The possibility of using intense relativistic electron beams (REBs) for heating plasmas in open systems is discussed. Within this context the following three sets of problems are discussed: REB transport in a vacuum with a strong magnetic field; beam equilibrium, stability and critical currents in a vacuum. Beam transport in a plasma; charge and current neutralization of the beam; reverse-current heating of the plasma, and macroscopic REB instabilities in the plasma. The theory of collective relaxation of REBs in a plasma, including quasi-linear and non-linear relaxation models; the role of plasma non-uniformity, and macroscopic effects during REB relaxation.

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