scholarly journals Perturbing an axisymmetric magnetic equilibrium to obtain a quasi-axisymmetric stellarator

2020 ◽  
Vol 86 (4) ◽  
Author(s):  
G. G. Plunk
Keyword(s):  
Magnetic Field ◽  
Field Strength ◽  
Numerical Optimization ◽  
External Rotation ◽  
Local Current ◽  
Rotational Transform ◽  
Average Size ◽  
Perturbed Magnetic Field ◽  
Magnetic Equilibrium ◽  
Axisymmetric Perturbations

It is demonstrated that finite-pressure, approximately quasi-axisymmetric stellarator equilibria can be directly constructed (without numerical optimization) via perturbations of given axisymmetric equilibria. The size of such perturbations is measured in two ways, via the fractional external rotation and, alternatively, via the relative magnetic field strength, i.e. the average size of the perturbed magnetic field, divided by the unperturbed field strength. It is found that significant fractional external rotational transform can be generated by quasi-axisymmetric perturbations, with a similar value of the relative field strength, despite the fact that the former scales more weakly with the perturbation size. High mode number perturbations are identified as a candidate for generating such transform with local current distributions. Implications for the development of a general non-perturbative solver for optimal stellarator equilibria are discussed.

scholarly journals Resistive evolution of toroidal field distributions and their relation to magnetic clouds

2019 ◽  
Vol 85 (1) ◽  
Author(s):  
C. B. Smiet ◽  
H. J. de Blank ◽  
T. A. de Jong ◽  
D. N. L. Kok ◽  
D. Bouwmeester
Keyword(s):  
Magnetic Field ◽  
Solar Wind ◽  
Field Strength ◽  
Magnetic Field Strength ◽  
Magnetic Clouds ◽  
Twisted Field ◽  
Field Lines ◽  
Rotational Transform ◽  
Universal Pattern ◽  
The Magnetic Field

We study the resistive evolution of a localized self-organizing magnetohydrodynamic equilibrium. In this configuration the magnetic forces are balanced by a pressure force caused by a toroidal depression in the pressure. Equilibrium is attained when this low-pressure region prevents further expansion into the higher-pressure external plasma. We find that, for the parameters investigated, the resistive evolution of the structures follows a universal pattern when rescaled to resistive time. The finite resistivity causes both a decrease in the magnetic field strength and a finite slip of the plasma fluid against the static equilibrium. This slip is caused by a Pfirsch–Schlüter-type diffusion, similar to what is seen in tokamak equilibria. The net effect is that the configuration remains in magnetostatic equilibrium whilst it slowly grows in size. The rotational transform of the structure becomes nearly constant throughout the entire structure, and decreases according to a power law. In simulations this equilibrium is observed when highly tangled field lines relax in a high-pressure (relative to the magnetic field strength) environment, a situation that occurs when the twisted field of a coronal loop is ejected into the interplanetary solar wind. In this paper we relate this localized magnetohydrodynamic equilibrium to magnetic clouds in the solar wind.

scholarly journals Direct construction of optimized stellarator shapes. Part 1. Theory in cylindrical coordinates

2018 ◽  
Vol 84 (6) ◽  
Author(s):  
Matt Landreman ◽  
Wrick Sengupta
Keyword(s):  
Magnetic Field ◽  
Field Strength ◽  
Magnetic Field Strength ◽  
Interesting Case ◽  
Magnetic Axis ◽  
Surface Shape ◽  
Cylindrical Coordinates ◽  
Direct Construction ◽  
Rotational Transform ◽  
The Magnetic Field

The confinement of the guiding-centre trajectories in a stellarator is determined by the variation of the magnetic field strength $B$ in Boozer coordinates $(r,\unicode[STIX]{x1D703},\unicode[STIX]{x1D711})$, but $B(r,\unicode[STIX]{x1D703},\unicode[STIX]{x1D711})$ depends on the flux surface shape in a complicated way. Here we derive equations relating $B(r,\unicode[STIX]{x1D703},\unicode[STIX]{x1D711})$ in Boozer coordinates and the rotational transform to the shape of flux surfaces in cylindrical coordinates, using an expansion in distance from the magnetic axis. A related expansion was done by Garren and Boozer (Phys. Fluids B, vol. 3, 1991a, 2805) based on the Frenet–Serret frame, which can be discontinuous anywhere the magnetic axis is straight, a situation that occurs in the interesting case of omnigenity with poloidally closed $B$ contours. Our calculation in contrast does not use the Frenet–Serret frame. The transformation between the Garren–Boozer approach and cylindrical coordinates is derived, and the two approaches are shown to be equivalent if the axis curvature does not vanish. The expressions derived here help enable optimized plasma shapes to be constructed that can be provided as input to VMEC and other stellarator codes, or to generate initial configurations for conventional stellarator optimization.

