The gravity potential and force field of the earth through fourth order
Gravity potential and force field of earth through fourth order to accurately determine spacecraft trajectories
EARTH↗
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The coronal field lines of an evolving bipolar magnetic region
A simple potential field model is presented to illustrate that loops of magnetic flux rise upward through the corona during the relatively short growth phase of a bipolar magnetic region but contract back to the sun's surface during the much longer decay phase of the photospheric region. To reconcile this behavior with the unidirectional, solar-wind-driven convection of flux outward from the sun, one must postulate the existence of an X-type neutral line in the middle corona where open field lines can be converted back to closed ones.
Sheeley, N. R., Jr.↗
Shear-induced inflation of coronal magnetic fields
Using numerical models of force-free magnetic fields, the shearing of footprints in arcade geometries leading to an inflation of the coronal magnetic field was examined. For each of the shear profiles considered, all of the field lines become elevated compared with the potential field. This includes cases where the shear is concentrated well away from the arcade axis, such that B(sub z), the component of field parallel to the axis, increases outward to produce an inward B(sub z)squared/8 pi magnetic pressure gradient force. These results contrast with an earlier claim, shown to be incorrect, that field lines can sometimes become depressed as a result of shear. It is conjectured that an inflation of the entire field will always result from the shearing of simple arcade configurations. These results have implications for prominence formation, the interplanetary magnetic flux, and possibly also coronal holes.
Klimchuk, James A.↗
Shear-induced inflation of coronal magnetic fields
Using numerical models of force-free magnetic fields, the shearing of footprints in arcade geometries leading to an inflation of the coronal magnetic field was examined. For each of the shear profiles considered, all of the field lines become elevated compared with the potential field. This includes cases where the shear is concentrated well away from the arcade axis, such that B(sub z), the component of field parallel to the axis, increases outward to produce an inward B(sub z) squared/8 pi magnetic pressure gradient force. These results contrast with an earlier claim, shown to be incorrect, that field lines can sometimes become depressed as a result of shear. It is conjectured that an inflation of the entire field will always result from the shearing of simple arcade configurations. These results have implications for prominence formation, the interplanetary magnetic flux, and possibly also coronal holes.
Klimchuk, James A.↗
Transformation of vector magnetograms and the problems associated with the effects of perspective and the azimuthal ambiguity
Off-center vector magnetograms which use all three components of the measured field provide the maximum information content from the photospheric field and can provide the most consistent potential field independent of the viewing angle by defining the normal component of the field. The required transformations of the magnetic field vector and the geometric mapping of the observed field in the image plane into the heliographic plane have been described. Here we discuss the total transformation of specific vector magnetograms to detail the problems and procedures that one should be aware of in analyzing observational magnetograms. The effect of the 180-deg ambiguity of the observed transverse field is considered as well as the effect of curvature of the photosphere. Specific results for active regions AR 2684 (September 23, 1980) and AR 4474 (April 26, 1984) from the Marshall Space Flight Center Vector magnetograph are described which point to the need for the heliographic projection in determining the field structure of an active region.
Gary, G. Allen↗
Coronal magnetic fields produced by photospheric shear
The magneto-frictional method is used for computing force free fields to examine the evolution of the magnetic field of a line dipole, when there is relative shearing motion between the two polarities. It found that the energy of the sheared field can be arbitrarily large compared with the potential field. It is also found that it is possible to fit the magnetic energy, as a function of shear, by a simple functional form.
Sturrock, P. A.↗
Coronal magnetic fields produced by photospheric shear
The magnetofrictional method for computing force-free fields is used to examine the evolution of the magnetic field of a line dipole, when there is relative shearing motion between the two polarities. It is found that the energy of the sheared field can be arbitrarily large compared with the potential field. It is also found that it is possible to fit the magnetic energy, as a function of shear amplitude, by a simple functional form. The fit parameters depend only on the distribution of normal field in the photosphere and the form of the shearing displacement. They show that the energy is relatively more enhanced if the shear occurs: (1) where the normal field is strongest; and/or (2) in the inner region of the dipole, near the axis; and/or (3) over a large fraction of the dipole area.
