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Results for “MAGNETOHYDROSTATICS”

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.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1973

On the possibility of constructing a radiative sunspot model in magnetohydrostatic equilibrium.

It is currently believed that it is impossible to construct a radiative sunspot model in magnetohydrostatic equilibrium unless magnetic fields below the surface are excessively large (greater than 100 kG). This belief is based on results obtained using the mixing length theory of convection. We wish to point out that by using a different theory of convection, due to Opik (1950), it is possible to compute a radiative sunspot model in which the field becomes no greater than 9000 G. By applying two boundary conditions (depth of spot equals depth of convection zone, and magnetic field has zero gradient at the base of the spot) we show that a radiative spot has a unique effective temperature for a given Wilson depression.

Mullan, D. J.↗
NASA NTRS1979

Non-force-free solar magnetic fields in magnetohydrostatic equilibrium

The objective of the paper is to examine a class of non-force-free fields analytically. Specifically, magnetic fields in magnetohydrostatic equilibrium with a plasma in a gravitational field are treated in an approximation of two independent variables but three vector components. Spherical coordinates are emphasized, although the formal results for cylindrical and Cartesian coordinates are presented in the appendices. Formal solutions for the magnetic-field components are obtained in terms of the plasma variables, and field line equations are derived. A final equation governing the plasma variables is then obtained. Procedures are developed for analyzing this equation and obtaining sets of self-consistent particular solutions to the governing equations; a number of such sets of solutions are presented. As an example, one solution set is examined, illustrating the application of the results to the analysis of solar observational data.

Comfort, R. H.↗
NASA NTRS1986

A coordinate free description of magnetohydrostatic equilibria

The question what geometrical restrictions are imposed on static magnetic fields by the magnetohydrostatic (MHS) equation is addressed. The general mathematical problem is therefore to determine the solutions of the MHS equations in the corona subject to an arbitrary normal component of the magnetic field at the boundary and arbitrary connectivity. What constraints the MHS equations impose on the geometry of the solutions, expressed in metric tensors, will be determined.

Martens, P. C. H.↗
NASA NTRS1988

The 2-D magnetohydrostatic configurations leading to flares or quiescent filament eruptions

To investigate the cause of flares and quiescent filament eruptions the quasi-static evolution of a magnetohydrostatic (MHS) model was studied. The results lead to a proposal that: the sudden disruption of an active-region filament field configuration and the accompanying flare result from the lack of a neighboring equilibrium state as magnetic shear is increased above the critical value; and a quiescent filament eruption is due to an ideal MHD kink instability of a highly twisted detached flux tube formed by the increase of plasma current flowing along the length of the filament. A numerical solution was developed for the 2-D MHS equation for the self-consistent equilibrium of a filament and overlying coronal magnetic field. Increase of the poloidal current causes increase of magnetic shear. As shear increases past a critical point, there is a discontinuous topological change in the equilibrium configuration. It was proposed that the lack of a neighboring equilibrium triggers a flare. Increase of the axial current results in a detached tube with enough helical twist to be unstable to ideal MHD kink modes. It was proposed that this is the condition for the eruption of a quiescent filament.

An, C.-H.↗
DOE OSTI2025

Metastability of stratified magnetohydrostatic equilibria and their relaxation

Motivated by explosive releases of energy in fusion, space and astrophysical plasmas, we consider the nonlinear stability of stratified magnetohydrodynamic equilibria against two-dimensional interchanges of straight magnetic-flux tubes. We demonstrate that, even within this restricted class of dynamics, the linear stability of an equilibrium does not guarantee its nonlinear stability: equilibria can be metastable. We show that the minimum-energy state accessible to a metastable equilibrium under non-diffusive two-dimensional dynamics can be found by solving a combinatorial optimisation problem. These minimum-energy states are, to good approximation, the final states reached by our simulations of destabilised metastable equilibria for which turbulent mixing is suppressed by viscosity. To predict the result of fully turbulent relaxation, we construct a statistical mechanical theory based on the maximisation of Boltzmann's mixing entropy. This theory is analogous to the Lynden-Bell statistical mechanics of collisionless stellar systems and plasma, and to the Robert–Sommeria–Miller theory of two-dimensional vortex turbulence. Our theory reproduces well the results of our numerical simulations for sufficiently large perturbations to the metastable equilibrium.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

