scholarly journals Steady plasma flows in a periodic non-symmetric domain

2021 ◽  
Vol 87 (6) ◽  
Author(s):  
Harold Weitzner ◽  
Wrick Sengupta
Keyword(s):  
Magnetic Field ◽  
Three Dimensional ◽  
Symmetric Domain ◽  
Steady Flows ◽  
Continuous Symmetry ◽  
Plasma Flows ◽  
Mhd Equilibrium ◽  
Mhd Model ◽  
Rotational Transform ◽  
The Magnetic Field

Steady plasma flows have been studied almost exclusively in systems with continuous symmetry or in open domains. In the absence of continuous symmetry, the lack of a conserved quantity makes the study of flows intrinsically challenging. In a toroidal domain, the requirement of double periodicity for physical quantities adds to the complications. In particular, the magnetohydrodynamics (MHD) model of plasma steady state with the flow in a non-symmetric toroidal domain allows the development of singularities when the rotational transform of the magnetic field is rational, much like the equilibrium MHD model. In this work, we show that steady flows can still be maintained provided the rotational transform is close to rational and the magnetic shear is weak. We extend the techniques developed in carrying out perturbation methods to all orders for static MHD equilibrium by Weitzner (Phys. Plasmas, vol. 21, 2014, p. 022515) to MHD equilibrium with flows. We construct perturbative MHD equilibrium in a doubly periodic domain with nearly parallel flows by systematically eliminating magnetic resonances order by order. We then utilize an additional symmetry of the flow problem, first discussed by Hameiri (J. Math. Phys., vol. 22, 1981, pp. 2080–2088, § III), to obtain a generalized Grad–Shafranov equation for a class of non-symmetric three-dimensional MHD equilibrium with flows both parallel and perpendicular to the magnetic field. For this class of flows, we can obtain non-symmetric generalizations of integrals of motion, such as Bernoulli's function and angular momentum. Finally, we obtain the generalized Hamada conditions, which are necessary to suppress singular currents in such a system when the magnetic field lines are closed. We do not attempt to address the question of neoclassical damping of flows.

scholarly journals Three-dimensional magnetohydrodynamic equilibria with continuous magnetic fields

2017 ◽  
Vol 83 (4) ◽  
Author(s):  
S. R. Hudson ◽  
B. F. Kraus
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Three Dimensional ◽  
Energy Functional ◽  
Equilibrium States ◽  
Equilibrium Solutions ◽  
Magnetic Islands ◽  
Continuity Properties ◽  
Rotational Transform ◽  
The Magnetic Field

A brief critique is presented of some different classes of magnetohydrodynamic equilibrium solutions based on their continuity properties and whether the magnetic field is integrable or not. A generalized energy functional is introduced that is comprised of alternating ideal regions, with nested flux surfaces with an irrational rotational transform, and Taylor-relaxed regions, possibly with magnetic islands and chaos. The equilibrium states have globally continuous magnetic fields, and may be constructed for arbitrary three-dimensional plasma boundaries and appropriately prescribed pressure and rotational-transform profiles.

Characterization of the flow past a truncated square cylinder in a duct under a spanwise magnetic field

2011 ◽  
Vol 691 ◽  
pp. 341-367 ◽  
Author(s):  
Vincent Dousset ◽  
Alban Pothérat
Keyword(s):  
Magnetic Field ◽  
Lorentz Force ◽  
Topological Analysis ◽  
Three Dimensional ◽  
Homogeneous Magnetic Field ◽  
Steady Flows ◽  
Square Cylinder ◽  
Electrically Conducting ◽  
Truncated Cylinder ◽  
The Magnetic Field

AbstractWe study the flow of an electrically conducting fluid past a truncated square cylinder in a rectangular duct under the influence of an externally applied homogeneous magnetic field oriented along the cylinder axis. Our aim is to bridge the gap between the non-magnetic regime, where we previously found a complex set of three-dimensional recirculations behind the cylinder (Dousset & Pothérat, J. Fluid Mech., vol. 653, 2010, pp. 519–536) and the asymptotic regime of dominating Lorentz force analysed by Hunt & Ludford (J. Fluid. Mech., vol. 33, 1968, pp. 693–714). The latter regime is characterized by a remarkable structure known as Hunt’s wake in the magnetohydrodynamics community, where the flow is deflected on either side of a stagnant zone, right above the truncated cylinder as if the latter would span the full height of the duct. In steady flows dominated by the Lorentz force, with negligible inertia, we provide the first numerical flow visualization of Hunt’s wake. In regimes of finite inertia, a thorough topological analysis of the steady flow regimes reveals how the Lorentz force gradually reorganizes the flow structures in the hydrodynamic wake of the cylinder as the Hartmann number $\mathit{Ha}$ (which gives a non-dimensional measure of the magnetic field) is increased. The nature of the vortex shedding follows from this rearrangement of the steady structures by the magnetic field. As $\mathit{Ha}$ is increased, we observe that the vortex street changes from a strongly symmetric one to the alternate procession of counter-rotating vortices typical of the non-truncated cylinder wakes.

