Rutkevich I, Mond M, Kaufman Y, Choi P, Favre M
Department of Mechanical Engineering, Ben-Gurion University, Beer Sheva 84105, Israel.
Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 2000 Oct;62(4 Pt B):5603-17. doi: 10.1103/physreve.62.5603.
A theory of propagation of cathode-directed ionization waves during the early stages of an electrical breakdown in a shielded, low-pressure capillary is developed. The discharge process occurs due to the ionization of the low-density gas in the capillary by an electron beam that is emanating from a hollow cathode. Due to the strong electric field in the capillary the electrons are in the fast acceleration regime. Consequently, the full momentum equation for the electrons is employed, rather than the electron drift velocity approach. The smallness of the ratio of the capillary radius to the characteristic length of the electric potential variation in the axial direction allows the construction of a quasi-one-dimensional model. The latter retains the important two-dimensional nature of the electron flow as well as the electrodynamic boundary conditions at the capillary wall and the conducting shield and results in a set of one-dimensional, time-dependent partial differential equations for the on-axis distributions of the physical quantities. It is shown that those equations admit self-similar solutions that represent ionization waves propagating with constant velocities. The resulting set of ordinary differential equations is solved numerically for various initial conditions representing a nonperturbed steady state ahead of the ionization front and the resulting features of the ionization waves are investigated and discussed. The obtained solutions describe both ionization growth and virtual anode propagation and represent fast ionization waves in plasma waveguides, for which the maximum value of the mean electron velocity is much higher than the wave velocity. The space-charge distribution associated with the ionization waves is found in the form of plasma oscillations with a continuously increasing frequency and a solitary envelope. The calculated wave velocity increases with the gas pressure and this tendency is in agreement with corresponding experimental observations.
本文建立了一种理论，用于描述屏蔽低压毛细管中电击穿早期阶段阴极定向电离波的传播。放电过程是由于空心阴极发射的电子束使毛细管内低密度气体电离而发生的。由于毛细管内存在强电场，电子处于快速加速状态。因此，采用了电子的完整动量方程，而不是电子漂移速度方法。毛细管半径与轴向电势变化特征长度之比很小，这使得可以构建一个准一维模型。该模型保留了电子流重要的二维特性以及毛细管壁和导电屏蔽层处的电动力学边界条件，并得出了一组关于物理量轴向分布的一维、时间相关的偏微分方程。结果表明，这些方程允许存在表示以恒定速度传播的电离波的自相似解。针对代表电离前沿之前未受扰动稳态的各种初始条件，对所得的常微分方程组进行了数值求解，并对电离波的结果特征进行了研究和讨论。所得解描述了电离增长和虚拟阳极传播，代表了等离子体波导中的快速电离波，其平均电子速度的最大值远高于波速。与电离波相关的空间电荷分布以频率不断增加的等离子体振荡和孤立包络的形式出现。计算得到的波速随气体压力增加，这一趋势与相应的实验观测结果一致。
