Magnetic driving energy of the collisional tearing modes

Adler, E. A.; Kulsrud, Russell M.; White, R. B.

doi:10.1063/1.863152

Cited by 27 publications

(20 citation statements)

References 5 publications

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“…In order to investigate this aspect let us now discuss the energetics of the collisionless tearing mode with electron inertia. Energetics of the collisional tearing mode were considered by Adler et al 26 Let us now write ͑x,y,t͒ϭ 0 ͑ x ͒ϩ 1 ͑ x ͒e ␥t cos ky…”

Section: Energetics Of the Linearized Collisionless Mhdmentioning

confidence: 99%

“…Finally, since the plasma pressure does not show up explicitly in the equations governing collisionless MHD, it is not clear what role, if any, the plasma pressure plays in this collisionless reconnected process. We will therefore consider the energetics of the collisionless tearing mode, which controls the collisionless MHD, to clarify this issue, following the work of Adler et al 26 for the collisional tearing mode.…”

Section: Introductionmentioning

confidence: 99%

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Electron-inertia effects on driven magnetic field reconnection

Al-Salti

Shivamoggi

2003

Physics of Plasmas

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Electron-inertia effects on the magnetic field reconnection induced by perturbing the boundaries of a slab of plasma with a magnetic neutral surface inside are considered. Energetics of the tearing mode dynamics with electron inertia which controls the linearized collisionless magnetohydrodynamics (MHD) are considered with a view to clarify the role of the plasma pressure in this process. Cases with the boundaries perturbed at rates slow or fast compared with the hydromagnetic evolution rate are considered separately. When the boundaries are perturbed at a rate slow compared with the hydromagnetic evolution rate and fast compared with the resistive diffusion rate, the plasma response for early times is according to ideal MHD. A current sheet formation takes place at the magnetic neutral surface for large times in the ideal MHD stage and plasma becomes motionless. The subsequent evolution of the current sheet is found to be divided into two distinct stages: (i) the electron-inertia stage for small times (when the current sheet is very narrow); (ii) the resistive-diffusion stage for large times. The current sheet mainly undergoes exponential damping in the electron-inertia regime while the bulk of the diffusion happens in the resistivity regime. For large times of the resistive-diffusion stage when plasma flow is present, the current sheet completely disappears and the magnetic field reconnection takes place. When the boundaries are perturbed at a rate fast compared even with the hydromagnetic evolution rate, there is no time for the development of a current sheet and the magnetic field reconnection has been found not to take place.

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Section: Energetics Of the Linearized Collisionless Mhdmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Electron-inertia effects on driven magnetic field reconnection

Al-Salti

Shivamoggi

2003

Physics of Plasmas

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“…Energy principles for the resistive equations have been obtained by Adler et al, 20 Bondeson and Sobel, 21 Tasso 22 and Wesson. 23 layer.…”

Section: Introductionmentioning

confidence: 99%

Energy principles for linear dissipative systems with application to resistive MHD stability

Pletzer¹

1997

Physics of Plasmas

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A formalism for the construction of energy principles for dissipative systems is presented. It is shown that dissipative systems satisfy a conservation law for the bilinear Hamiltonian provided the Lagrangian is time invariant. The energy on the other hand, differs from the Hamiltonian by being quadratic and by having a negative definite time derivative ͑positive power dissipation͒. The energy is a Lyapunov functional whose definiteness yields necessary and sufficient stability criteria. The stability problem of resistive magnetohydrodynamic ͑MHD͒ is addressed: the energy principle for ideal MHD is generalized and the stability criterion by Tasso ͓Phys. Lett. 147, 28 ͑1990͔͒ is shown to be necessary in addition to sufficient for real growth rates. An energy principle is found for the inner layer equations that yields the resistive stability criterion D R Ͻ0 in the incompressible limit, whereas the tearing mode criterion ⌬ЈϽ0 is shown to result from the conservation law of the bilinear concomitant in the resistive layer.

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“…Once these variational parameters have been determined, the trial functions are again inserted into Eq. (14) and the dispersion relation for these trial functions is determined by setting S = 0 . This variational principle will be utilized later in a calculation of the dispersion relation for the tearing mode.…”

Section: Coupled Equations For Q and Allmentioning

confidence: 99%

Turbulent stabilization of the tearing mode in tokamak plasmas

Esarey

Freidberg

Molvig

et al. 1986

The Physics of Fluids

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The effect of turbulent electron diffusion from stochastic electron orbits on the stability of low-beta fluctuations is considered through the use of the Normal Stochastic Approximation. A set of coupled, self-adjoint equations is derived for the fluctuation potentials 4 and All. Solutions to this set of equations describe both unstable finite-# drift waves when analyzed for high m modes and the tearing mode when analyzed for low m modes. For the tearing mode, it is shown that stability is obtained for sufficiently large values of the diffusion coefficient. Provided De ~ 1/n, this implies that a density threshold must be surpassed before the tearing mode is observed. Physically, turbulent electron diffusion prohibits the formation of a perturbed current within a finite region about the rational surface. At higher densities, the inclusion of a finite electrostatic potential, 4, gives an additional stabilizing term to the dispersion relation, which physically represents ion inertial effects. This ion inertial effect implies that, in the absence of diffusion, the tearing mode is stabilized for ion betas, #i, above some critical value.

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Magnetic driving energy of the collisional tearing modes

Cited by 27 publications

References 5 publications

Electron-inertia effects on driven magnetic field reconnection

Electron-inertia effects on driven magnetic field reconnection

Energy principles for linear dissipative systems with application to resistive MHD stability

Turbulent stabilization of the tearing mode in tokamak plasmas

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