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.

An Interpretation on Kinetics of Martensitic Transformation

2011 ◽  
Vol 172-174 ◽  
pp. 90-98 ◽  
Author(s):  
Tomoyuki Kakeshita ◽  
Takashi Fukuda ◽  
Yong-Hee Lee
Keyword(s):  
Magnetic Field ◽  
Hydrostatic Pressure ◽  
Martensitic Transformation ◽  
Magnetic Fields ◽  
Martensitic Transformations ◽  
Phenomenological Theory ◽  
Time Dependent ◽  
Isothermal Process ◽  
Kinetics Of ◽  
Transformation Processes

We have investigated athermal and isothermal martensitic transformations (typical displacive transformations) in Fe–Ni, Fe–Ni–Cr, and Ni-Co-Mn-In alloys under magnetic fields and hydrostatic pressures in order to understand the time-dependent nature of martensitic transformation, that is, the kinetics of martensitic transformation. We have confirmed that the two transformation processes are closely related to each other, that is, the athermal process changes to the isothermal process and the isothermal process changes to the athermal one under a hydrostatic pressure or a magnetic field. These findings can be explained by the phenomenological theory, which gives a unified explanation for the two transformation processes previously proposed by our group.

Kompressionswellen in einer isothermen Atmosphäre mit vertikalem Magnetfeld

1966 ◽  
Vol 21 (7) ◽  
pp. 1098-1106 ◽  
Author(s):  
R. Lust ◽  
M. Scholer
Keyword(s):  
Magnetic Field ◽  
Strong Influence ◽  
Vertical Direction ◽  
Time Dependent ◽  
Solar Chromosphere ◽  
Magnetohydrodynamic Equation ◽  
One Dimensional ◽  
Spatial Dimensions ◽  
Propagation Of Waves ◽  
The Waves

The propagation of waves in the solar atmosphere is investigated with respect to the problem of the chromospheric spiculae and of the heating of the solar chromosphere and corona. In particular the influence of external magnetic fields is considered. Waves of finite amplitudes are numerically calculated by solving the time-dependent magnetohydrodynamic equation for two spatial dimensions by assuming axial symmetry. For the case without a magnetic field the comparison between one dimensional and two dimensional treatment shows the strong influence of the radial propagation on the steepening of waves in the vertical direction. In the presence of a magnetic field it is shown that the propagation is strongly guided along the lines of force. The steepening of the waves along the field is much larger as compared to the case where no field is present.

FROM RELATIVISTIC VECTOR MESONS IN CONSTANT MAGNETIC FIELDS TO NONRELATIVISTIC (PSEUDO)SUPERSYMMETRIES

1995 ◽  
Vol 10 (19) ◽  
pp. 2783-2797 ◽  
Author(s):  
J. BECKERS ◽  
N. DEBERGH
Keyword(s):  
Magnetic Field ◽  
Quantum Mechanics ◽  
Magnetic Fields ◽  
Constant Magnetic Field ◽  
Vector Mesons ◽  
One Dimensional ◽  
Recent Developments

Results coming from the study of relativistic vector mesons interacting with a constant magnetic field are examined through Johnson-Lippmann implications on one-dimensional oscillatorlike systems. We obtain specific nonrelativistic Hamiltonians showing new properties in quantum mechanics and leading to superpositions of bosons and pseudofermions. Moreover, two “potentials” are introduced and discussed in comparison with recent developments usually obtained in p=2 parasupersymmetric quantum mechanics. Pseudofermions are also examined, particularly with respect to orthofermions.

