Pulsation dampener

The device has a pressure generator, an injector with injection opening and a fuel line between the pressure generator and the injector. A damping element is provided between the pressure generator and the injection opening for reduction of fuel fluid-pressure waves. The damping element has multiple flow paths with free flowing middle cross-sectional surface having the cross section diameter or with free flowing pores having pore diameter. A length of the damping element aligned in flow direction of the fuel fluid is between 1 and 100 millimeter large. An independent claim is also included for an injection unit.