transfers can be accomplished under clear sky conditions with an error rate of less than 1%. The delay introduced by the satellite (1/4 sec) was transparent to synchronization of satellite modem as well as to the PV/diesel-hybrid computer. End-to-end communications link recovery times were less than 36 seconds for loss of power and less than one second for loss of link. The system recovered by resuming operation without any manual intervention, which is important since the 4 dB margin is not sufficient to prevent loss of the satellite link during moderate to heavy rain. Hybrid operations during loss of communications link continued seamlessly but real-time monitoring was interrupted. For this sub-tropical region, the estimated amount of time that the signal fade will exceed the 4 dB margin is about 10%. These results suggest that data rates of 4800 bps and a link margin of 4 dB with a 1/4 Watt transmitter are sufficient for end-to-end operation in this SCADA application.

Kalu, A.↗

Advanced interactive display formats for terminal area traffic control

The basic design considerations for perspective Air Traffic Control displays are described. A software framework has been developed for manual viewing parameter setting (MVPS) in preparation for continued, ongoing developments on automated viewing parameter setting (AVPS) schemes. The MVPS system is based on indirect manipulation of the viewing parameters. Requests for changes in viewing parameter setting are entered manually by the operator by moving viewing parameter manipulation pointers on the screen. The motion of these pointers, which are an integral part of the 3-D scene, is limited to the boundaries of screen. This arrangement has been chosen, in order to preserve the correspondence between the new and the old viewing parameter setting, a feature which contributes to preventing spatial disorientation of the operator. For all viewing operations, e.g. rotation, translation and ranging, the actual change is executed automatically by the system, through gradual transitions with an exponentially damped, sinusoidal velocity profile, in this work referred to as 'slewing' motions. The slewing functions, which eliminate discontinuities in the viewing parameter changes, are designed primarily for enhancing the operator's impression that he, or she, is dealing with an actually existing physical system, rather than an abstract computer generated scene. Current, ongoing efforts deal with the development of automated viewing parameter setting schemes. These schemes employ an optimization strategy, aimed at identifying the best possible vantage point, from which the Air Traffic Control scene can be viewed, for a given traffic situation.

Grunwald, Arthur J.↗

Winds From Luminous Late-Type Stars: The Effects of Nonlinear Alfven Waves - 1

We present the results of magnetohydrodynamic (MHD) modeling of winds from luminous late-type stars using a 2.5-dimensional, nonlinear MHD computer code. We assume that the wind is generated within an initially hydrostatic atmosphere and is driven by torsional Alfven waves generated at the stellar surface. Two cases of atmospheric topology are considered: case I has longitudinally uniform density distribution and isotropic radial magnetic field over the stellar surface, and case II has an isotropic, radial magnetic field with a transverse density gradient, which we refer to as an "atmospheric hole." We use the same set of boundary conditions for both models. The calculations are designed to model a cool luminous star, for which we assume an initial hydrostatic pressure scale height of 0.072 Stellar Radius, an Alfven wave speed of 92 km/s at the surface, and a wave period of 76 days, which roughly corresponds with the convective turnover time. For case I the calculations produce a wind with terminal velocity of about 22 km/s and a mass loss rate comparable to the expected value of 10(exp -6) Solar Mass/yr. For case II we predict a two-component wind: a fast (25 km/s) and relatively dense wind outside of the atmospheric hole and a slow (1.5 km/s), rarefied wind inside of the hole.

Airapetian, V. S.↗

Flow Simulation of Supersonic Inlet with Bypass Annular Duct

A relaxed isentropic compression supersonic inlet is a new concept that produces smaller cowl drag than a conventional inlet, but incurs lower total pressure recovery and increased flow distortion in the (radially) outer flowpath. A supersonic inlet comprising a bypass annulus to the relaxed isentropic compression inlet dumps out airflow of low quality through the bypass duct. A reliable computational fluid dynamics solution can provide considerable useful information to ascertain quantitatively relative merits of the concept, and further provide a basis for optimizing the design. For a fast and reliable performance evaluation of the inlet performance, an equivalent axisymmetric model whose area changes accounts for geometric and physical (blockage) effects resulting from the original complex three-dimensional configuration is proposed. In addition, full three-dimensional calculations are conducted for studying flow phenomena and verifying the validity of the equivalent model. The inlet-engine coupling is carried out by embedding numerical propulsion system simulation engine data into the flow solver for interactive boundary conditions at the engine fan face and exhaust plane. It was found that the blockage resulting from complex three-dimensional geometries in the bypass duct causes significant degradation of inlet performance by pushing the terminal normal shock upstream.

