scholarly journals Bifurcations of the magnetic axis and the alternating-hyperbolic sawtooth

2020 ◽  
Vol 60 (8) ◽  
pp. 084005
Author(s):  
C.B. Smiet ◽  
G.J. Kramer ◽  
S.R. Hudson
Keyword(s):  
Magnetic Axis

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.

scholarly journals Direct construction of optimized stellarator shapes. Part 3. Omnigenity near the magnetic axis

2019 ◽  
Vol 85 (6) ◽  
Author(s):  
Gabriel G. Plunk ◽  
Matt Landreman ◽  
Per Helander
Keyword(s):  
Numerical Method ◽  
Plasma Phys ◽  
Magnetic Axis ◽  
Direct Construction ◽  
Numerical Construction ◽  
First Order

The condition of omnigenity is investigated, and applied to the near-axis expansion of Garren & Boozer (Phys. Fluids B, vol. 3 (10), 1991a, pp. 2805–2821). Due in part to the particular analyticity requirements of the near-axis expansion, we find that, excluding quasi-symmetric solutions, only one type of omnigenity, namely quasi-isodynamicity, can be satisfied at first order in the distance from the magnetic axis. Our construction provides a parameterization of the space of such solutions, and the cylindrical reformulation and numerical method of Landreman & Sengupta (J. Plasma Phys., vol. 84 (6), 2018, 905840616); Landreman et al. (J. Plasma Phys., vol. 85 (1), 2019, 905850103), enables their efficient numerical construction.

scholarly journals Effect of magnetic field on the burning of a neutron star

2018 ◽  
Vol 27 (10) ◽  
pp. 1850083 ◽  
Author(s):  
Ritam Mallick ◽  
Amit Singh
Keyword(s):  
Magnetic Field ◽  
Neutron Star ◽  
Initial Density ◽  
Considerable Effect ◽  
Magnetic Axis ◽  
Small Window ◽  
Exothermic Process ◽  
Text Density ◽  
The Magnetic Field ◽  
Observational Aspect

In this paper, we present the effect of a strong magnetic field in the burning of a neutron star (NS). We have used relativistic magneto-hydrostatic (MHS) conservation equations for studying the PT from nuclear matter (NM) to quark matter (QM). We found that the shock-induced phase transition (PT) is likely if the density of the star core is more than three times nuclear saturation ([Formula: see text]) density. The conversion process from NS to quark star (QS) is found to be an exothermic process beyond such densities. The burning process at the star center most likely starts as a deflagration process. However, there can be a small window at lower densities where the process can be a detonation one. At small enough infalling matter velocities the resultant magnetic field of the QS is lower than that of the NS. However, for a higher value of infalling matter velocities, the magnetic field of QM becomes larger. Therefore, depending on the initial density fluctuation and on whether the PT is a violent one or not the QS could be more magnetic or less magnetic. The PT also have a considerable effect on the tilt of the magnetic axis of the star. For smaller velocities and densities the magnetic angle are not affected much but for higher infalling velocities tilt of the magnetic axis changes suddenly. The magnetic field strength and the change in the tilt axis can have a significant effect on the observational aspect of the magnetars.

scholarly journals Near-axis expansion of stellarator equilibrium at arbitrary order in the distance to the axis

2020 ◽  
Vol 86 (1) ◽  
Author(s):  
R. Jorge ◽  
W. Sengupta ◽  
M. Landreman
Keyword(s):  
Magnetic Field ◽  
Aspect Ratio ◽  
Magnetic Flux ◽  
Arbitrary Order ◽  
Analytical Framework ◽  
Field Vector ◽  
Magnetic Axis ◽  
Direct Construction ◽  
Geometrical Properties ◽  
Rotational Transform

