Paschen’s law is one of the most important discoveries in the gas discharge. There are still some problems related to Paschen’s Law

such as it is solely applicable for the condition of the uniform field. To understand some problems related to Paschen’s law and Paschen’s curve

we investigated the breakdown of low-pressure gap between two plane-parallel electrodes and simulated the process using a numerical method. The separation and intersection of the Paschen’s curves for different gaps with nonuniform electric field were experimentally observed. It is found that the breakdown voltage depends not only on the product of gas pressure and gap length but also on the ratio of gap length to electrode radius

i.e.

Ub=f（pd

d/r）. Based on the distribution of the electric field

the separation of the Paschen’s curves was explained. The intersection of the Paschen’s curves was reproduced by the numerical computation of the gas breakdown. Based on the distribution of the electric field and the dependence of the electron free path length on gas pressure

the reason for the intersection of the Paschen’s curves was given. It will extend the Paschen’s law to the non-uniform electric field which helps people use Paschen’s law correctly.