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NASA NTRS1991

Space plasma and its origin at the sun

This paper provides a concise review of the large picture of space plasmas, concentrating on the heliosphere and the origin of the X-ray corona and coronal hole at the sun. It is tentatively suggested that the active X-ray corona is heated primarily by the dissipation of magnetic energy at the spontaneous tangential discontinuities (current sheets) in the confining bipolar magnetic fields of active regions. The discontinuities arise because of the continuous mapping of the footpoints of the field by the photospheric convection. The coronal holes appear to be heated by a combination of Alfven waves, providing the high-speed streams in the solar wind, and the microflaring in the small-scale network fields.

Parker, E. N.↗

DOE OSTI2022

Removing numerical pathologies in a turbulence parameterization through convergence testing

Discretized numerical models of the atmosphere are usually intended to faithfully represent an underlying set of continuous equations, but this necessary condition is violated sometimes by subtle pathologies that have crept into the discretized equations. Such pathologies can introduce undesirable artifacts, such as sawtooth noise, into the model solutions. The presence of these pathologies can be detected by numerical convergence testing. This study employs convergence testing to verify the discretization of the Cloud Layers Unified By Binormals (CLUBB) model of clouds and turbulence. That convergence testing identifies two aspects of CLUBB's equation set that contribute to undesirable noise in the solutions. First, numerical limiters (i.e. clipping) used by CLUBB introduce discontinuities or slope discontinuities in model fields. Second, this noise can be amplified by an advective term in CLUBB's background diffusion. Smoothing the limiters and removing the advective component of the background diffusion reduces the noise and restores the expected first-order convergence in CLUBB's solutions. These model reformulations improve the results at coarser, near-operational grid spacing and time step in cumulus cloud and dry turbulence tests. In addition, convergence testing is proved to be a valuable tool for detecting pathologies, including unintended discontinuities and grid dependence, in the model equation set.

Mathematics and Computing, Geosciences↗

NASA NTRS1986

Equilibrium of magnetic fields with arbitrary interweaving of the lines of force. I - Discontinuities in the torsion

Consideration is given to the static force-free equilibrium of a magnetic field in which all of the lines of force connect without knotting between parallel planes. The field is formed by continuous deformation from an initial uniform field, and is conventiently described in terms of the scalar function psi, which is the stream function for the incompressible wrapping and interweaving of the lines of force. Local compression and expansion of the lines of force is described in terms of the scalar function Phi. Equilibrium in the field requires satisfaction of two independent equations which cannot be accomplished without the full freedom of both psi and Phi. It is shown that discontinuities in the torsional characteristics of the lines occur when psi is predetermined by an arbitrary pattern. Discontinuities in the winding pattern of the lines can lead to discontinuities in the associated current sheets.

Parker, E. N.↗

DOE OSTI2023

Removing Numerical Pathologies in a Turbulence Parameterization Through Convergence Testing

Abstract Discretized numerical models of the atmosphere are usually intended to faithfully represent an underlying set of continuous equations, but this necessary condition is violated sometimes by subtle pathologies that have crept into the discretized equations. Such pathologies can introduce undesirable artifacts, such as sawtooth noise, into the model solutions. The presence of these pathologies can be detected by numerical convergence testing. This study employs convergence testing to verify the discretization of the Cloud Layers Unified By Binormals (CLUBB) model of clouds and turbulence. That convergence testing identifies two aspects of CLUBB's equation set that contribute to undesirable noise in the solutions. First, numerical limiters (i.e., clipping) used by CLUBB introduce discontinuities or slope discontinuities in model fields. Second, nonlinear artificial diffusion employed for improving numerical stability can introduce unintended small‐scale features into the solution of the model equations. Smoothing the limiters and using linear artificial diffusion reduces the noise and restores the expected first‐order convergence in CLUBB's solutions. These model reformulations enhance our confidence in the trustworthiness of solutions from CLUBB by eliminating the unphysical oscillations in high‐resolution simulations. The improvements in the results at coarser, near‐operational grid spacing and timestep are also seen in cumulus cloud and dry turbulence tests. In addition, convergence testing is proven to be a valuable tool for detecting pathologies, including unintended discontinuities and grid dependence, in the model equation set.

