Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Power Law”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 181 records · Page 10
All sourcesNASA NTRSDOE OSTI
NASA NTRS1986

X-ray spectroscopy of five BL Lacertae objects

Five X-ray bright BL Lacertae objects were observed in the energy range 0.6-4.5 keV with the solid state spectrometer (SSS) of the Einstein Observatory. The 14 SSS spectra obtained represent most of the X-ray spectra of BL Lac objects with resolution better than approximately 3. These data do not reveal the presence of large amounts of thermal gas, with upper limits for the equivalent width of individual spectral features typically less that about 100 eV. However, the SSS spectra are the first set of X-ray data to indicate low-energy absorption in excess of that caused by the cold interstellar matter in the Galaxy. Comparison with contemporaneous, lower energy X-ray data implies that this absorption does not arise in cold neutral material, but in hotter, highly ionized material, probably intrinsic to the source. All five BL Lac objects have X-ray continua that are well fitted by power-law models, with power-law energy indices usually greater than about 1. In a few cases, a flattening at higher energies is observed; these and other data suggest that two-component X-ray spectra, steep at low energies and flat at high energies, are a common feature of BL Lac objects. Three of the five sources clearly vary between SSS observations, with time scales ranging from days to years. A historical synopsis of the X-ray spectral data confirms the tendency for BL Lacertae objects to be highly variable in the X-ray band but reveals no correlation between spectral and intensity changes.

Urry, C. M.↗
NASA NTRS1989

Fractal statistics of cloud fields

Landsat Multispectral Scanner (MSS) and Thematic Mapper (TM) data, with 80 and 30 m spatial resolution, respectively, have been employed to study the spatial structure of boundary-layer and intertropical convergence zone (ITCZ) clouds. The probability distributions of cloud areas and cloud perimeters are found to approximately follow a power-law, with a different power (i.e., fractal dimension) for each cloud type. They are better approximated by a double power-law behavior, indicating a change in the fractal dimension at a characteristic size which depends upon cloud type. The fractal dimension also changes with threshold. The more intense cloud areas are found to have a higher perimeter fractal dimension, perhaps indicative of the increased turbulence at cloud top. A detailed picture of the inhomogeneous spatial structure of various cloud types will contribute to a better understanding of basic cloud processes, and also has implications for the remote sensing of clouds, for their effects on remote sensing of other parameters, and for the parameterization of clouds in general circulation models, all of which rely upon plane-parallel radiative transfer algorithms.

Cahalan, Robert F.↗
NASA NTRS1997

Observation of a Long-Term Spin-up Trend in 4U 1538-52

The high-mass X-ray pulsar 4U 153 8-52 has been continually monitored by the Burst and Transient Source Experiment (BATSE) on Compton Gamma-Ray Observatory. These observations permit the construction of long-term pulse frequency and intensity histories. The frequency history reveals that a reversal of the long-term trend in the accretion torque, from spinning down to spinning up, has occurred, probably in 1988. This is the first time a long-term change is known to have occurred for this source, The magnitude of the average absolute value of (dot-nu / nu) is approximately 10(exp -11)/s over an interval of approximately 5 year is similar during spin-down and spin-up. Shorter term pulse frequency variations of either sign are also observed. The power density spectrum of fluctuations in angular acceleration is consistent with white noise on timescales from 16 to 1600 days. It can be well fit with a power law with a power-law index of 0.10 plus or minus 0.21 and white noise strength of (7.6 +/- 1.6) x 10(exp -21) (Hz/s(exp 2)/Hz). These observations are also used to set 95% confidence level lower and upper limits on the rate of orbital period change, -3.9< dot-P orb /P orb <2. 1, in units of 10(exp -6) yr(exp -1).

Rubin, B. C.↗
NASA NTRS2002

ISTP Solar Maximum Extended Science Program

We have studied the entry of solar energetic particles (SEPS) into the magnetosphere by following particles in the time dependent magnetic and electric field from global magnetohydrodynamic (MHD) simulations of the magnetosphere. The MHD simulations can either be for idealized interplanetary magnetic field (IMF) conditions, or for upstream conditions measured by spacecraft. An important part of the analysis is understanding the response of the magnetosphere to the IMF conditions. In the idealized case, the MHD simulation included a steady interplanetary magnetic field (IMF) B(sub x), velocity and density, while the B(sub y) and B(sub z) components were varied from southward IMF to dawnward and finally to northward IMF. We launched more than ten million protons, as well as about 1 million He-3 ions and a few thousand electrons upstream of the magnetosphere into the solar wind. They were initialized using a kappa distribution, which is a power law distribution with a power law coefficient of 1.5 at high energies. The particles had energies between 0. 1 and 50 MeV. The particles were run in time dependent MHD fields that were advanced in time as the particles moved through the system.

