scholarly journals On the groundstate energy of tight knots

2009 ◽  
Vol 465 (2109) ◽  
pp. 2761-2783 ◽  
Author(s):  
Francesca Maggioni ◽  
Renzo L. Ricca
Keyword(s):  
Magnetic Field ◽  
Magnetic Energy ◽  
Energy Levels ◽  
Minimum Energy ◽  
Internal Field ◽  
Exact Expression ◽  
Torus Knots ◽  
Tube Cross Section ◽  
The Magnetic Field ◽  
Groundstate Energy

New results on the groundstate energy of tight, magnetic knots are presented. Magnetic knots are defined as tubular embeddings of the magnetic field in an ideal, perfectly conducting, incompressible fluid. An orthogonal, curvilinear coordinate system is introduced and the magnetic energy is determined by the poloidal and toroidal components of the magnetic field. Standard minimization of the magnetic energy is carried out under the usual assumptions of volume- and flux-preserving flow, with the additional constraints that the tube cross section remains circular and that the knot length (ropelength) is independent from internal field twist (framing). Under these constraints the minimum energy is determined analytically by a new, exact expression, function of ropelength and framing. Groundstate energy levels of tight knots are determined from ropelength data obtained by the SONO tightening algorithm. Results for torus knots are compared with previous work, and the groundstate energy spectrum of the first prime knots — up to 10 crossings — is presented and analysed in detail. These results demonstrate that ropelength and framing determine the spectrum of magnetic knots in tight configuration.

The energy and helicity of knotted magnetic flux tubes

1995 ◽  
Vol 451 (1943) ◽  
pp. 609-629 ◽  
Keyword(s):  
Magnetic Field ◽  
Magnetic Energy ◽  
Minimum Energy ◽  
Circular Cross Section ◽  
Parametric Representation ◽  
Energy Functional ◽  
Helical Axis ◽  
Torus Knots ◽  
Flux Tubes ◽  
Kink Mode

Magnetic relaxation of a magnetic field embedded in a perfectly conducting incompressible fluid to minimum energy magnetostatic equilibrium states is considered. It is supposed that the magnetic field is confined to a single flux tube which may be knotted. A local non-orthogonal coordinate system, zero-framed with respect to the knot, is introduced, and the field is decomposed into toroidal and poloidal ingredients with respect to this system. The helicity of the field is then determined; this vanishes for a field that is either purely toroidal or purely poloidal. The magnetic energy functional is calculated under the simplifying assumptions that the tube is axially uniform and of circular cross-section. The case of a tube with helical axis is first considered, and new results concerning kink mode instability and associated bifurcations are obtained. The case of flux tubes in the form of torus knots is then considered and the ‘ground-state’ energy function ͞m ( h ) (where h is an internal twist parameter) is obtained; as expected, ͞m ( h ), which is a topological invariant of the knot, increases with increasing knot complexity. The function ͞m ( h ) provides an upper bound on the corresponding function m ( h ) that applies when the above constraints on tube structure are removed. The technique is applicable to any knot admitting a parametric representation, on condition that points of vanishing curvature are excluded.

Formation of the SN1987A Ring due to magnetic pressure

1997 ◽  
Vol 180 ◽  
pp. 473-473
Author(s):  
M. Mori ◽  
H. Washimi ◽  
S. Shibata
Keyword(s):  
Magnetic Field ◽  
Radio Emission ◽  
Blast Wave ◽  
Magnetic Energy ◽  
Minimum Energy ◽  
Magnetic Pressure ◽  
Interaction Region ◽  
Stellar Winds ◽  
Fast Wind ◽  
The Magnetic Field

