## 4 Discussion
### Inference of Phase States Distribution and Peak Orepersive of Shockwave  
Figure 3, Figure 5, and Figure 6, respectively, show the test and analysis results for the pulse current, the explosion product, and the peak overpressure. The experimental results were compared with the calculated results of the skin effect in Equation (8). The extreme simplification and qualitative derivation of the phase distribution of a wire electric explosion is presented in Figure 9.  
As shown in Figure 9a, the current density, \(J(r)\), showed a Bessel function distribution. The wire is heated unevenly in the radial direction because of the impulse current distribution. Therefore, the wire will rapidly undergo a phase state transition. Under the spatial structure properties (diameter and hollow ratio), the temperature inhomogeneity caused by phase state components' coexistence is dynamically changing. They may exist simultaneously in the solid-liquid-gas-plasma state, or in two of the four states. The study of the characteristic parameters of temperature and resistance values is always a difficult issue in the field of electrical explosion. The signals of temperature and resistance change too fast and the amplitude is very large. They are far beyond the range of existing sensors. The characteristic parameters can only be inferred qualitatively from existing  
Figure 9: The extreme simplification and qualitative derivation of the phase distribution. (**a**) Phase states distribution and energy flow of wire guided by its current density. (**b**) Parallel model of load wires with different phase states during electrical explosion. (**c**) The resistance and temperature distribution along the wire radial direction. theoretical relations. The following change processes and mechanisms can be derived from the theoretical relationships. The sequence of phase transitions in the radial direction of the wire is shown in Figure 9a. The plasma's heat is dissipated radially outwards and transferred inward to heat the inner wire. The heavy cations pinch inward to concentrate energy. The high temperature and pressure of the Cu plasma and water vapor are compressed outward into a shockwave. As shown in Figure 9b, it can be defined as the parallel model of Cu wires in different phase states because of its spatial inhomogeneity during the electrical explosion. When the current density of the Bezier distribution drives the phase state components of a specific mass fraction, the resistance and temperature values are different. As shown in Figure 9c, the resistance value of the Cu wire is closely related to temperature. The resistance value of Cu increases first and then decreases with the increase of its temperature. The resistance value increases significantly at the point of the phase transition temperature of the Cu wire and decreases to the minimum value instantaneously when ionization occurs. The positive feedback mechanism results in a more intense Bessel function distribution in the radial direction. The collected products of small particle size may be the high-temperature plasma during the electrical explosion. Moreover, the coarse particle size may be the splashed metal droplets. The fine and the coarse particles may come from the wire's surface and core, respectively. The heat conduction accompanying the phase distribution has two effects on the subsequent evolution of the wire. For the surface of the wire, the dissipative heat conduction wastes the deposited energy in the plasma. For the core of the wire, the dual action of heat conduction and internal current density can vaporize the core Cu wire in the subsequent time. In the wire electric explosion test, the essence of increasing shockwave energy is to improve energy conversion efficiency. When the wire is heated by an impulse current, the skin effect causes the transition of phase states inside the wire to be uneven in time and space. Finally, the energy conversion efficiency of electrical energy to mechanical energy of the shockwave is reduced.