Ashour-Abdalla, Maha↗
NASA NTRS1999

Heart rate dynamics before spontaneous onset of ventricular fibrillation in patients with healed myocardial infarcts

The traditional methods of analyzing heart rate (HR) variability have failed to predict imminent ventricular fibrillation (VF). We sought to determine whether new methods of analyzing RR interval variability based on nonlinear dynamics and fractal analysis may help to detect subtle abnormalities in RR interval behavior before the onset of life-threatening arrhythmias. RR interval dynamics were analyzed from 24-hour Holter recordings of 15 patients who experienced VF during electrocardiographic recording. Thirty patients without spontaneous or inducible arrhythmia events served as a control group in this retrospective case control study. Conventional time- and frequency-domain measurements, the short-term fractal scaling exponent (alpha) obtained by detrended fluctuation analysis, and the slope (beta) of the power-law regression line (log power - log frequency, 10(-4)-10(-2) Hz) of RR interval dynamics were determined. The short-term correlation exponent alpha of RR intervals (0.64 +/- 0.19 vs 1.05 +/- 0.12; p <0.001) and the power-law slope beta (-1.63 +/- 0.28 vs -1.31 +/- 0.20, p <0.001) were lower in the patients before the onset of VF than in the control patients, but the SD and the low-frequency spectral components of RR intervals did not differ between the groups. The short-term scaling exponent performed better than any other measurement of HR variability in differentiating between the patients with VF and controls. Altered fractal correlation properties of HR behavior precede the spontaneous onset of VF. Dynamic analysis methods of analyzing RR intervals may help to identify abnormalities in HR behavior before VF.

Non-NASA Center↗
NASA NTRS2003

A Chandra X-Ray Study of NGC 1068 IL the Luminous X-Ray Source Population

We present an analysis of the compact X-ray source population in the Seyfert 2 galaxy NGC 1068, imaged with a approx. 50 ks Chandra observation. We find a total of 84 compact sources on the S3 chip, of which 66 are located within the 25.0 B-mag/arcsec isophote of the galactic disk of NGC 1068. Spectra have been obtained for the 21 sources with at least 50 counts and modeled with both multicolor disk blackbody and power-law models. The power-law model provides the better description of the spectrum for 18 of these sources. For fainter sources, the spectral index has been estimated from the hardness ratio. Five sources have 0.4 - 8 keV intrinsic luminosities greater than 10(exp 39)ergs/ s, assuming that their emission is isotropic and that they are associated with NGC 1068. We refer to these sources as intermediate-luminosity X-ray objects (ISOs). If these five sources are X-ray binaries accreting with luminosities that are both sub-Eddington and isotropic, then the implied source masses are approx greater than 7 solar mass, and so they are inferred to be black holes. Most of the spectrally modeled sources have spectral shapes similar to Galactic black hole candidates. However, the brightest compact source in NGC 1068 has a spectrum that is much harder than that found in Galactic black hole candidates and other ISOs. The brightest source also shows large amplitude variability on both short-term and long-term timescales, with the count rate possibly decreasing by a factor of 2 in approx. 2 ks during our Chundra observation, and the source flux decreasing by a factor of 5 between our observation and the grating observations taken just over 9 months later. The ratio of the number of sources with luminosities greater than 2.1 x 10(exp 38) ergs/s in the 0.4 - 8 keV band to the rate of massive (greater than 5 solar mass) star formation is the same, to within a factor of 2, for NGC 1068, the Antennae, NGC 5194 (the main galaxy in M51), and the Circinus galaxy. This suggests that the rate of production of X-ray binaries per massive star is approximately the same for galaxies with currently active star formation, including "starbursts."

