scholarly journals Low-shear three-dimensional equilibria in a periodic cylinder

2019 ◽  
Vol 85 (1) ◽  
Author(s):  
Erin Jaquiery ◽  
Wrick Sengupta
Keyword(s):  
Three Dimensional ◽  
Power Series Expansion ◽  
Flat Torus ◽  
Flux Surface ◽  
Mhd Equilibria ◽  
Convergence Proofs ◽  
Field Lines ◽  
Ideal Magnetohydrodynamic ◽  
Physical Quantities ◽  
Low Shear

We carry out expansions of non-symmetric toroidal ideal magnetohydrodynamic (MHD) equilibria with nested flux surfaces about a periodic cylinder, in which physical quantities are periodic of period$2\unicode[STIX]{x03C0}$in the cylindrical angle$\unicode[STIX]{x1D703}$and$z$. The cross-section of a flux surface at a constant toroidal angle is assumed to be approximately circular, and data are given on the cylindrical flux surface$r=1$. Furthermore, we assume that the magnetic field lines are closed on the lowest-order flux surface, and the magnetic shear is relatively small. We extend earlier work in a flat torus by Weitzner (Phys. Plasmas, vol. 23, 2016, 062512) and demonstrate that a power series expansion can be carried out to all orders using magnetic flux as an expansion parameter. The cylindrical metric introduces certain new features to the expansions compared to the flat torus. However, the basic methodology of dealing with resonance singularities remains the same. The results, even though lacking convergence proofs, once again support the possibility of smooth, low-shear non-symmetric toroidal MHD equilibria.

scholarly journals New classes of three-dimensional ideal-MHD equilibria

1997 ◽  
Vol 57 (2) ◽  
pp. 425-448 ◽  
Author(s):  
R. KAISER ◽  
A. SALAT
Keyword(s):  
Magnetic Field ◽  
Three Dimensional ◽  
Poloidal Magnetic Field ◽  
The Third ◽  
Cylindrical Coordinate ◽  
Mhd Equilibria ◽  
Vacuum Fields ◽  
Free Function ◽  
Field Lines ◽  
Ideal Magnetohydrodynamic

Six ansatzes are investigated for their potential to allow three-dimensional (3D) ideal magnetohydrodynamic (MHD) equilibria. The ansatzes are based on a Clebsch representation for the magnetic field, B=∇H × ∇k, and a ‘generalized Clebsch representation’, B=∇×(∇K × ∇k), with ∇k being one of the coordinate directions of a cylindrical coordinate system. Three classes of equilibria, all with a straight magnetic axis, are obtained. Equilibria of the first class have a purely poloidal magnetic field of the Clebsch type with k=z and include the 3D equilibria already known. Equilibria of the other two classes have a purely toroidal (i.e. here longitudinal) magnetic field and pressure surfaces that can be chosen such that poloidal sections are closed. The second class is based on a Clebsch representation with k=θ. Solutions contain a free function of θ that determines the poloidal sections of the pressure surfaces at, say, z=0. The behaviour in the toroidal direction is then fixed but not periodic. For the third class, the generalized Clebsch representation with k=z is used. The equilibria are similar to those of the second class, with two important differences. They contain no free function and field lines are not planar. Finally, 3D vacuum fields, which exhibit 3D magnetic surfaces, are presented. They have the same geometry as the equilibria of the third class, and in fact can be obtained as a certain limit from these equilibria. Possible applications of the equilibria found are mentioned.

Localized Ideal and Resistive Instabilities in 3-dimensional MHD Equilibria with Closed Field Lines

1990 ◽  
Vol 45 (9-10) ◽  
pp. 1074-1076
Author(s):  
Dario Correa-Restrepo
Keyword(s):  
Radial Direction ◽  
Mhd Equations ◽  
Closed Field ◽  
Stability Criteria ◽  
Energy Principle ◽  
3 Dimensional ◽  
Pressure Surface ◽  
Mhd Equilibria ◽  
Field Lines ◽  
Low Shear

Abstract A class of stability criteria is derived for MHD equilibria with closed field lines. The destabilizing perturbations have finite gradients along the field and are localized around a field line, the localiza-tion being stronger on the pressure surface than in the radial direction. By contrast, in sheared configurations the localization is comparable in both directions. The derived stability criteria are less stringent than those obtained for MHD equilibria with shear for similarly localized perturbations in the limit of low shear. These results, obtained from the energy principle, are a particular case of those obtained by solving the linearized resistive MHD equations with an appropriate ansatz and subsequently taking the limit of vanishing shear and resistivity.

