We study instability of plasmons in a dual-grating-gate graphene field-effect transistor induced by dc current injection using self-consistent simulations with the Boltzmann equation. With only the acoustic-phonon-limited electron scattering, it is demonstrated that a total growth rate of the plasmon instability, with the terahertz/mid-infrared range of the frequency, can exceed $4times10^{12}$ s$^{-1}$ at room temperature, which is an order of magnitude larger than in two-dimensional electron gases based on usual semiconductors. By Comparing the simulation results with existing theory, it is revealed that the giant total growth rate originates from simulataneous occurence of the so-called Dyakonov-Shur and Ryzhii-Satou-Shur instabilities.
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