Parker's Theory Research Articles

Topological nature of the Parker magnetostatic theorem

The two-plate initial boundary-value problem of Parker is reviewed, treating the relaxation of a 3D magnetic field prescribed with an arbitrary topology to a terminal force-free field in a cold, viscous, electrically perfect fluid conductor. Anchored by their foot-points at the perfectly conducting rigid plates, the relaxing field preserves its topology. The Parker magnetostatic theorem states that for most prescribed field topologies, the terminal field must embed current sheets. The elements of this theorem are reviewed and analyzed to relate this initial boundary-value problem to (i) the variational problem for a force-free field of a given topology and (ii) the direct construction of a force-free field in terms of its pair of Euler flux functions. New insights and understanding are presented on the theorem as the compelling basis of the Parker theory of solar coronal heating.

Continuous synthesis of nickel/cobalt/manganese hydroxide microparticles in Taylor–Couette reactors

Taylor–Couette flow based reactors have been used to prepare nickel/cobalt/manganese hydroxide particles. The experiments performed in small volume reactors at the laboratory level have yielded satisfactory results. However, to commercialize Taylor–Couette reactors, parametric studies considering various operating conditions must be conducted. In this work, the synthesis of nickel/cobalt/manganese hydroxides was examined in two reactors with different size and operating conditions. Specifically, the effects of the RPM and pH were investigated by measuring the mean diameter and tap density after the saturation of the particle growth in the given reactors. The results were used to define the design criteria to determine the mean diameter and tap density by comparing the experimental results with the results reported in the literature. Furthermore, the correlation between the shear rate and particle size was analyzed to predict the particle growth in scale-up reactors based on Parker's theory.

TRUCKS AS INSPIRATION FOR BABY BED CREATION

Baby bed is one type of furniture which the existence is very necessary to meet the needs of the community, especially in family groups who have children / babies. The idea of creating the work is divided into two problem formulations, namely, how to design a baby bed in the form of a truck with decorative elements of Punakawan and how to visualize the design into works of art. The approach used is Dewitt H. Parker's aesthetic theory. The method of creation includes 3 stages, namely: the exploration stage, the design stage, and the embodiment stage. The baby bed produced in this artistic research is a work that has functional and aesthetic values with reference to the character of Punakawan. The symbolic value contains the exemplary teachings of Punakawan become a substance in this baby bed artwork. These baby beds are created creatively and innovatively for the renewal of baby bed shapes.

PENERAPAN SURAT PEMBERITAHUAN ELEKTRONIK (E-SPT) MASA PPN TERHADAP PEMENUHAN PEMERIKSAAN PADA WAJIB PAJAK BADAN (STUDI KASUS KPP MADYAMAKASSAR)

The purpose of this study is to answer the problem of how to implement an online service system, namely the application of electronic notification letters (E-SPT) which is carried out on tax audit compliance in accordance with Parker's theory (2011: 1) in the form of optimal information or optimal information services such as availability. , easy to understand, relevant, useful, timely, reliable, accurate and consistent. The basis of this research is a qualitative descriptive type of research. The techniques used in data collection are field observation, in-depth interviews, and documentation. Then the data and interview results obtained were analyzed descriptively qualitatively. From the results of the research conducted, it shows that there is data stating that the process of implementing an Online-based System for the fulfillment of the inspection has been implemented properly, it is proven that there is a very synchronous answer between service informants and tax audit informants and shows consistency by requiring all taxpayers to be registered at KPP Madya Makassar uses a sustainable online system. Therefore, in-depth socialization is needed so that all parties served and the parties served can optimize the online system.

What it takes to get proactive: An integrative multilevel model of the antecedents of personal initiative.

Building upon and extending Parker, Bindl, and Strauss's (2010) theory of proactive motivation, we develop an integrated, multilevel model to examine how contextual factors shape employees' proactive motivational states and, through these proactive motivational states, influence their personal initiative behavior. Using data from a sample of hotels collected from 3 sources and over 2 time periods, we show that establishment-level initiative-enhancing human resource management (HRM) systems were positively related to departmental initiative climate, which was positively related to employee personal initiative through employee role-breadth self-efficacy. Further, department-level empowering leadership was positively related to initiative climate only when initiative-enhancing HRM systems were low. These findings offer interesting implications for research on personal initiative and for the management of employee proactivity in organizations. (PsycINFO Database Record

