Computation of zero. beta. three-dimensional equilibria with magnetic islands

Abstract The sawtooth-like oscillations resulting from the m/n=2/1 double tearing mode (DTM) are numerically investigated through the three-dimensional, toroidal, nonlinear resistive-MHD code (CLT). We find that the nonlinear evolution of the m/n=2/1 DTM can lead to sawtooth-like oscillations, which are similar to those driven by the kink mode. The perpendicular thermal conductivity and the external heating rate can significantly alter the behaviors of the DTM driven sawtooth-like oscillations. With a high perpendicular thermal conductivity, the system quickly evolves into a steady state with m/n=2/1 magnetic islands and helical flow. However, with a low perpendicular thermal conductivity, the system tends to exhibit sawtooth-like oscillations. With a sufficiently high or low heating rate, the system exhibits sawtooth-like oscillations, while with an intermediate heating rate, the system quickly evolves into a steady state. At the steady state, there exist the non-axisymmetric magnetic field and strong radial flow, and both are with helicity of m/n=2/1. Like the steady state with m/n=1/1 radial flow, which is beneficial for preventing the Helium ash accumulation in the core, the steady state with m/n=2/1 radial flow might also be a good candidate for the advanced steady-state operations in future fusion reactors. We also find that the behaviors of the sawtooth-like oscillations are almost independent of Tokamak geometry, which implies that the steady state with saturated m/n=2/1 islands might exist in different Tokamaks.

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Implementation of Hamada principle in calculations of nested 3-D equilibria

Journal of Plasma Physics ◽

10.1017/s0022377815001440 ◽

2015 ◽

Vol 81 (6) ◽

Cited By ~ 2

Author(s):

Leonid E. Zakharov

Keyword(s):

Magnetic Field ◽

Three Dimensional ◽

Numerical Algorithms ◽

Magnetic Islands ◽

Plasma Confinement ◽

Equilibrium Equations ◽

Flux Function ◽

Magnetic Surfaces

Plasma confinement is based on the use of nested toroidal magnetic surfaces. In axisymmetric configurations the nestedness is provided by the existence of a flux function describing the magnetic surfaces explicitly. In the case of a three-dimensional magnetic field, the nested surfaces represent an exception. More typically, magnetic islands are formed on the resonant surfaces. The islands could degrade the plasma performance. The rigorous condition for the existence of nested surfaces without islands was formulated by Hamada (Nucl. Fusion, vol. 2, 1962, pp. 23–37) but was not implemented directly into numerical codes used, for example, for designing the stellarator configurations. This paper introduces a method of implementation of the Hamada principle in numerical algorithms. The proposed approach allows for simple linearized equilibrium equations (LEE) and potentially very efficient three-dimensional calculations of nested equilibria.

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Three-dimensional magnetohydrodynamic equilibria with continuous magnetic fields

Journal of Plasma Physics ◽

10.1017/s0022377817000538 ◽

2017 ◽

Vol 83 (4) ◽

Cited By ~ 11

Author(s):

S. R. Hudson ◽

B. F. Kraus

Keyword(s):

Magnetic Field ◽

Magnetic Fields ◽

Three Dimensional ◽

Energy Functional ◽

Equilibrium States ◽

Equilibrium Solutions ◽

Magnetic Islands ◽

Continuity Properties ◽

Rotational Transform ◽

The Magnetic Field

A brief critique is presented of some different classes of magnetohydrodynamic equilibrium solutions based on their continuity properties and whether the magnetic field is integrable or not. A generalized energy functional is introduced that is comprised of alternating ideal regions, with nested flux surfaces with an irrational rotational transform, and Taylor-relaxed regions, possibly with magnetic islands and chaos. The equilibrium states have globally continuous magnetic fields, and may be constructed for arbitrary three-dimensional plasma boundaries and appropriately prescribed pressure and rotational-transform profiles.

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Measurements of three-dimensional flows induced by magnetic islands

Physical Review Research ◽

10.1103/physrevresearch.2.023285 ◽

2020 ◽

Vol 2 (2) ◽

Author(s):

C. M. Samuell ◽

J. D. Lore ◽

W. H. Meyer ◽

M. W. Shafer ◽

S. L. Allen ◽

...