A three-dimensional kinematic dynamo

1975 ◽  
Vol 344 (1637) ◽  
pp. 235-258 ◽  
Keyword(s):  
Magnetic Field ◽  
Three Dimensional ◽  
Characteristic Size ◽  
Steady Flows ◽  
Dynamo Action ◽  
Ohmic Dissipation ◽  
The Earth ◽  
Induction Equation ◽  
High Degree ◽  
The Magnetic Field

A number of steady (marginal) solutions of the induction equation governing the magnetic field created by a particular class of threedimensional flows in a sphere of conducting fluid surrounded by an insulator are derived numerically. These motions possess a high degree of symmetry which can be varied to confirm numerically that the corresponding asymptotic limit of Braginsky is attained. The effect of altering the spatial scale of the motions without varying their vigour can also be examined, and it is found that dynamo action is at first eased by decreasing their characteristic size. There are, however, suggestions that the regenerative efficiency does not persistently increase to very small length scales, but ultimately decreases. It is further shown that time varying motions, in which the asymmetric components of flow travel as a wave round lines of latitude, can sustain fields having co-rotating asymmetric parts. It is demonstrated that, depending on their common angular velocity, these may exist at slightly smaller magnetic Reynolds numbers than the corresponding models having steady flows and fields. The possible bearing of the integrations on the production of the magnetic field of the Earth is considered, and the implied ohmic dissipation of heat in the core of the Earth is estimated for different values of the parameters defining the model.

scholarly journals Hamiltonian Approach to Magnetic Fields with Toroidal Surfaces

1985 ◽  
Vol 40 (10) ◽  
pp. 959-967
Author(s):  
A. Salat
Keyword(s):  
Magnetic Field ◽  
Hamiltonian System ◽  
Magnetic Fields ◽  
Constant Pressure ◽  
Time Dependent ◽  
Hamiltonian Approach ◽  
One Dimensional ◽  
Mhd Equilibrium ◽  
Magnetic Surfaces ◽  
Rotational Transform

The equivalence of magnetic field line equations to a one-dimensional time-dependent Hamiltonian system is used to construct magnetic fields with arbitrary toroidal magnetic surfaces I = const. For this purpose Hamiltonians H which together with their invariants satisfy periodicity constraints have to be known. The choice of H fixes the rotational transform η(I). Arbitrary axisymmetric fields, and nonaxisymmetric fields with constant η(I) are considered in detail.Configurations with coinciding magnetic and current density surfaces are obtained. The approach used is not well suited, however, to satisfying the additional MHD equilibrium condition of constant pressure on magnetic surfaces.

scholarly journals Magnetic Field Structure of Star Forming Regions: VLBI Spectral Line Results

1984 ◽  
Vol 110 ◽  
pp. 333-334
Author(s):  
J.A. Garcia-Barreto ◽  
B. F. Burke ◽  
M. J. Reid ◽  
J. M. Moran ◽  
A. D. Haschick
Keyword(s):  
Magnetic Field ◽  
Three Dimensional ◽  
Aperture Synthesis ◽  
Stokes Parameters ◽  
Hii Region ◽  
Star Forming ◽  
Star Forming Regions ◽  
Vlbi Observations ◽  
The Magnetic Field ◽  
Synthesis Experiment

Magnetic fields play a major role in the general dynamics of astronomical phenomena and particularly in the process of star formation. The magnetic field strength in galactic molecular clouds is of the order of few tens of μG. On a smaller scale, OH masers exhibit fields of the order of mG and these can probably be taken as representative of the magnetic field in the dense regions surrounding protostars. The OH molecule has been shown to emit highly circular and linearly polarized radiation. That it was indeed the action of the magnetic field that would give rise to the highly polarized spectrum of OH has been shown by the VLBI observations of Zeeman pairs of the 1720 and 6035 MHz by Lo et. al. and Moran et. al. VLBI observations of W3 (OH) revealed that the OH emission was coming from numerous discrete locations and that all spots fell within the continuum contours of the compact HII region. The most detailed VLBI aperture synthesis experiment of the 1665 MHz emission from W3 (OH) was carried out by Reid et. al. who found several Zeeman pairs and a characteristic maser clump size of 30 mas. In this work, we report the results of a 5 station VLBI aperture synthesis experiment of the 1665 MHz OH emission from W3 (OH) with full polarization information. We produced VLBI synthesis maps of all Stokes parameters of 16 spectral features that showed elliptical polarization. The magnitude and direction of the magnetic field have been obtained by the detection of 7 Zeeman pairs. The three dimensional orientation of the magnetic field can be obtained, following the theoretical arguments of Goldreich et. al., from the observation of π and σ components.

