Ionization in a magnetically confined argon discharge has been studied by the use of a Monte Carlo simulation. Especially, influences of the transverse magnetic field have been investigated for a pressure range of 30 Pa-4 kPa. It is found that the magnetic field acts effectively only in a definite range of pressure( < 600 Pa), and within the range there is an optimum strength for the field. Analyses for the results and consideration of applying the discharge in ion lasers as well as in sputtering-based metal vapor lasers have been given.