A constrained-transport embedded boundary method for compressible resistive magnetohydrodynamics

Motivated by the increased interest in pulsed-power magneto-inertial fusion devices in recent years, we present a method for implementing an arbitrarily shaped embedded boundary on a Cartesian mesh while solving the equations of compressible resistive magnetohydrodynamics. The method is built around a finite volume formulation of the equations in which a Riemann solver is used to compute fluxes on the faces between grid cells, and a face-centered constrained transport formulation of the induction equation. The small time step problem associated with the cut cells is avoided by always computing fluxes on the faces and edges of the Cartesian mesh. We extend the method to model a moving interface between two materials with different properties using a ghost-fluid approach, and show some preliminary results including shock-wave-driven and magnetically-driven dynamical compressions of magnetohydrostatic equilibria. In conclusion, we present a thorough verification of the method and show that it converges at second order in the absence of discontinuities, and at first order with a discontinuity in material properties.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Stellarator equilibrium axis-expansion to all orders in distance from the axis for arbitrary plasma beta

A systematic theory of the asymptotic expansion of the magnetohydrostatics (MHS) equilibrium in the distance from the magnetic axis is developed to include arbitrary smooth currents near the magnetic axis. Compared with the vacuum and the force-free system, an additional magnetic differential equation must be solved to obtain the pressure-driven currents. It is shown that there exist variables in which the rest of the MHS system closely mimics the vacuum system. Thus, a unified treatment of MHS fields is possible. The mathematical structure of the near-axis expansions to arbitrary order is examined carefully to show that the double-periodicity of physical quantities in a toroidal domain can be satisfied order by order. The essential role played by the leading-order Birkhoff–Gustavson normal form in solving the magnetic differential equations is highlighted. Several explicit examples of vacuum, force-free and MHS equilibrium in different geometries are presented.

Physics↗
DOE OSTI2024

Exploration of the parameter space of quasisymmetric stellarator vacuum fields through adjoint optimisation

Optimising stellarators for quasisymmetry leads to strongly reduced collisional transport and energetic particle losses compared with unoptimised configurations. Although stellarators with precise quasisymmetry have been obtained in the past, it remains unclear how broad the parameter space is where good quasisymmetry may be achieved. We study the range of aspect ratios and rotational transform values for which stellarators with excellent quasisymmetry on the boundary can be obtained. A large number of Fourier harmonics is included in the boundary representation, which is made computationally tractable by the use of adjoint methods to enable fast gradient-based optimisation and by the direct optimisation of vacuum magnetic fields, which converge more robustly compared with solutions from magnetohydrostatics. Several novel configurations are presented, including stellarators with record levels of quasisymmetry on a surface, three field period quasiaxisymmetric stellarators with substantial magnetic shear, and compact quasisymmetric stellarators at low aspect ratios similar to tokamaks.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Characterization of admissible quasisymmetries

We solve ‘half’ the problem of finding three-dimensional quasisymmetric magnetic fields that do not necessarily satisfy magnetohydrostatic force balance. This involves determining which hidden symmetries are admissible as quasisymmetries, and then showing explicitly how to construct quasisymmetric magnetic fields given an admissible symmetry. The admissibility conditions take the form of a system of overdetermined nonlinear partial differential equations involving second derivatives of the symmetry's infinitesimal generator.

Burby, J. W. (ORCID:0000000317727647)↗
DOE OSTI2024

A Novel Method to Train Classification Models for Structure Detection in In Situ Spacecraft Data

We present a method for creating spacecraft-like data which can be used to train Machine Learning (ML) models to detect and classify structures in in situ spacecraft data. First, we use the Grad-Shafranov equation to numerically solve for several magnetohydrostatic equilibria which are variations on a known analytic equilibrium. These equilibria are then used as the initial conditions for Particle-In-Cell simulations in which the structures of interest are observed and labeled. We then take one-dimensional slices through the simulations to replicate what a spacecraft collecting data from the simulation would observe. This sliced data then can be used as training data for the initial training of ML models intended for use on spacecraft data. We demonstrate the method applied to the problem of detecting small-scale plasmoids in the magnetotail, which is important for understanding complex magnetotail reconnection dynamics. The simple 1D classifier we train is able to detect more than 70% of the plasmoid points in the data set but also produces a large number of false positives. Our further work on this example problem is detailed, and further potential uses of the method are discussed.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Verification of the Shafranov shift in free-boundary VMEC, DESC, and SPEC calculations with elliptical geometry