Kim, HyoungJin↗

Generalized environmental control and life support system computer program (G1894), phase 3

The work performed during Phase 3 of the Generalized Environmental Control Life Support System (ECLSS) Computer Program is reported. Phase 3 of this program covered the period from December 1977 to September 1978. The computerized simulation of the Shuttle Orbiter ECLSS was upgraded in the following areas: (1) the payload loop of the Shuttle simulation was completely recoded and checked out; (2) the Shuttle simulation water and freon loop initialization logic was simplified to permit easier program input for the user; (3) the computerized simulation was modified to accept the WASP subroutine, which is a subroutine to evaluate thermal properties of water and freon; (4) the 1108 operating system was upgraded by LEC; (5) the Shuttle simulation was modified to permit failure cases which simulate zero component flow values; and (6) the Shuttle SEPS version was modified and secure files were setup on the 1108 and 1110 systems to permit simulation runs to be made from remote terminals.

Mcenulty, R. E.↗

Ka-band propagation studies using the ACTS propagation terminal and the CSU-CHILL multiparameter, Doppler radar

An increase in the demand for satellite communications has led to an overcrowding of the current spectrums being used - mainly at C and Ku bands. To alleviate this overcrowding, new technology is being developed to open up the Ka-band for communications use. One of the first experimental communications satellites using this technology is NASA's Advanced Communications Technology Satellite (ACTS). In Sept. 1993, ACTS was deployed into a geostationary orbit near 100 deg W longitude. The ACTS system employs two Ka-band beacons for propagation experiments, one at 20.185 GHz and another at 27.505 GHz. Attenuation due to rain and tropospheric scintillations will adversely affect new technologies proposed for this spectrum. Therefore, before being used commercially, propagation effects at Ka-band must be studied. Colorado State University is one of eight sites across the United States and Canada conducting propagations studies; each site is equipped with the ACTS propagation terminal (APT). With each site located in a different climatic zone, the main objective of the propagation experiment is to obtain monthly and yearly attenuation statistics. Each site also has secondary objectives that are site dependent. At CSU, the CSU-CHILL radar facility is being used to obtain polarimetric radar data along the ACTS propagation path. During the expected two to four year period of the project, it is hoped to study several significant weather events. The S-band radar will be used to obtain Ka-band attenuation estimates and to initialize propagation models that have been developed, to help classify propagation events measured by the APT. Preliminary attenuation estimates for two attenuation events will be shown here - a bright band case that occurred on 13 May 1994 and a convective case that occurred on 20 Jun. 1994. The computations used to obtain Ka-band attenuation estimates from S-band radar data are detailed. Results from the two events are shown.

Beaver, J.↗

Using DSCOVR EPIC as a Transfer Radiometer to Scale Leo Imagers to the Same Calibration Reference

The NASA CERES project provides climate-quality observed TOA and computed surface fluxes to the climate community. The CERES instruments are on board the Terra, Aqua, Suomi-NPP, and NOAA-20 low earth orbiting (LEO) satellites, where they are used in tandem with the MODIS and VIIRS instruments to retrieve cloud properties required for converting CERES radiance observations into fluxes. The CERES project radiometrically scales the MODIS and VIIRS imager visible channel radiances to the Aqua-MODIS reference to retrieve consistent imager cloud properties between sensors. The NPP, NOAA-20, and the future NOAA-21 VIIRS imagers will be in the same sun-synchronous orbit but spaced equally apart, allowing for no simultaneous nadir overpasses (SNO) to inter-calibrate the VIIRS imagers to each other. Currently, the CERES project uses Aqua-MODIS to radiometrically scale between VIIRS imagers. Once the Terra and Aqua satellites start drifting toward the terminator, Aqua can no longer be utilized as the transfer radiometer between VIIRS sensors and there will be no SNOs in common between neither MODIS nor VIIRS imagers. The DSCOVR satellite orbits the Lagrange-1 (L1) point about 1.5 million kilometers from Earth. The Earth Polychromatic Imaging Camera (EPIC) instrument on the Earth-facing side of DSCOVR takes images ranging from the UV to the NIR of the sunlit side of the Earth. While the EPIC sensor has no onboard calibration systems, multiple inter-calibration studies have indicated that the EPIC instrument response is radiometrically stable. The stability of the EPIC instrument allows it to be used as a transfer radiometer between all MODIS and VIIRS imagers. The study will demonstrate the use of EPIC to radiometrically scale VIIRS and MODIS imagers to the same Aqua-MODIS calibration reference. The EPIC-based NPP and N20-VIIRS scaling factors will be compared with the Aqua-MODIS based NPP and N20-VIIRS scaling factors.

