  We present a theory for plasmonic crystal instability in a semiconductor
field-effect transistor with a dual grating gate, designed with strong
asymmetry in the crystal elementary cell. Under the action of a dc current
bias, we demonstrate that Bloch plasma waves in the resulting plasmonic
crystal, formed in this transistor, develop the Dyakonov-Shur instability
across the entire Brillouin zone. By calculating the energy spectrum of the
plasmonic crystal and its instability increments, we analyze the dependence of
the latter on the electron drift velocity and the extent of the structural
asymmetry. Our results point to the possibility of exciting radiating
steady-state plasma oscillations at room temperature, in transistors with
asymmetric gate arrays that should be readily implementable via standard
nanofabrication techniques. Long-range coherence of the unstable plasma
oscillations, generated in the elementary cells of the crystal, should
dramatically increase the radiated THz electromagnetic power, making this
approach a promising pathway to the generation of THz signals.
