High-frequency gas-discharge breakdown in helium
High-frequency gas-discharge breakdown in helium
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氦气中的高频气体放电击穿
DOI：
10.1103/physrev.75.411
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发表时间：
1949
期刊：
影响因子：
--
通讯作者：
S. Brown
中科院分区：
文献类型：
--
作者：
A. D. Macdonald;S. Brown
对低压氦气中高频击穿电场进行了理论预测和实验验证。电子的能量分布是从玻尔兹曼输运方程，考虑到所有重要的去除过程。分布函数展开球谐函数和由此产生的二阶线性微分方程求解的合流超几何函数。该分布函数与动力学理论公式相结合，允许计算电离率和电子扩散系数。由此确定高频电离系数。通过扩散方程，该电离系数与击穿电场有关。因此，击穿电场的理论预测，而不使用任何气体放电数据以外的激发电位和碰撞截面的氦的实验值。测量了氦气在大气压范围内不同尺寸微波腔中的击穿电场。理论电场，不涉及可调参数，检查在6%的最大实验误差。高频气体放电击穿在氦介绍当高频电场施加到气体，击穿发生时，电离产生的电子数等于扩散损失的数量。电离率和扩散系数将根据动力学理论进行理论计算。这些使我们能够预测高频电离系数和击穿电场。通过建立电子连续性方程，考虑相空间中电子的产生和损失，确定了电子分布函数。这样确定的分布函数用于标准动力学理论公式，以找到电离率和扩散系数。结果用高频电离系数1表示。球谐展开相空间连续性方程电子的（玻尔兹曼输运方程）可以写为2.3 P = a+ + Vf，（1）其中f是电子能量分布函数，P是每单位相空间的电子产生速率，并且可以通过找到弹性和非弹性碰撞的电子能量变化而用f表示; v是速度，加速度，t是时间，Vv是速度空间中的梯度算子。与气体原子的碰撞往往会扰乱电子的任何非随机运动，因此几乎是球对称的。因此如果f以球谐函数f = fo +（？）l）/v +。. .; 4球对称项f占主导地位。的？L项表示可从其计算电流的矢量漂移项。然后，该系列是迅速收敛的，我们只考虑那些情况下，前两项足以计算系统的性能。2.将电场视为时间上的正弦曲线;展开后，方程。(1)变为a P = at + 3u auE l）+ 3°V l（2）
Breakdown electric fields in low-pressure helium at high frequencies have been theoretically predicted and experimentally verified. The energy distribution of electrons is derived from the Boltzmann transport equation by taking into account all significant removal processes. The distribution function is expanded in spherical harmonics and the resulting second-order linear differential equation is solved in terms of the confluent hypergeometric function. This distribution function combined with kinetic theory formulas permits calculation of the ionization rate and the electron diffusion coefficient. From these the high-frequency ionization coefficient is determined. Through the diffusion equation this ionization coefficient is related to breakdown electric fields. Thus breakdown electric fields are predicted theoretically without using any gas-discharge data other than experimental values of the excitation potential and collision cross section of helium. Breakdown electric fields are measured for helium in microwave cavities of various sizes with a large range of pressure. The theoretical electric fields, involving no adjustable parameters, are checked within the maximum experimental error of 6 per cent. HIGH-FREQUELNCY GAS-DISCHARGE BREAKDOWN IN HELIUM Introduction When a high-frequency electric field is applied to a gas, breakdown occurs when the number of electrons produced by ionization equals the number lost by diffusion. The ionization rate and the diffusion coefficient will be computed theoretically on the basis of kinetic theory. These enable us to predict high-frequency ionization coefficients and breakdown electric fields. The electron distribution function is determined by setting up the electron continuity equation, accounting for production and loss of electrons in phase space. The distribution functions so determined are used in standard kinetic theory formulas in order to find ionization rates and diffusion coefficients. The results are expressed in terms of the high-frequency ionization coefficient 1. Spherical Harmonic Expansion The phase space continuity equation (Boltzmann transport equation) for electrons may be written as2,3 P = a+ + Vf, (1) where f is the electron energy distribution function, P is the production rate of electrons per unit phase space and may be expressed in terms of f by finding the energy changes in electrons for elastic and inelastic collisions; v the velocity, the acceleration, t the time,and Vv the gradient operator in velocity space. Collisions with gas atoms tend to disorder any non-random motion of the electrons so that is almost spherically symmetric. Thus if f is expanded in spherical harmonics f = fo + ( ? 1l)/v + . . .;4 the spherically symmetrical term f is predominant. The ?l term represents a vector drift term from which the current may be calculated. The series then is rapidly convergent and we consider only those cases where the first two terms suffice to calculate the properties of the system. 2. The Differential Euation for fo Consider the electric field as sinusoidal in time; on expansion, Eq. (1) becomes afo a P = at + 3u auE l) + 3°V l (2)