scholarly journals Hamilton–Jacobi theory for continuation of magnetic field across a toroidal surface supporting a plasma pressure discontinuity

2010 ◽  
Vol 374 (33) ◽  
pp. 3308-3314 ◽  
Author(s):  
M. McGann ◽  
S.R. Hudson ◽  
R.L. Dewar ◽  
G. von Nessi
Keyword(s):  
Magnetic Field ◽  
Plasma Pressure ◽  
Toroidal Surface ◽  
Pressure Discontinuity

Plasma equilibrium in toroidal l = 3 stellarators

1980 ◽  
Vol 24 (3) ◽  
pp. 453-478 ◽  
Author(s):  
P. J. Fielding ◽  
W. N. G. Hitchon
Keyword(s):  
Magnetic Field ◽  
Aspect Ratio ◽  
Plasma Pressure ◽  
Large Aspect Ratio ◽  
Plasma Equilibrium ◽  
Density Profiles ◽  
Vertical Field ◽  
Mhd Equilibrium ◽  
Vacuum Fields

The equations of MHD equilibrium are solved by including plasma pressure and current in a large aspect-ratio ordering scheme for the calculation of toroidal, l = 3 stellarator vacuum fields. The extended ordering unifies the low-beta equilibrium theory for tokamaks and l = 3 stellarators, and allows solutions to be obtained simply for arbitrarily prescribed pressure and current density profiles. Expressions are given for the equilibrium magnetic field and the equation for the flux surfaces is calculated, including the effects of l = 3 shaping and toroidal displacement. These results are used to calculate equilibria for the parameters of CLEO stellarator, and we examine the role of an externally applied vertical field in reducing pressure-induced flux surface distortion and destruction.

Magnetohydrodynamic Equilibria

2020 ◽  
Author(s):  
Thomas Wiegelmann
Keyword(s):  
Magnetic Field ◽  
Boundary Conditions ◽  
Lorentz Force ◽  
Plasma Flow ◽  
Plasma Pressure ◽  
Mhd Equations ◽  
The Sun ◽  
Planetary Magnetospheres ◽  
Mhd Equilibria ◽  
The Magnetic Field

Magnetohydrodynamic equilibria are time-independent solutions of the full magnetohydrodynamic (MHD) equations. An important class are static equilibria without plasma flow. They are described by the magnetohydrostatic equations j×B=∇p+ρ∇Ψ,∇×B=μ0j,∇·B=0. B is the magnetic field, j the electric current density, p the plasma pressure, ρ the mass density, Ψ the gravitational potential, and µ0 the permeability of free space. Under equilibrium conditions, the Lorentz force j×B is compensated by the plasma pressure gradient force and the gravity force. Despite the apparent simplicity of these equations, it is extremely difficult to find exact solutions due to their intrinsic nonlinearity. The problem is greatly simplified for effectively two-dimensional configurations with a translational or axial symmetry. The magnetohydrostatic (MHS) equations can then be transformed into a single nonlinear partial differential equation, the Grad–Shafranov equation. This approach is popular as a first approximation to model, for example, planetary magnetospheres, solar and stellar coronae, and astrophysical and fusion plasmas. For systems without symmetry, one has to solve the full equations in three dimensions, which requires numerically expensive computer programs. Boundary conditions for these systems can often be deduced from measurements. In several astrophysical plasmas (e.g., the solar corona), the magnetic pressure is orders of magnitudes higher than the plasma pressure, which allows a neglect of the plasma pressure in lowest order. If gravity is also negligible, Equation 1 then implies a force-free equilibrium in which the Lorentz force vanishes. Generalizations of MHS equilibria are stationary equilibria including a stationary plasma flow (e.g., stellar winds in astrophysics). It is also possible to compute MHD equilibria in rotating systems (e.g., rotating magnetospheres, rotating stellar coronae) by incorporating the centrifugal force. MHD equilibrium theory is useful for studying physical systems that slowly evolve in time. In this case, while one has an equilibrium at each time step, the configuration changes, often in response to temporal changes of the measured boundary conditions (e.g., the magnetic field of the Sun for modeling the corona) or of external sources (e.g., mass loading in planetary magnetospheres). Finally, MHD equilibria can be used as initial conditions for time-dependent MHD simulations. This article reviews the various analytical solutions and numerical techniques to compute MHD equilibria, as well as applications to the Sun, planetary magnetospheres, space, and laboratory plasmas.