Nonlinear stationary magnetoconvection in a rotating fluid

1997 ◽  
Vol 58 (3) ◽  
pp. 395-408 ◽  
Author(s):  
S. G. TAGARE
Keyword(s):  
Magnetic Field ◽  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Pitchfork Bifurcation ◽  
Time Dependent ◽  
Vertical Magnetic Field ◽  
Stationary Convection ◽  
Rotating Fluid ◽  
Order Ordinary Differential Equation ◽  
One Dimensional

We investigate finite-amplitude magnetoconvection in a rotating fluid in the presence of a vertical magnetic field when the axis of rotation is parallel to a vertical magnetic field. We derive a nonlinear, time-dependent, one-dimensional Landau–Ginzburg equation near the onset of stationary convection at supercritical pitchfork bifurcation whenformula hereand a nonlinear time-dependent second-order ordinary differential equation when Ta=T*a (from below). Ta=T*a corresponds to codimension-two bifurcation (or secondary bifurcation), where the threshold for stationary convection at the pitchfork bifurcation coincides with the threshold for oscillatory convection at the Hopf bifurcation. We obtain steady-state solutions of the one-dimensional Landau–Ginzburg equation, and discuss the solution of the nonlinear time-dependent second-order ordinary differential equation.

Solidification of AlSi Alloys in the ARTEMIS and ARTEX Facilities Including Rotating Magnetic Fields – A Combined Experimental and Numerical Analysis

2006 ◽  
Vol 508 ◽  
pp. 199-204 ◽  
Author(s):  
Marc Hainke ◽  
Sonja Steinbach ◽  
Johannes Dagner ◽  
Lorenz Ratke ◽  
Georg Müller
Keyword(s):  
Magnetic Field ◽  
Numerical Modeling ◽  
Numerical Analysis ◽  
Temperature Gradient ◽  
Magnetic Fields ◽  
Time Dependent ◽  
Flow Conditions ◽  
Rotating Magnetic Fields ◽  
Microstructural Parameters ◽  
Wide Range

The solidification microstructure is the consequence of a wide range of process parameters, like the growth velocity, the temperature gradient and the composition. Although the influence of these parameters is nowadays considerably well understood, an overall theory of the influence of convection on microstructural features is still lacking. The application of time dependent magnetic fields during directional solidification offers the possibility to create defined solidification and flow conditions. In this work, we report about solidification experiments in the ARTEMIS and ARTEX facilities including rotating magnetic fields (RMF). The effect of the forced melt flow on microstructural parameters like the primary and secondary dendrite arm spacing is analyzed for a wide range of magnetic field parameters. The experimental analysis is supported by a rigorous application of numerical modeling. An important issue is hereby the prediction of the resulting macrosegregation, i.e., differences in the composition on the scale of the sample (macroscale) due to the RMF. For the considered configuration and parameters an axial enrichment of Si is found beyond a certain magnetic field strength. The results are compared to available theories and their applicability is discussed.

scholarly journals CMEs ‘en rafale’ observations and simulations

2008 ◽  
Vol 4 (S257) ◽  
pp. 251-255
Author(s):  
Cristiana Dumitrache
Keyword(s):  
Magnetic Field ◽  
Magnetic Reconnection ◽  
Solar Disk ◽  
Large Scale ◽  
Stable Equilibrium ◽  
Time Dependent ◽  
Kink Mode ◽  
Mhd Equilibrium ◽  
Ideal Mhd ◽  
Slow Evolution

AbstractA CME is triggered by the disappearance of a stable equilibrium as a result of the slow evolution of the photospheric magnetic field. This disappearance may be due to a loss of ideal-MHD equilibrium or stability as in the kink mode, or to a loss of resistive-MHD equilibrium as a result of magnetic reconnection. We have obtained CMEs in sequence by a time dependent magnetohydrodynamic computation performed on three solar radii. These successive CMEs resulted from a prominence eruption. Velocities of these CMEs decrease in time, from a CME to another. We present observational evidences for large-scale magnetic reconnections that caused the destabilization of a sigmoid filament. These reconnections covered half of the solar disk and produced CMEs in squall (sequential CMEs).