Several weeks after the explosion of supernova (SN) SN1987A, the UV flash of the SN illuminated a ring-like structure in the circumstellar material at about 0.65 ly from the SN. The interaction between the stellar winds from the SN progenitor is considered to be the candidate for the formation of the circumstellar structure. In the case that the stellar winds are spherically symmetric, the interaction should result in a shell-like structure. However, Washimi, Shibata & Mori (1996) show that the magnetic field in the winds causes an anisotropy which leads to the formation of a ring-like structure. When the fast wind of the blue supergiant phase of the progenitor sweeps up the surrounding slow wind of the red-supergiant phase, the magnetic field as well as the wind material are piled up in the interaction region. Since the magnetic energy increases in proportion to the square of the amplitude, the magnetic field exhibits its effect prominently at the interaction region; due to the magnetic pressure force the material at lower latitudes is compressed into a ring-like structure. It is suggested that this magnetic process can also explain the newly observed pair of rings of the SN1987A nebula. We note that the idea of a magnetic field effect is consistent with the radio observation of a supernova remnant, detected by Staveley-Smith et al. (1992) at about 1200 days after the explosion. This radio emission is explained by the collision of the supernova blast wave with the shocked blue wind. This position corresponds to the averaged expansion speed of the supernova ejecta ∼ 0.08 ly which is consistent with the estimation by Shigeyama and Nomoto (1990). The estimated magnetic-energy density by the minimum-energy argument is ∼ 4 × 10–8f–4/7N m–2, where f is the fractional volume of the radiating acceleration region, suggesting a magnetic field of a few milli-Gauss or more (Chevalier 1992). This field intensity is consistent with an intensity of ≈ 2 · 10–4 Gauss obtained between the reverse shock and the contact surface shown, if one takes into account a further enhancement of the field due to the sweeping-up process by the supernova blast wave. When the SN ejector collides with the ring at the end of this century or at the beginning of the next one, we can also expect more intense radio emission at rather middle and high latitudes where the magnetic intensity is greater, rather than at the equator where the ring-like structure is located.

scholarly journals The role of magnetic energy on plasma localization during the glow discharge under reduced pressure

Nukleonika ◽  
2016 ◽  
Vol 61 (2) ◽  
pp. 191-194 ◽  
Author(s):  
Rafal Chodun ◽  
Katarzyna Nowakowska-Langier ◽  
Krzysztof Zdunek ◽  
Sebastian Okrasa
Keyword(s):  
Magnetic Field ◽  
Glow Discharge ◽  
Breakdown Voltage ◽  
Magnetic Energy ◽  
Minimum Energy ◽  
Electrode System ◽  
Reduced Pressure ◽  
First Results ◽  
Paschen Curve ◽  
The Magnetic Field

Abstract In this work, we present the first results of our research on the synergy of fields, electric and magnetic, in the initiation and development of glow discharge under reduced pressure. In the two-electrode system under reduced pressure, the breakdown voltage characterizes a minimum energy input of the electric field to initiate and sustain the glow discharge. The glow discharge enhanced by the magnetic field applied just above the surface of the cathode influences the breakdown voltage decreasing its value. The idea of the experiment was to verify whether the contribution of potential energy of the magnetic field applied around the cathode is sufficiently effective to locate the plasma of glow discharge to the grounded cathode, which, in fact, is the part of a vacuum chamber wall (the anode is positively biased in this case). In our studies, we used the grounded magnetron unit with positively biased anode in order to achieve favorable conditions for the deposition of thin films on fibrous substrates such as fabrics for metallization, assuming that locally applied magnetic field can effectively locate plasma. The results of our studies (Paschen curve with the participation of the magnetic field) seem to confirm the validity of the research assumption. What is the most spectacular - the glow discharge was initiated between introduced into the chamber anode and the grounded cathode of magnetron ‘assisted’ by the magnetic field (discharge did not include the area of the anode, which is a part of the magnetron construction).

