An electrosurgical generator supplies, during operation, a high-frequency alternating current to an electrosurgical instrument for plasma cutting of body tissue. The electrosurgical generator has outputs for connecting an electrosurgical instrument to supply an electrosurgical instrument connected to the outputs with a high-frequency alternating current, and for determining the impedance of a load connected to the outputs. The electrosurgical generator features impedance and voltage measuring units as well as an output voltage control unit. The output voltage control unit is designed to control the AC output voltage depending on a maximum output voltage value that is set during operation depending on an output value of the impedance measuring unit and/or depending on an output value of the voltage measuring unit, such that the maximum output voltage value predefines a lower AC output voltage during a vaporization phase than during an ignition phase occurring subsequently to the vaporization phase.