Smith, David A.↗
NASA NTRS2007

An Investigation of Synchrony in Transport Networks

The cumulative degree distributions of transport networks, such as air transportation networks and respiratory neuronal networks, follow power laws. The significance of power laws with respect to other network performance measures, such as throughput and synchronization, remains an open question. Evolving methods for the analysis and design of air transportation networks must address network performance in the face of increasing demands and the need to contain and control local network disturbances, such as congestion. Toward this end, we investigate functional relationships that govern the performance of transport networks; for example, the links between the first nontrivial eigenvalue of a network's Laplacian matrix - a quantitative measure of network synchronizability - and other global network parameters. In particular, among networks with a fixed degree distribution and fixed network assortativity (a measure of a network's preference to attach nodes based on a similarity or difference), those with the small eigenvalue are shown to be poor synchronizers, to have much longer shortest paths and to have greater clustering in comparison to those with large. A simulation of a respiratory network adds data to our investigation. This study is a beginning step in developing metrics and design variables for the analysis and active design of air transport networks.

Kincaid, Rex K.↗
NASA NTRS2012

Fermi Large Area Telescope Second Source Catalog

We present the second catalog of high-energy gamma-ray sources detected by the Large Area Telescope (LAT), the primary science instrument on the Fermi Gamma-ray Space Telescope (Fermi), derived from data taken during the first 24 months of the science phase of the mission, which began on 2008 August 4. Source detection is based on the average flux over the 24-month period. The Second Fermi-LAT catalog (2FGL) includes source location regions, defined in terms of elliptical fits to the 95% confidence regions and spectral fits in terms of power-law, exponentially cutoff power-law, or log-normal forms. Also included are flux measurements in 5 energy bands and light curves on monthly intervals for each source. Twelve sources in the catalog are modeled as spatially extended. We provide a detailed comparison of the results from this catalog with those from the first Fermi-LAT catalog (1FGL). Although the diffuse Galactic and isotropic models used in the 2FGL analysis are improved compared to the 1FGL catalog, we attach caution flags to 162 of the sources to indicate possible confusion with residual imperfections in the diffuse model. The 2FGL catalog contains 1873 sources detected and characterized in the 100 11eV to 100 GeV range of which we consider 127 as being firmly identified and 1171 as being reliably associated with counterparts of known or likely gamma-ray-producing source classes.

Nolan, P. L.↗
NASA NTRS2023

Electron Acceleration and Heating during Magnetic Reconnection in the Earth's Quasi-parallel Bow Shock

We perform a 2.5-dimensional particle-in-cell simulation of a quasi-parallel shock, using parameters for the Earth's bow shock, to examine electron acceleration and heating due to magnetic reconnection. The shock transition region evolves from the ion-coupled reconnection dominant stage to the electron-only reconnection dominant stage, as time elapses. The electron temperature enhances locally in each reconnection site, and ion-scale magnetic islands generated by ion-coupled reconnection show the most significant enhancement of the electron temperature. The electron energy spectrum shows a power law, with a power-law index around 6. We perform electron trajectory tracing to understand how they are energized. Some electrons interact with multiple electron-only reconnection sties, and Fermi acceleration occurs during multiple reflections. Electrons trapped in ion-scale magnetic islands can be accelerated in another mechanism. Islands move in the shock transition region, and electrons can obtain larger energy from the in-plane electric field than the electric potential in those islands. These newly found energization mechanisms in magnetic islands in the shock can accelerate electrons to energies larger than the achievable energies by the conventional energization due to the parallel electric field and shock drift acceleration. This study based on the selected particle analysis indicates that the maximum energy in the nonthermal electrons is achieved through acceleration in ion-scale islands, and electron-only reconnection accounts for no more than half of the maximum energy, as the lifetime of sub-ion-scale islands produced by electron-only reconnection is several times shorter than that of ion-scale islands.