Photodetachment microscopy of H– ion in time-dependent electric and magnetic fields

2018 ◽  
Vol 96 (9) ◽  
pp. 961-968
Author(s):  
De-hua Wang
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Electric Field ◽  
Interference Pattern ◽  
Current Distribution ◽  
Time Dependent ◽  
Electron Current ◽  
Detector Plane ◽  
Electron Trajectories ◽  
Electric And Magnetic Fields

We examine the dynamics of electrons photodetached from the H– ion in time-dependent electric and magnetic fields for the first time. The photodetachment microscopy patterns caused by a time-dependent gradient electric field and magnetic field have been analyzed in great detail based on the semiclassical theory. The interplay of the gradient electric field and magnetic field forces causes an intricate shape of the electron wave and multiple electron trajectories generated by a fixed energy point source can arrive at a given point on the microchannel-plate detector. The interference effects between these electron trajectories cause the oscillatory structures of the electron probability density and electron current distribution, and a set of concentric interference fringes are found at the detector. Our calculation results suggest that the photodetachment microscopy interference pattern on the detector can be adjusted by the electron energy, magnetic field strength, and position of the detector plane. Under certain conditions, the interference pattern in the electron current distribution might be seen on the detector plane localized at a macroscopic distance from the photodetachment source, which can be observed in an actual photodetachment microscopy experiment. Therefore, we make predictions that our work should serve as a guide for future photodetachment microscopy experiments in time-dependent electric and magnetic fields.

Almost-invariant surfaces for magnetic field-line flows

1996 ◽  
Vol 56 (2) ◽  
pp. 361-382 ◽  
Author(s):  
S. R. Hudson ◽  
R. L. Dewar
Keyword(s):  
Magnetic Field ◽  
Field Line ◽  
Magnetic Field Line ◽  
Gradient Flow ◽  
Invariant Surface ◽  
Infinite Dimensional ◽  
Invariant Surfaces ◽  
Magnetic Surfaces ◽  
Rotational Transform ◽  
The Magnetic Field

Two approaches to defining almost-invariant surfaces for magnetic fields with imperfect magnetic surfaces are compared. Both methods are based on treating magnetic field-line flow as a 1½-dimensional Hamiltonian (or Lagrangian) dynamical system. In thequadratic-flux minimizing surfaceapproach, the integral of the square of the action gradient over the toroidal and poloidal angles is minimized, while in theghost surfaceapproach a gradient flow between a minimax and an action-minimizing orbit is used. In both cases the almost-invariant surface is constructed as a family of periodic pseudo-orbits, and consequently it has a rational rotational transform. The construction of quadratic-flux minimizing surfaces is simple, and easily implemented using a new magnetic field-line tracing method. The construction of ghost surfaces requires the representation of a pseudo field line as an (in principle) infinite-dimensional vector and also is inherently slow for systems near integrability. As a test problem the magnetic field-line Hamiltonian is constructed analytically for a topologically toroidal, non-integrable ABC-flow model, and both types of almost-invariant surface are constructed numerically.

Quasi-static electric and magnetic fields in vacuum

2018 ◽  
Author(s):  
J. Pierrus
Keyword(s):  
Magnetic Field ◽  
Nineteenth Century ◽  
Magnetic Fields ◽  
Electric Field ◽  
Electromagnetic Induction ◽  
Point Of View ◽  
Time Dependent ◽  
Important Phenomenon ◽  
Electric And Magnetic Fields ◽  
Practical Standpoint

In this chapter, the transition from time-independent to time-dependent source densities and fields is made. It is here that Faraday’s famous nineteenth-century experiments on electromagnetic induction are first encountered. This important phenomenon—whereby a changing magnetic field produces an induced electric field (whose curl is now no longer zero)—forms the basis of most of the questions and solutions which follow. Some new and interesting examples—not usually found in other textbooks—are introduced. These are treated both from an analytical and numerical point of view. Also considered here is the standard yet important topic (at least from a practical standpoint) of mutual and self-inductance. Several questions deal with this concept.

Sign in / Sign up

Export Citation Format

Share Document