Linear stability analysis of collisionless reconnection in the presence of an equilibrium flow aligned with the guide field

The influence of a velocity jet, directed along a magnetic guide field, on the linear evolution of collisionless reconnection is investigated both analytically and numerically. The analysis covers both the small and large. Delta' regimes, with Delta' indicating the standard tearing stability parameter, and is carried out, in slab geometry, by means of a reduced four-field model for magnetic reconnection accounting for two-fluid effects. Analytical dispersion relations are derived in both regimes and their predictions on the growth rates are tested against numerical simulations. In both regimes the presence of the flow is shown to have a stabilizing effect, with growth rates decreasing when increasing the amplitude of the equilibrium flow. The analytical results predict that a decrease in the growth rate could be obtained also by reducing the characteristic width of the equilibrium flow profile. Such stabilizing effects appear to be stronger in the small Delta' regime. A very good quantitative agreement is found between the analytical predictions and the numerical results. As a complement to the analysis, we also consider, in the small Delta' regime, the dispersion relation in the absence of equilibrium flow, which extends a previously derived dispersion relation by including a corrective term due to plasma parallel compressibility. It is shown that such correction can have a stabilizing effect and yields a better agreement with the numerical results.