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Title: Riemannian geometry of twisted magnetic flux tubes in almost helical plasma flows

Abstract

Riemannian geometry of curves applied recently by Ricca [Fluid Dyn. Res 36, 319 (2005)] in the case of inflectional disequilibrium of twisted magnetic flux tubes is used here to compute the magnetic helicity force-free field case. Here the application of Lorentz force-free to the magnetic flux tube in tokamaks allows one to obtain an equation that generalizes the cylindrical tokamak equation by a term that contains the curvature of the magnetic flux tube. Another example of the use of the magnetic flux tube is done by taking the electron magnetohydrodynamics (MHD) fluid model (EMHD) of plasma physics that allows one to compute the velocity of the fluid in helical and almost helical flows in terms of the Frenet torsion of thin magnetic flux tubes. The cases of straight and curved twisted tubes are examined. Second-order effects on the Frenet torsion arise on the poloidal component of the magnetic field, while curvature effects appear in the toroidal component. The magnetic fields are computed in terms of the penetration depth used in superconductors. The ratio between poloidal and toroidal components of the magnetic field depends on the torsion and curvature of the magnetic flux tube. It is shown that the rotation ofmore » the almost helical plasma flow contributes to the twist of the magnetic flux tube through the total Frenet torsion along the tube.« less

Authors:
 [1]
  1. Departamento de Fisica Teorica, Instituto de Fisica-UERJ Rua Sao Fco. Xavier 524, Rio de Janeiro, RJ Maracana, CEP:20550-003 (Brazil)
Publication Date:
OSTI Identifier:
20782501
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physics of Plasmas; Journal Volume: 13; Journal Issue: 2; Other Information: DOI: 10.1063/1.2172363; (c) 2006 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY; ELECTRONS; EQUATIONS; FLUID FLOW; GEOMETRY; HELICITY; LORENTZ FORCE; MAGNETIC FIELDS; MAGNETIC FLUX; MAGNETOHYDRODYNAMICS; PENETRATION DEPTH; PLASMA; PLASMA CONFINEMENT; PLASMA SIMULATION; ROTATION; TOKAMAK DEVICES; TORSION; TUBES

