scholarly journals Nonlinear Evolution of the Resistive Tearing Mode

1985 ◽  
Vol 107 ◽  
pp. 273-276
Author(s):  
R. S. Steinolfson ◽  
G. van Hoven
Keyword(s):  
Numerical Solutions ◽  
Nonlinear Evolution ◽  
Magnetic Energy ◽  
Nonlinear Behavior ◽  
Mhd Equations ◽  
Tearing Mode ◽  
Magnetic Island ◽  
Long Wavelength ◽  
Nonlinear Growth ◽  
Tearing Instability

Numerical solutions of the MHD equations are used to investigate the nonlinear behavior of the tearing instability. The mode evolves from a linearly growing excitation, followed by a period of greatly reduced nonlinear growth. Constant-Ψ solutions evolve much more slowly than comparable nonconstant-Ψ modes with orders of magnitude less conversion of the stored magnetic energy. The nonconstant-Ψ computations indicate a reduction by approximately 20% of the energy in the initial shear layer. For long–wavelength solutions, secondary–flow vortices, opposite in direction to the linear vortices, generate a new magnetic island centered at the initial x-point.

Turbulent excitation of spontaneous reconnection

1989 ◽  
Vol 42 (2) ◽  
pp. 269-290 ◽  
Author(s):  
D. Deeds ◽  
G. Van Hoven
Keyword(s):  
Nonlinear Evolution ◽  
Turbulence Energy ◽  
Tearing Mode ◽  
Computational System ◽  
Turbulent Environment ◽  
Tearing Instability ◽  
Magnetic Tearing ◽  
The Relationship ◽  
Initial Turbulence

We explore the long-term nonlinear evolution of a tearing-mode-unstable sheared-field plasma in a turbulent environment. Two different physical configurations are modeled, and a different computational system is used for each. Results of both sets of calculations show that magnetic tearing arises spontaneously provided that the initial turbulence energy level is below the natural saturation level of the tearing instability.We discuss briefly the relationship between our results and those of previous calculations, concluding that there are no significant unexplainable disagreements.

scholarly journals Nonlinear growth of strongly unstable tearing modes

1993 ◽  
Vol 50 (3) ◽  
pp. 477-494 ◽  
Author(s):  
F. L. Waelbroeck
Keyword(s):  
Magnetic Islands ◽  
Long Wavelength ◽  
Tearing Modes ◽  
Nonlinear Growth ◽  
Tearing Instability ◽  
Aspect Ratios ◽  
Secondary Instabilities

Rutherford's theory of the tearing instability is extended to cases where current nonlinearities are important, such as long-wavelength modes in current slabs and the m = 1 instability in tokamaks with moderately large aspect ratios. Of particular interest is the possibility that the associated magnetic islands, as a result of secondary instabilities, have a singular response to the Ohmic diffusion of the current. A family of islands is used to test this possibility; it is found that the response remains bounded.

Activated Prominences; Mechanisms for Activation and Eruption

1979 ◽  
Vol 44 ◽  
pp. 307-313
Author(s):  
D.S. Spicer
Keyword(s):  
Pressure Gradient ◽  
Density Gradient ◽  
Current Density ◽  
Convective Instability ◽  
Tearing Mode ◽  
Magnetic Shear ◽  
Long Wavelength ◽  
Ideal Mhd ◽  
Gradient Change ◽  
Accelerated Particles

A possible relationship between the hot prominence transition sheath, increased internal turbulent and/or helical motion prior to prominence eruption and the prominence eruption (“disparition brusque”) is discussed. The associated darkening of the filament or brightening of the prominence is interpreted as a change in the prominence’s internal pressure gradient which, if of the correct sign, can lead to short wavelength turbulent convection within the prominence. Associated with such a pressure gradient change may be the alteration of the current density gradient within the prominence. Such a change in the current density gradient may also be due to the relative motion of the neighbouring plages thereby increasing the magnetic shear within the prominence, i.e., steepening the current density gradient. Depending on the magnitude of the current density gradient, i.e., magnetic shear, disruption of the prominence can occur by either a long wavelength ideal MHD helical (“kink”) convective instability and/or a long wavelength resistive helical (“kink”) convective instability (tearing mode). The long wavelength ideal MHD helical instability will lead to helical rotation and thus unwinding due to diamagnetic effects and plasma ejections due to convection. The long wavelength resistive helical instability will lead to both unwinding and plasma ejections, but also to accelerated plasma flow, long wavelength magnetic field filamentation, accelerated particles and long wavelength heating internal to the prominence.

scholarly journals Effects of plasma turbulence on the nonlinear evolution of magnetic island in tokamak

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Minjun J. Choi ◽  
Lāszlo Bardōczi ◽  
Jae-Min Kwon ◽  
T. S. Hahm ◽  
Hyeon K. Park ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Nonlinear Evolution ◽  
Plasma Turbulence ◽  
Magnetized Plasmas ◽  
Tokamak Plasmas ◽  
Magnetic Islands ◽  
Magnetic Island ◽  
Reconnection Site ◽  
Ambient Turbulence

AbstractMagnetic islands (MIs), resulting from a magnetic field reconnection, are ubiquitous structures in magnetized plasmas. In tokamak plasmas, recent researches suggested that the interaction between an MI and ambient turbulence can be important for the nonlinear MI evolution, but a lack of detailed experimental observations and analyses has prevented further understanding. Here, we provide comprehensive observations such as turbulence spreading into an MI and turbulence enhancement at the reconnection site, elucidating intricate effects of plasma turbulence on the nonlinear MI evolution.