A direct construction of equilibrium magnetic fields with toroidal topology at arbitrary order in the distance from the magnetic axis is carried out, yielding an analytical framework able to explore the landscape of possible magnetic flux surfaces in the vicinity of the axis. This framework can provide meaningful analytical insight into the character of high-aspect-ratio stellarator shapes, such as the dependence of the rotational transform and the plasma beta limit on geometrical properties of the resulting flux surfaces. The approach developed here is based on an asymptotic expansion on the inverse aspect ratio of the ideal magnetohydrodynamics equation. The analysis is simplified by using an orthogonal coordinate system relative to the Frenet–Serret frame at the magnetic axis. The magnetic field vector, the toroidal magnetic flux, the current density, the field line label and the rotational transform are derived at arbitrary order in the expansion parameter. Moreover, a comparison with a near-axis expansion formalism employing an inverse coordinate method based on Boozer coordinates (the so-called Garren–Boozer construction) is made, where both methods are shown to agree at lowest order. Finally, as a practical example, a numerical solution using a W7-X equilibrium is presented, and a comparison between the lowest-order solution and the W7-X magnetic field is performed.

scholarly journals Circular Polarimetry of AM Herculis

1983 ◽  
Vol 72 ◽  
pp. 207-210
Author(s):  
V. Piirola ◽  
O. Vilhu ◽  
I. Tuominen
Keyword(s):  
Circular Polarization ◽  
Magnetic Axis ◽  
Light Curves ◽  
Short Term ◽  
Probable Explanation ◽  
Photometric Observations ◽  
Peak Value

ABSTRACTCircular polarimetry in the red and simultaneous photometric observations in the UBVRI bands during the period June 1-3, 1981, are discussed. The peak value of negative circular polarization PV ~ -15 % is stronger than observed in 1976-79. Variations in the shape of the polarization and light curves occur from night to night. The positive crossover and reversal of the sign of the circular polarization are only marginal. A probable explanation of the short term variations seems to be the changing shape and position of the accretion columns with respect to the magnetic axis

scholarly journals A Geometrical origin of the Pulsar Core and Conal Emissions

1996 ◽  
Vol 160 ◽  
pp. 229-230 ◽  
Author(s):  
R.C. Kapoor ◽  
C.S. Shukre
Keyword(s):  
Polar Angle ◽  
Quadratic Equation ◽  
Magnetic Axis ◽  
Polar Cap ◽  
The Core ◽  
The North ◽  
Polar Caps ◽  
Inclination Angles ◽  
Field Geometry ◽  
Field Lines

We have analysed the dipole magnetic field geometry for the general case of an oblique rotator and have found that open field lines which define the polar cap divide into two branches (Kapoor and Shukre 1996) which appear naturally relevant for distinguishing the core and conal emissions. The polar cap shape is actually determined by a quadratic equation having two roots leading to two values of the polar angle,θ+andθ−with respect to the magnetic axis for a given azimuth φ. For the north pole bothθ+andθ−branches are shown as polar plots in Fig. 1 for various inclination angles α and a typical pulsar period. The discussion of pulsar polar caps hitherto (e.g. Biggs 1990) had not distinguished between theθ+and theθ−solutions. The region defined by theθ+solution is completely contained inside the polar cap. It has a peculiar triangular shape whose lowest vertex is always on the magnetic axis. This naturally suggests an identification of theθ+and theθ−regions with the core and conal emission zones.

Toroidal plasma configuration with non-planar magnetic axis

1984 ◽  
Vol 32 (2) ◽  
pp. 179-196
Author(s):  
Hussain M. Rizk
Keyword(s):  
Cross Section ◽  
Ohmic Heating ◽  
Circular Cross Section ◽  
Magnetic Axis ◽  
Toroidal Plasma ◽  
Mhd Equilibrium ◽  
Special Cases ◽  
Magnetic Surfaces ◽  
Plasma Configuration ◽  
The Ideal

The ideal MHD equilibrium, stability, classical diffusion, effective thermal conductivity, and Ohmic heating of a zero-shear toroidal plasma configuration with a single non-planar magnetic axis of variable torsion and curvature are investigated. The plasma has a circular cross-section through which a longitudinal current density with arbitrary profile flows. In this type of magnetic configuration, the magnetic surfaces arbitrarily rotate around the magnetic axis. This magnetic toroidal configuration is of a stellarator type with a non-planar magnetic axis. The present work also covers as special cases tokamak and a magnetic toroidal plasma configuration with a magnetic axis of arbitrarily modulated curvature.

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