Collisionless tearing instability in a non-Maxwellian neutral sheet: An integrodifferential formulation

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Abstract
An integro-differential formalism is developed to study the collisionless tearing instability in a non-Maxwellian neutral sheet. The exact unperturbed particle orbits are used analytically in the orbit integrals. The treatment is linear, self-consistent, and kinetic for both ions and electrons. The analysis is carried out for low-frequency, purely growing electromagnetic perturbations (‖ω‖≪ωci). Using the Galerkin method, the integro-differential equation is solved to obtain the dispersion relation and the eigenmode structure. A sufficient condition for instability is given on the basis of a quadratic form and the eigenvalues of a self-adjoint integro-differential operator. The formalism is applied to a specific model distribution. For the case where the electrons and ions are both non-Maxwellian, it is found that the instability is dominated by the axis-crossing electrons and that the eigenmode is strongly localized to a region of the order of ( ρezp)1/2 at the null plane, where ρe is a measure of the electron gyroradius in the asymptotic magnetic field and zp is the sheet thickness. It is shown that the growth rate can be enhanced by several orders of magnitude over the isotropic case and that short wavelength perturbations are strongly preferred. The dispersion relation has the general form γ/kve∥=const where k∥B0 and ve∥ is the electron thermal velocity along B0, the equilibrium magnetic field.

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