The unstable eigenmodes of a neutral sheet

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Abstract
The linear stability of a Harris current sheet is examined using the Vlasov description for both ions and electrons. Orbit integrals are treated numerically using the exact particle orbits and including the global structure of the perturbation inside the integral. Both electromagnetic and electrostatic contributions to the field perturbation are retained and the eigenvalue problem for the system of integro-differential equations is solved using a Hermite expansion of the eigenfunction. For the tearing mode, results are in excellent agreement with established theory. For the recently discovered kink mode, results are consistent with kinetic simulations at low mass ratio m i /m e ⩽16. However, in the limit of realistic electron mass, the growth rate of the kink mode is substantially reduced in contrast to results from kinetic simulations. It is demonstrated that a background population may dramatically alter the growth rate of the kink mode at realistic values of the mass ratio. This result may have relevance to the stability of the Earth’s geomagnetic tail.