A waste water cleaning apparatus for cleaning waste water with shock waves, comprising: a reactor body that stretches out between opposing ends and comprising a first water inlet and a first water outlet; and a plasma-hydraulic shock wave generator comprising: a pair of plasma pencils, each plasma pencil being mounted to a respective end among said opposing ends of the reactor body and comprising: an elongated core configured to form a cathode of the plasma pencil; an elongated insulating sleeve that is provided coaxially around the elongated core; and an elongated metallic sleeve that is provided coaxially around the elongated insulating sleeve and that is configured to form an anode of the plasma pencil, wherein each plasma pencil has a tip part that is arranged inside the reactor body, said tip part being formed by a part of the elongated core extending in longitudinal direction out of the insulating sleeve, and a part of the insulating sleeve extending in longitudinal direction out of the metallic sleeve, a voltage pulse generator connected, for each plasma pencil, to the anode and to the cathode, wherein the voltage pulse generator is configured to generate an electric field between the anode and the cathode having a strength exceeding 40 kV/m and wherein a power density at each cathode exceeds 4 kW/cm 2, wherein an exposed area of the elongated core is such that the power density of at least 4 kW/cm 2 is achieved in use, as a result of which a plasma is created around the part of the elongated core that extends out of the insulating sleeve, wherein the plasma generates shock waves; wherein the elongated core comprises tungsten; wherein the insulator sleeve is made of ceramic material: wherein the metallic sleeve comprises a metal that is configured to, during operation, form a self-healing porous metallic oxide layer on its surface, wherein the metallic sleeve comprises aluminum and/or titanium; wherein the insulating sleeve is set back from the core and the metallic sleeve is set back from the insulating sleeve. a reactor body that stretches out between opposing ends and comprising a first water inlet and a first water outlet; and a plasma-hydraulic shock wave generator comprising: a pair of plasma pencils, each plasma pencil being mounted to a respective end among said opposing ends of the reactor body and comprising: an elongated core configured to form a cathode of the plasma pencil; an elongated insulating sleeve that is provided coaxially around the elongated core; and an elongated metallic sleeve that is provided coaxially around the elongated insulating sleeve and that is configured to form an anode of the plasma pencil, wherein each plasma pencil has a tip part that is arranged inside the reactor body, said tip part being formed by a part of the elongated core extending in longitudinal direction out of the insulating sleeve, and a part of the insulating sleeve extending in longitudinal direction out of the metallic sleeve, a voltage pulse generator connected, for each plasma pencil, to the anode and to the cathode, wherein the voltage pulse generator is configured to generate an electric field between the anode and the cathode having a strength exceeding 40 kV/m and wherein a power density at each cathode exceeds 4 kW/cm 2, wherein an exposed area of the elongated core is such that the power density of at least 4 kW/cm 2 is achieved in use, as a result of which a plasma is created around the part of the elongated core that extends out of the insulating sleeve, wherein the plasma generates shock waves; an elongated core configured to form a cathode of the plasma pencil; an elongated insulating sleeve that is provided coaxially around the elongated core; and an elongated metallic sleeve that is provided coaxially around the elongated insulating sleeve and that is configured to form an anode of the plasma pencil, wherein each plasma pencil has a tip part that is arranged inside the reactor body, said tip part being formed by a part of the elongated core extending in longitudinal direction out of the insulating sleeve, and a part of the insulating sleeve extending in longitudinal direction out of the metallic sleeve, a voltage pulse generator connected, for each plasma pencil, to the anode and to the cathode, wherein the voltage pulse generator is configured to generate an electric field between the anode and the cathode having a strength exceeding 40 kV/m and wherein a power density at each cathode exceeds 4 kW/cm 2, wherein an exposed area of the elongated core is such that the power density of at least 4 kW/cm 2 is achieved in use, as a result of which a plasma is created around the part of the elongated core that extends out of the insulating sleeve, wherein the plasma generates shock waves; wherein the elongated core comprises tungsten; wherein the insulator sleeve is made of ceramic material: wherein the metallic sleeve comprises a metal that is configured to, during operation, form a self-healing porous metallic oxide layer on its surface, wherein the metallic sleeve comprises aluminum and/or titanium; wherein the insulating sleeve is set back from the core and the metallic sleeve is set back from the insulating sleeve. wherein the metallic sleeve comprises a metal that is configured to, during operation, form a self-healing porous metallic oxide layer on its surface, wherein the metallic sleeve comprises aluminum and/or titanium; wherein the insulating sleeve is set back from the core and the metallic sleeve is set back from the insulating sleeve.