58 GEOSCIENCES↗

NASA NTRS1994

Ulysses field and plasma observations of magnetic holes in the solar wind and their relation to mirror-mode structures

The term 'magnetic hole' has been used to denote isolated intervals when the magnitude of the interplanetary magnetic field drops to a few tenths, or less, of its ambient value for a time that corresponds to a linear dimension of tens to a few hundreds of proton gyro-radii. Data obtained by the Ulysses magnetometer and solar wind anlayzer have been combined to study the properties of such magnetic holes in the solar wind between 1 AU and 5.4 AU and to 23 deg south latitude. In order to avoid confusion with decreases in field strength at interplanetary discontinuities, the study has focused on linear holes across which the field direction changed by less than 5 deg. The holes occurred preferentially, but not without exception, in the interaction regions on the leading edges of high-speed solar wind streams. Although the plasma surrounding the holes was generally stable against the mirror instability, there are indications that the holes may have been remnants of mirror-mode structures created upstream of the points of observation. Those indications include the following: (1) For the few holes for which proton of alpha-particle pressure could be measured inside the hole, the ion thermal pressure was always greater than in the plasma adjacent to the holes. (2) The plasma surrounding many of the holes was marginally stable for the mirror mode, while the plasma environment of all holes was significantly closer to mirror instability than was the average solar wind. (3) The plasma containing trains of closely spaced holes was closer to mirror instability than was the plasma containing isolated holes. (4) The near-hole plasma had much higher ion beta (ratio of thermal to magnetic pressure) than did the average solar wind. (5) Near the holes, T(sub perp)/T(sub parallel) tended to be either greater than 1 or larger than in the average wind. (6) The proton and alpha-particle distribution functions measured inside the holes occasionally exhibited the flattened phase-space-density contoures in nu(sub perp)/nu(sub parallel) space found in some numerical simulations of the mirror instability.

Winterhalter, Daniel↗

DOE OSTI2017

The twist of the draped interstellar magnetic field ahead of the heliopause: a magnetic reconnection driven rotational discontinuity

Based on the difference between the orientation of the interstellar B {sub ISM} and the solar magnetic fields, there was an expectation that the magnetic field direction would rotate dramatically across the heliopause (HP). However, the Voyager 1 spacecraft measured very little rotation across the HP. Previously, we showed that the B {sub ISM} twists as it approaches the HP and acquires a strong T component (east–west). Here, we establish that reconnection in the eastern flank of the heliosphere is responsible for the twist. On the eastern flank the solar magnetic field has twisted into the positive N direction and reconnects with the southward pointing component of the B {sub ISM}. Reconnection drives a rotational discontinuity (RD) that twists the B {sub ISM} into the −T direction and propagates upstream in the interstellar medium toward the nose. The consequence is that the N component of B {sub ISM} is reduced in a finite width band upstream of the HP. Voyager 1 currently measures angles (δ=sin{sup −1}(B{sub N}/B)) close to solar values. We present MHD simulations to support this scenario, suppressing reconnection in the nose region while allowing it in the flanks, consistent with recent ideas about reconnection suppression from diamagnetic drifts. The jump in plasma β (the plasma to magnetic pressure) across the nose of HP is much greater than in the flanks because the heliosheath β is greater there than in the flanks. Large-scale reconnection is therefore suppressed in the nose but not at the flanks. Simulation data suggest that B {sub ISM} will return to its pristine value 10–15 au past the HP.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

Photon topology

The topology of photons in vacuum is interesting because there are no photons with k = 0, creating a hole in momentum space. We show that while the set of all photons forms a trivial vector bundle $γ$ over this momentum space, the R and L photons form topologically nontrivial subbundles $γ±$ with first Chern numbers ∓2. In contrast, $γ$ has no linearly polarized subbundles, and there is no Chern number associated with linear polarizations. It is a known difficulty that the standard version of Wigner’s little group method produces singular representations of the Poincaré group for massless particles. By considering representations of the Poincaré group on vector bundles we obtain a version of Wigner’s little group method for massless particles which avoids these singularities. Here we show that any massless bundle representation of the Poincaré group can be canonically decomposed into irreducible bundle representations labeled by helicity, which in turn can be associated to smooth irreducible Hilbert space representations. This proves that the R and L photons are globally well defined as particles and that the photon wave function can be uniquely split into R and L components. This formalism offers a method of quantizing the electromagnetic field without invoking discontinuous polarization vectors as in the traditional scheme. We also demonstrate that the spin-Chern number of photons is not a purely topological quantity. Lastly, there has been an extended debate on whether photon angular momentum can be split into spin and orbital parts. Our work explains the precise issues that prevent this splitting. Photons do not admit a spin operator; instead, the angular momentum associated with photons’ internal degree of freedom is described by a helicity-induced subalgebra corresponding to the translational symmetry of $γ$.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2022

A multi-resolution approach to hydraulic fracture simulation

Abstract We present a multi-resolution approach for constructing model-based simulations of hydraulic fracturing, wherein flow through porous media is coupled with fluid-driven fracture. The approach consists of a hybrid scheme that couples a discrete crack representation in a global domain to a phase-field representation in a local subdomain near the crack tip. The multi-resolution approach addresses issues such as the computational expense of accurate hydraulic fracture simulations and the difficulties associated with reconstructing crack apertures from diffuse fracture representations. In the global domain, a coupled system of equations for displacements and pressures is considered. The crack geometry is assumed to be fixed and the displacement field is enriched with discontinuous functions. Around the crack tips in the local subdomains, phase-field sub-problems are instantiated on the fly to propagate fractures in arbitrary, mesh independent directions. The governing equations and fields in the global and local domains are approximated using a combination of finite-volume and finite element discretizations. The efficacy of the method is illustrated through various benchmark problems in hydraulic fracturing, as well as a new study of fluid-driven crack growth around a stiff inclusion.

