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We examine linear and quasi-liner stages of Cherenkov-drift instability in the relativistic magnetized electron-positron plasma. The external magnetic field lines are assumed to be slightly curved. In this case the curvature drift of relativistic beam particles plays decisive role in the development of the instability. Quasi-linear relaxation of the relativistic beam leads to diffusion of the resonant particles in the momenta space. The expressions for diffusion coefficients of Cherenkov-drift instability are obtained.

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