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Calculations in the theory of tearing instability
Recent studies have suggested that the tearing instability may play a significant role in magnetic turbulence. In this work we review the theory of the magnetohydrodynamic tearing instability in the general case of an arbitrary tearing parameter, which is relevant for applications in turbulence. We discuss a detailed derivation of the results for the standard Harris profile and accompany it by the derivation of the results for a lesser known sine-shaped profile. We devote special attention to the exact solution of the inner equation, which is the central result in the theory of tearing instability. We also briefly discuss the influence of shear flows on tearing instability in magnetic structures. Our presentation is self-contained; we expect it to be accessible to researchers in plasma turbulence who are not experts in magnetic reconnection
Computations of the current profile influence on tearing instability
Results of computations of tearing instability of a plasma column in a strong longitudinal magnetic field are presented for different current profiles. The power current profiles j=j sub 0(1-(r/a)(P))(nu) are considered and analyzed for various values of the parameters p and v. The tearing instability of the smoothed two-step profiles is studied. Optimal smoothed two-step profiles are constructed which are stable with respect to all helical largescale perturbations.
Multimodal Prediction of Tearing Instabilities in a Tokamak
Tokamak is a torus-shaped nuclear fusion device that uses magnetic fields to confine fusion fuel in the form of plasma. Tearing instability in plasma is a major issue in which the magnetic field breaks and recombines in tokamak. Here, this instability can lead to plasma disruption that terminates the fusion power generation and damages the plasma-facing wall materials. For a successful steady operation of a large-scale tokamak without disruption, it is required to predict and alarm the tearing instabilities well in advance to avoid them. In this work, we develop and validate a deep neural network-based multimodal prediction system that estimates the future tearing instability likelihood from multi-diagnostics signals in the DIII-D tokamak.
Avoiding fusion plasma tearing instability with deep reinforcement learning
For stable and efficient fusion energy production using a tokamak reactor, it is essential to maintain a high-pressure hydrogenic plasma without plasma disruption. Therefore, it is necessary to actively control the tokamak based on the observed plasma state, to manoeuvre high-pressure plasma while avoiding tearing instability, the leading cause of disruptions. This presents an obstacle-avoidance problem for which artificial intelligence based on reinforcement learning has recently shown remarkable performance. However, the obstacle here, the tearing instability, is difficult to forecast and is highly prone to terminating plasma operations, especially in the ITER baseline scenario. Previously, we developed a multimodal dynamic model that estimates the likelihood of future tearing instability based on signals from multiple diagnostics and actuators. Here we harness this dynamic model as a training environment for reinforcement-learning artificial intelligence, facilitating automated instability prevention. We demonstrate artificial intelligence control to lower the possibility of disruptive tearing instabilities in DIII-D, the largest magnetic fusion facility in the United States. The controller maintained the tearing likelihood under a given threshold, even under relatively unfavourable conditions of low safety factor and low torque. In particular, it allowed the plasma to actively track the stable path within the time-varying operational space while maintaining H-mode performance, which was challenging with traditional preprogrammed control. This controller paves the path to developing stable high-performance operational scenarios for future use in ITER.
The beta dependence of the collisionless tearing instability at the dayside magnetopause
The beta dependence (where beta is the ratio between plasma pressure to magnetic pressure) of the collisionless tearing instability at the dayside magnetopause current sheet was investigated analytically for several current sheet models. The results show that, when the asymmetry of the dayside magnetopause current sheet is taken into account, the beta dependence of the collisionless tearing instability at the dayside magnetopause is controlled by the magnetic field profile across the magnetopause current sheet.
Streaming sausage, kink and tearing instabilities in a current sheet with applications to the earth's magnetotail
This paper investigates the growth rates and eigenmode structures of the streaming sausage, kink, and tearing instabilities in a current sheet with a super-Alfvenic flow. The growth rates and eigenmode structures are first considered in the ideal incompressible limit by using a four-layer model, as well as a more realistic case in which all plasma parameters and the magnetic field vary continuously along the direction perpendicular to the magnetic field and plasma flow. An initial-value method is applied to obtain the growth rate and eigenmode profiles of the fastest growing mode, which is either the sausage mode or kink mode. It is shown that, in the earth's magnetotail, where super-Alfvenic plasma flows are observed in the plasma sheet and the ratio between the plasma and magnetic pressures far away from the current layer is about 0.1-0.3 in the lobes, the streaming sausage and streaming tearing instabilities, but not kink modes, are likely to occur.
Linear, collisionless, bi-Maxwellian neutral-sheet tearing instability
The problem of linear bi-Maxwellian neutral-sheet tearing instability has been solved, using neither an approximation of the orbits nor the constant-psi approximation. The present method has a larger range of validity than the best previous approximation, the three-region approximation. It is found that as the temperature anisotropy is increased, the growth rate increases and the wavelength associated with the peak growth decreases. It is suggested that if small-island formation is experimentally observed, then temperature anisotropy may be present.
Does the resistive tearing instability nonlinearly evolve to a fast reconnection mode
A fundamental problem in applying linear tearing instability theory to the rapid processes (particle acceleration, heating) in flares was the characteristically slow rate of reconnection. This problem can be at least partially overcome if the tearin mode nonlinearly evolves to a regime in which the reconnection rate is substantially enhanced, such as that for the Petschek configuration. This possibility was often suggested, and some numerical simulations appear to provide support for such a view. Numerical simulation are used to study the nonlinear evolution of the tearing stability and show that a fast Petschek-like regime may not be achieved. This conclusion follows when there are sufficient grid points within the diffusion region to completely resolve the nonlinear dynamic interactions in the diffusion layer. When the numerical resolution is not adequate, the solution does appear to approach a Petschek configuration. The resolved solution contains reverse flow vortices and current sheets, terminated with a current reversal, similar to those obtained by Syrovatsky (JEPT, 33, 933, 1971).
