Abstract: In the paper, the “cold” cavity is designed by a 3D electromagnetic software to provide the corresponding radio frequency (RF) field, which is required in the 2D particle in cell (PIC)simulation (with the electron beam). Though the rf field is TM01 mode in the modulation cavity in a relativistic klystron amplifier, the structure of the cavity is the 3D one because a special connection is needed between the seeding rf source and the cavity. So the 3D design of a modulation cavity is necessary. The designed cavity is tested in the 3D PIC simulation, then the electron beam is modulated in the cavity, and the modulation can meet the requirement for the 2D PIC simulation.