Force balance near an X line in a collisionless plasma

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<jats:p>We investigate the balance of forces near an X line in a collisionless plasma having a reconnection electric field along the X line. Near an X line the generalized Ohm's law reduces to the electron momentum equation. We use a two‐dimensional magnetic field model and apply a simplified model of particle motion to evaluate terms in this momentum equation. Our results show that the gyroviscosity associated with off‐diagonal elements of the pressure tensor can balance the electric field at and near the X line, as has recently been suggested by Dungey. Particle velocity moments do not become large at the X line, and we conclude that neither collisions nor wave turbulence are necessary for an electric field along an X line to be maintained. Gyroviscosity results from single‐particle motion in the presence of the magnetic field gradients near the X line, but we find that large values for these gradients are not required. We find that conditions expected to occur in the distant geomagnetic tail yield reasonable values for the physical parameters associated with reconnection. However, the equations provide no actual constraints on parameters other than the requirement for force balance. Thus gyroviscosity does not impose restraints on the reconnection rate. The present application is to the geomagnetic tail, but our results should apply as well to collisionless reconnection in many situations.</jats:p>

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