Using SUPERFISH and PARMELA, we simulate the back bombardment dynamics of electrons in rf thermionic guns. First, we shed light on some basic physical pictures of the back bombardment by means of the simulation results. Then the solution to this problem is investigated through applying a transverse magnetic field vertically traversing the cathode cavity. The Glaser profile is assumed for the magnetic field. It shows that for the total emitted charge of 1.65 nC and the rf duty factor of 2.5 X 10(-5) the average back bombardment power can be reduced from more than 10 W to about 2 W with the varying magnetic field up to 150 G. The influence of the magnetic field on the normal electrons out of the gun cavity is examined. The correction to this influence is investigated. Some conclusions are drawn finally.