Magnetic reconnection: from the Sweet–Parker model to stochastic plasmoid chains

Magnetic reconnection is the topological reconfiguration of the magnetic field in a plasma, accompanied by the violent release of energy and particle acceleration. Reconnection is as ubiquitous as plasmas themselves, with solar flares perhaps the most popular example. Other fascinating processes where reconnection plays a key role include the magnetic dynamo, geomagnetic storms and the sawtooth crash in tokamaks.Over the last few years, the theoretical understanding of magnetic reconnection in large-scale fluid systems has undergone a major paradigm shift. The steady-state model of reconnection described by the famous Sweet–Parker (SP) theory, which dominated the field for ∼50 years, has been replaced with an essentially time-dependent, bursty picture of the reconnection layer, dominated by the continuous formation and ejection of multiple secondary islands (plasmoids). Whereas in the SP model reconnection was predicted to be slow, a major implication of this new paradigm is that reconnection in fluid systems is fast (i.e. independent of the Lundquist number), provided that the system is large enough. This conceptual shift hinges on the realization that SP-like current layers are violently unstable to the plasmoid (tearing) instability—implying, therefore, that such current sheets are super-critically unstable and thus can never form in the first place. This suggests that the formation of a current sheet and the subsequent reconnection process cannot be decoupled, as is commonly assumed.This paper provides an introductory-level overview of the recent developments in reconnection theory and simulations that led to this essentially new framework. We briefly discuss the role played by the plasmoid instability in selected applications, and describe some of the outstanding challenges that remain at the frontier of this subject. Amongst these are the analytical and numerical extension of the plasmoid instability to (i) 3D and (ii) non-magnetohydrodynamics (MHD) regimes. New results are reported in both cases.

An overview of recent physics results from NSTX

The National Spherical Torus Experiment (NSTX) is currently being upgraded to operate at twice the toroidal field and plasma current (up to 1 T and 2 MA), with a second, more tangentially aimed neutral beam (NB) for current and rotation control, allowing for pulse lengths up to 5 s. Recent NSTX physics analyses have addressed topics that will allow NSTX-Upgrade to achieve the research goals critical to a Fusion Nuclear Science Facility. These include producing stable, 100% non-inductive operation in high-performance plasmas, assessing plasma–material interface (PMI) solutions to handle the high heat loads expected in the next-step devices and exploring the unique spherical torus (ST) parameter regimes to advance predictive capability. Non-inductive operation and current profile control in NSTX-U will be facilitated by co-axial helicity injection (CHI) as well as radio frequency (RF) and NB heating. CHI studies using NIMROD indicate that the reconnection process is consistent with the 2D Sweet–Parker theory. Full-wave AORSA simulations show that RF power losses in the scrape-off layer (SOL) increase significantly for both NSTX and NSTX-U when the launched waves propagate in the SOL. Toroidal Alfvén eigenmode avalanches and higher frequency Alfvén eigenmodes can affect NB-driven current through energy loss and redistribution of fast ions. The inclusion of rotation and kinetic resonances, which depend on collisionality, is necessary for predicting experimental stability thresholds of fast growing ideal wall and resistive wall modes. Neutral beams and neoclassical toroidal viscosity generated from applied 3D fields can be used as actuators to produce rotation profiles optimized for global stability. DEGAS-2 has been used to study the dependence of gas penetration on SOL temperatures and densities for the MGI system being implemented on the Upgrade for disruption mitigation. PMI studies have focused on the effect of ELMs and 3D fields on plasma detachment and heat flux handling. Simulations indicate that snowflake and impurity seeded radiative divertors are candidates for heat flux mitigation in NSTX-U. Studies of lithium evaporation on graphite surfaces indicate that lithium increases oxygen surface concentrations on graphite, and deuterium–oxygen affinity, which increases deuterium pumping and reduces recycling. In situ and test-stand experiments of lithiated graphite and molybdenum indicate temperature-enhanced sputtering, although that test-stand studies also show the potential for heat flux reduction through lithium vapour shielding. Non-linear gyro kinetic simulations have indicated that ion transport can be enhanced by a shear-flow instability, and that non-local effects are necessary to explain the observed rapid changes in plasma turbulence. Predictive simulations have shown agreement between a microtearing-based reduced transport model and the measured electron temperatures in a microtearing unstable regime. Two Alfvén eigenmode-driven fast ion transport models have been developed and successfully benchmarked against NSTX data. Upgrade construction is moving on schedule with initial physics research operation of NSTX-U planned for mid-2015.