58 GEOSCIENCES↗

DOE OSTI2014

The onset of massive star formation: The evolution of temperature and density structure in an infrared dark cloud

We present new NH{sub 3} (1, 1), (2, 2), and (4, 4) observations from the Karl G. Jansky Very Large Array compiled with work in the literature to explore the range of conditions observed in young, massive star-forming regions. To sample the effects of evolution independent from those of distance/resolution, abundance, and large-scale environment, we compare clumps in different evolutionary stages within a single infrared dark cloud (IRDC), G32.02+0.06. We find that the early stages of clustered star formation are characterized by dense, parsec-scale filamentary structures interspersed with complexes of dense cores (<0.1 pc cores clustered in complexes separated by ∼1 pc) with masses from about 10 to 100 M {sub ☉}. The most quiescent core is the most extended while the star forming cores are denser and more compact, showing very similar column density structure before and shortly after the onset of massive star formation, with peak surface densities Σ ≳ 1 g cm{sup –2}. Quiescent cores and filaments show smoothly varying temperatures from 10 to 20 K, rising to over 40 K in star-forming cores. We calculate virial parameters for 16 cores and find that the level of support provided by turbulence is generally insufficient to support them against gravitational collapse ((α{sub vir}) ∼ 0.6). The star-forming filaments show smooth velocity fields, punctuated by discontinuities at the sites of active star formation. We discuss the massive molecular filament (M ∼ 10{sup 5} M {sub ☉}, length >60 pc) hosting the IRDC, hypothesizing that it may have been shaped by previous generations of massive stars.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS1972

Energy Distributions and spectra of Orion B stars

New MK spectral types and energy distributions are presented for B stars in Orion for which far ultraviolet flux excesses have recently been discovered. Significant differences between HD spectral energy distributions show the Orion late B stars to have smaller Balmer discontinuities than do field stars of the same spectral types. For the late B stars, these effects cause the 1500 A fluxes to be under-estimated by approximately 0.5 mag. No comparable systematic effects were found for the early B stars.

Schild, R. E.↗

NASA NTRS1981

Numerical Boundary Condition Procedures

Topics include numerical procedures for treating inflow and outflow boundaries, steady and unsteady discontinuous surfaces, far field boundaries, and multiblock grids. In addition, the effects of numerical boundary approximations on stability, accuracy, and convergence rate of the numerical solution are discussed.

Source record↗

NASA NTRS1988

The origins of the stellar corona

A critical review is presented of present observational facts and theoretical developments related to the causes of the active X-ray corona and to coronal holes in the sun and other late-type stars. Observations indicate that the active X-ray corona represents a superposition of large numbers of nanoflares. Presumably individual nanoflares occur at the many small tangential discontinuities in the field. Nothing about the active corona can be asserted with scientific confidence until the Fourier spectrum of the motions of the magnetic fibrils at the photosphere has been determined observationally.

Parker, E. N.↗

NASA NTRS1996

Approximate Analysis for Interlaminar Stresses in Composite Structures with Thickness Discontinuities

An efficient, approximate analysis for calculating complete three-dimensional stress fields near regions of geometric discontinuities in laminated composite structures is presented. An approximate three-dimensional local analysis is used to determine the detailed local response due to far-field stresses obtained from a global two-dimensional analysis. The stress results from the global analysis are used as traction boundary conditions for the local analysis. A generalized plane deformation assumption is made in the local analysis to reduce the solution domain to two dimensions. This assumption allows out-of-plane deformation to occur. The local analysis is based on the principle of minimum complementary energy and uses statically admissible stress functions that have an assumed through-the-thickness distribution. Examples are presented to illustrate the accuracy and computational efficiency of the local analysis. Comparisons of the results of the present local analysis with the corresponding results obtained from a finite element analysis and from an elasticity solution are presented. These results indicate that the present local analysis predicts the stress field accurately. Computer execution-times are also presented. The demonstrated accuracy and computational efficiency of the analysis make it well suited for parametric and design studies.