On the Configuration of the Magnetic Field of β CrB

1976 ◽  
Vol 32 ◽  
pp. 613-622
Author(s):  
I.A. Aslanov ◽  
Yu.S. Rustamov
Keyword(s):  
Magnetic Field ◽  
Field Strength ◽  
Radial Velocity ◽  
Magnetic Field Strength ◽  
Complex Shape ◽  
Rotation Period ◽  
Field Variation ◽  
Magnetic Field Variation ◽  
Secular Variations ◽  
The Magnetic Field

SummaryMeasurements of the radial velocities and magnetic field strength of β CrB were carried out. It is shown that there is a variability with the rotation period different for various elements. The curve of the magnetic field variation measured from lines of 5 different elements: FeI, CrI, CrII, TiII, ScII and CaI has a complex shape specific for each element. This may be due to the presence of magnetic spots on the stellar surface. A comparison with the radial velocity curves suggests the presence of a least 4 spots of Ti and Cr coinciding with magnetic spots. A change of the magnetic field with optical depth is shown. The curve of the Heffvariation with the rotation period is given. A possibility of secular variations of the magnetic field is shown.

2D analysis of magnetic field strength in GO SiFe steel sheets

1998 ◽  
Vol 08 (PR2) ◽  
pp. Pr2-579-Pr2-582 ◽  
Author(s):  
S. Tumanski ◽  
M. Stabrowski
Keyword(s):  
Magnetic Field ◽  
Field Strength ◽  
Magnetic Field Strength ◽  
Steel Sheets

MAGNETIC FIELD, PRESSURE AND TEMPERATURE DEPENDENT OPTICAL PROPERTIES IN A GaAs 9.0 P 1.0 QUANTUM DOT

2014 ◽  
Vol 6 (2) ◽  
pp. 1178-1190
Author(s):  
A. JOHN PETER ◽  
Ada Vinolin
Keyword(s):  
Magnetic Field ◽  
Optical Properties ◽  
Quantum Dot ◽  
Field Strength ◽  
Magnetic Field Strength ◽  
Photon Energy ◽  
Nonlinear Optical ◽  
Binding Energies ◽  
Nonlinear Optical Properties ◽  
Optical Rectification

Simultaneous effects of magnetic field, pressure and temperature on the exciton binding energies are found in a 9.0 1.0 6.0 4.0 GaAs P / GaAs P quantum dot. Numerical calculations are carried out taking into consideration of spatial confinement effect. The cylindrical system is taken in the present problem with the strain effects. The electronic properties and the optical properties are found with the combined effects of magnetic field strength, hydrostatic pressure and temperature values. The exciton binding energies and the nonlinear optical properties are carried out taking into consideration of geometrical confinement and the external perturbations.Compact density approach is employed to obtain the nonlinear optical properties. The optical rectification coefficient is obtained with the photon energy in the presence of pressure, temperature and external magnetic field strength. Pressure and temperature dependence on nonlinear optical susceptibilities of generation of second and third order harmonics as a function of incident photon energy are brought out in the influence of magnetic field strength. The result shows that the electronic and nonlinear optical properties are significantly modified by the applications of external perturbations in a 9.0 1.0 6.0 4.0 GaAs P / GaAs P quantum dot.

Magnetic field strength dependence of chemical shift artifacts

1988 ◽  
Vol 12 (2) ◽  
pp. 89-96 ◽  
Author(s):  
R. Lufkin ◽  
M. Anselmo ◽  
J. Crues ◽  
W. Smoker ◽  
W. Hanafee
Keyword(s):  
Magnetic Field ◽  
Chemical Shift ◽  
Field Strength ◽  
Magnetic Field Strength ◽  
Strength Dependence

scholarly journals Figures of merit for stellarators near the magnetic axis

2021 ◽  
Vol 87 (1) ◽  
Author(s):  
Matt Landreman
Keyword(s):  
Magnetic Field ◽  
Field Strength ◽  
Magnetic Axis ◽  
Configuration Design ◽  
New Paradigm ◽  
First Order ◽  
Figures Of Merit ◽  
Minor Radius ◽  
Error Field ◽  
Quantities Of Interest