THE SOLAR CHROMOSPHERE OBSERVED AT 1 Hz AND 0.″2 RESOLUTION

We recently reported extremely rapid changes in chromospheric fine structure observed using the IBIS instrument in the red wing of H alpha. Here, we examine data obtained during the same observing run (August 7 2010), of a mature active region NOAA 11094. We analyze more IBIS data including wavelength scans and data from the Solar Dynamics Observatory, all from within a 30 minute interval. Using a slab radiative transfer model, we investigate the physical nature of fibrils in terms of tube-like vs. sheet-like structures. Principal Component Analysis shows that the very rapid H alpha variations in the line wings depend mostly on changes of line width and line shift, but for Ca II 854.2 the variations are dominated by changes in column densities. The tube model must be rejected for a small but significant class of fibrils undergoing very rapid changes. If our wing data arise from the same structures leading to "type II spicules", our analysis calls into question much recent work. Instead the data do not reject the hypothesis that some fibrils are optical superpositions of plasma collected into sheets. We review how Parker's theory of tangential discontinuities naturally leads to plasma collecting into sheets, and show that the sheet picture is falsifiable. Chromospheric fine structures seem to be populated by both tubes and sheets. We assess the merits of spectral imaging versus slit spectroscopy for future studies.

NEWTONIAN AND NON-NEWTONIAN MAGNETIC-FIELD RELAXATIONS IN SOLAR-CORONAL MHD

This paper treats the relaxation of a magnetic field into a minimum-energy force-free state in a cold (pressure-less) viscous fluid, under the frozen-in condition of perfect electrical conductivity and letting the viscosity-dissipated energy be completely lost. A non-Newtonian fluid in popular use is studied in relation to the Newtonian viscous fluid, as two alternative numerical means to (1) construct force-free fields representing solar coronal structures in realistic geometry and (2) investigate the Parker theory of spontaneous formation of electric current sheets as a basic MHD process. Faraday's induction equation imposes an independent condition on the fluid velocity at rigid, perfectly conducting boundaries. This boundary condition is quite compatible with Newtonian mechanics but not with the non-Newtonian fluid model where velocity is equated to the Lorentz force with a free, positive multiplicative-factor. This defining property gives rise to unphysical or artificial singularities not previously known that are completely distinct from the physically admissible singularities representing the current sheets of the Parker theory. In particular, the non-Newtonian fluid takes a magnetic field with neutral points from any one of a continuum of initial states into an unphysical state instead of the proper force-free end-state accessible by Newtonian relaxation. The validity of previously published MHD results based on this non-Newtonian fluid, including some counterclaims against the Parker theory, is dubious. Investigating the Parker theory requires numerical relaxation models capable of anticipating and accurately describing inevitable current-sheet singularities. By including a weak resistivity to dissipate the inevitable current sheets as they form, the field can change topology intermittently to seek a terminal force-free state free of singularities. The minimum-energy state of this more complete model corresponds to the long-lived relaxed structures in the corona.

On spontaneous formation of current sheets: Untwisted magnetic fields

This is a study of the spontaneous formation of electric current sheets in an incompressible viscous fluid with perfect electrical conductivity, governed by the magnetohydrodynamic Navier–Stokes equations. Numerical solutions to two initial value problems are presented for a three-dimensional, periodic, untwisted magnetic field evolving, with no change in magnetic topology under the frozen-in condition and at characteristic fluid Reynolds numbers of the order of 500, from a nonequilibrium initial state with the fluid at rest. The evolution converts magnetic free energy into kinetic energy to be all dissipated away by viscosity so that the field settles into a minimum-energy, static equilibrium. The solutions demonstrate that, as a consequence of the frozen-in condition, current sheets must form during the evolution despite the geometric simplicity of the prescribed initial fields. In addition to the current sheets associated with magnetic neutral points and field reversal layers, other sheets not associated with such magnetic features are also in evidence. These current sheets form on magnetic flux surfaces. This property is used to achieve a high degree of the frozen-in condition in the simulations, by describing the magnetic field entirely in terms of the advection of its flux surfaces and integrating the resulting governing equations with a customized version of a general-purpose high-resolution (viz., nonoscillatory) hydrodynamical simulation code EULAG [J. M. Prusa et al., Comput. Fluids 37, 1193 (2008)]. Incompressibility imposes the additional global constraint that the flux surfaces must evolve with no change in the spatial volumes they enclose. In this approach, current sheet formation is demonstrated graphically by the progressive pressing together of suitably selected flux surfaces until their separation has diminished below the minimal resolved distance on a fixed grid. The frozen-in condition then fails in the simulation as the field reconnects through an effecting numerical resistivity. The principal results are related to the Parker theory of current-sheet formation and dissipation in the solar corona.