Keyword(s):

Three Dimensional ◽

Magnetic Islands

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The three-dimensional equilibrium with magnetic islands and MHD instabilities in the CFQS quasi-axisymmetric stellarator

Nuclear Fusion ◽

10.1088/1741-4326/abd3ec ◽

2021 ◽

Vol 61 (3) ◽

pp. 036021

Author(s):

X.Q. Wang ◽

Y. Xu ◽

A. Shimizu ◽

M. Isobe ◽

S. Okamura ◽

...

Keyword(s):

Three Dimensional ◽

Magnetic Islands ◽

Mhd Instabilities

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Inverse energy transfer in decaying, three dimensional, nonhelical magnetic turbulence due to magnetic reconnection

Monthly Notices of the Royal Astronomical Society ◽

10.1093/mnras/staa3849 ◽

2020 ◽

Author(s):

Pallavi Bhat ◽

Muni Zhou ◽

Nuno F Loureiro

Keyword(s):

Magnetic Field ◽

Magnetic Reconnection ◽

Magnetic Energy ◽

Three Dimensional ◽

Conserved Quantities ◽

Magnetic Islands ◽

Magnetic Turbulence ◽

Dynamo Effect ◽

2D And 3D ◽

The Magnetic Field

Abstract It has been recently shown numerically that there exists an inverse transfer of magnetic energy in decaying, nonhelical, magnetically dominated, magnetohydrodynamic turbulence in 3-dimensions (3D). We suggest that magnetic reconnection is the underlying physical mechanism responsible for this inverse transfer. In the two-dimensional (2D) case, the inverse transfer is easily inferred to be due to smaller magnetic islands merging to form larger ones via reconnection. We find that the scaling behaviour is similar between the 2D and the 3D cases, i.e., the magnetic energy evolves as t−1, and the magnetic power spectrum follows a slope of k−2. We show that on normalizing time by the magnetic reconnection timescale, the evolution curves of the magnetic field in systems with different Lundquist numbers collapse onto one another. Furthermore, transfer function plots show signatures of magnetic reconnection driving the inverse transfer. We also discuss the conserved quantities in the system and show that the behaviour of these quantities is similar between the 2D and 3D simulations, thus making the case that the dynamics in 3D could be approximately explained by what we understand in 2D. Lastly, we also conduct simulations where the magnetic field is subdominant to the flow. Here, too, we find an inverse transfer of magnetic energy in 3D. In these simulations, the magnetic energy evolves as t−1.4 and, interestingly, a dynamo effect is observed.

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Computation of zero β three-dimensional equilibria with magnetic islands

Journal of Computational Physics ◽

10.1016/0021-9991(90)90257-2 ◽

1990 ◽

Vol 87 (2) ◽

pp. 349-365 ◽

Cited By ~ 19

Author(s):

A.H. Reiman ◽

H.S. Greenside

Keyword(s):

Three Dimensional ◽

Magnetic Islands

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The orbit of Pluto over a long interval of time

Symposium - International Astronomical Union ◽

10.1017/s0074180900105509 ◽

1966 ◽

Vol 25 ◽

pp. 227-229 ◽

Cited By ~ 1

Author(s):

D. Brouwer

Keyword(s):

Periodic Orbit ◽

Numerical Integration ◽

Restricted Problem ◽

Three Dimensional ◽

The Third ◽

Circular Restricted Problem ◽

Resonance Relation

The paper presents a summary of the results obtained by C. J. Cohen and E. C. Hubbard, who established by numerical integration that a resonance relation exists between the orbits of Neptune and Pluto. The problem may be explored further by approximating the motion of Pluto by that of a particle with negligible mass in the three-dimensional (circular) restricted problem. The mass of Pluto and the eccentricity of Neptune's orbit are ignored in this approximation. Significant features of the problem appear to be the presence of two critical arguments and the possibility that the orbit may be related to a periodic orbit of the third kind.

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