Solar magnetic reconnection↗
DOE OSTI2020

Inflation and Dark Energy from spectroscopy at $\mathcal{z} > 2$

The expansion of the Universe is understood to have accelerated during two epochs: in its very first moments during a period of Inflation and much more recently, at $\mathcal{z} < 1$, when Dark Energy is hypothesized to drive cosmic acceleration. The undiscovered mechanisms behind these two epochs represent some of the most important open problems in fundamental physics. Most of the processes involved during Inflation impact observations on the very largest spatial scales. Traditionally, these have been accessed through observations of the Cosmic Microwave Background (CMB). While very powerful, the CMB originates from a 2D surface and the finite number of modes that it contains will largely be measured by experiments over the next decade. Observations of large 3D volumes with large-scale structure (LSS) access similar scales and will dramatically increase the number of available modes. For example, LSS observations in the range $2 \lesssim z \lesssim 5$ can more than triple the volume surveyed at $z \lesssim 2$, and, together with the sufficiently high galaxy number in this interval, strongly motivates a future spectroscopic survey that exploits this opportunity. In addition, tomography allows mapping the growth of structure with redshift, which provides robust constraints on Dark Energy and neutrino masses while relaxing restrictive assumptions such as a power-law primordial power spectrum. Finally, cross-correlation with external tracers, such as CMB lensing, Intensity Mapping or the Lyman-$\alpha$ forest, immunises the constraints to the systematics that make measurement challenging and further improves the precision through ‘sample variance cancellation’ and degeneracy breaking.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

The importance of round-robin validation when assessing machine-learning-based vertical extrapolation of wind speeds

The extrapolation of wind speeds measured at a meteorological mast to wind turbine rotor heights is a key component in a bankable wind farm energy assessment and a significant source of uncertainty. Industry-standard methods for extrapolation include the power-law and logarithmic profiles. The emergence of machine-learning applications in wind energy has led to several studies demonstrating substantial improvements in vertical extrapolation accuracy in machine-learning methods over these conventional power-law and logarithmic profile methods. In all cases, these studies assess relative model performance at a measurement site where, critically, the machine-learning algorithm requires knowledge of the rotor-height wind speeds in order to train the model. This prior knowledge provides fundamental advantages to the site-specific machine-learning model over the power-law and log profiles, which, by contrast, are not highly tuned to rotor-height measurements but rather can generalize to any site. Furthermore, there is no practical benefit in applying a machine-learning model at a site where winds at the heights relevant for wind energy production are known; rather, its performance at nearby locations (i.e., across a wind farm site) without rotor-height measurements is of most practical interest. To more fairly and practically compare machine-learning-based extrapolation to standard approaches, we implemented a round-robin extrapolation model comparison, in which a random-forest machine-learning model is trained and evaluated at different sites and then compared against the power-law and logarithmic profiles. We consider 20 months of lidar and sonic anemometer data collected at four sites between 50 and 100 km apart in the central United States. We find that the random forest outperforms the standard extrapolation approaches, especially when incorporating surface measurements as inputs to include the influence of atmospheric stability. When compared at a single site (the traditional comparison approach), the machine-learning improvement in mean absolute error was 28 % and 23 % over the power-law and logarithmic profiles, respectively. Using the round-robin approach proposed here, this improvement drops to 20 % and 14 %, respectively. These latter values better represent practical model performance, and we conclude that round-robin validation should be the standard for machine-learning-based wind speed extrapolation methods.

17 WIND ENERGY↗
NASA NTRS1992

High-energy spectral breaks in gamma-ray bursts

Model fits are presented for 18 gamma-ray burst spectra from 100 keV to 27 MeV made with the BATSE spectroscopy detectors on the Compton Gamma Ray Observatory. Most of the bursts are well fitted as power laws with spectral indices between -1.36 and -2.29; however, five bursts show definite departures from a simple power-law fit at high energies. Three of these bursts are well fitted with broken power-law spectra and break energies of from 400 to 690 keV, such as might arise from photon-photon interactions. If so, then the source compactness and hence distance will be sharply constrained. Two of the bursts have spectra with sharply confined slope changes and are well fitted with broken power-law spectra with break energies of 1.2 and 1.6 MeV at peak, such as might arise from photon-magnetic field interactions. If so, then these spectral breaks provide strong evidence for the existence of high magnetic fields in the burst emission region.