Rose, Cheryl A.↗

NASA NTRS1989

The structure of rotational discontinuities

This study examines the structures of a set of rotational discontinuities detected in the solar wind by the ISEE-3 spacecraft. It is found that the complexity of the structure increases as the angle theta between the propagation vector k and the magnetic field decreases. For rotational discontinuities that propagate at a large angle to the field with an ion (left-hand) sense of rotation, the magnetic hodograms tend to be flattened, in agreement with prior numerical simulations. When theta is large, angular 'overshoots' are often observed at one or both ends of the discontinuity. When the propagation is nearly parallel to the field (when theta is small), many different types of structure are seen, ranging from straight lines, to S-shaped curves, to complex, disorganized shapes.

Neugebauer, M.↗

NASA NTRSDate not supplied

Flare Ribbon Signatures of Plasmoids

Solar flares are explosive space weather events that rapidly convert stored magnetic energy into bulk motion, plasma heating, and particle acceleration. Understanding the structure and dynamics of the magnetic reconnection that powers flares is critical for predicting the energy release. In particular, the amount of energy transferred to energetic particles is thought to be highly dependent on whether the reconnection is primarily turbulent (e.g., plasmoid dominated) or instead laminar. We present new high-resolution MHD simulations of three-dimensional reconnection in an eruptive flare and compare the results to recent data. Although flare reconnection is challenging to observe directly in the corona, highly detailed constraints on its dynamics can be obtained from observations of flare ribbons that track the chromospheric footpoints of newly reconnected field lines. The analogues of flare ribbons in our simulations are identified by tracking discontinuous changes in field-line magnetic connectivity due to the reconnection. In our highest-resolution calculations, we find that these ribbon analogues are highly structured and exhibit many ‘whorl’ patterns that are linked to turbulent plasmoids in the reconnecting current sheet. Such flare ribbon fine structure therefore reveals crucial information about the fundamental turbulent vs. laminar nature of the reconnection. Plasmoid-driven particle acceleration models would therefore predict co-location of energetic particle signatures with plasmoid-associated ribbon fine structure.

J T Dahlin↗

NASA NTRSDate not supplied

Flare Ribbon Signatures of Reconnection Plasmoids

Solar flares are explosive space weather events that rapidly convert stored magnetic energy into bulk motion, plasma heating, and particle acceleration. Understanding the structure and dynamics of the magnetic reconnection that powers flares is critical for predicting the energy release. In particular, the amount of energy transferred to energetic particles is thought to be highly dependent on whether the reconnection is primarily turbulent (e.g., plasmoid dominated) or instead laminar. We present high-resolution MHD simulations of three-dimensional reconnection in an eruptive flare and compare the results to recent data. Although flare reconnection is challenging to observe directly in the corona, highly detailed constraints on its dynamics can be obtained from observations of flare ribbons that track the chromospheric footpoints of newly reconnected field lines. The analogues of flare ribbons in our simulations are identified by tracking discontinuous changes in field-line magnetic connectivity due to the reconnection. In our highest-resolution calculations, we find that these ribbon analogues are highly structured and exhibit many ‘whorl’ patterns that are linked to turbulent plasmoids in the reconnecting current sheet. Flare ribbon fine structure therefore reveals crucial information about the fundamental turbulent vs. laminar nature of the reconnection. We discuss the implications of these results for understanding reconnection-driven energy release throughout the heliosphere.

J. T. Dahlin↗

NASA NTRS1973

Shock system of February 2, 1969

The shock system observed in the solar wind by Pioneer 9 and Ogo 5 on Feb. 2, 1969, consisted of the following major discontinuities: a forward slow shock; a forward fast shock; a tangential discontinuity at which the density dropped sharply and the flow direction changed; a tangential discontinuity at which the magnetic field strength jumped to an unusually high value; two closely spaced tangential discontinuities that bracketed a region of even greater field strength and that fronted a region of very cool, very dense, helium-enriched plasma; a reverse fast shock of low Mach number; and a second reverse fast shock of very low Mach number. The event had aspects of both corotating and flare-induced shock systems; it is suggested that the source of the disturbances was a flare occurring at or near an M region.

Unti, T.↗

NASA NTRS1987

A boundary layer model for magnetospheric substorms

An alternative framework for understanding magnetospheric substorm activity is presented. It is argued that observations of magnetic field and plasma flow variations in the magnetotail can be explained in terms of the passage of the plasma sheet boundary layer over the satellite detecting the tail signatures. It is shown that field-aligned currents and particle acceleration processes on magnetic field lines threading the ionospheric Harang discontinuity lead to the distinctive particle and field signatures observed in the magnetotail during substorms. It is demonstrated that edge effects of field-aligned currents associated with the westward traveling surge can lead to the negative B(z) perturbations observed in the tail that are presently attributed to observations made on the anti-earthward side of a near-earth neutral line. Finally, it is shown that the model can provide a physical explanation of both the driven system and the loading-unloading system whose combined effects provide the observed substorm perturbation pattern in the magnetosphere and ionosphere.

Rostoker, Gordon↗