scholarly journals Nonlinear equilibrium structure of thin currents sheets: influence of electron pressure anisotropy

2004 ◽  
Vol 11 (5/6) ◽  
pp. 579-587 ◽  
Author(s):  
L. M. Zelenyi ◽  
H. V. Malova ◽  
V. Yu. Popov ◽  
D. Delcourt ◽  
A. S. Sharma
Keyword(s):  
Magnetic Field ◽  
Current Sheet ◽  
Magnetic Energy ◽  
Plasma Pressure ◽  
Quasi Equilibrium ◽  
Electrostatic Effects ◽  
Current Sheets ◽  
Thin Current Sheet ◽  
Field Lines ◽  
The Magnetic Field

Abstract. Thin current sheets represent important and puzzling sites of magnetic energy storage and subsequent fast release. Such structures are observed in planetary magnetospheres, solar atmosphere and are expected to be widespread in nature. The thin current sheet structure resembles a collapsing MHD solution with a plane singularity. Being potential sites of effective energy accumulation, these structures have received a good deal of attention during the last decade, especially after the launch of the multiprobe CLUSTER mission which is capable of resolving their 3D features. Many theoretical models of thin current sheet dynamics, including the well-known current sheet bifurcation, have been developed recently. A self-consistent 1D analytical model of thin current sheets in which the tension of the magnetic field lines is balanced by the ion inertia rather than by the plasma pressure gradients was developed earlier. The influence of the anisotropic electron population and of the corresponding electrostatic field that acts to restore quasi-neutrality of the plasma is taken into account. It is assumed that the electron motion is fluid-like in the direction perpendicular to the magnetic field and fast enough to support quasi-equilibrium Boltzmann distribution along the field lines. Electrostatic effects lead to an interesting feature of the current density profile inside the current sheet, i.e. a narrow sharp peak of electron current in the very center of the sheet due to fast curvature drift of the particles in this region. The corresponding magnetic field profile becomes much steeper near the neutral plane although the total cross-tail current is in all cases dominated by the ion contribution. The dependence of electrostatic effects on the ion to electron temperature ratio, the curvature of the magnetic field lines, and the average electron magnetic moment is also analyzed. The implications of these effects on the fine structure of thin current sheets and their potential impact on substorm dynamics are presented.

scholarly journals Magnetohydrostatic modeling of AR11768 based on a SUNRISE/IMaX vector magnetogram

2020 ◽  
Vol 640 ◽  
pp. A103 ◽  
Author(s):  
X. Zhu ◽  
T. Wiegelmann ◽  
S K. Solanki
Keyword(s):  
Magnetic Field ◽  
High Resolution ◽  
Field Measurements ◽  
Plasma Pressure ◽  
Photospheric Magnetic Field ◽  
Solar Photosphere ◽  
Free Layer ◽  
Lower Boundary Condition ◽  
Magnetic Field Measurements ◽  
The Magnetic Field

Context. High-resolution magnetic field measurements are routinely only done in the solar photosphere. Higher layers, such as the chromosphere and corona, can be modeled by extrapolating these photospheric magnetic field vectors upward. In the solar corona, plasma forces can be neglected and the Lorentz force vanishes. This is not the case in the upper photosphere and chromosphere where magnetic and nonmagnetic forces are equally important. One way to deal with this problem is to compute the plasma and magnetic field self-consistently, in lowest order with a magnetohydrostatic (MHS) model. The non-force-free layer is rather thin and MHS models require high-resolution photospheric magnetic field measurements as the lower boundary condition. Aims. We aim to derive the magnetic field, plasma pressure, and density of AR11768 by applying the newly developed extrapolation technique to the SUNRISE/IMaX data embedded in SDO/HMI magnetogram. Methods. We used an optimization method for the MHS modeling. The initial conditions consist of a nonlinear force-free field (NLFFF) and a gravity-stratified atmosphere. During the optimization procedure, the magnetic field, plasma pressure, and density are computed self-consistently. Results. In the non-force-free layer, which is spatially resolved by the new code, Lorentz forces are effectively balanced by the gas pressure gradient force and gravity force. The pressure and density are depleted in strong field regions, which is consistent with observations. Denser plasma, however, is also observed at some parts of the active region edges. In the chromosphere, the fibril-like plasma structures trace the magnetic field nicely. Bright points in SUNRISE/SuFI 3000 Å images are often accompanied by the plasma pressure and electric current concentrations. In addition, the average of angle between MHS field lines and the selected chromospheric fibrils is 11.8°, which is smaller than those computed from the NLFFF model (15.7°) and linear MHS model (20.9°). This indicates that the MHS solution provides a better representation of the magnetic field in the chromosphere.