Schaefer, Bradley E.↗
NASA NTRS1987

X-ray spectra of PG quasars. II - The X-ray-ultraviolet excess of PG 1211 + 143

Observations of the quasar PG 1211 + 143 are presented and its continuum is modelled in terms of an accretion disk and an underlying power law. The X-ray spectrum in the Einstein imaging proportional counter band is well described by a power law with the very steep spectral index 2.2 + or - 0.4. The overall continuum spectral energy distribution can be described as a power law with alpha roughly 1.2 from the infrared to about 1 keV, with the optical, ultraviolet, and soft X-rays forming a large excess above this power law. If the soft X-ray excess is attributed to emission from a physically thin, optically thick accretion disk, then the implied accretion rate is super-Eddington, from which it is concluded that the application of this simple model is not valid. The observed broad-line ratios in PG 1211 + 143 imply broad-line cloud densities that are somewhat higher than those usually derived for quasars.

Bechtold, Jill↗
DOE OSTI2020

Entanglement properties of disordered quantum spin chains with long-range antiferromagnetic interactions

Entanglement measures are useful tools in characterizing otherwise unknown quantum phases and indicating transitions between them. Here we examine the concurrence and entanglement entropy in quantum spin chains with random long-range couplings, spatially decaying with a power-law exponent $\textit{α}$. Using the strong disorder renormalization group (SDRG) technique, we find by analytical solution of the master equation a strong disorder fixed point, characterized by a fixed point distribution of the couplings with a finite dynamical exponent, which describes the system consistently in the regime $α > \frac{1}{2}$ . A numerical implementation of the SDRG method yields a power-law spatial decay of the average concurrence, which is also confirmed by exact numerical diagonalization. However, we find that the lowest-order SDRG approach is not sufficient to obtain the typical value of the concurrence. We therefore implement a correction scheme which allows us to obtain the leading-order corrections to the random singlet state. This approach yields a power-law spatial decay of the typical value of the concurrence, which we derive both by a numerical implementation of the corrections and by analytics. Next, using numerical SDRG, the entanglement entropy (EE) is found to be logarithmically enhanced for all $\textit{α}$, corresponding to a critical behavior with an effective central charge $\textit{c}$ = ln(2), independent of $\textit{α}$. This is confirmed by an analytical derivation. Using numerical exact diagonalization (ED), we confirm the logarithmic enhancement of the EE and a weak dependence on $\textit{α}$. For a wide range of partition size $\textit{l}$, the EE fits a critical behavior with a central charge close to $\textit{c}$ = 1, which is the same as for the clean Haldane-Shastry model with a power-law-decaying interaction with $\textit{α}$ = 2. Only for small $l \ll L$, in a range which increases with the number of spins N, we find deviations which are rather consistent with the strong disorder fixed point central charge $\textit{c}$ = ln(2). Furthermore, we find using ED that the concurrence shows power-law decay, albeit with smaller power exponents than obtained by SDRG. Finally, we also present results obtained with DMRG and find agreement with ED for sufficiently small $\textit{α}$ < 2, whereas for larger $\textit{α}$ DMRG tends to underestimate the entanglement entropy and finds a faster decaying concurrence.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
NASA NTRS2008

A New Bond Albedo for Performing Orbital Debris Brightness to Size Transformations

We have developed a technique for estimating the intrinsic size distribution of orbital debris objects via optical measurements alone. The process is predicated on the empirically observed power-law size distribution of debris (as indicated by radar RCS measurements) and the log-normal probability distribution of optical albedos as ascertained from phase (Lambertian) and range-corrected telescopic brightness measurements. Since the observed distribution of optical brightness is the product integral of the size distribution of the parent [debris] population with the albedo probability distribution, it is a straightforward matter to transform a given distribution of optical brightness back to a size distribution by the appropriate choice of a single albedo value. This is true because the integration of a powerlaw with a log-normal distribution (Fredholm Integral of the First Kind) yields a Gaussian-blurred power-law distribution with identical power-law exponent. Application of a single albedo to this distribution recovers a simple power-law [in size] which is linearly offset from the original distribution by a constant whose value depends on the choice of the albedo. Significantly, there exists a unique Bond albedo which, when applied to an observed brightness distribution, yields zero offset and therefore recovers the original size distribution. For physically realistic powerlaws of negative slope, the proper choice of albedo recovers the parent size distribution by compensating for the observational bias caused by the large number of small objects that appear anomalously large (bright) - and thereby skew the small population upward by rising above the detection threshold - and the lower number of large objects that appear anomalously small (dim). Based on this comprehensive analysis, a value of 0.13 should be applied to all orbital debris albedo-based brightness-to-size transformations regardless of data source. Its prima fascia genesis, derived and constructed from the current RCS to size conversion methodology (SiBAM Size-Based Estimation Model) and optical data reduction standards, assures consistency in application with the prior canonical value of 0.1. Herein we present the empirical and mathematical arguments for this approach and by example apply it to a comprehensive set of photometric data acquired via NASA's Liquid Mirror Telescopes during the 2000-2001 observing season.