THE TOPOLOGICAL CHANGES OF SOLAR CORONAL MAGNETIC FIELDS. III. RECONNECTED FIELD TOPOLOGY PRODUCED BY CURRENT-SHEET DISSIPATION

In this paper, the third in a series of papers on topological changes of magnetic fields, we study how the dissipation of an initial current sheet (CS) in a closed three-dimensional (3D) field affects the field topology. The initial field is everywhere potential except at the location of the CS which is in macroscopic equilibrium under the condition of perfect conductivity. In the physical world of extremely high, but finite, conductivity, the CS dissipates and the field seeks a new equilibrium state in the form of an everywhere potential field since the initial field is everywhere untwisted. Our semi-analytical study indicates that the dissipation of the single initial CS must induce formation of additional CSs in extensive parts of the magnetic volume. The subsequent dissipation of these other sheets brings about topological changes by magnetic reconnection in order for the global field to become potential. In 2D fields, the magnetic reconnection due to the dissipation of a CS is limited to the magnetic vicinity of the dissipating sheet. Thus, the consequence of CS dissipation is physically and topologically quite different in 2D and 3D fields. A discussion of this result is given in general relation to the Parker theory of spontaneous CSs and heating in the solar corona and solar flares.

The Craig – Sneyd Analytic Solutions to the Parker Problem

This paper follows up on the conclusion by Craig and Sneyd (2005) that the solutions to a linearized magnetostatic problem are counterexamples to the magnetostatic model of Parker (1972), demonstrating a general absence of continuous equilibrium for a magnetic field with an arbitrarily prescribed topology. The analysis presented here shows that Craig and Sneyd had incorrectly rejected an important subset of those solutions in a misunderstanding of the Parker model. The complete set of solutions when correctly interpreted is, in fact, physically consistent with the Parker model. A general discussion of the Parker theory of spontaneous current sheets is given.

Corona-like atmospheric escape from KBOs: I. Gas dynamics

We show that for low temperatures ( T ∼ 30 K ) and small, but non-negligible, gravitational fields the hydrodynamic escape of gas can be treated by Parker's theory of coronal expansion [Parker, E.N., 1963. Interplanetary Dynamical Processes. Interscience Publishers, New York]. We apply this theory to gas escape from Kuiper belt objects. We derive limits on the density and radius of the bodies for which this theory is applicable, and show how the flow depends on the mean molecular weight and internal degrees of freedom of the gas molecules. We use these results to explain the CH 4 dichotomy seen on KBOs [Schaller, E.L., Brown, M.E., 2007. Astrophys. J., 659, L61–L64].

THE TOPOLOGICAL CHANGES OF SOLAR CORONAL MAGNETIC FIELDS. I. SPONTANEOUS CURRENT SHEETS IN THREE-DIMENSIONAL FIELDS

We present mathematical models to demonstrate the inevitability of current-sheet formation in a cylindrical magnetic field governed by the ideal hydromagnetic induction equation, as described by the Parker theory. This process, central to the heating of the solar corona, is radically different in fully three-dimensional fields as compared with two-dimensional fields. Magnetic neutral points or separatrix flux surfaces are necessary for sheet formation in two-dimensional fields. In fully three-dimensional fields, current sheets form readily even in the complete absence of neutral points and separatrix surfaces, and these sheets can form densely throughout the field in response to changes in the magnetic volume. This general result is established for cylindrical fields that are topologically untwisted, including the first direct demonstration of sheet formation in the absence of any magnetic neutral point. We discuss simple implications of this basic result for solar flares and coronal heating. In subsequent papers, we apply our result to coronal mass ejections and solar flares.

On the possibility of electric-current sheets in dense formation

This is a mathematical study of the formation of tangential discontinuities, or current sheets, in a magnetic field evolving in an electrically perfectly conducting fluid in response to deformation of its domain, an effect first treated by Hahm and Kulsrud [Phys. Fluids 28, 2412 (1985)]. Explicit examples are presented of three-dimensional, untwisted fields, anchored to the boundary, that cannot assume a force-free state in the absence of current sheets. The underlying physics of this process is as described by the Parker theory of spontaneous current sheets, namely, that for most continuous magnetic fields in complex three-dimensional geometry, there is an incompatibility between the preservation of field topology and point-by-point force balance to achieve equilibrium. This incompatibility is removed through discontinuous plasma displacements that produce magnetic tangential discontinuities. In contrast to the twisted magnetic fields central to the Parker theory, fixing the connectivity between the anchored magnetic footpoints alone is sufficient to lead to current-sheet formation in untwisted fields. This mode of sheet formation may produce spatially dense multitudes of sheets to heat a plasma throughout its macroscopic volume such as implied by several phenomena in the solar corona.

