scholarly journals Equilibrium 𝛽-limits in classical stellarators

2017 ◽  
Vol 83 (6) ◽  
Author(s):  
J. Loizu ◽  
S. R. Hudson ◽  
C. Nührenberg ◽  
J. Geiger ◽  
P. Helander
Keyword(s):  
Scaling Laws ◽  
Magnetic Islands ◽  
Stochastic Field ◽  
Cambridge University ◽  
Minor Radius ◽  
Ideal Mhd ◽  
Pressure Equilibrium ◽  
Field Lines ◽  
High Beta ◽  
Shafranov Shift

A numerical investigation is carried out to understand the equilibrium $\unicode[STIX]{x1D6FD}$-limit in a classical stellarator. The stepped-pressure equilibrium code (Hudson et al., Phys. Plasmas, vol. 19 (11), 2012) is used in order to assess whether or not magnetic islands and stochastic field-lines can emerge at high $\unicode[STIX]{x1D6FD}$. Two modes of operation are considered: a zero-net-current stellarator and a fixed-iota stellarator. Despite the fact that relaxation is allowed (Taylor, Rev. Mod. Phys., vol. 58 (3), 1986, pp. 741–763), the former is shown to maintain good flux surfaces up to the equilibrium $\unicode[STIX]{x1D6FD}$-limit predicted by ideal-magnetohydrodynamics (MHD), above which a separatrix forms. The latter, which has no ideal equilibrium $\unicode[STIX]{x1D6FD}$-limit, is shown to develop regions of magnetic islands and chaos at sufficiently high $\unicode[STIX]{x1D6FD}$, thereby providing a ‘non-ideal $\unicode[STIX]{x1D6FD}$-limit’. Perhaps surprisingly, however, the value of $\unicode[STIX]{x1D6FD}$ at which the Shafranov shift of the axis reaches a fraction of the minor radius follows in all cases the scaling laws predicted by ideal-MHD. We compare our results to the High-Beta-Stellarator theory of Freidberg (Ideal MHD, 2014, Cambridge University Press) and derive a new prediction for the non-ideal equilibrium $\unicode[STIX]{x1D6FD}$-limit above which chaos emerges.

scholarly journals Theory of Protostellar Disk Formation

2015 ◽  
Vol 11 (S315) ◽  
pp. 118-125
Author(s):  
Zhi-Yun Li ◽  
Ruben Krasnopolsky ◽  
Hsien Shang
Keyword(s):  
Magnetic Field ◽  
Rotation Axis ◽  
Misalignment Angle ◽  
Disk Formation ◽  
Magnetic Field Rotation ◽  
Ideal Mhd ◽  
Magnetic Braking ◽  
Field Rotation ◽  
Field Lines ◽  
Protostellar Collapse

AbstractHow large, 100-AU scale, rotationally supported disks form around protostars remains unsettled, both observationally and theoretically. In this contribution, we discuss the theoretical difficulties with disk formation in the presence of a dynamically significant magnetic field and their possible resolutions. These difficulties are caused by the concentration of magnetic field lines close to the forming star by protostellar collapse, and the strong magnetic braking associated with the concentrated field. Possible resolutions include magnetic field-rotation axis misalignment, non-ideal MHD effects, and turbulence. The field-rotation misalignment has been shown to promote disk formation, especially when the field is relatively weak and the misalignment angle is relatively large. Non-ideal MHD effects can enable the formation of small disks at early times. How such disks grow at later times remains to be fully quantified. Turbulence has been found to enable disk formation in a number of simulations, but the exact reason for its beneficial effect is debated.