C. O. Haney↗

Realistic NLTE Radiative Transfer for Modeling Stellar Winds

This NASA grant supported the development of codes to solve the non-LTE multi-level spherical radiative transfer problem in the presence of velocity fields. Much of this work was done in collaboration with Graham Harper (CASA, University of Colorado). These codes were developed for application to the cool, low-velocity winds of evolved late-type stars. Particular emphasis was placed on modeling the wind of lambda Velorum (K4 lb), the brightest K supergiant in the sky, based on extensive observations of the ultraviolet spectrum with the HST/GHRS from GO program 5307. Several solution techniques were examined, including the Eddington factor Approach described in detail by Bennett & Harper (1997). An Eddington factor variant of Harper's S-MULTI code (Harper 1994) for stationary atmospheres was developed and implemented, although full convergence was not realized. The ratio of wind terminal velocity to turbulent velocity is large (approx. 0.3-0.5) in these cool star winds so this assumption of stationarity provides reasonable starting models. Final models, incorporating specified wind laws, were converged using the comoving CRD S-MULTI code. Details of the solution procedure were published by Bennett & Harper (1997). Our analysis of the wind of lambda Vel, based on wind absorption superimposed on chromospheric emission lines in the ultraviolet, can be found in Carpenter et al. (1999). In this paper, we compare observed wind absorption features to an exact CRD calculation in the comoving frame, and also to a much quicker, but approximate, method using the SEI (Sobolev with Exact Integration) code of Lamers, Cerruti-Sola, & Perinotto (1987). Carpenter et al. (1999) provide detailed comparisons of the exact CRD and approximate SEI results and discuss when SEI is adequate to use for computing wind line profiles. Unfortunately, the observational material is insufficient to unambiguously determine the wind acceleration law for lambda Vel. Relatively few unblended Fe II lines of optical depth sensitive to the wind acceleration region are present in the existing HST/GHRS data set. Most of the Fe II lines are either too optically thick (resulting in a board, black wind absorption profile) or too optically thin (resulting in no wind absorption feature present). Also, most of the ultraviolet spectra obtained from HST GO-5307 was at medium resolution (R approx. 40,000, corresponding to a velocity resolution of 7.5 km/s). This is simply inadequate to resolve the turbulence in the outer wind; a key parameter in theoretical wind models. We can now say that an unambiguous determination of the wind velocity law in lambda Vel will require complete coverage of the ultraviolet spectrum at high dispersion (R approx. 10(exp 5), or 3 km/s). This is now feasible usin, the STIS echelle spectrograph on-board HST.

Bennett, Philip D.↗

The archives of the future

The term “artificial intelligence” (AI) - essentially programming machines to think like humans - conjures up different emotions in different people. Some view it with fear, imagining a malevolent AI similar to Skynet in the Terminator movies. Others see something benevolent, such as the character Data in Star Trek: The Next Generation . Still others see it as a means to advance the frontiers of science, engineering and technology to new levels not possible through traditional means. At the National Security Research Center (NSRC or the Center), which is the classified library at Los Alamos National Laboratory, we see AI as a tool to help us go through the monumental tasks we have in digitizing, cataloging, and searching our collections.

