A recently developed analytical expression relating $\frac{\alpha }{p}$ with $\frac{E}{p}$ ($\alpha$ is the Townsend ionization coefficient, $E$ the applied field strength, $p$ the pressure) is used in conjunection with an appropriate breakdown criterion to theoretically formulate the experimental Paschen's law. Variations of both temperature and pressure are considered in this derivation. Theoretical and experimental values of both $\alpha d$ ($d$ is the length of the discharge gap) and the minimum breakdown voltage for air are in close agreement in the region of validity of the streamer theory, i.e., for $\mathrm{pd}>\mathrm{}500\mathrm{}$ mm Hg×cm.

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