Klimchuk, J. A.↗
Modeling a simple coronal streamer during whole sun month
The solar minimum streamer structure observed during the whole sun month was modeled. The Van de Hulst inversion was used in order to determine the coronal electron density profiles and scale-height temperature profiles. The axisymmetric magnetostatic model of Gibson, Bagenal and Low was also used. The density, temperature, and magnetic field distribution were quantified using both coronal white light data and photospheric magnetic field data from the Wilcox Solar Observatory. The densities and temperatures obtained by the Van de Hulst and magnetostatic models are compared to the magnetic field predicted by the magnetostatic model to a potential field extrapolated from the photosphere.
Gibson, S. E.↗
CME Interaction with Coronal Holes and Their Interplanetary Consequences
A significant number of interplanetary (IP) shocks (-17%) during cycle 23 were not followed by drivers. The number of such "driverless" shocks steadily increased with the solar cycle with 15%, 33%, and 52% occurring in the rise, maximum, and declining phase of the solar cycle. The solar sources of 15% of the driverless shocks were very close the central meridian of the Sun (within approx.15deg), which is quite unexpected. More interestingly, all the driverless shocks with their solar sources near the solar disk center occurred during the declining phase of solar cycle 23. When we investigated the coronal environment of the source regions of driverless shocks, we found that in each case there was at least one coronal hole nearby suggesting that the coronal holes might have deflected the associated coronal mass ejections (CMEs) away from the Sun-Earth line. The presence of abundant low-latitude coronal holes during the declining phase further explains why CMEs originating close to the disk center mimic the limb CMEs, which normally lead to driverless shocks due to purely geometrical reasons. We also examined the solar source regions of shocks with drivers. For these, the coronal holes were located such that they either had no influence on the CME trajectories. or they deflected the CMEs towards the Sun-Earth line. We also obtained the open magnetic field distribution on the Sun by performing a potential field source surface extrapolation to the corona. It was found that the CMEs generally move away from the open magnetic field regions. The CME-coronal hole interaction must be widespread in the declining phase, and may have a significant impact on the geoeffectiveness of CMEs.
Gopalswamy, N.↗
Nanoflare Heating Frequency of an X-ray Bright Point Observed by MaGIXS
Nanoflares have been considered to be one of the most likely candidates for heating the solar corona to multi-million kelvin temperatures. Individual nanoflares are difficult to detect with today's instruments, but their presence may be established by comparing simulated nanoflare-heated plasma emissions to observed emissions. We present a simulation of emission from an X-ray Bright Point (XBP) detected by the MaGIXS, as well as simultaneous observations from SDO/AIA and Hinode/XRT. To simulate the XBP loops, we utilize the HYDRAD code. The length and magnetic field strength of these loops are determined using potential field extrapolation of SDO/HMI's observed photospheric magnetogram. Each loop is considered to be heated by random nanoflares, the amplitude and frequency of which are governed by the length of the loop and the strength of the magnetic field. The simulated outputs are used to estimate the intensity of spectrally pure maps of Fe-18, Fe-17, Ne-9, O-8, O-9, Ne-9, and so on, which is then compared to the intensity determined from MaGIXS observations. In addition, we derived the intensity maps obtained by AIA and XRT and compared them to the observed data. The composite distribution of the delay time of the nanoflares for which the simulated loops morphology and intensities match with observation shows a peak at 200s-500s, indicating that most of the nanoflares have a high/intermediate frequency.
coronal heating↗
The potential and electric field at the surface of the moon
Potential and electric field of lunar surface under conditions of normal incidence of solar radiation
LUNAR SURFACE↗
Full-potential modeling of blade-vortex interactions
A comparison is made of four different models for predicting the unsteady loading induced by a vortex passing close to an airfoil. (1) The first model approximates the vortex effect as a change in the airfoil angle of attack. (2) The second model is related to the first but, instead of imposing only a constant velocity on the airfoil, the distributed effect of the vortex is computed and used. This is analogous to a lifting surface method. (3) The third model is to specify a branch cut discontinuity in the potential field. The vortex is modeled as a jump in potential across the branch cut, the edge of which represents the center of the vortex. (4) The fourth method models the vortex expressing the potential as the sum of a known potential due to the vortex and an unknown perturbation due to the airfoil. The purpose of the current study is to investigate the four vortex models described above and to determine their relative merits and suitability for use in large three-dimensional codes.
