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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Paschen's law ： ウィキペディア英語版 Paschen's law Paschen's Law is an equation that gives the breakdown voltage, that is the voltage necessary to start a discharge or electric arc, between two electrodes in a gas as a function of pressure and gap length. It is named after Friedrich Paschen who discovered it empirically in 1889. Paschen studied the breakdown voltage of various gases between parallel metal plates as the gas pressure and gap distance were varied. The voltage necessary to arc across the gap decreased as the pressure was reduced and then increased gradually, exceeding its original value. He also found that at normal pressure, the voltage needed to cause an arc reduced as the gap size was reduced but only to a point. As the gap was reduced further, the voltage required to cause an arc began to rise and again exceeded its original value. For a given gas, the voltage is a function only of the product of the pressure and gap length.〔〔 The curve he found of voltage versus the pressure-gap length product ''(right)'' is called Paschen's curve. He found an equation that fit these curves, which is now called Paschen's law.〔 At higher pressures and gap lengths, the breakdown voltage is approximately ''proportional'' to the product of pressure and gap length, and the term Paschen's law is sometimes used to refer to this simpler relation. However this is only roughly true, over a limited range of the curve. ==Paschen curve== Early vacuum experimenters found a rather surprising behavior. An arc would sometimes take place in a long irregular path rather than at the minimum distance between the electrodes. For example, in air, at a pressure of 10−3 atmospheres, the distance for minimum breakdown voltage is about 7.5 mm. The voltage required to arc this distance is 327 V which is insufficient to ignite the arcs for gaps that are either wider or narrower. For a 3.75 mm gap, the required voltage is 533 V, nearly twice as much. If 500 V were applied, it would not be sufficient to arc at the 2.85 mm distance, but would arc at a 7.5 mm distance. It was found that breakdown voltage was described by the equation: : $V\_B=\backslash frac\})"\; TITLE="ln(1+\backslash frac$ Where $V$ is the breakdown voltage in Volts, $p$ is the pressure in Pascals, $d$ is the gap distance in meters,$\backslash gamma\_$ is the secondary electron emission coefficient at the cathode, $A$ is the saturation ionization in the gas at a particular $E/p$ (electric field/pressure), and $B$ is related to the excitation and ionization energies. The constants $A$ and $B$ are determined experimentally and found to be roughly constant over a restricted range of $E/p$ for any given gas. For example, air with an $E/p$ in the range of 450 to 7500 V·(kPa·cm)−1, $A$ = 112.50 (kPa·cm)−1 and $B$ = 2737.50 V·(kPa·cm)−1. The graph of this equation is the Paschen curve. By differentiating it with respect to $pd$ and setting the derivative to zero, the minimum voltage can be found. This yields : $pd=e^$ and predicts the occurrence of a minimum breakdown voltage for $pd$ = 7.5×10−6 m·atm. This is 327 V in air at standard atmospheric pressure at a distance of 7.5 µm. The composition of the gas determines both the minimum arc voltage and the distance at which it occurs. For argon, the minimum arc voltage is 137 V at a larger 12 µm. For sulfur dioxide, the minimum arc voltage is 457 V at only 4.4 µm. For air at STP, the voltage needed to arc a 1 meter gap is about 3.4 MV. The intensity of the electric field for this gap is therefore 3.4 MV/m. The electric field needed to arc across the minimum voltage gap is much greater than that is necessary to arc a gap of one meter. For a 7.5 µm gap the arc voltage is 327 V which is 43 MV/m. This is about 13 times greater than the field strength for the 1 meter gap. The phenomenon is well verified experimentally and is referred to as the Paschen minimum. The equation loses accuracy for gaps under about 10 µm in air at one atmosphere and incorrectly predicts an infinite arc voltage at a gap of about 2.7 micrometers. Breakdown voltage can also differ from the Paschen curve prediction for very small electrode gaps when field emission from the cathode surface becomes important. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Paschen's law」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.