CHOICE OF CONDITIONS FOR MHD SIMULATIONS ABOVE THE ACTIVE REGION, ALLOWING THE STUDY OF THE SOLAR FLARE MECHANISM

2021 ◽  
Vol 44 ◽  
pp. 92-95
Author(s):  
A.I. Podgorny ◽  
◽  
I.M. Podgorny ◽  
A.V. Borisenko ◽  
N.S. Meshalkina ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Active Region ◽  
Solar Flare ◽  
Magnetic Energy ◽  
Solar Radius ◽  
Computational Domain ◽  
Mhd Simulations ◽  
Flare Energy ◽  
Numerical Instabilities ◽  
The Magnetic Field

Primordial release of solar flare energy high in corona (at altitudes 1/40 - 1/20 of the solar radius) is explained by release of the magnetic energy of the current sheet. The observed manifestations of the flare are explained by the electrodynamical model of a solar flare proposed by I. M. Podgorny. To study the flare mechanism is necessary to perform MHD simulations above a real active region (AR). MHD simulation in the solar corona in the real scale of time can only be carried out thanks to parallel calculations using CUDA technology. Methods have been developed for stabilizing numerical instabilities that arise near the boundary of the computational domain. Methods are applicable for low viscosities in the main part of the domain, for which the flare energy is effectively accumulated near the singularities of the magnetic field. Singular lines of the magnetic field, near which the field can have a rather complex configuration, coincide or are located near the observed positions of the flare.

scholarly journals The development of magnetic field line wander by plasma turbulence

2017 ◽  
Vol 83 (4) ◽  
Author(s):  
Gregory G. Howes ◽  
Sofiane Bourouaine
Keyword(s):  
Magnetic Field ◽  
Field Line ◽  
Magnetic Field Line ◽  
Large Scale ◽  
Magnetic Energy ◽  
Plasma Turbulence ◽  
Alfven Wave ◽  
Astrophysical Plasmas ◽  
Field Lines ◽  
The Magnetic Field

Plasma turbulence occurs ubiquitously in space and astrophysical plasmas, mediating the nonlinear transfer of energy from large-scale electromagnetic fields and plasma flows to small scales at which the energy may be ultimately converted to plasma heat. But plasma turbulence also generically leads to a tangling of the magnetic field that threads through the plasma. The resulting wander of the magnetic field lines may significantly impact a number of important physical processes, including the propagation of cosmic rays and energetic particles, confinement in magnetic fusion devices and the fundamental processes of turbulence, magnetic reconnection and particle acceleration. The various potential impacts of magnetic field line wander are reviewed in detail, and a number of important theoretical considerations are identified that may influence the development and saturation of magnetic field line wander in astrophysical plasma turbulence. The results of nonlinear gyrokinetic simulations of kinetic Alfvén wave turbulence of sub-ion length scales are evaluated to understand the development and saturation of the turbulent magnetic energy spectrum and of the magnetic field line wander. It is found that turbulent space and astrophysical plasmas are generally expected to contain a stochastic magnetic field due to the tangling of the field by strong plasma turbulence. Future work will explore how the saturated magnetic field line wander varies as a function of the amplitude of the plasma turbulence and the ratio of the thermal to magnetic pressure, known as the plasma beta.

scholarly journals Spin-1/2 Particles under the Influence of a Uniform Magnetic Field in the Interior Schwarzschild Solution

Universe ◽  
2021 ◽  
Vol 7 (12) ◽  
pp. 467
Author(s):  
Fayçal Hammad ◽  
Alexandre Landry ◽  
Parvaneh Sadeghi
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Total Mass ◽  
Uniform Magnetic Field ◽  
Energy Levels ◽  
Relativistic Wave Equation ◽  
Relativistic Wave ◽  
Schwarzschild Solution ◽  
Relativistic Regime ◽  
The Magnetic Field

The relativistic wave equation for spin-1/2 particles in the interior Schwarzschild solution in the presence of a uniform magnetic field is obtained. The fully relativistic regime is considered, and the energy levels occupied by the particles are derived as functions of the magnetic field, the radius of the massive sphere and the total mass of the latter. As no assumption is made on the relative strengths of the particles’ interaction with the gravitational and magnetic fields, the relevance of our results to the physics of the interior of neutron stars, where both the gravitational and the magnetic fields are very intense, is discussed.