The off-axis pressure crash associated with the nonlinear evolution of the m/n = 2/1 double tearing mode

2020 ◽  
Vol 27 (12) ◽  
pp. 122509
Author(s):  
W. Zhang ◽  
X. Lin ◽  
Z. W. Ma ◽  
X. Q. Lu ◽  
H. W. Zhang
Keyword(s):  
Nonlinear Evolution ◽  
Tearing Mode

Fully developed MHD turbulence near critical magnetic Reynolds number

1981 ◽  
Vol 104 ◽  
pp. 419-443 ◽  
Author(s):  
J. Léorat ◽  
A. Pouquet ◽  
U. Frisch
Keyword(s):  
Reynolds Number ◽  
Kinetic Energy ◽  
Isotropic Turbulence ◽  
Magnetic Energy ◽  
Reynolds Numbers ◽  
Magnetic Reynolds Number ◽  
Mhd Equations ◽  
Liquid Sodium ◽  
Turbulent Heat ◽  
Mhd Turbulence

Liquid-sodium-cooled breeder reactors may soon be operating at magnetic Reynolds numbers RM where magnetic fields can be self-excited by a dynamo mechanism (as first suggested by Bevir 1973). Such flows have kinetic Reynolds numbers RV of the order of 107 and are therefore highly turbulent.This leads us to investigate the behaviour of MHD turbulence with high RV and low magnetic Prandtl numbers. We use the eddy-damped quasi-normal Markovian closure applied to the MHD equations. For simplicity we restrict ourselves to homogeneous and isotropic turbulence, but we do include helicity.We obtain a critical magnetic Reynolds number RMc of the order of a few tens (non-helical case) above which magnetic energy is present. RMc is practically independent of RV (in the range 40 to 106). RMc can be considerably decreased by the presence of helicity: when the overall size of the flow L is much larger than the integral scale l0, RMc can drop below unity as suggested by an α-effect argument. When L ≈ l0 the drop can still be substantial (factor of 6) when helicity is a maximum. We examine how the turbulence is modified when RM crosses RMc: presence of magnetic energy, decreased kinetic energy, steepening of kinetic-energy spectrum, etc.We make no attempt to obtain quantitative estimates for a breeder reactor, but discuss some of the possible consequences of exceeding RMc, such as decreased turbulent heat transport. More precise information may be obtained from numerical simulations and experiments (including some in the subcritical regime).

scholarly journals The non-modal onset of the tearing instability

2018 ◽  
Vol 84 (5) ◽  
Author(s):  
D. MacTaggart
Keyword(s):  
Initial Conditions ◽  
Linear Equations ◽  
Initial Perturbation ◽  
Transient Growth ◽  
Tearing Mode ◽  
Eigenvalue Spectrum ◽  
Tearing Instability ◽  
Set Up ◽  
Solution Behaviour ◽  
Physical Quantities

We investigate the onset of the classical magnetohydrodynamic (MHD) tearing instability (TI) and focus on non-modal (transient) growth rather than the tearing mode. With the help of pseudospectral theory, the operators of the linear equations are shown to be highly non-normal, resulting in the possibility of significant transient growth at the onset of the TI. This possibility increases as the Lundquist number$S$increases. In particular, we find evidence, numerically, that the maximum possible transient growth, measured in the$L_{2}$-norm, for the classical set-up of current sheets unstable to the TI, scales as$O(S^{1/4})$on time scales of$O(S^{1/4})$for$S\gg 1$. This behaviour is much faster than the time scale$O(S^{1/2})$when the solution behaviour is dominated by the tearing mode. The size of transient growth obtained is dependent on the form of the initial perturbation. Optimal initial conditions for the maximum possible transient growth are determined, which take the form of wave packets and can be thought of as noise concentrated at the current sheet. We also examine how the structure of the eigenvalue spectrum relates to physical quantities.

Magnetic island suppression by electron cyclotron current drive as converse of a forced reconnection problem

2018 ◽  
Vol 84 (3) ◽  
Author(s):  
D. Grasso ◽  
D. Borgogno ◽  
L. Comisso ◽  
E. Lazzaro
Keyword(s):  
Robust Control ◽  
Control Strategy ◽  
Electron Cyclotron ◽  
Current Drive ◽  
Magnetic Islands ◽  
Tearing Mode ◽  
Magnetic Island ◽  
Technical Approach ◽  
Physical Conditions ◽  
Secondary Instabilities

This paper addresses one aspect of the problem of the suppression of tearing mode magnetic islands by electron cyclotron current drive (ECCD) injection, formulating the problem as the converse of a forced reconnection problem. New physical conditions are discussed which should be considered in the technical approach towards a robust control strategy. Limits on the ECCD deposition are determined to avoid driving the system into regimes where secondary instabilities develop. Numerical simulations confirming the theory are also presented.

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