We have developed the calculation method for ion bombardment traces. When an M type dispenser cathode is operated in a cathode ray tube (CRT), the surface coating film is subjected to ion bombardment due to ionized residual gas. With long-time use, the coating film is dissipated and a change to an S type occurs. This occurrence of an S type causes a deterioration of emission and focus characteristics. A method for calculating the life time dependency of the shape of ion bombardment traces using the degree of vacuum in the tube, the grid voltage, and the cathode current was studied. The calculated results and measured results were in close agreement. As a result, it was confirmed that modeling is possible using (1) an electron and ion beam trajectory calculation program, and (2) formulas for calculating the ionization cross-section and sputtering yield. (C) 2002 Elsevier Science B.V. All rights reserved.