Universal instability for wavelengths below the ion Larmor scale

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 \(L_x \gg \rho_i\), where \(L_x\) is the scale length of the mode in the radial direction, and \(\rho_i\) is the ion Larmor radius. Here we instead use a gyrokinetic approach which does not have this same limitation. Instability is found for perpendicular wavenumbers \(k_y\) in the range \(0.7 \lesssim k_y \rho_i \lesssim 100\), and for sufficiently weak magnetic shear: \(L_s / L_n \ge 17\), 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.