Jones, H. E.↗
Full potential modeling of blade-vortex interactions
A comparison is made of four different models for predicting the unsteady loading induced by a vortex passing close to an airfoil. (1) The first model approximates the vortex effect as a change in the airfoil angle of attack. (2) The second model is related to the first but, instead of imposing only a constant velocity on the airfoil, the distributed effect of the vortex is computed and used. This is analogous to a lifting surface method. (3) The third model is to specify a branch cut discontinuity in the potential field. The vortex is modeled as a jump in potential across the branch cut, the edge of which represents the center of the vortex. (4) The fourth method models the vortex expressing the potential as the sum of as known potential due to the vortex and an unknown perturbation due to the airfoil. The purpose of the current study is to investigate the four vortex models described above and to determine their relative merits and suitability for use in large three-dimensional codes.
Jones, H. E.↗
Evidence for the interaction of large scale magnetic structures in solar flares
By modeling the observed vertical magnetic field of an active region AR 2372 by the potential field of an ensemble of magnetic dipoles, the likely location of the separatrices, surfaces that separates cells of different field line connectivities, and of the separator which is the intersection of the separatrices, is derived. Four of the five off-band H-alpha kernels of a flare that occurred less than 20 minutes before obtaining the magnetogram are shown to have taken place near or at the separatrices. These H-alpha kernels are connected by field lines that pass near the separator. This indicates that the flare may have resulted from the interaction in the separator region of large scale magnetic structures.
Mandrini, C. H.↗
Constructing the Coronal Magnetic Field by Correlating Parameterized Magnetic Field Lines with Observed Coronal Plasma Structures
A method is presented for constructing the coronal magnetic field from photospheric magnetograms and observed coronal loops. A set of magnetic field lines generated from magnetogram data is parameterized and then deformed by varying the parameterized values. The coronal flux tubes associated with this field are adjusted until the correlation between the field lines and the observed coronal loops is maximized. A mathematical formulation is described which ensures that (1) the normal component of the photospheric field remains unchanged, (2) the field is given in the entire corona over an active region, (3) the field remains divergence-free, and 4electric currents are introduced into the field. It is demonstrated that a parameterization of a potential field, comprising a radial stretching of the field, can provide a match for a simple bipolar active region, AR 7999, which crossed the central meridian on 1996 November 26. The result is a non-force-free magnetic field with the Lorentz force being of the order of 10(exp -5.5) g per s(exp 2) resulting from an electric current density of 0.79 micro A per m(exp 2). Calculations show that the plasma beta becomes larger than unity at a strong non-radial currents requires low height of about 0.25 solar radii supporting the non-force-free conclusion. The presence of such strong non-radial currents requires large transverse pressure gradients fo maintain a magnetostatic atmosphere, required by the relatively persistent nature of the coronal structures observed in AR 7999. This scheme is an important tool in generating a magnetic field solution consistent with the coronal flux tube observations and the observed photospheric magnetic field.