scholarly journals Adjoint approach to calculating shape gradients for three-dimensional magnetic confinement equilibria

2019 ◽  
Vol 85 (2) ◽  
Author(s):  
Thomas Antonsen ◽  
Elizabeth J. Paul ◽  
Matt Landreman
Keyword(s):  
Figure Of Merit ◽  
Transport Coefficients ◽  
Three Dimensional ◽  
Direct Calculation ◽  
Flux Surface ◽  
Shape Gradient ◽  
Onsager Symmetry ◽  
Mhd Equilibria ◽  
Gradient Based ◽  
Adjoint Approach

The shape gradient quantifies the change in some figure of merit resulting from differential perturbations to a shape. Shape gradients can be applied to gradient-based optimization, sensitivity analysis and tolerance calculation. An efficient method for computing the shape gradient for toroidal three-dimensional magnetohydrodynamic (MHD) equilibria is presented. The method is based on the self-adjoint property of the equations for driven perturbations of MHD equilibria and is similar to the Onsager symmetry of transport coefficients. Two versions of the shape gradient are considered. One describes the change in a figure of merit due to an arbitrary displacement of the outer flux surface; the other describes the change in the figure of merit due to the displacement of a coil. The method is implemented for several example figures of merit and compared with direct calculation of the shape gradient. In these examples the adjoint method reduces the number of equilibrium computations by factors of$O(N)$, where$N$is the number of parameters used to describe the outer flux surface or coil shapes.

Exact nonlinear wave solutions of the incompressible magnetohydrodynamic equations in a sheared magnetic field

1990 ◽  
Vol 44 (1) ◽  
pp. 25-32 ◽  
Author(s):  
Hiromitsu Hamabata
Keyword(s):  
Magnetic Field ◽  
Incompressible Fluid ◽  
Large Amplitude ◽  
Uniform Magnetic Field ◽  
Magnetohydrodynamic Equations ◽  
Wave Solutions ◽  
Field Lines ◽  
Incompressible Magnetohydrodynamic Equations ◽  
Physical Quantities ◽  
Nonlinear Wave Solutions

Exact wave solutions of the nonlinear jnagnetohydrodynamic equations for a highly conducting incompressible fluid are obtained for the cases where the physical quantities are independent of one Cartesian co-ordina.te and for where they vary three-dimensionally but both the streamlines and magnetic field lines lie in parallel planes. It is shown that there is a class of exact wave solutions with large amplitude propagating in a straight but non-uniform magnetic field with constant or non-uniform velocity.

Instability of isolated three-dimensional magnetic null points

1998 ◽  
Vol 59 (3) ◽  
pp. 537-541 ◽  
Author(s):  
MANUEL NÚÑEZ
Keyword(s):  
Linear Stability ◽  
Three Dimensional ◽  
Null Point ◽  
Static Equilibrium ◽  
Flux Surface ◽  
Form Part ◽  
Magnetic Null ◽  
Transverse Oscillations

Although most magnetic neutral points occurring in nature seem to form part of a continuum, recent studies of reconnection have centred on static equilibria in the neighbourhood of an isolated three-dimensional null point. The linear stability of this configuration is studied here. It is found that one may choose a flux surface so that transverse oscillations localized around the surface and polarized within it must grow exponentially in time. This means that any static equilibrium containing an isolated three-dimensional null point is linearly unstable.

scholarly journals The Formation of a Cavity in a 3D Flux Rope

2013 ◽  
Vol 8 (S300) ◽  
pp. 147-150 ◽  
Author(s):  
Donald Schmit ◽  
Sarah Gibson
Keyword(s):  
Ad Hoc ◽  
Numerical Models ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Flux Rope ◽  
Multiple Structures ◽  
Field Lines ◽  
Hydrostatic Balance ◽  
Distinct Field ◽  
Three Dimensional Space

AbstractThere are currently no three dimensional numerical models which describe the magnetic and energetic formation of prominences self-consistently. Consequently, there has not been significant progress made in understanding the connection between the dense prominence plasma and the coronal cavity. We have taken an ad-hoc approach to understanding the energetic implications of the magnetic models of prominence structure. We extract one dimensional magnetic field lines from a 3D MHD model of a flux rope and solve for hydrostatic balance along these field lines incorporating field-aligned thermal conduction, uniform heating, and radiative losses. The 1D hydrostatic solutions for density and temperature are then mapped back into three dimensional space, which allows us to consider the projection of multiple structures. We find that the 3D flux rope is composed of several distinct field line types. A majority of the flux rope interior field lines are twisted but not dipped. These field lines are density-reduced relative to unsheared arcade field lines. We suggest the cavity may form along these short interior field lines which are surrounded by a sheath of dipped field lines. This geometric arrangement would create a cavity on top of a prominence, but the two structures would not share field lines or plasma.

