等离子体焦点的Gratton-Vargas二维分析雪犁模型的再评价和推广.第II部分：观察奇点
Re-appraisal and extension of the Gratton-Vargas two-dimensional analytical snowplow model of plasma focus - Part II: Looking at the singularity
摘要：
最近重新访问和扩展的Gratton-Vargas雪犁模型（S K H Auluck，Physics of Plasmas，20，112501（2013））已经引起了对致密等离子体焦点（DPF）的某些方面的重要的新见解，尽管其是不涉及等离子体现象的纯运动学描述。它能够提供一个很好的适合在至少4个大型设施的实验电流波形。它已被用于构造一个局部曲线参考系，其中的质量，动量和能量守恒定律可以有效地减少到一维双曲守恒定律方程。它的效用在全局参数优化的器件参数已被证明。这些特征表明，Gratton-Vargas模型值得仔细研究其在DPF奇异相附近的假定限制。本文在Gratton和Vargas原有工作的基础上，讨论了它在器件轴附近的发展，但有一些不同之处。它示出的Gratton-Vargas偏微分方程的解决方案的时间后，电流奇异性，表现出一个不断扩大的有界体积，（它可以作为模型的扩大等离子体柱）和减少的动态电感的放电，尽管没有内置的流体动力学。这使得该模型能够定性地再现DPF实验中的电流导数的特征形状，而不参考任何等离子体现象，如不稳定性，异常电阻或流体动力冲击波从轴的反射。轴向传播的解决方案表现出幂律依赖于无量纲的时间从奇异性的时间，这是类似的幂律关系的理论预测的点爆炸在理想气体中，这也已被观察到的实验。
英文摘要：
The Gratton-Vargas snowplow model, recently revisited and expanded (S K H Auluck, Physics of Plasmas, 20, 112501 (2013)), has given rise to significant new insights into some aspects of the Dense Plasma Focus (DPF), in spite of being a purely kinematic description having no reference to plasma phenomena. It is able to provide a good fit to the experimental current waveforms in at least 4 large facilities. It has been used for construction of a local curvilinear frame of reference, in which conservation laws for mass, momentum and energy can be reduced to effectively-one-dimensional hyperbolic conservation law equations. Its utility in global parameter optimization of device parameters has been demonstrated. These features suggest that the Gratton-Vargas model deserves a closer look at its supposed limitations near the singular phase of the DPF. This paper presents a discussion of its development near the device axis, based on the original work of Gratton and Vargas, with some differences. It is shown that the Gratton-Vargas partial differential equation has solutions for times after the current singularity, which exhibit an expanding bounded volume, (which can serve as model of an expanding plasma column) and decreasing dynamic inductance of the discharge, in spite of having no built-in hydrodynamics. This enables the model to qualitatively reproduce the characteristic shape of the current derivative in DPF experiments without reference to any plasma phenomena such as instabilities, anomalous resistance or reflection of hydrodynamic shock wave from the axis. The axial propagation of the solution exhibits a power-law dependence on the dimensionless time starting from the time of singularity, which is similar to the power-law relations predicted by theory of point explosions in ideal gases and which has also been observed experimentally.
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