scholarly journals INCREASING THE EFFICIENCY OF MULTY-VARIANT CALCULATIONS OF ELECTROMAGNETIC FIELD DISTRIBUTION IN MATRIX OF A POLYGRADIENT SEPARATOR

2021 ◽  
Author(s):  
Jasim Mohmed Jasim Jasim ◽  
Iryna Shvedchykova ◽  
Igor Panasiuk ◽  
Julia Romanchenko ◽  
Inna Melkonova
Keyword(s):  
Magnetic Field ◽  
Field Distribution ◽  
Three Dimensional ◽  
Magnetic Potential ◽  
Geometric Parameters ◽  
Two Dimensional ◽  
Air Gaps ◽  
Vector Magnetic Potential ◽  
Electromagnetic Separator ◽  
The Magnetic Field

An approach is proposed to carry out multivariate calculations of the magnetic field distribution in the working gaps of a plate polygradient matrix of an electromagnetic separator, based on a combination of the advantages of two- and three-dimensional computer modeling. Two-dimensional geometric models of computational domains are developed, which differ in the geometric dimensions of the plate matrix elements and working air gaps. To determine the vector magnetic potential at the boundaries of two-dimensional computational domains, a computational 3D experiment is carried out. For this, three variants of the electromagnetic separator are selected, which differ in the size of the working air gaps of the polygradient matrices. For them, three-dimensional computer models are built, the spatial distribution of the magnetic field in the working intervals of the electromagnetic separator matrix and the obtained numerical values of the vector magnetic potential at the boundaries of the computational domains are investigated. The determination of the values of the vector magnetic potential for all other models is carried out by interpolation. The obtained values of the vector magnetic potential are used to set the boundary conditions in a computational 2D experiment. An approach to the choice of a rational version of a lamellar matrix is substantiated, which provides a solution to the problem according to the criterion of the effective area of the working area. Using the method of simple enumeration, a variant of the structure of a polygradient matrix with rational geometric parameters is selected. The productivity of the electromagnetic separator with rational geometric parameters of the matrix increased by 3–5 % with the same efficiency of extraction of ferromagnetic inclusions in comparison with the basic version of the device

Quantitative Research on Cracks in Pipe Based on Magnetic Field Response Method of Eddy Current Testing

2021 ◽  
Vol 36 (1) ◽  
pp. 99-107
Author(s):  
Feng Jiang ◽  
Shulin Liu ◽  
Li Tao
Keyword(s):  
Magnetic Field ◽  
Eddy Current ◽  
Quantitative Research ◽  
Three Dimensional ◽  
Impedance Analysis ◽  
Eddy Current Testing ◽  
Element Analysis ◽  
Defect Parameter ◽  
Current Testing ◽  
The Magnetic Field

The quantitative evaluation of defects in eddy current testing is of great significance. Impedance analysis, as a traditional method, is adopted to determine defects in the conductor, however, it is not able to depict the shape, size and location of defects quantitatively. In order to obtain more obvious characteristic quantities and improve the ability of eddy current testing to detect defects, the study of cracks in metal pipes is carried out by utilizing the analysis method of three-dimensional magnetic field in present paper. The magnetic field components in the space near the crack are calculated numerically by using finite element analysis. The simulation results confirm that the monitoring of the crack change can be achieved by measuring the magnetic field at the arrangement positions. Besides, the quantitative relationships between the shape, length of the crack and the magnetic field components around the metal pipe are obtained. The results show that the axial and radial magnetic induction intensities are affected more significantly by the cross-section area of the crack. Bz demonstrates obvious advantages in analyzing quantitatively crack circumference length. Therefore, the response signal in the three-dimensional direction of the magnetic field gets to intuitively reflect the change of the defect parameter, which proves the effectiveness and practicability of this method.