scholarly journals Velocity Shear Instabilities in the Anisotropic Solar Wind

1985 ◽  
Vol 107 ◽  
pp. 371-374
Author(s):  
Stefano Migliuolo
Keyword(s):  
Magnetic Field ◽  
Growth Rate ◽  
Solar Wind ◽  
Magnetic Energy ◽  
Equilibrium Temperature ◽  
Acoustic Mode ◽  
Plasma Pressure ◽  
Velocity Shear ◽  
Linear Growth Rate ◽  
Quasilinear Theory

The linear and quasilinear theory of perturbations in finite-β (β is the ratio of plasma pressure to magnetic energy density), collisionless plasmas, that have sheared (velocity) flows, is developed. A simple, one-dimensional magnetic field geometry is assumed to adequately represent solar wind conditions near the sun (i.e., at R ≃ 0.3 AU). Two modes are examined in detail: an ion-acoustic mode (finite-β stabilized) and a compressional Alfven mode (finite-β threshold, high-β stabilization). The role played by equilibrium temperature anisotropies, in the linear stability of these modes, is also presented. From the quasilinear theory, two results are obtained. First, the feedback of these waves on the state of the wind is such as to heat (cool) the ions in the direction perpendicular (parallel) to the equilibrium magnetic field. The opposite effect is found for the electrons. This is in qualitative agreement with the observed anisotropies of ions and electrons, in fast solar wind streams. Second, these quasilinear temperature changes are shown to result in a quasilinear growth rate that is lower than the linear growth rate, suggesting saturation of these instabilities.

scholarly journals Cluster observations of flux rope structures in the near-tail

2006 ◽  
Vol 24 (2) ◽  
pp. 651-666 ◽  
Author(s):  
P. D. Henderson ◽  
C. J. Owen ◽  
I. V. Alexeev ◽  
J. Slavin ◽  
A. N. Fazakerley ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Plasma Sheet ◽  
Lower Estimate ◽  
Flux Rope ◽  
Plasma Pressure ◽  
Magnetic Pressure ◽  
Total Force ◽  
Core Field ◽  
Flux Ropes ◽  
The Magnetic Field

