## 1 Introduction  
Wire electric explosion technology is a unique auxiliary technology to stimulate oil and gas well stimulation. Compared with conventional acidizing and hydraulic fracturing technology, electric explosion technology has the advantages of a simple construction process, short construction period, and environmental protection. Since the 1960s, there has been much research on this technology's basic theory and principle prototype [1; 2; 3; 4; 5].  
The study of electrical load resistivity is the theoretical basis of wire explosion. The results of high-purity Cu by experiments at high pressures show that the antagonistic effects of pressure and temperature interpret the resistivity of solid and liquid [6]. The resistivity of neutral copper gas is measured by the dark pause effect in a wire explosion [7]. Meanwhile, the weakening effects of water resistivity and phase state on an underwater electric explosion are also studied [8; 9]. Shockwaves generated in electrical explosion tests have also been extensively studied. The peak overpressure of the shockwave is discussed by conducting a wire explosion under the different spatial arrangements and ambient pressure [10; 11; 12]. The magnitude and efficiency of the deposited energy are the fundamental reasons for experimental parameters' effects on the shockwave's peak overpressure in the process of a wire electric explosion [13; 14; 15; 16]. However, quantitatively determining the process by which an electric wire explosion achieves a target shockwave is complex. The temporal and spatial evolution of a wire electric explosion is studied through optical tests [17], and the result parameters of the investigation are estimated by an empirical approach [18; 19].  
Meanwhile, the implementation scheme of electric explosion technology is related to the micromorphology of its nanoproducts [20]. In addition, the dispersive property of an electric explosion was used to prepare binary and complex nanoalloys [21; 22]. The spatial-temporal distribution of the wire's inner electromagnetic field generated by the pulsed current is a basis for pulsed power technology, such as a wire electric explosion. Studies on the skin effect show that the current density satisfies the Bessel function distribution on the cross-section of the wire when a pulsed electromagnetic field is loaded [23; 24; 25]. Furthermore, the magnetic field distribution calculated by combining the axial measurement and laser ablation technology indicates that the magnetic field is 5-15 T at a radial position of 5-7 mm [26]. The investigation of plasma evolution dynamics of the exploding thin Al liner shows that the effective current radius gets bigger with time because of the time-varying magnetic diffusion process [27].  
In order to make the shockwaves generated by electric explosion technology reach the index of overpressure and deposition efficiency required by petroleum engineering, they need to match the driving energy and wire spatial structure to overcome or alleviate the influence of the skin effect. In this paper, the hollow cylindrical copper wire is proposed as an electric explosion medium when the circuit parameters are controllable and fixed. The correlation between the phase state distribution of products and the peak overpressure of the shockwave is studied to match the driving energy and wire spatial structure during the electric explosion process. Moreover, through the qualitative derivation of the spatial-temporal evolution of a wire electric explosion, the design of the wire spatial structure blunts the harmful effects and takes advantage of the beneficial effects to obtain the ideal peak overpressure of a shockwave.