In this paper, the breakdown phenomenon is explored in low pressure DC discharges by introducing a new variable (L/R). The various gases and cathode materials are tried experimentally to obtain data for the breakdown voltage. For the experiments, E/p is remained constant while pL value is changing. In literature, Paschen’s law illustrates that the breakdown voltage is a function of p (pressure) and L (the discharge gap). However, Townsend and McCallum showed that for the same pL values, the voltage is significantly higher for higher L values. This implies there should be another factor affecting the voltage. This parameter is decided as L/R, where R is the radius of the discharge vessel.
Theoretical description depends on the previous works of the separate groups. By expressing mobility, diffusivity and Townsend’s first coefficient in open forms, the set of equations are represented in terms of L/R. For the minimum of the breakdown curve, the minimum pL and voltage can be obtained by taking the derivative of the original equation and equating to zero. According to the results, when R is fixed, an increase in L shifts both the voltage and pL values. This means the growth of the losses of charged particle on the walls of the discharge tube because of the diffusion across the electric field. With different cathode materials, which affects the secondary emission coefficient, and gases, the same results relating the breakdown voltage with pL and L/R are attained. The coordinate axes are manipulated to see the regimes in breakdown curves. The measured and calculated data are compared with the new model which gives a simple representation for different gases. The equations are rearranged by accounting losses to the walls which is assumed proportional to L/R too. The way to obtain an accurate breakdown curve is to fix L and then change p in experiments.
One of the drawback of this model, they did not include the effects of charges on the walls. Before the breakdown in Townsend regime, quasineutrality is distorted by the increased number of ions which can accumulate on the walls. Therefore, the breakdown curve can be affected if the space charges are accounted. On the other hand, this paper gives a complete interpretation for low-pressure breakdown voltage that is a function of pL and L/R. The Paschen’s law is still valid in the discharges for which L/R–>0.
Reference: Lisovskiy, V. A., S. D. Yakovin, and V. D. Yegorenkov. “Low-pressure gas breakdown in uniform dc electric field.” Journal of Physics D: Applied Physics 33, no. 21 (2000): 2722.
Course: AME 60637
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