Allen, Gary G.↗
Simulation of Turbine Tone Noise Generation Using a Turbomachinery Aerodynamics Solver
As turbofan engine bypass ratios continue to increase, the contribution of the turbine to the engine noise signature is receiving more attention. Understanding the relative importance of the various turbine noise generation mechanisms and the characteristics of the turbine acoustic transmission loss are essential ingredients in developing robust reduced-order models for predicting the turbine noise signature. A computationally based investigation has been undertaken to help guide the development of a turbine noise prediction capability that does not rely on empiricism. As proof-of-concept for this approach, two highly detailed numerical simulations of the unsteady flow field inside the first stage of a modern high-pressure turbine were carried out. The simulations were computed using TURBO, which is an unsteady Reynolds-Averaged Navier-Stokes code capable of multi-stage simulations. Spectral and modal analysis of the unsteady pressure data from the numerical simulation of the turbine stage show a circumferential modal distribution that is consistent with the Tyler-Sofrin rule. Within the high-pressure turbine, the interaction of velocity, pressure and temperature fluctuations with the downstream blade rows are all possible tone noise source mechanisms. We have taken the initial step in determining the source strength hierarchy by artificially reducing the level of temperature fluctuations in the turbine flowfield. This was accomplished by changing the vane cooling flow temperature in order to mitigate the vane thermal wake in the second of the two simulations. The results indicated that, despite a dramatic change in the vane cooling flow, the computed modal levels changed very little indicating that the contribution of temperature fluctuations to the overall pressure field is rather small compared with the viscous and potential field interaction mechanisms.
VanZante, Dale↗
Nanoflare Heating of an X-Ray Bright Point
Nanoflares are thought to be one of the prime candidates that can keep the solar corona to its multimillion kelvin temperature. Individual nanoflares are difficult to detect with the present generation instruments, however their presence can be inferred by comparing the nanoflare heated simulated plasma emissions with the observed emission. Here, we present a simulation of emission from an X-ray Bright Point (XBP) that was observed by the Marshall Grazing Incidence X-ray Spectrometer (MaGIXS), along with concurrent observations from SDO/AIA and Hinode/XRT. We use EBTEL hydrodynamic code to simulate the XBP loops. Length and magnetic field strength of these loops are derived from the potential field extrapolation of the observed photospheric magnetogram by HMI/SDO. Each loop is assumed to be heated by random nanoflares, whose magnitude and frequency are determined by the looplength and magnetic field strength. The simulated outputs are used to predict the intensity of spectrally pure map of Fe-18, Fe-17, Ne-9 ,O-8, O-9, Ne-9 etc, which are then compared with the derived intensity from MaGIXS observation. Further we have predicted the intensity map as observed by AIA and XRT and compared them with the observation. We also estimated the temperature distribution of the XBP from the simulation and found a good agreement with the derived distribution from MaGIXS observation.
coronal heating↗
Role of Small-Scale Impulsive Events in Heating the X-Ray Bright Points of the Quiet Sun
Small-scale impulsive events, known as nanoflares, are thought to be one of the prime candidates that can keep the solar corona hot at its multimillion-Kelvin temperature. Individual nanoflares are difficult to detect with the current generation of instruments; however, their presence can be inferred through indirect techniques such as Differential Emission Measure (DEM) analysis. Here, we employ this technique to investigate the possibility of nanoflare heating of the quiet corona during the minimum of solar cycle 24. We estimate the DEM of disk-integrated quiet Sun and X-ray bright points (XBP) using the observations from XSM on board the Chandrayaan-2 orbiter and AIA on board the Solar Dynamic Observatory. XBPs are found to be the dominant contributor to disk-integrated X-rays, with a radiative flux of ∼2 × 10 5 erg cm −2 s −1 . XBPs consist of small-scale loops associated with bipolar magnetic fields. We simulate such XBP loops using the EBTEL hydrodynamic code. The lengths and magnetic field strengths of these loops are obtained through a potential field extrapolation of the photospheric magnetogram. Each loop is assumed to be heated by random nanoflares having an energy that depends on the loop properties. The composite nanoflare energy distribution for all the loops has a power-law slope close to −2.5. The simulation output is then used to obtain the integrated DEM. It agrees remarkably well with the observed DEM at temperatures above 1 MK, suggesting that the nanoflare distribution, as predicted by our model, can explain the XBP heating.
Solar coronal heating↗