A New Technology for Three-Dimensional Cell Culture: The Hydrodynamic Focusing Bioreactor

1999 ◽  
Author(s):  
Yow-Min D. Tsao ◽  
Steve R. Gonda
Keyword(s):  
Cell Culture ◽  
New Technology ◽  
Three Dimensional ◽  
Culture Vessel ◽  
Air Bubbles ◽  
Hydrodynamic Focusing ◽  
Shaped Cell ◽  
Fluid Environment ◽  
Dimensional Cell ◽  
Low Shear

Abstract The Hydrodynamic Focusing Bioreactor (HDFB) developed by NASA at the Johnson Space Center provides a unique hydrofocusing capability that simultaneously enables a low-shear culture environment and a unique hydrofocusing-based “herding” of suspended cells, cell aggregates, and air bubbles. The HDFB is a rotating dome-shaped cell culture vessel with a centrally located sampling port and an internal rotating viscous spinner attached to a rotating base. The vessel and viscous spinner can rotate at different speeds and in either the same or different directions. Adjusting the differential rotation rate between the vessel and spinner results in a controllable hydrodynamic focusing force. The resultant hydrodynamic force suspends the cells in a low-shear fluid environment that supports the formation of delicate three-dimensional tissue assemblies. Both suspension and anchorage-dependent cells have been successfully cultured.

Indentation of a Transversely Isotropic Thermoporoelastic Half-Space by a Rigid Circular Cylindrical Punch

2017 ◽  
Vol 84 (11) ◽  
Author(s):  
Yilan Huang ◽  
Guozhan Xia ◽  
Weiqiu Chen ◽  
Xiangyu Li
Keyword(s):  
Half Space ◽  
Original Problem ◽  
Three Dimensional ◽  
Transversely Isotropic ◽  
The Finite Element Method ◽  
Thermal Fields ◽  
Cylindrical Punch ◽  
The One ◽  
Physical Quantities ◽  
Potential Theory Method

Exact solutions to the three-dimensional (3D) contact problem of a rigid flat-ended circular cylindrical indenter punching onto a transversely isotropic thermoporoelastic half-space are presented. The couplings among the elastic, hydrostatic, and thermal fields are considered, and two different sets of boundary conditions are formulated for two different cases. We use a concise general solution to represent all the field variables in terms of potential functions and transform the original problem to the one that is mathematically expressed by integral (or integro-differential) equations. The potential theory method is extended and applied to exactly solve these integral equations. As a consequence, all the physical quantities of the coupling fields are derived analytically. To validate the analytical solutions, we also simulate the contact behavior by using the finite element method (FEM). An excellent agreement between the analytical predictions and the numerical simulations is obtained. Further attention is also paid to the discussion on the obtained results. The present solutions can be used as a theoretical reference when practically applying microscale image formation techniques such as thermal scanning probe microscopy (SPM) and electrochemical strain microscopy (ESM).

scholarly journals Characteristic Mode Analysis of surface current distributions on metallic structures exposed to HIRF- and DCI-excitations

2020 ◽  
Vol 18 ◽  
pp. 33-41
Author(s):  
Jan Ückerseifer ◽  
Frank Gronwald
Keyword(s):  
Three Dimensional ◽  
Surface Current ◽  
Resonance Region ◽  
Mode Analysis ◽  
Surface Currents ◽  
Characteristic Mode ◽  
Metallic Structures ◽  
Current Distributions ◽  
Characteristic Modes ◽  
Physical Quantities

Abstract. This paper treats Characteristic Mode Analyses of three-dimensional test objects in the context of EMC. Based on computed Characteristic Modes and mode-specific physical quantities, series expansions for HIRF- and DCI-induced surface currents are deduced. The contribution of single Characteristic Modes to surface currents at different test frequencies is analyzed. HIRF- and DCI-excitations are compared with regard to their surface current distributions in their resonance region determined by Characteristic Mode Analysis.

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