Zur Begrenzung der radial en Ausdehnung des Li chtbogenstromes durch ein axiales Magnetfeld. II. Skalengesetze und Vergleich mit Experimenten / On Limitation of the Radial Extent of the Arc Current by Means of an Axial Magnetic Field. II. Scaling Laws and Comparison with Experimental Results

1972 ◽  
Vol 27 (4) ◽  
pp. 652-670
Author(s):  
O. Klüber
Keyword(s):  
Magnetic Field ◽  
Cross Sections ◽  
Scaling Laws ◽  
Axial Magnetic Field ◽  
Angular Frequency ◽  
Model Calculations ◽  
Simple Geometry ◽  
Radial Extent ◽  
Arc Current ◽  
Field Lines

Abstract In an arc with superimposed axial magnetic field, radial current components cause a rotational motion of the plasma column and produce azimuthal Hall currents and hence electromotive forces such that the arc current is guided by the magnetic field lines. In the first part of this paper the steady-state plasma equations have been solved for a homogeneous plasma in simple geometry, allowance being made for finite viscosity. Here, scaling laws giving the radial extent of the arc current are obtained. In addition, electrodes with finite cross sections are treated. The results of model calculations agree well with experimental data. Generally, the model is applicable, if the angular frequency of the plasma is small compared with the ion gyration frequency.

scholarly journals Impact of ideal MHD stability limits on high-beta hybrid operation

2016 ◽  
Vol 59 (1) ◽  
pp. 014027 ◽  
Author(s):  
P Piovesan ◽  
V Igochine ◽  
F Turco ◽  
D A Ryan ◽  
M R Cianciosa ◽  
...  
Keyword(s):  
Hybrid Operation ◽  
Ideal Mhd ◽  
Mhd Stability ◽  
High Beta ◽  
Stability Limits

scholarly journals Ideal MHD stability of very high beta tokamaks

1990 ◽  
Author(s):  
M.S. Chance ◽  
S.C. Jardin ◽  
C. Kessel ◽  
J. Manickam ◽  
D. Monticello ◽  
...  
Keyword(s):  
Ideal Mhd ◽  
Mhd Stability ◽  
High Beta ◽  
Very High

On the accuracy of the symmetric ergodic magnetic limiter map in tokamaks

2010 ◽  
Vol 76 (5) ◽  
pp. 777-794 ◽  
Author(s):  
A. R. SOHRABI ◽  
S. M. JAZAYERI ◽  
M. MOLLABASHI
Keyword(s):  
Delta Function ◽  
Mapping Technique ◽  
Error Criterion ◽  
Flux Function ◽  
Energy Error ◽  
Chaotic Field ◽  
Shafranov Equation ◽  
Field Lines ◽  
Poloidal Flux ◽  
Shafranov Shift

AbstractA new symmetric symplectic map for an ergodic magnetic limiter (EML) is proposed. A rigorous mapping technique based on the Hamilton–Jacobi equation is used for its derivation. The system is composed of the equilibrium field, which is fully integrable, and a Hamiltonian perturbation. The equilibrium poloidal flux function is a solution of the Grad–Schlüter–Shafranov equation. This equation is written in polar toroidal coordinate in order to take into account the outward Shafranov shift. The static perturbation field breaks the exact axisymmetry of the equilibrium field and creates a region of chaotic field lines near the plasma edge. The new symmetric EML map is compared with the conventional (asymmetric) EML map which is derived by applying delta-function method. The accuracy of the maps is considered through mean energy error criterion and maximal Lyapunov exponents. For asymmetric and symmetric maps the approximate location of the main cantorus near the edge of plasma is determined with high accuracy by using mean energy error. The forward–backward error criterion is applied to show the relation between the accuracy of the symmetric EML map and the number of EML rings. We also report on the effect of the number of EML rings on the maximal Lyapunov exponent of the symmetric EML map.

scholarly journals A mechanism for heating electrons in the magnetopause current layer and adjacent regions

2011 ◽  
Vol 29 (12) ◽  
pp. 2305-2316 ◽  
Author(s):  
A. Roux ◽  
P. Robert ◽  
O. Le Contel ◽  
V. Angelopoulos ◽  
U. Auster ◽  
...  
Keyword(s):  
Low Frequency ◽  
Sheet Thickness ◽  
Equatorial Region ◽  
Current Layer ◽  
Electron Temperature Gradient ◽  
Spatial Gradients ◽  
Short Transverse ◽  
Field Lines ◽  
High Beta ◽  
String Of Pearls

