**1. Introduction**

28 Hydrodynamics

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The electrical explosion of conductors, such as metallic foils and wires, refers to rapid changes of physical states when the large pulsed current (tens or hundreds of kA or more, the current density j106 A/cm2) flows through the conductors in very short time(sub microsecond or several microseconds), which may produce and radiate shock waves, electrical magnetic waves, heat and so on. There are many applications using some characteristics of the electrical explosion of conductors.

The Techniques of metallic foil electrical explosion had been developed since 1961, which was first put forward by Keller, Penning[1] and Guenther et al[2]. However, it develops continually until now because of its wide uses in material science, such as preparation of nanometer materials and plating of materials[3,4], shock wave physics[5-7] , high energy density physics[8] and so on. Especially the techniques of metallic foil electrically exploding driving highvelocity flyers, are widely used to research the dynamics of materials, hypervelocity impact phenomena and initiation of explosives in weapon safety and reliability. Therefore, in this chapter we focus on the physical process of metallic foil explosion and the techniques of metallic foil electrically exploding driving highvelocity flyers. Here the explosion of metallic foils are caused by the large current flowing through in sub microsecond or 1~2 microsecond or less. During the whole physical process, not only does the temperature rising, melting, vaporizing and plasma forming caused by instantaneously large current, but also the electrical magnetic force exists and acts on. Because the whole process is confined by rigid face and barrel, and the time is very short of microsecond or sub microsecond or less, and the phynomena is similar to the explosion of explosives, we call the process electrical explosion of metallic foils. This process is a typically hydrodynamic phenomena. It is also a magnetohydrodynamic process because of the exist and action of the magnetic force caused by large current and self-induction magnetic field.

Magnetically driven quasi-isentropic compression is an relatively new topic, which was developed in 1972[9]. At that time the technique of magnetically driven quasi-isentropic compression was used to produce high pressure and compress the cylindrical sample materials. Until 2000, the planar loading technique of magnetically driven quasi-isentropic

Magnetohydrodynamics of Metallic Foil Electrical

foil.

Explosion and Magnetically Driven Quasi-Isentropic Compression 349

Fig. 2. The typically discharging current and voltage histories between bridge Aluminum

point of the discharging current shown in Fig.2 exhibits the feature.

phase transition can be used to described it well[16].

According to the density changing extent of metallic foil when the first pulsed current flows through it, the whole process of electrical explosion of metallic foil can be classified to two stages. The initial stage includes the heating stage , the melting stage and the heating stage of liquid metal before vaporizing. During this process, the density of metallic foil changes relatively slow. The second stage includes the vaporizing stage and the following plasma forming. The typical feature of electrical explosion of metallic foil is that the foil expands rapidly and violently, and that the resistance increases to be two or more orders than that of initial time (*R*/*R*0~100). The resistance increases to be maximum when the state of metallic foil is at the vaporizing stage. During this stage, the voltage of between foil also increases to be maximum, and then the breakdown occurs and the plamas is forming. The inflection

At the initial satge, the expansion of metallic foil is not obvious, and the change of physical states can be described with one thermodynamic variable *T* (temperature) or specific enthalpy. The energy loss of the interaction between the foil and the ambient medium can be neglected when there is no surface voltaic arcs. Therefore, some assumptions can be used to simplify the problem. We can think that the heating of the metallic foil is uniform and the instability, heat conduction and skin effect can not be considered at initial stage. For this stage, the physical states of metallic foil vary from solid to liquid, and the model of melting

For the second stage, the physical states varies from liquid to gas, and then from gas to plasma. There are several vaporizing mechanisms to describe this transition, such as surface evaporation and whole boil[16]. The rapid vaporizing of liquid metal make its resistance increases violently, and the current decreases correspondingly. At this time, the induction voltage between bridge foil increases fastly. If the induction voltage can make the metallic vapor breakdown and the plasma is formed, the circuit is conducted again. Of course, the

compression was firstly presented by J.R. Asay at Sandia National Laboratory[10]. In last decade, this planar loading technique had being developed fastly and accepted by many researchers in the world, such as France[11], United Kingdom[12],and China[13]. As J.R. Asay said, it will be a new experimental technique widely used in shock dynamics, astrophysics, high energy density physics, material science and so on. The process of magnetically driven quasi-isentropic compression is typical magnetodynamics[14], which refers to dynamic compression, magnetic field diffusion, heat conduction and so on.

As described above, the electrical explosion of metallic foil and magnetically driven quasiisentropic compression is typically magnetohydrodynamic problem. Although it develops fastly and maybe many difficulties and problems exist in our work, we present our important and summary understanding and results to everyone in experiments and simulations of electrical explosion of metallic foil and magnetically driven quasi-isentropic compression in last decade.

In the following discussions, more attentions are paid to the physical process, the experimental techniques and simulation of electrical explosion of metallic foil and magnetically driven quasi-isentropic compression.