Collisionless tearing instability of a bi-Maxwellian neutral sheet - An integrodifferential treatment with exact particle orbits
The integrodifferential equation describing the linear tearing instability in the bi-Maxwellian neutral sheet is solved without approximating the particle orbits or the eigenfunction psi. Results of this calculation are presented. Comparison between the exact solution and the three-region approximation motivates the piecewise-straight-line approximation, a simplification that allows faster solution of the integrodifferential equation, yet retains the important features of the exact solution.
Tearing Instability in Alfvén and Kinetic-Alfvén Turbulence
Recently, it has been realized that magnetic plasma turbulence and magnetic field reconnection are inherently related phenomena. Turbulent fluctuations generate regions of sheared magnetic field that become unstable to the tearing instability and reconnection, thus modifying turbulence at the corresponding scales. In this contribution, we give a brief review of some recent results on tearing-mediated magnetic turbulence. We illustrate the main ideas of this rapidly developing field of study by concentrating on two important examples—magnetohydrodynamic Alfvén turbulence and small-scale kinetic-Alfvén turbulence. Due to various potential applications of these phenomena in space physics and astrophysics, we specifically try not to overload the text by heavy analytical derivations but rather present a qualitative discussion accessible to a non-expert in the theories of turbulence and reconnection.
Tearing Instability in Alfven and Kinetic-Alfven Turbulence
Recently, it has been realized that magnetic plasma turbulence and magnetic field reconnection are inherently related phenomena. Turbulent fluctuations generate regions of sheared magnetic field that become unstable to the tearing instability and reconnection, thus modifying turbulence at the corresponding scales. In this contribution, we give a brief review of some recent results on tearing-mediated magnetic turbulence.We illustrate the main ideas of this rapidly developing field of study by concentrating on two important examples—magnetohydrodynamic Alfven turbulence and small-scale kinetic-Alfven turbulence. Due to various potential applications of these phenomena in space physics and astrophysics, we specifically try not to overload the text by heavy analytical derivations but rather present a qualitative discussion accessible to a non-expert in the theories of turbulence and reconnection.
Collsionless tearing instability in a non-Maxwellian neutral sheet - An integro-differential formulation
In the present investigation, a general integro-differential formalism is derived for the study of the collisionless tearing mode in a highly non-Maxwellian neutral sheet in which both electrons and ions are treated kinetically. The obtained formalism is applied to a specific non-Maxwellian distribution. The dispersion relation for the considered system is determined, taking into account the fundamental harmonic of the orbital frequency. It is found that the dispersion relation is dominated by the electrons. The results are presented in a number of graphs. The growth rates of non-Maxwellian distributions are generally much greater than the growth rate of the conventional isotropic tearing instability.
The effect of shear flow on the resistive tearing instability
We develop a new scaling theory for the resistive tearing mode instability of a current sheet with a strong shear flow across the layer. The growth rate decreases with increasing flow shear and is completely stabilized as the shear flow becomes Alfvénic: both in the constant-Ψ regime, as in previous results, but we also show that the growth rate is in fact suppressed more strongly in the nonconstant-Ψ regime. As a consequence, for sufficiently large flow shear, the maximum of the growth rate is always affected by the shear suppression, and the wavenumber at which this maximum growth rate is attained is an increasing function of the strength of the flow shear. These results may be important for the onset of reconnection in imbalanced MHD turbulence.
Collisional tearing instability in the current sheet with a low magnetic Lundquist number
An MHD model is used to calculate the growth rate of the collisional tearing mode instability in a current layer with a Lundquist number in the range 3-100,000. The maximum growth rate is found to be a function of the Alfven transit time in the current sheet and the Lundquist number. When the Lundquist number is below 50, the growth rate asymptotically approaches a value of about -0.075/transit time. The discovery of the dependence of the asymptotic value is considered to be of use in studies of the current sheet in the diffusion region of a magnetic reconnection configuration, where the Lundquist number will be in the range 2-100.
High conductivity magnetic tearing instability
Linearized equations of magnetohydrodynamics are used to investigate the tearing mode, for arbitrary values of the conductivity, through a consideration of the additional effect of the electron-inertia contribution to Ohm's law. A description is provided of the equilibrium and subsequent instability in the magnetohydrodynamic approximation. A method for solving the perturbation equations in the linear approximation is discussed and attention is given to the results in the high conductivity limit.
Nonlinear 3-D evolution of bounded kinetic Alfven waves due to shear flow and collisionless tearing instability
The three-dimensional nonlinear simulation of the evolution of a kinetic Alfven wave is presented for simple boundary conditions that resemble those of a discrete auroral breakup arc. The model used is a variant of the reduced megnetohydrodynamic description that includes, in addition, the important dispersive effect of electron inertia. It is found that with a 'generator' boundary condition corresponding to a current generator and a fully conducting 'load' boundary, the wave evolves three-dimensionally through a combination of shear flow and collisionless tearing mode instability.
Collisionless tearing instability in magnetotail plasmas
The problem of the linear stability of collisionless tearing modes in the earth's magnetotail is revisited. It is found that the collisionless tearing mode is linearly unstable with wavelengths of the order of 10 R(E). It is shown that an important feature neglected in earlier theories is a nonzero equilibrium B(y)-field. The physics of the instability is elucidated in the context of a simple slab model and a sheared parabolic model which is representative of the magnetotail in which all three components of the magnetic field are nonzero. The dispersion equation for the instability is obtained by a boundary-layer analysis. The implications of the theory for recent observations on current disruption and diversion during substorms is discussed.