Individual particle trajectories are determined analytically and numerically in two possible configurations of electric and magnetic fields in the geomagnetic tail. The models are based on reconnection models incorporating a neutral point with associated neutral or current sheet and on the observed neutral sheet in the geomagnetic tail. Both models contain magnetic field lines oppositely directed on either side of a current sheet, with some field line connection through the sheet and with an electric field perpendicular to the magnetic field and parallel to the sheet. The models differ in the rate of variation of a magnetic field component perpendicular to the neutral sheet and hence in the rate of field line crossing of the neutral sheet. For the two models, particles are accelerated and turned toward the earth within the neutral sheet and are ejected from the neutral sheet with small pitch angles to a magnetic line of force, with energies of tens of kilovolts. For the first model, a dipole and tail model, electrons are ejected at about 150 RE and protons about 50 RE back in the tail. For the second model, an extended tail model, electrons are ejected at about 500 RE, and protons at about 400 RE. Proton auroras would be expected about ½° lower latitude than electron auroras, and isotropic fluxes should be measurable out to distances of the order of 2.5 RE from the earth. Extremely thin sheets of incoming particles are produced, about 1 km for electrons between 1 and 10 kev. These results are obtained from an approximate, nonadiabatic theory and are verified by machine computations. To map the thin output sheets onto the earth, a three-dimensional dipole and tail model is used for the numerical computations of many proton trajectories. Thin output sheets of accelerated particles are found using Liouville's theorem. These thin sheets or spatially intense regions are near the auroral zones when mapped onto the earth; they move to lower latitudes on the earth with an increase in the strength of the tail field, and their thickness is roughly proportional to the thermal velocity of the particles incident on the tail. The geomagnetic tail may sometimes be quite long without field-line merging and may sometimes be shorter with merging. These models may therefore be useful in the description of auroral acceleration whenever the merging process is going on. The models may be applicable to other situations where neutral points or sheets may exist, such as the day-side magnetospheric current sheet, the interplanetary field, solar flares, etc. If He auroral emission occurs as suggested by Eather, these results imply that alphas should be found equatorward of precipitating protons with about twice the proton energy.