Here, given a set of current-carrying filaments that create a magnetic field with rotating elliptical flux surfaces, we present verification calculations using the VMEC, DESC, and SPEC free-boundary magnetohydrostatic equilibrium codes for both the “vacuum” equilibrium, for which there is no plasma pressure and no plasma currents, and for a non-zero pressure, zero toroidal current equilibrium. For the vacuum case, these codes are quantitatively compared to the magnetic field produced by the coils. For the non-zero pressure case, they are compared to each other. As the stepped pressure profile used in SPEC approaches the continuous profile used in VMEC and DESC, the SPEC magnetic axis approaches the VMEC and DESC axes. To within an error given by the difference between the pressure profiles, the VMEC, DESC, and SPEC calculations give the same pressure-induced geometric shift of the magnetic axis, known as the Shafranov shift.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Periodic Korteweg–de Vries soliton potentials generate quasisymmetric magnetic field strength in a finite plasma- β equilibrium

Quasisymmetry (QS) is a hidden symmetry of the magnetic field strength, B , that enables effective confinement of charged particles in a fully three-dimensional (3D) toroidal plasma equilibrium. Such equilibria are typically modeled by the ideal magnetohydrostatic (MHS) equations. The nonlinear, overdetermined nature of the QS MHS equations severely complicates our understanding of the interplay between 3D shaping, equilibrium properties such as pressure and rotational transform, and B . Progress has been made through expansions near the magnetic axis; however, a more comprehensive theory is desirable. Using a combination of analysis and regression on a large dataset of numerically optimized quasisymmetric stellarators, we demonstrate that there is a hidden lower dimensionality of B on a magnetic flux surface with connections to the theory of periodic solitons. We show that B on a flux surface is determined by three or at most four flux functions, each of which determines a critical value of the derivative of B along the field line. While being consistent with the near-axis models, our results are global and hold even on the last closed flux surface.

Differential geometry↗
NASA NTRS1976

Basic properties of magnetic flux tubes and restrictions on theories of solar activity

It is shown that the mean longitudinal field in a magnetic flux tube is reduced, rather than enhanced, by twisting the tube to form a rope. It is shown that there is no magnetohydrostatic equilibrium when one twisted rope is wound around another. Instead there is rapid line cutting (neutral point annihilation). It is shown that the twisting increases, and the field strength decreases, along a flux tube extending upward through a stratified atmosphere. These facts are at variance with Piddington's (1975) recent suggestion that solar activity is to be understood as the result of flux tubes which are enormously concentrated by twisting, which consist of several twisted ropes wound around each other, and which came untwisted where they emerge through the photosphere.

Parker, E. N.↗
NASA NTRS1978

Magnetohydrodynamics of atmospheric transients. II - Two-dimensional numerical results for a model solar corona

A systematic study of dynamic response of the inner solar corona is made within the context of two-dimensional, time-dependent plane hydromagnetics. The governing equations are written in r-phi coordinates (i.e., in the solar equatorial plane), and numerical solutions are obtained by introducing an impulsive temperature enhancement within a rectangular region (i.e., 'box') in an initially isothermal corona in magnetohydrostatic equilibrium. Effects of the magnetic field configuration are illustrated for initially open (radial) and closed (azimuthal) magnetic fields by comparison with the nonmagnetic response. The channeling or blocking effects by the magnetic fields on the mass motion of solar plasma as the consequence of the evolution of fast and slow mode MHD shock waves are demonstrated. Some physically significant applications of the results, useful for the interpretation of observations, are discussed. It is noted, for example, that coronal transients observed in white light probably occur within essentially radial field topologies.

Wu, S. T.↗
NASA NTRS1979

Formation, support and stability of quiescent prominences

The most prevalent hypotheses and theories that treat the formation and support of quiescent prominences are reviewed, along with current ideas concerning the stability of such prominences. Observational clues to the formation of quiescent prominences are described, condensation of coronal material is examined, and injection mechanisms of prominence formation are considered. Questions pertaining to the support and stability of quiescent prominences are discussed in terms of magnetohydrostatic equilibrium, prominence equilibria, and breakdown of stability conditions.

Tandberg-Hanssen, E.↗