Hydromagnetic Stabilization of Toroidal Systems without the Use of Shear in the Presence of Rotational Transform

1964 ◽  
Vol 7 (11) ◽  
pp. 1875 ◽  
Author(s):  
Andrew Lenard
Keyword(s):  
Rotational Transform

scholarly journals Hamiltonian Approach to Magnetic Fields with Toroidal Surfaces

1985 ◽  
Vol 40 (10) ◽  
pp. 959-967
Author(s):  
A. Salat
Keyword(s):  
Magnetic Field ◽  
Hamiltonian System ◽  
Magnetic Fields ◽  
Constant Pressure ◽  
Time Dependent ◽  
Hamiltonian Approach ◽  
One Dimensional ◽  
Mhd Equilibrium ◽  
Magnetic Surfaces ◽  
Rotational Transform

The equivalence of magnetic field line equations to a one-dimensional time-dependent Hamiltonian system is used to construct magnetic fields with arbitrary toroidal magnetic surfaces I = const. For this purpose Hamiltonians H which together with their invariants satisfy periodicity constraints have to be known. The choice of H fixes the rotational transform η(I). Arbitrary axisymmetric fields, and nonaxisymmetric fields with constant η(I) are considered in detail.Configurations with coinciding magnetic and current density surfaces are obtained. The approach used is not well suited, however, to satisfying the additional MHD equilibrium condition of constant pressure on magnetic surfaces.

Rotational Transform Angle of the Stellarator Field with Twisted Coils

1977 ◽  
Vol 16 (5) ◽  
pp. 813-816 ◽  
Author(s):  
Kazumi Ohasa ◽  
Kenro Miyamoto
Keyword(s):  
Rotational Transform

Effect of Rotational Transform on Toroidal Confinement

1972 ◽  
Vol 28 (16) ◽  
pp. 1022-1025 ◽  
Author(s):  
M. A. Hellberg ◽  
N. K. Winsor ◽  
J. M. Dawson
Keyword(s):  
Rotational Transform

Rotational Transform for Smoothing Correlated Field Data

1991 ◽  
Vol 7 (4) ◽  
pp. 393-399 ◽  
Author(s):  
A. L. Dillard ◽  
A. W. Thomas ◽  
W. M. Snyder
Keyword(s):  
Field Data ◽  
Rotational Transform

Drift resonance of impurity ions in a toroidal magnetic trap with rotational transform

2000 ◽  
Vol 7 (12) ◽  
pp. 5023-5032 ◽  
Author(s):  
A. A. Shishkin ◽  
A. V. Zolotukhin
Keyword(s):  
Magnetic Trap ◽  
Impurity Ions ◽  
Rotational Transform

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 Kinetic infernal modes for Wendelstein 7-X-like -profiles

2019 ◽  
Vol 85 (6) ◽  
Author(s):  
Alessandro Zocco ◽  
Alexey Mishchenko ◽  
Axel Könies
Keyword(s):  
Electron Temperature ◽  
High Performance ◽  
Ion Temperature ◽  
Electron Temperature Gradient ◽  
Average Value ◽  
Toroidal Plasma ◽  
Rotational Transform ◽  
Ideal Magnetohydrodynamic ◽  
The One ◽  
Sawtooth Oscillations

We show analytically that for $\unicode[STIX]{x1D704}$ -profiles similar to the one of the Wendelstein 7-X stellarator, where $\unicode[STIX]{x1D704}$ is the rotational transform of the equilibrium magnetic field, a highly conducting toroidal plasma is unstable to kinetically mediated pressure-driven long-wavelength reconnecting modes, of the infernal type. The modes are destabilized either by the electron temperature gradient or by a small amount of current, depending on how far from unity the average value of $\unicode[STIX]{x1D704}$ is, which is assumed to be slowly varying. We argue that, for W7-X, a broad mode with toroidal and poloidal mode numbers $(n,m)=(1,1)$ can be destabilized due to the strong geometric side-band coupling of the resonant kinetic electron response at locations where $\unicode[STIX]{x1D704}$ is rational for harmonics that belong to the mode family of the $(n,m)=(1,1)$ mode itself. In many regimes, the growth rate is insensitive to the plasma density, thus it is likely to persist in high performance W7-X discharges. For a peaked electron temperature, with a maximum of $T_{e}=5~\text{keV}$ , larger than the ion temperature, $T_{i}=2.5~\text{keV}$ , and a density $n_{0}=10^{19}~\text{m}^{-3}$ , instability is found in regimes which show plasma sawtooth activity, with growth rates of the order of tens of kiloHertz. Frequencies are either electron diamagnetic or of the ideal magnetohydrodynamic type, but sub-Alfvénic. The kinetic infernal mode is thus a good candidate for the explanation of sawtooth oscillations in present-day stellarators and poses a new challenge to the problem of stellarator reactor optimization.

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.

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