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A cold-cathode Penning ion generator (PIG) has been developed in our laboratory to study the interaction of charged particles with matter. The ignition voltage was measured in the presence of the axial magnetic field in the range of 460-580 G. The performed measurements with stainless steel cathodes were in argon gas at pressure of 4 × 10−2 mbar. A PIC-MCC (particle-in-cell, Monte Carlo collision) technique has been used to calculate the electron multiplication coefficient M for various strength of axial magnetic field and applied voltage. An approach based on the coefficient M and the experimental values of the secondary electron emission coefficient γ, was proposed to determine the ignition voltages, theoretically. Applying the values of secondary coefficient γ leads to the average value of γM(V, B) to be = 1.05 ± 0.03 at the ignition of the PIG which satisfies the proposed ignition criterion. Thus, the ion-induced secondary electrons emitted from the cathode have dominant contribution to self-sustaining of the discharge process in a PIG.