The Topological Nature of Boundary Value Problems for Force‐Free Magnetic Fields

The difficulties of constructing a three-dimensional, continuous force-free magnetic field in the solar corona are investigated through a boundary value problem posed for the unbounded domain external to a unit sphere. The normal field component Bn and the boundary value αb of the twist function α on the unit sphere, combined with the demand for a vanishing field at infinity, do constitute sufficient conditions for determining a solution if it exists, but Bn and αb cannot be prescribed independently. An exhaustive classification of the admissible (Bn,αb)-pairs is developed, using the topological properties of the α flux surfaces implied by their footprints described by the constant-αb curves on the unit sphere. The incompatibilities arising from boundary conditions contradicting the field equations are distinguished from the interesting one of (Bn,αb) being, in principle, admissible but requiring a weak solution describing a force-free field containing inevitable magnetic tangential discontinuities. This particular incompatibility relates the boundary value problem to the Parker theory of spontaneous current sheets in magnetic fields embedded in electrically perfectly conducting fluids. Our investigation strategically skirts around some important but formidable mathematical problems to arrive at physically definite conclusions and insights on the construction of force-free fields, both in the practical task of modeling coronal magnetic fields with magnetopolarimetric data and in the basic understanding of the Parker theory. Two specific demonstrations of (Bn,αb) are given to illustrate circumstances under which a continuous solution to the boundary value may or may not exist.

The power of loving humane care in nursing

This study aimed to develop an approach about the power of humane care within the concept of nursing through the building of a theoretical structure. Spiegelberg's methodology was used to seek the meaning of the power of humane care for new nurses and for patients. The resulting theoretical structure is based on Parker's theory of power, Patterson and Zderad's humane care, Watson's theories and Larrañaga's concept of love. The elements of this structure are: the nurse, the ill or healthy person, the environment and nursing, all bound by an affectionate humane care. The final reflection was that all of them are included within the technical-scientific paradigm of modernity and that the patients hope to be care for by humane nurses.

Spontaneous Current Sheets in an Ideal Hydromagnetic Fluid

Parker's theory of spontaneous current sheets, or magnetic tangential discontinuities, in electrically perfectly conducting fluids is demonstrated for globally untwisted magnetic fields in the Chandrasekhar-Kendall representation. All the three-dimensional, globally untwisted fields sharing the same flux distribution, fixed at the rigid boundary of the domain, span an infinity of different field topologies, each preserved in a field under the frozen-in condition. The general result is obtained and illustrated that only one of these topologies allows a field to relax into an everywhere continuous force-free state, namely, the potential field uniquely determined by the boundary flux distribution. All other topologies require the field to find a force-free state containing inevitable tangential magnetic discontinuities. This result extends a class of two-dimensional demonstrations of the Parker theory to three dimensions. A field of a fixed topology and boundary flux distribution can be in a continuous state in one equilibrium but may have to contain inevitable tangential discontinuities on transition to another equilibrium. This property, demonstrated here with untwisted fields, is probably the hydromagnetic origin of flares occurring in the course of slow evolution in the solar corona.

The Parker Problem and the Theory of Coronal Heating

To illustrate his theory of coronal heating, Parker initially considers the problem of disturbing a homogeneous vertical magnetic field that is line-tied across two infinite horizontal surfaces. It is argued that, in the absence of resistive effects, any perturbed equilibrium must be independent of z. As a result random footpoint perturbations give rise to magnetic singularities, which generate strong Ohmic heating in the case of resistive plasmas. More recently these ideas have been formalized in terms of a magneto-static theorem but no formal proof has been provided. In this paper we investigate the Parker hypothesis by formulating the problem in terms of the fluid displacement. We find that, contrary to Parker's assertion, well-defined solutions for arbitrary compressibility can be constructed which possess non-trivial z-dependence. In particular, an analytic treatment shows that small-amplitude Fourier disturbances violate the symmetry ∂ z = 0 for both compact and non-compact regions of the (x, y) plane. Magnetic relaxation experiments at various levels of gas pressure confirm the existence and stability of the Fourier mode solutions. More general footpoint displacements that include appreciable shear and twist are also shown to relax to well-defined non-singular equilibria. The implications for Parker's theory of coronal heating are discussed.

A uniqueness result for a simple force-free magnetic field submitted to a topological constraint

A proof is given of the following statement: if B is a smooth force-free magnetic field contained in a cylindrical domain of axis parallel toand of star-shaped cross-section, and if B is topologically equivalent to the uniform field B0 = B0 ˆ, then B = B0. In addition to being a very first step in the general study of the uniqueness of a magnetostatic equilibrium subject to a topological constraint, this result has a direct relevance to the approach recently developed by Ng & Bhattacharjee (1998, Phys. Plasma, 5, 4028) to support Parker's theory of current sheets formation in the solar corona.