The linear stability of a current sheet is of interest in connection with t
he dynamics of the magnetotail and in particular as a triggering mechanism
for substorms. Until recently, most theoretical work in this area has conce
ntrated on the collisionless tearing mode. Recent simulations suggest that
for thin current sheets another long wavelength electromagnetic mode, these
-called drift kink instability, may also be of importance. The linear stabi
lity analysis for a Harris-type equilibrium is formulated using a kinetic d
escription for both ions and electrons. The orbit integrals are treated num
erically using the exact unperturbed particle orbits and including the glob
al structure of the perturbation inside the integral. It is found that the
drift kink has a significant electrostatic component which strongly alters
the mode structure and real frequency relative to the case of a purely elec
tromagnetic mode. The resulting growth rates, mode structure and parametric
dependences are presented and compared with previous results. The effect o
f finite parallel wavelength is considered, and the relevance of the drift
kink mode to the magnetotail is discussed.