It was shown previously that the current-carrying state of a Field Effect Transistor with asymmetric source and drain boundary conditions may become unstable against spontaneous generation of plasma waves [1]. By extending the analysis to the two-dimensional case we find that the dominant instability modes correspond to waves propagating in the direction perpendicular to the current and localized near the boundaries. This new type of instability should result in plasma turbulency with a broad frequency spectrum. More generally, it is shown that a similar instability might exist, when a strong enough current goes through a single boundary between the gated and ungated regions. PACS: 85.30.Tv, 72.15.Nj

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