We demonstrate that the universal mode driven by the density gradient in a plasma slab can be absolutely unstable even in the presence of reasonable magnetic shear. Previous studies from the 1970s that reached the opposite conclusion used an eigenmode equation limited to L_x ≫ρ_i, where L_x is the scale length of the mode in the radial direction, and ρ_i is the ion Larmor radius. Here we instead use a gyrokinetic approach which does not have this same limitation. Instability is found for

more »

... icular wavenumbers k_y in the range 0.7 ≲ k_y ρ_i ≲ 100, and for sufficiently weak magnetic shear: L_s / L_n > 17, where L_s and L_n are the scale lengths of magnetic shear and density. Thus, the plasma drift wave in a sheared magnetic field may be unstable even with no temperature gradients, no trapped particles, and no magnetic curvature.