Abstract. An investigation of the 2003 Cluster tail season has revealed small flux ropes in the near-tail plasma sheet of Earth. These flux ropes manifest themselves as a bipolar magnetic field signature (usually predominantly in the Z-component) associated with a strong transient peak in one or more of the other components (usually the Y-component). These signatures are interpreted as the passage of a cylindrical magnetic structure with a strong axial magnetic field over the spacecraft position. On the 2 October 2003 all four Cluster spacecraft observed a flux rope in the plasma sheet at X (GSM) ~-17 RE. The flux rope was travelling Earthward and duskward at ~160 kms-1, as determined from multi-spacecraft timing. This is consistent with the observed south-then-north bipolar BZ signature and corresponds to a size of ~0.3 RE (a lower estimate, measuring between the inflection points of the bipolar signature). The axis direction, determined from multi-spacecraft timing and the direction of the strong core field, was close to the intermediate variance direction of the magnetic field. The current inside the flux rope, determined from the curlometer technique, was predominantly parallel to the magnetic field. However, throughout the flux rope, but more significant in the outer sections, a non-zero component of current perpendicular to the magnetic field existed. This shows that the flux rope was not in a "constant α" force-free configuration, i.e. the magnetic force, J×B was also non-zero. In the variance frame of the magnetic field, the components of J×B suggest that the magnetic pressure force was acting to expand the flux rope, i.e. directed away from the centre of the flux rope, whereas the smaller magnetic tension force was acting to compress the flux rope. The plasma pressure is reduced inside the flux rope. A simple estimate of the total force acting on the flux rope from the magnetic forces and surrounding plasma suggests that the flux rope was experiencing an expansive total force. On 13 August 2003 all four Cluster spacecraft observed a flux rope at X (GSM) ~-18 RE. This flux rope was travelling tailward at 200 kms-1, consistent with the observed north-then-south bipolar BZ signature. The bipolar signature corresponds to a size of ~0.3 RE (lower estimate). In this case, the axis, determined from multi-spacecraft timing and the direction of the strong core field, was directed close to the maximum variance direction of the magnetic field. The current had components both parallel and perpendicular to the magnetic field, and J×B was again larger in the outer sections of the flux rope than in the centre. This flux rope was also under expansive magnetic pressure forces from J×B, i.e. directed away from the centre of the flux rope, and had a reduced plasma pressure inside the flux rope. A simple total force calculation suggests that this flux rope was experiencing a large expansive total force. The observations of a larger J×B signature in the outer sections of the flux ropes when compared to the centre may be explained if the flux ropes are observed at an intermediate stage of their evolution after creation by reconnection at multiple X lines near the Cluster apogee. It is suggested that these flux ropes are in the process of relaxing towards the force-free like configuration often observed further down the tail. The centre of the flux ropes may contain older reconnected flux at a later evolutionary stage and may therefore be more force-free.

scholarly journals Sustainment of High-Beta Mirror Plasma by Neutral Beams

2018 ◽  
Vol 5 (3) ◽  
pp. 125-127
Author(s):  
T. D. Akhmetov ◽  
V. I. Davydenko ◽  
A. A. Ivanov ◽  
S. V. Murakhtin
Keyword(s):  
Magnetic Field ◽  
Plasma Pressure ◽  
Budker Institute ◽  
Maximum Plasma ◽  
Axially Symmetric ◽  
Field Reversal ◽  
Neutral Beams ◽  
Gas Dynamic ◽  
High Beta ◽  
Fast Ion

The report presents two experiments carried out in Budker Institute for obtaining the maximum plasma beta (ratio of the plasma pressure to magnetic field pressure) in axially symmetric magnetic field. The experiments are based on injection of powerful focused neutral beams with high neutral power density in the plasma. The produced fast ion population significantly increases the plasma pressure. It the axially symmetric GDT experiment (Gas Dynamic Trap) the plasma beta exceeded 0.6 at the fast ion turning points. The CAT experiment (Compact Axisymmetric Toroid) is being prepared for obtaining a plasmoid with extremely high diamagnetism in axially symmetric magnetic field. Reversal of magnetic field in the plasmoid is possible in this experiment.

The evolution of magnetic flux ropes in sheared plasma flows

2000 ◽  
Vol 64 (1) ◽  
pp. 41-55 ◽  
Author(s):  
J. M. SCHMIDT ◽  
P. J. CARGILL
Keyword(s):  
Magnetic Field ◽  
Magnetic Flux ◽  
Shear Layer ◽  
Cross Section ◽  
Circular Cross Section ◽  
Flux Rope ◽  
Plasma Pressure ◽  
Magnetic Flux Ropes ◽  
Flux Ropes ◽  
The Magnetic Field

The evolution of magnetic flux ropes in a sheared plasma flow is investigated. When the magnetic field outside the flux rope lies parallel to the axis of the flux rope, a flux rope of circular cross-section, whose centre is located at the midpoint of the shear layer, has its shape distorted, but remains in the shear layer. Small displacements of the flux-rope centre above or below the midpoint of the shear layer lead to the flux-rope being expelled from the shear layer. This motion arises because small asymmetries in the plasma pressure around the flux-rope boundary leads to a force that forces the flux rope into a region of uniform flow. When the magnetic field outside the flux rope lies in a plane perpendicular to the flux-rope axis, the flux rope and external magnetic field reconnect with each other, leading to the destruction of the flux rope.

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