96 KNOWLEDGE MANAGEMENT AND PRESERVATION↗

An Exploration of Discontinuous Time Synchronous Averaging for Helicopter HUMS Using Cruise and Terminal Area Vibration Data

Recent research using NASA Ames AH-1 and OH-58C helicopters, and NASA Glenn test rigs, has shown that in-flight vibration data are typically non-stationary [l-4]. The nature and extent of this non-stationarity is most likely produced by several factors operating simultaneously. The aerodynamic flight environment and pilot commands provide continuously changing inputs, with a complex dynamic response that includes automatic feedback control from the engine regulator. It would appear that the combined effects operate primarily through an induced torque profile, which causes concomitant stress modulation at the individual internal gear meshes in the transmission. This notion is supported by several analyses, which show that upwards of 93% of the vibration signal s variance can be explained by knowledge of torque alone. That this relationship is stronger in an AH-1 than an OH-58, where measured non-stationarity is greater, suggests that the overall mass of the vehicle is an important consideration. In the lighter aircraft, the unsteady aerodynamic influences transmit relatively greater unsteady dynamic forces on the mechanical components, quite possibly contributing to its greater non-stationarity . In a recent paper using OH-58C pinion data [5], the authors have shown that in computing a time synchronous average (TSA) for various single-value metric computations, an effective trade-off can be obtained between sample size and measured stationarity by using data from only a single mesh cycle. A mesh cycle, which is defined as the number of rotations required for the gear teeth to return to their original mating position, has the property of representing all of the discrete phase angles of the opposing gears exactly once in the average. Measured stationarity is probably maximized because a single mesh cycle of the pinion gear occurs over a very short span of time, during which time-dependent non-stationary effects are kept to a minimum. Clearly, the advantage of local stationarity diminishes as the temporal duration of the cycle increases. This is most evident for a planetary mesh cycle, which can take several minutes to complete.

Huff, Edward M.↗

DACS II - A distributed thermal/mechanical loads data acquisition and control system

A distributed data acquisition and control system has been developed for the NASA Flight Loads Research Facility. The DACS II system is composed of seven computer systems and four array processors configured as a main computer system, three satellite computer systems, and 13 analog input/output systems interconnected through three independent data networks. Up to three independent heating and loading tests can be run concurrently on different test articles or the entire system can be used on a single large test such as a full scale hypersonic aircraft. Thermal tests can include up to 512 independent adaptive closed loop control channels. The control system can apply up to 20 MW of heating to a test specimen while simultaneously applying independent mechanical loads. Each thermal control loop is capable of heating a structure at rates of up to 150 F per second over a temperature range of -300 to +2500 F. Up to 64 independent mechanical load profiles can be commanded along with thermal control. Up to 1280 analog inputs monitor temperature, load, displacement and strain on the test specimens with real time data displayed on up to 15 terminals as color plots and tabular data displays. System setup and operation is accomplished with interactive menu-driver displays with extensive facilities to assist the users in all phases of system operation.

Zamanzadeh, Behzad↗

Continuity conditions for tensor product Q-Bézier surfaces of degree (m, n)

Based on a kind of Q-Bézier surfaces with shape parameters, the basic properties of the surfaces and the geometric significance of the shape parameters are analyzed. To resolve the problem of shape control and adjustment of composite surfaces, the continuity conditions for Q-Bézier surfaces of degree (m, n) are investigated. Taking advantage of the terminal properties of generalized Bernstein basis functions, we derive the conditions of G{sup 1} and G{sup 2} continuity between two adjacent Q-Bézier surfaces. In addition, the specific steps of smooth continuity between Q-Bézier surfaces and the shape adjustment function of shape parameters for composite surfaces are discussed. The modeling examples show that the proposed smooth continuity conditions are not only intuitive and easy to implement, but also greatly enhance the shape adjustability, which provide a useful method for constructing complex surfaces in engineering design.