Kinematic dynamo problem in a linear velocity field

1984 ◽  
Vol 144 ◽  
pp. 1-11 ◽  
Author(s):  
Ya. B. Zel'Dovich ◽  
A. A. Ruzmaikin ◽  
S. A. Molchanov ◽  
D. D. Sokoloff
Keyword(s):  
Magnetic Field ◽  
Spatial Distribution ◽  
Velocity Field ◽  
Random Matrix ◽  
Magnetic Energy ◽  
Linear Velocity ◽  
Finite Conductivity ◽  
Kinematic Dynamo ◽  
Linear Velocity Field ◽  
The Magnetic Field

A magnetic field is shown to be asymptotically (t → ∞) decaying in a flow of finite conductivity with v = Cr, where C = Cζ(t) is a random matrix. The decay is exponential, and its rate does not depend on the conductivity. However, the magnetic energy increases exponentially owing to growth of the domain occupied by the field. The spatial distribution of the magnetic field is a set of thin ropes and (or) layers.

Fast magnetic field penetration into low resistivity plasma

2017 ◽  
Vol 83 (1) ◽  
Author(s):  
Amnon Fruchtman
Keyword(s):  
Magnetic Field ◽  
Energy Dissipation ◽  
Electric Field ◽  
Density Gradient ◽  
Magnetic Energy ◽  
Measured Velocity ◽  
Magnetic Field Penetration ◽  
The Magnetic Field ◽  
Uniform Plasma ◽  
Field Penetration

Penetration of a magnetic field into plasma that is faster than resistive diffusion can be induced by the Hall electric field in a non-uniform plasma. This mechanism explained successfully the measured velocity of the magnetic field penetration into pulsed plasmas. Major related issues have not yet been resolved. Such is the theoretically predicted, but so far not verified experimentally, high magnetic energy dissipation, as well as the correlation between the directions of the density gradient and of the field penetration.

Existence and Energy Balance of the Solar Dynamo

1993 ◽  
Vol 157 ◽  
pp. 19-23
Author(s):  
J.H.G.M. van Geffen
Keyword(s):  
Magnetic Field ◽  
Energy Balance ◽  
Energy Method ◽  
Magnetic Energy ◽  
Mean Field ◽  
Solar Dynamo ◽  
Ensemble Averaging ◽  
Dynamo Theory ◽  
The Magnetic Field ◽  
Mean Field Dynamo

The idea behind the use of ensemble averaging and the finite magnetic energy method of van Geffen and Hoyng (1992) is briefly discussed. Applying this method to the solar dynamo shows that the turbulence — an essential ingredient of traditional mean field dynamo theory — poses grave problems: the turbulence makes the magnetic field so unstable that it becomes impossible to recognize any period.

scholarly journals Spin Polarization Oscillations and Coherence Time in the Random Interaction Approach

2019 ◽  
Vol 2019 ◽  
pp. 1-10
Author(s):  
P. Pereyra
Keyword(s):  
Magnetic Field ◽  
Time Evolution ◽  
Spin Polarization ◽  
Energy Levels ◽  
Coherence Time ◽  
Environment Interaction ◽  
Interaction Picture ◽  
Gaussian Orthogonal Ensemble ◽  
Interaction Approach ◽  
The Magnetic Field

We study the time evolution of the survival probability and the spin polarization of a dissipative nondegenerate two-level system in the presence of a magnetic field in the Faraday configuration. We apply the Extended Gaussian Orthogonal Ensemble approach to model the stochastic system-environment interaction and calculate the survival and spin polarization to first and second order of the interaction picture. We present also the time evolution of the thermal average of these quantities as functions of the temperature, the magnetic field, and the energy-levels density, for ρ(ϵ)∝ϵs, in the subohmic, ohmic, and superohmic dissipation forms. We show that the behavior of the spin polarization calculated here agrees rather well with the time evolution of spin polarization observed and calculated, recently, for the electron-nucleus dynamics of Ga centers in dilute (Ga,N)As semiconductors.

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