Modification of Paschen´s law for the nonuniform electric field between two plane-parallel electrodes

Summary form only given. Paschen´s law, U_b = f(pd), is the most famous result in the study of low-pressure gas discharge. However, many researchers observed the deviation from Paschen´s law in their experiments in which, with a same value of pd, the breakdown voltage for a longer gap is higher than that for a shorter gap, i.e., U_b = f(p, d) rather than U_b = f(pd), which leads to the curves of the breakdown voltage as a function of pd for the gaps with different length not superimposing onto each other. In this paper, the results from the investigation on the deviation from Paschen´s law mentioned above were presented. In the investigation low-pressure argon gaps between two plane-parallel electrodes were used. It was found by experiments that the difference in the distribution of the electric field is the reason for this deviation from Paschen´s law and that Paschen´s law could be modified as Ub = f(pd, d/r) where r is the radius of the electrodes. It was theoretically showed that Paschen´s law is just a special case of a more general similarity theorem of gas discharge and should be modified as Ub = f(pd, E/p) which is equivalent to Ub = f(pd, d/r) when two plane-parallel electrodes are used. Furthermore, the intersection of Paschen´s curves was observed in the experiments in which the radius of the electrode varied while the gap length was kept unchanged. The phenomenon of the intersection could be reproduced in the calculation of Paschen´s curves based on the condition for initiating a self-sustaining Townsend discharge when the effect of the nonunifrom electric field on the electron impact ionization coefficient was taken into account.