We theoretically consider the amplification of THz radiation in a superlattice Bloch oscillator. The main dilemma in the realization of THz Bloch oscillator is finding operational conditions which allow simultaneously to achieve gain at THz frequencies and to avoid destructive space-charge instabilities. A possible solution to this dilemma is the extended Limited Space-Charge Accumulation scheme of Kroemer (H. Kroemer, cond-mat/0009311). Within the semiclassical miniband transport approach we extend its range of applicability by considering a difference in the relaxation times for electron velocity and electron energy. The kinetics of electrons and fields establishing a stationary signal in the oscillator is also discussed.

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