A new paradigm for rapid stellarator configuration design has been recently demonstrated, in which the shapes of quasisymmetric or omnigenous flux surfaces are computed directly using an expansion in small distance from the magnetic axis. To further develop this approach, here we derive several other quantities of interest that can be rapidly computed from this near-axis expansion. First, the $\boldsymbol {\nabla }\boldsymbol {B}$ and $\boldsymbol {\nabla }\boldsymbol {\nabla }\boldsymbol {B}$ tensors are computed, which can be used for direct derivative-based optimization of electromagnetic coil shapes to achieve the desired magnetic configuration. Moreover, if the norm of these tensors is large compared with the field strength for a given magnetic field, the field must have a short length scale, suggesting it may be hard to produce with coils that are suitably far away. Second, we evaluate the minor radius at which the flux surface shapes would become singular, providing a lower bound on the achievable aspect ratio. This bound is also shown to be related to an equilibrium beta limit. Finally, for configurations that are constructed to achieve a desired magnetic field strength to first order in the expansion, we compute the error field that arises due to second-order terms.

Effect of external magnetic field on lane formation in driven pair-ion plasmas

2021 ◽  
Vol 87 (2) ◽  
Author(s):  
Swati Baruah ◽  
U. Sarma ◽  
R. Ganesh
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Field Strength ◽  
Electric Field ◽  
Electric Field Strength ◽  
Coupling Parameter ◽  
Critical Parameters ◽  
Coulomb Coupling ◽  
Lane Formation ◽  
Parameter Values

Lane formation dynamics in externally driven pair-ion plasma (PIP) particles is studied in the presence of external magnetic field using Langevin dynamics (LD) simulation. The phase diagram obtained distinguishing the no-lane and lane states is systematically determined from a study of various Coulomb coupling parameter values. A peculiar lane formation-disintegration parameter space is identified; lane formation area extended to a wide range of Coulomb coupling parameter values is observed before disappearing to a mixed phase. The different phases are identified by calculating the order parameter. This and the critical parameters are calculated directly from LD simulation. The critical electric field strength value above which the lanes are formed distinctly is obtained, and it is observed that in the presence of the external magnetic field, the PIP system requires a higher value of the electric field strength to enter into the lane formation state than that in the absence of the magnetic field. We further find out the critical value of electric field frequency beyond which the system exhibits a transition back to the disordered state and this critical frequency is found as an increasing function of the electric field strength in the presence of an external magnetic field. The movement of the lanes is also observed in a direction perpendicular to that of the applied electric and magnetic field directions, which reveals the existence of the electric field drift in the system under study. We also use an oblique force field as the external driving force, both in the presence and absence of the external magnetic field. The application of this oblique force changes the orientation of the lane structures for different applied oblique angle values.

scholarly journals Simulations of Switchback, Fragmentation and Sunspot Pair in δ-Sunspots during Magnetic Flux Emergence

Sensors ◽  
2021 ◽  
Vol 21 (2) ◽  
pp. 586
Author(s):  
Che-Jui Chang ◽  
Jean-Fu Kiang
Keyword(s):  
Magnetic Field ◽  
Solar System ◽  
Field Strength ◽  
Magnetic Flux ◽  
Initial Conditions ◽  
Observation Data ◽  
Flux Emergence ◽  
Polarity Inversion ◽  
Simulation Results ◽  
Spot Type

Strong flares and coronal mass ejections (CMEs), launched from δ-sunspots, are the most catastrophic energy-releasing events in the solar system. The formations of δ-sunspots and relevant polarity inversion lines (PILs) are crucial for the understanding of flare eruptions and CMEs. In this work, the kink-stable, spot-spot-type δ-sunspots induced by flux emergence are simulated, under different subphotospheric initial conditions of magnetic field strength, radius, twist, and depth. The time evolution of various plasma variables of the δ-sunspots are simulated and compared with the observation data, including magnetic bipolar structures, relevant PILs, and temperature. The simulation results show that magnetic polarities display switchbacks at a certain stage and then split into numerous fragments. The simulated fragmentation phenomenon in some δ-sunspots may provide leads for future observations in the field.

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