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A substantial narrowing of the plume of the cylindrical Hall thruster (CHT) was observed upon the enhancement of the electron emission from the hollow-cathode discharge, which implies the possibility for the thruster efficiency increase due to the ion-beam focusing. It is demonstrated that the miniaturized CHT can be operated in the non-self-sustained regime, with the discharge current being controlled by the cathode electron emission. The thruster operation in this mode greatly expands the range of the plasma and discharge parameters normally accessible for the CHT. The observed variation of the plasma potential, electron temperature, and plasma density with the cathode current in the non-self-sustained regime points to the fact that the cathode discharge can affect the electron cross-field transport in the CHT plasma.