Abstract. Taking advantage of the string-of-pearls configuration of the five THEMIS spacecraft during the early phase of their mission, we analyze observations taken simultaneously in the magnetosheath, the magnetopause current layer and the magnetosphere. We find that electron heating coincides with ultra low frequency waves. It seems unlikely that electrons are heated by these waves because the electron thermal velocity is much larger than the Alfvén velocity (Va). In the short transverse scale (k⊥ρi >> 1) regime, however, short scale Alfvén waves (SSAWs) have parallel phase velocities much larger than Va and are shown to interact, via Landau damping, with electrons thereby heating them. The origin of these waves is also addressed. THEMIS data give evidence for sharp spatial gradients in the magnetopause current layer where the highest amplitude waves have a large component δB perpendicular to the magnetopause and k azimuthal. We suggest that SSAWs are drift waves generated by temperature gradients in a high beta, large Ti/Te magnetopause current layer. Therefore these waves are called SSDAWs, where D stands for drift. SSDAWs have large k⊥ and therefore a large Doppler shift that can exceed their frequencies in the plasma frame. Because they have a small but finite parallel electric field and a magnetic component perpendicular to the magnetopause, they could play a key role at reconnecting magnetic field lines. The growth rate depends strongly on the scale of the gradients; it becomes very large when the scale of the electron temperature gradient gets below 400 km. Therefore SSDAW's are expected to limit the sharpness of the gradients, which might explain why Berchem and Russell (1982) found that the average magnetopause current sheet thickness to be ~400–1000 km (~500 km in the near equatorial region).

The use of scaling laws for the design of high beta tokamaks

1987 ◽  
Vol 27 (2) ◽  
pp. 313-324 ◽  
Author(s):  
M.E. Mauel
Keyword(s):  
Scaling Laws ◽  
High Beta

Resistively induced plasma diffusion due to the trivial marginal modes of ideal MHD

1988 ◽  
Vol 39 (1) ◽  
pp. 157-168
Author(s):  
W. Liebert ◽  
E. Rebhan
Keyword(s):  
Magnetic Field ◽  
Heat Conduction ◽  
Perturbation Analysis ◽  
Cross Diffusion ◽  
Magnetic Surfaces ◽  
Ideal Mhd ◽  
Reductive Perturbation ◽  
Plasma Diffusion ◽  
Field Lines ◽  
The Magnetic Field

The influence of nonlinearities and plasma resistivity on the so-called trivial marginal modes of ideal MHD is investigated. It turns out that to lowest significant order of a reductive perturbation analysis nonlinearities have no influence, while in toroidal confinement configurations resistivity induces a local plasma diffusion across the magnetic surfaces. This is demonstrated for tokamaks with zero poloidal current density. In addition, the appearance of singularities in the plasma motion parallel to the magnetic field lines suggests a profile condition at the edge of the plasma. Heat conduction would directly tend to keep these effects at lower level, while indirectly it creates a reinforcement mechanism through the coupling to usual cross diffusion.

Plasma transport in stochastic magnetic fields. Part 3. Kinetics of test particle diffusion

1983 ◽  
Vol 30 (1) ◽  
pp. 11-56 ◽  
Author(s):  
John A. Krommes ◽  
Carl Oberman ◽  
Robert G. Kleva
Keyword(s):  
Magnetic Fields ◽  
Test Particle ◽  
Scaling Laws ◽  
Direct Interaction ◽  
Stochastic Field ◽  
Common Procedure ◽  
Correlation Lengths ◽  
Direct Interaction Approximation ◽  
Stochastic Magnetic Fields ◽  
Autocorrelation Length

A discussion is given of test particle transport in the presence of specified stochastic magnetic fields, with particular emphasis on the collisional limit. Certain paradoxes and inconsistencies in the literature regarding the form of the scaling laws are resolved by carefully distinguishing a number of physically distinct correlation lengths, and thus identifying several collisional subregimes. The common procedure of averaging the conventional fluid equations over the statistics of a random field is shown to fail in some important cases because of breakdown of the Chapman-Enskog ordering in the presence of a stochastic field component with short autocorrelation length. A modified perturbation theory is introduced which leads to a Kubo-like formula valid in all collisional regimes. The direct-interaction approximation is shown to fail in the interesting limit in which the orbit exponentiation length LK appears explicitly. A higher-order renormalized kinetic theory in which LK appears naturally is discussed and used to rederive more systematically the results of the heuristic scaling arguments.

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