97 MATHEMATICS AND COMPUTING↗

Physics of Rotation Powered Pulsars and Their Nebulae

This letter is my progress report for the Astrophysics Theory grant. The first goal of the research supported by this grant is to produce a time dependent theory of the unsteady relativistic collisionless shock wave terminating the relativistic wind from a pulsar, and compare the predicted surface brightness fluctuations to Hubble Space Telescope observations of the wisps in the Crab Nebula. The second goal is to model the production of electron-positron pairs over the polar caps of rotation powered pulsars, and use the results to predict the heating of the surface due to particle trapping and bombardment of the atmosphere at the base of the polar field lines. We have succeeded in creating a one dimensional hybrid code, in which the electron-positron pairs incident on the shock structure are modeled as a relativistic, adiabatic, ideal MHD fluid, while the heavy ions are treated as particles using a particle-in-cell algorithm. The electromagnetic fields are evaluated from the currents and charge densities in the pairs and the ions, while the particles and the fluid accelerate in response to the computed self-consistent electromagnetic fields. The results are promising, in that the underlying ion cyclotron instability generates finite amplitude, propagating magnetosonic waves in the pairs, whose wavelengths and frequencies, when translated into physical units, are comparable to the observed running waves of brightness observed by HST near the Crab pulsar. The code is undergoing a number of tests, to assure us that this preliminary correspondence is not an artifact. In the coming year, the observational appearance of the models will be computed and compared to the HST observations of the Crab now in hand, and used to predict the HST results which will be obtained the year after next. WE also developed a one dimensional cascade theory for pair creation over pulsars' polar caps. A linear integral equation describing the synchrotron cascade has been derived and solved by iterative techniques, in the case when a high energy electron moving parallel to a star centered dipole magnetic field initiates the cascade through curvature gamma ray emission.

Arons, Jonathan↗

High-Temperature Probe Station Developed to Characterize Microwave Devices Through 500 C

A photograph and a block diagram of the high-temperature probe station are shown. The system consists of the ceramic heater mounted on a NASA shuttle tile insulator, a direct current power supply, a personal-computer-based data acquisition and temperature controller, microwave probes, a microscope, and a network analyzer. The ability to perform microwave tests at high temperatures is becoming necessary. There is now a need for sensors and communication circuits that can operate at 500 C and above for aircraft engine development and monitoring during flight. To address this need, researchers have fabricated devices using wide bandgap semiconductors such as SiC with targeted operating temperatures of 500 to 600 C. However, the microwave properties of these devices often change drastically with temperature, so any designs that are intended to be used in such an environment must be characterized at high temperatures. For some reliability, lifetime, and direct-current testing, the device under test can be packaged and characterized in an oven. However, for RF and microwave measurements, it is usually not possible to establish a calibrated reference plane at the device terminals within a package. In addition, the characteristics of the package would vary over a 500 C temperature range, and this would have to be accounted for when the data were analyzed. A high temperature probe station allows circuits and devices to be characterized through on wafer measurements across a broad temperature range with known reference plane. The conventional, commercially available thermal wafer-probe stations that are used to evaluate microwave devices across a controlled temperature range have a typical upper limit of 200 C. Standalone thermal heating chucks are available with an extended upper temperature range of 300 to 400 C. To effectively characterize devices at temperatures up to and surpassing 500 C, Glenn researchers developed a custom probe station. In the past, custom probe stations have been developed to test devices under other extreme environments, such as cryogenic temperatures as low as 37 K. Similarly, this custom probe station was specifically modified for high-temperature use. It allows devices to be measured quickly and flexibly, without the use of wire bonds and test fixtures. The probe station is shown making scattering parameter measurements from 1 to 50 GHz with a Hewlett-Packard 8510C Network Analyzer. There is a half-wafer of silicon directly on top of the heater to provide a uniform heated platform for our sample. A quarter wafer of silicon carbide forms the substrate for our test circuit of several transmission lines.

Downey, Alan N.↗

Observations of the Magnetic Field and Plasma in the Heliosheath by Voyager 2 from 2007.7 to 2009.4

The density and temperature profiles of the plasma measured by Voyager 2 (V2) behind the termination shock changed abruptly near 2008.6 from relatively large average values and large fluctuations during 2007.7 to 2008.6 (interval A) to relatively low average values and very small-amplitude fluctuations during 2008.6 to 2009.4 (interval B). This paper shows that the change in the magnetic field strength B(t) was less abrupt than the plasma changes, and the fluctuations of the magnetic field strength in interval B were of moderate amplitude, with indications of a quasiperiodic structure in part of the interval. The magnetic field was directed away from the sun (positive polarity) approx. 78% +/- 5% of the time in both interval A and interval B, changing in an irregular way from positive to negative polarities throughout the interval. The polarity distribution indicates that the minimum latitudinal extent of the heliospheric current sheet (HCS) was near V2 throughout the interval, consistent with the extrapolated minimum latitudes of the HCS computed from solar magnetic field observations. Thus, V2 was observing magnetic fields from the southern polar coronal hole most of the time. The distribution of B was lognormal in interval A and Gaussian interval B.

Burlaga, L. F.↗