The invention relates to a process a system and a high pressure pump for the preparation of a copolymer of ethylene and a di- or higher functional (meth)acrylate in a tubular reactor, comprising the steps of: injecting ethylene at a pressure of 100 MPa to 350 MPa into the reactor from a high pressure compressor and injecting the (meth)acrylate at a pressure of 100 MPa to 350 MPa into the reactor from a high pressure pump, wherein the high pressure pump comprises—a pump suction chamber for receiving a medium to be compressed; —a cylinder for receiving the medium to be compressed from the pump suction chamber; —an outlet for discharging a compressed medium from the cylinder, —a seal fixed to the inner wall of the cylinder at an end of the cylinder distal to the outlet and—a plunger movable in the cylinder by sliding through the seal, wherein a leakage gap is present along the plunger and the leakage gap is fluidly connected to the pump suction chamber.