  We apply a kinetic model to predict the existence of an instability mechanism
in elongated Bose-Einstein condensates. Our kinetic description, based on the
Wigner formalism, is employed to highlight the existence of unstable Bogoliubov
waves that may be excited in the counterpropagation configuration. We identify
a dimensionless parameter, the Mach number at T = 0, that tunes different
regimes of stability. We also estimate the magnitude of the main parameters at
which two-stream instability is expected to be observed under typical
experimental conditions.
