The effect of a constant cross-tail magnetic field By on the collisionless conductivity produced by chaotic scattering and stochastic diffusion of particles in the current sheet for a parabolic geometry is considered. We show that the correlation time scales as (By/Bz)2 and from this strong By scaling, we infer a strong tendency toward stabilization of the linear tearing modes with increasing values of By. This effect of increased dawn-dusk mobility is particularly dramatic when electrons are introduced in the calculation, and is in agreement with the results of kinetic particle simulations. The By-stabilizing effect complements the earlier Bz-stabilizing effect reported by Galeev and Zelenyiˇ (1976) and Lemb¿ge and Pellat (1982) due to electron compression. The collisionless conductivity is expressed in terms of the ensemble-averaged power spectrum of the single particle trajectories. This allows us to calculate directly the linear conductivity instead of deriving it from the calculation of the irreversible heating rates as in Horton and Tajima (1991a). The importance of determining the collisionless conductivity (or dawn-dusk mobility) in terms of the power spectrum cannot be overstated since the power spectrum gives direct evidence of the effect of the chaotic particle dynamics in the generation of a collisionless irreversible resistivity. ¿ American Geophysical Union 1993