Inertial Effects on Tearing Instability
Keywords:resistive instabilities, Ohm’s law, current relaxation
AbstractIn this work, we explore inertial effects, due to charged species in a resistive plasma, on the tearing instability. The standard theory of tearing modes assumes a long wavelength limit. At shorter wave lengths, inertial effects can become important and the current density flowing in the fluid can acquire a finite relaxation time. The introduction of such a correction into the problem leads to an extension of the standard dispersion relation. In the long wave length limit, we recover the standard scaling of the growth rate γ with the plasma resistivity η, namely γ ≈ η3/5. However, in the short wavelength limit, we find that the scaling of γ with the relevant plasma parameters changes significantly due to the influence of inertia. Notwithstanding, the dependence of γ on the relaxation time of the current density is not determined. In order to achieve such a description, we propose to further rediscuss the problem in the framework of the boundary layer technique.
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