Mulrooney, Mark K.↗
NASA NTRS1981

Radio occultation of Jupiter's ring - Bounds on optical depth and particle size and a comparison with infrared and optical results

A comparison of Voyager 1 data of the Jovian ring at radio, infrared and optical wavelengths suggests a population density that either falls more rapidly than the inverse square of the linear size, or is sharply bounded in maximum particle size. A fragmentation power law is used to estimate a minimum particle radius of 1-2 microns, and a specific model is developed which consists of a power law distribution of lossless or slightly absorbent Mie scatterers with a refractive index near 1.62, a power law index of -3.5, and a minimum particle size of 1.5 microns. The maximum particle radius is not critical, provided that it is greater than 4 microns, and the power law polydispersion of lossless or low absorbent Mie scatterers is consistent with previously reported observations as long as the parameter size minimum is 20 and the power index is about -3.5.

Tyler, G. L.↗
NASA NTRS1995

OSSE observations of GX 339-4

The Oriented Scintillation Spectrometer Experiment (OSSE) on the Compton Gamma Ray Observatory (CGRO) observed the Galactic black hole candidate GX 339-4 as a target of oppurtunity in 1991 September, in response to the outburst reported by Burst and Transient Source Experiment (BATSE). We report here on energy spectra in the 50 keV-10 MeV range obtained by OSSE. The source was detected from 50 to 400 keV at a level relative to the Crab Nebula of approximately 30%. The observed spectrum was prescribed reasonably well by a power law with an exponential cutoff; a least-squares fit yielded a photon index of 0.88 +/- 0.05 and a cutoff energy of 68 +/- 2 keV. The addition of a Compton reflection component did not significantly improve the overall fit. An optically thin thermal bremsstrahlung spectrum also provides a good fit, and the thermal Comptonization model of Sunyaev & Titarchuk, while deficient in describing the data above approximately 200 keV, cannot formally be ruled out. A pure power law with reflection does not fit the observed spectrum. During a follow-up observation made in 1991 November the intensity of the source below 100 keV had dropped by more than a factor of 40, and it was no longer detected above approximately 100 keV. The energy spectrum during the November observation could be characterized by a power law with a photon index of 2.3 +/- 0.3; the spectrum was fitted equally well with the same exponentially cutoff power-law model applied to the September observation, reduced in intensity by a factor of approximately 40. During the 1991 September observation, the luminosity in the 50-400 keV band was approximately 2 x 10(exp 37) ergs/s (assuming a distance of 4 kpc), no more than a factor of 5 below the soft X-ray luminosity of GX 339-4 observed in its X-ray high state. The luminosity during the 1991 November observation was approximately 5 x 10(exp 35) ergs/s. Extrapolations of both the exponentially cutoff power-law and Sunyaev-Titarchuk models to the approximately 5-20 keV X-ray band yield flux levels very close to that observed by Ginga during an overlapping interval in 1991 September, when GX 339-4 was reported to be in its low state. This may be one of the strongest indications to date of a direct correspondence between the low X-ray state and gamma-ray outbursts of GX 339-4.

Grabelsky, D. A.↗
NASA NTRS1991

Interrelation of soft and hard X-ray emissions during solar flares. I - Observations

The interrelation between the acceleration and heating of electrons and ions during impulsive solar flares is determined on the basis of simulataneous observations of hard and soft X-ray emission from the Solar Maximum Mission at high time resolution (6 s). For all the flares, the hard X-rays are found to have a power-law spectrum which breaks down during the rise phase and beginning of the decay phase. After that, the spectrum changes to either a single power law or a power law that breaks up at high energies. The characteristics of the soft X-ray are found to depend on the flare position. It is suggested that small-scale quasi-static electric fields are important for determining the acceleration of the X-ray-producing electrons and the outflowing chromospheric ions.

Winglee, R. M.↗