Non-linear numerical studies of the tearing mode

Schnack, D. D.

doi:10.2172/5056702

Cited by 7 publications

(8 citation statements)

References 22 publications

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“…[14][15][16][17][18][19][20][21][22][23][24][25][26][27][28] These usually employ strongly implicit time advance algorithms, and are able to advance the solution accurately and stably over very large time steps. The advantage is that all the underlying physics is retained, the model remains valid across a wide range of parameters, the boundary conditions are obvious, and the same algorithm can be applied to a wide variety of problems pertaining to magnetized plasmas.…”

Section: Introductionmentioning

confidence: 99%

Computational modeling of fully ionized magnetized plasmas using the fluid approximation

et al. 2006

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Strongly magnetized plasmas are rich in spatial and temporal scales, making a computational approach useful for studying these systems. The most accurate model of a magnetized plasma is based on a kinetic equation that describes the evolution of the distribution function for each species in six-dimensional phase space. High dimensionality renders this approach impractical for computations for long time scales. Fluid models are an approximation to the kinetic model. The reduced dimensionality allows a wider range of spatial and/or temporal scales to be explored. Computational modeling requires understanding the ordering and closure approximations, the fundamental waves supported by the equations, and the numerical properties of the discretization scheme. Several ordering and closure schemes are reviewed and discussed, as are their normal modes, and algorithms that can be applied to obtain a numerical solution.

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Section: Introductionmentioning

confidence: 99%

Computational modeling of fully ionized magnetized plasmas using the fluid approximation

et al. 2006

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“…The distinction between the DT mode and the CASDI mode is subtle and deserves some explanation. The DT mode is a magnetic tearing-type instability in which two points having k Á B = 0, called singular points, exist in the equilibrium profile [Schnack and Killeen, 1978;Pritchett et al, 1980;Seyler and Wu, 2001]. In the collisionless case, when these points are within a few l e , the perturbation fields and flows about these points are strongly coupled.…”

Section: Introductionmentioning

confidence: 99%

Particle‐in‐cell simulations of current shear‐driven instabilities and the generation of broadband ELF fluctuations

Liu¹,

Seyler²,

Xu³

2006

J. Geophys. Res.

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[1] Three-dimensional electromagnetic particle-in-cell (PIC) simulations are performed to study the properties of current shear-driven (CSD) instabilities, which are driven by the free energy stored in the inhomogeneous transverse magnetic field and associated with the transverse gradient of the field-aligned current. Current shear-driven instabilities are unstable in both a static field-aligned current equilibrium and the sheared field-aligned current sheet embedded in a transversely finite Alfvén wave. The simulation results demonstrate that the electromagnetic fluctuations generated by CSD instabilities have characteristics similar to the broadband ELF (BBELF) fluctuations observed in the topside auroral region and at higher altitudes. It is also shown that CSD instabilities have the capacity to accelerate ions transversely. Comparison of the PIC simulations with the satellite observations and three-dimensional, two-fluid MHD simulations supports CSD instabilities as potential candidates for the generation of BBELF fluctuations and the correlated transverse acceleration of ions.

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“…This has been verified in earlier studies of multiple current sheets that are highly relevant to our present work. The earliest studies of the evolution of MCS were focused on the double tearing layer, which can occur in magnetic fusion devices [Schnack and Killeen, 1977;Pritchett et al, 1980]. Instability growth rates for the double tearing mode were found to greatly exceed those for the comparable isolated tearing layer, because the flow due to the tearing in one layer helps to drive the tearing in the other layer.…”

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confidence: 99%

A triple current sheet model for adjoining coronal helmet streamers

Dahlburg¹,

Karpen²

1995

J. Geophys. Res.

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The highly structured magnetic field and plasma properties observed in the heliospheric extension of the coronal streamer belt have been interpreted as evidence for multiple current sheets originating at coronal helmet streamers. We explore the linear stability of a simple case: a triple current sheet, as would exist above two neighboring helmets of the same polarity. The behavior of the triple current sheet when perturbed by small disturbances can be described (in the incompressible limit) by MHD Orr-Sommerfeld and Squire equations, which we solve with a Chebyshev-, method. We show the velocity and magnetic fields which characterize the three unstable modes and describe the modal dependence on fieldwise wavenumber and current sheet separation. At long wavelengths an unexpected phenomenon occurs: two modes degenerate into unstable traveling modes. We also explore the three-dimensional behavior and the modal variation with both large and small values of the resistivity and viscosity. We conclude that the magnetic topology in closely packed streamers is susceptible to instabilities with growth times of the order of hours. Our predictions indicate that the resultant plasmoid structures should be observable with the large angle and spectrometric coronagraph (LASCO) and ultraviolet coronagraph spectrometer (UVCS) instruments on the upcoming Solar and Heliospheric Observatory (SOHO) mission. IntroductionHelmet streamers have been observed essentially as long as solar eclipses, yet their formation and evolution remain poorly understood. Once the basic magnetic flux element has emerged through the solar photosphere, it is unclear how the characteristic cusp and current sheet structure of the helmet streamer is formed: either partial opening of the closed, stressed magnetic field or reconnection of previously open field is thought to occur with the aid of the solar wind [Kopp, 1992, and references therein]. At solar minimum the streamer belt around the solar equator appears closest to a laminar configuration, which can be idealized as a wavy, azimuthal torus; farther from the Sun the streamers form a thick plasma sheet, in which a much narrower, complex current structure is em- bedded [e.g., Borrini et al., 1981; Gosling et al., 1981; Winterhalter et al., 1994]. On closer inspection the streamer belt consists of discrete low-latitude structures distributed irregularly in longitude, with both two-and three-dimensional (3D) structure. The 3D aspects become prominent near solar maximum, when the Sun is most likely to have numerous complex, neighboring flux systems over a range of latitudes.Once thought to be entirely stable, long-lived phenomena, helmet streamers now are known to be capable of rapid changes. The best studied and most disruptive manifestations of such transient activity are coronal mass ejections. However, the complexity of the current configuration within the heliospheric plasma sheet suggests another mechanism for short-This paper is not subject to U.S. copyright. Published in 1995 by the American Geophysic...

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Non-linear numerical studies of the tearing mode

Cited by 7 publications

References 22 publications

Computational modeling of fully ionized magnetized plasmas using the fluid approximation

Computational modeling of fully ionized magnetized plasmas using the fluid approximation

Particle‐in‐cell simulations of current shear‐driven instabilities and the generation of broadband ELF fluctuations

A triple current sheet model for adjoining coronal helmet streamers

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