In 1889, F. Pashchen published a paper set out what has become known as Paschen's Law. The law essentially states that the breakdown characteristics of a gap are a function (generally not linear) of the product of the gas pressure and the gap length, usually written as V= f( pd ), where p is the pressure and d is the gap distance. In actuality, the pressure should be replaced by the gas density.
For air, and gaps on the order of a millimeter, the breakdown is roughly a linear function of the gap length: V = 30pd + 1.35 kV, where d is in centimeters, and p is in atmospheres.
Much research has been done since then to provide a theoretical basis for the law and to develop a greater understanding of the mechanisms of breakdown. Some of this will be described in the rest of this section, but it should be realized that there are many, many factors which have an effect on the breakdown of a gap, such as radiation, dust, surface irregularities. Excessive theoretical analysis might help understanding why a gap breaks down, but won't necessarily provide a more accurate value for the breakdown voltage in any given situation.
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