The magnetic field about a three-dimensional block neodymium magnet

2021 ◽  
Vol 62 ◽  
pp. 386-405
Author(s):  
Graham John Weir ◽  
George Chisholm ◽  
Jerome Leveneur
Keyword(s):  
Magnetic Field ◽  
Permanent Magnets ◽  
Hard Disk Drives ◽  
Three Dimensional ◽  
Transverse Magnetic ◽  
Observation Point ◽  
Magnetization Direction ◽  
Potential Approach ◽  
Neodymium Magnet ◽  
The Magnetic Field

Neodymium magnets were independently discovered in 1984 by General Motors and Sumitomo. Today, they are the strongest type of permanent magnets commercially available. They are the most widely used industrial magnets with many applications, including in hard disk drives, cordless tools and magnetic fasteners. We use a vector potential approach, rather than the more usual magnetic potential approach, to derive the three-dimensional (3D) magnetic field for a neodymium magnet, assuming an idealized block geometry and uniform magnetization. For each field or observation point, the 3D solution involves 24 nondimensional quantities, arising from the eight vertex positions of the magnet and the three components of the magnetic field. The only unknown in the model is the value of magnetization, with all other model quantities defined in terms of field position and magnet location. The longitudinal magnetic field component in the direction of magnetization is bounded everywhere, but discontinuous across the magnet faces parallel to the magnetization direction. The transverse magnetic fields are logarithmically unbounded on approaching a vertex of the magnet.   doi:10.1017/S1446181120000097

scholarly journals Filaments and striations: anisotropies in observed, supersonic, highly magnetized turbulent clouds

2019 ◽  
Vol 492 (1) ◽  
pp. 668-685 ◽  
Author(s):  
James R Beattie ◽  
Christoph Federrath
Keyword(s):  
Magnetic Field ◽  
Column Density ◽  
Three Dimensional ◽  
High Density ◽  
Systematic Analysis ◽  
Guide Field ◽  
Degree Of Anisotropy ◽  
Mach Numbers ◽  
Magnetohydrodynamic Simulations ◽  
The Magnetic Field

ABSTRACT Stars form in highly magnetized, supersonic turbulent molecular clouds. Many of the tools and models that we use to carry out star formation studies rely upon the assumption of cloud isotropy. However, structures like high-density filaments in the presence of magnetic fields and magnetosonic striations introduce anisotropies into the cloud. In this study, we use the two-dimensional power spectrum to perform a systematic analysis of the anisotropies in the column density for a range of Alfvén Mach numbers ($\operatorname{\mathcal {M}_{\text{A}}}=0.1{\!-\!10}$) and turbulent Mach numbers ($\operatorname{\mathcal {M}}=2{\!-\!20}$), with 20 high-resolution, three-dimensional turbulent magnetohydrodynamic simulations. We find that for cases with a strong magnetic guide field, corresponding to $\operatorname{\mathcal {M}_{\text{A}}}\lt 1$, and $\operatorname{\mathcal {M}}\lesssim 4$, the anisotropy in the column density is dominated by thin striations aligned with the magnetic field, while for $\operatorname{\mathcal {M}}\gtrsim 4$ the anisotropy is significantly changed by high-density filaments that form perpendicular to the magnetic guide field. Indeed, the strength of the magnetic field controls the degree of anisotropy and whether or not any anisotropy is present, but it is the turbulent motions controlled by $\operatorname{\mathcal {M}}$ that determine which kind of anisotropy dominates the morphology of a cloud.

scholarly journals Observations of diffusion in the electron halo and strahl

2016 ◽  
Vol 34 (12) ◽  
pp. 1175-1189 ◽  
Author(s):  
Chris Gurgiolo ◽  
Melvyn L. Goldstein
Keyword(s):  
Magnetic Field ◽  
Energy Range ◽  
Lower Energy ◽  
Three Dimensional ◽  
Distribution Functions ◽  
Electron Velocity ◽  
Electron Velocity Distribution ◽  
Velocity Distribution Functions ◽  
The Magnetic Field ◽  
Solar Wind Electron

Abstract. Observations of the three-dimensional solar wind electron velocity distribution functions (VDF) using ϕ–θ plots often show a tongue of electrons that begins at the strahl and stretches toward a new population of electrons, termed the proto-halo, that exists near the projection of the magnetic field opposite that associated with the strahl. The energy range in which the tongue and proto-halo are observed forms a “diffusion zone”. The tongue first appears in energy generally near the lower-energy range of the strahl and in the absence of any clear core/halo signature. While the ϕ–θ plots give the appearance that the tongue and proto-halo are derived from the strahl, a close examination of their density suggests that their source is probably the upper-energy core/halo electrons which have been scattered by one or more processes into these populations.

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