Citation Formats

Garcia de Andrade, L.C.. Riemannian geometry of twisted magnetic flux tubes in almost helical plasma flows. United States: N. p., 2006. Web. doi:10.1063/1.2172363.
Garcia de Andrade, L.C.. Riemannian geometry of twisted magnetic flux tubes in almost helical plasma flows. United States. doi:10.1063/1.2172363.
Garcia de Andrade, L.C.. Wed . "Riemannian geometry of twisted magnetic flux tubes in almost helical plasma flows". United States. doi:10.1063/1.2172363.
@article{osti_20782501,
title = {Riemannian geometry of twisted magnetic flux tubes in almost helical plasma flows},
author = {Garcia de Andrade, L.C.},
abstractNote = {Riemannian geometry of curves applied recently by Ricca [Fluid Dyn. Res 36, 319 (2005)] in the case of inflectional disequilibrium of twisted magnetic flux tubes is used here to compute the magnetic helicity force-free field case. Here the application of Lorentz force-free to the magnetic flux tube in tokamaks allows one to obtain an equation that generalizes the cylindrical tokamak equation by a term that contains the curvature of the magnetic flux tube. Another example of the use of the magnetic flux tube is done by taking the electron magnetohydrodynamics (MHD) fluid model (EMHD) of plasma physics that allows one to compute the velocity of the fluid in helical and almost helical flows in terms of the Frenet torsion of thin magnetic flux tubes. The cases of straight and curved twisted tubes are examined. Second-order effects on the Frenet torsion arise on the poloidal component of the magnetic field, while curvature effects appear in the toroidal component. The magnetic fields are computed in terms of the penetration depth used in superconductors. The ratio between poloidal and toroidal components of the magnetic field depends on the torsion and curvature of the magnetic flux tube. It is shown that the rotation of the almost helical plasma flow contributes to the twist of the magnetic flux tube through the total Frenet torsion along the tube.},
doi = {10.1063/1.2172363},
journal = {Physics of Plasmas},
number = 2,
volume = 13,
place = {United States},
year = {Wed Feb 15 00:00:00 EST 2006},
month = {Wed Feb 15 00:00:00 EST 2006}
}
  • The nonlinear response of an axisymmetric magnetic flux tube under the influence of an azimuthal twist force is studied. For a constant twist force, the tube approaches an inertial collapse phase in finite time. The competing pinch and magnetic pressure forces cause radial oscillation during the collapse. The plasma pressure is negligible in the process. When the tube is subject to a random twist, each end of the tube absorbs angular momentum preferentially in the direction of the initial field line winding. Thus again, the tube is twisted up and collapses in finite time. For typical solar parameters, the collapsemore » time is a few tens of the coronal Alfven time. Both magnetic and kinetic energy increase explosively near the collapse as a result of the twist. The tube contracts to about one-tenth of its original size before reaching the kink threshold twist angle. {copyright} {ital 1995} {ital American} {ital Institute} {ital of} {ital Physics}.« less
  • The equilibrium structure of an axisymmetric twisted magnetic flux tube, confined by an external plasma pressure p/sub e/(z) which varies along the tube, is studied. Previous results for cylindrical twisted tubes, and for untwisted tubes in an inhomogeneous atmosphere, are generalized to take into account the effect of twist, of a varying pressure and of a radial field component.
  • The three-dimensional dynamical evolution of twisted magnetic flux tubes is studied using a time-dependent magnetohydrodynamic (MHD) model. The flux tubes are intended to model solar coronal loops, and include the stabilizing effect of photospheric line tying. The model permits the complete evolution of flux tubes to be followed self-consistently, including the formation, equilibrium, linear instability, and nonlinear behavior. Starting from an initial uniform background magnetic field, a twisted flux tube is created by the application of slow, localized photospheric vortex flows. The flux tube evolves quasi-statically through sequences of equilibria with increasing twist, until it becomes linearly unstable to anmore » ideal MHD kink mode. In this paper, the equilibrium properties and the linear stability behavior are discussed. The application of the method to the uniform-twist, Gold-Hoyle field confirms the previous stability threshold for kink instability and provides estimates of the resulting growth rate. 29 refs.« less
  • We present the new results of the two-dimensional numerical experiments on the cross-sectional evolution of a twisted magnetic flux tube rising from the deeper solar convection zone (-20,000 km) to the corona through the surface. The initial depth is 10 times deeper than most of the previous calculations focusing on the flux emergence from the uppermost convection zone. We find that the evolution is illustrated by the following two-step process. The initial tube rises due to its buoyancy, subject to aerodynamic drag due to the external flow. Because of the azimuthal component of the magnetic field, the tube maintains itsmore » coherency and does not deform to become a vortex roll pair. When the flux tube approaches the photosphere and expands sufficiently, the plasma on the rising tube accumulates to suppress the tube's emergence. Therefore, the flux decelerates and extends horizontally beneath the surface. This new finding owes to our large-scale simulation, which simultaneously calculates the dynamics within the interior as well as above the surface. As the magnetic pressure gradient increases around the surface, magnetic buoyancy instability is triggered locally and, as a result, the flux rises further into the solar corona. We also find that the deceleration occurs at a higher altitude than assumed in our previous experiment using magnetic flux sheets. By conducting parametric studies, we investigate the conditions for the two-step emergence of the rising flux tube: field strength {approx}> 1.5 x 10{sup 4} G and the twist {approx}> 5.0 x 10{sup -4} km{sup -1} at -20,000 km depth.« less
  • Magnetic flux tubes in the solar wind can be twisted as they are transported from the solar surface, where the tubes are twisted due to photospheric motions. It is suggested that the twisted magnetic tubes can be detected as the variation of total (thermal+magnetic) pressure during their passage through the observing satellite. We show that the total pressure of several observed twisted tubes resembles the theoretically expected profile. The twist of the isolated magnetic tube may explain the observed abrupt changes of magnetic field direction at tube walls. We have also found some evidence that the flux tube walls canmore » be associated with local heating of the plasma and elevated proton and electron temperatures. For the tubes aligned with the Parker spiral, the twist angle can be estimated from the change of magnetic field direction. Stability analysis of twisted tubes shows that the critical twist angle of the tube with a homogeneous twist is 70°, but the angle can further decrease due to the motion of the tube with respect to the solar wind stream. The tubes with a stronger twist are unstable to the kink instability, therefore they probably cannot reach 1 AU.« less