## 1 Introduction
The erosion depth of the pulsating water jet is much greater than that of the CWJ [26]. During their research, [PERSON] et al. [27] analyzed the corresponding relationship between acoustic emission signals and the degree of jet erosion to further conduct non-destructive testing of the erosion process. The enhanced technology of disc-truncated pulsed water jets has been studied for efficient rock crushing. [PERSON] et al. [20] captured the flow field structure of a truncated pulsed water jet using high-speed photography and verified it by conducting numerical simulations. Rock-breaking experiments show that there are two main modes of breaking hard rock with a truncated pulsed water jet: deep hole erosion and macroscopic fracture. [PERSON] et al. [28] studied the flow field characteristics of a truncated pulsed water jet and found that the jet deflected after being intercepted by a rotating disk. Therefore, the positional relationship between the disc and the nozzle was analyzed in detail. After the research, it was found that the depth of the erosion pit first increased and then decreased with an increase in the ratio between the distance from the cutting disc to the nozzle and the distance between the cutting disc and the target. Additionally, [PERSON] et al. [29] analyzed the damage to a hard rock surface and subsurface eroded by an interrupted PWJ. It was found that the length and frequency of the pulse are the main factors leading to internal damage. Moreover, it was shown that the propagation of subcritical cracks in the interior has a stronger correlation with the length of the pulse. The micro-cracks in the impacted rock mass were measured, and the effective damage of the truncated pulsed water jet to the interior of the rock mass was verified. [PERSON] et al. [30] fitted the generalized equation of rock-cutting efficiency by using the experimental data of a rock mass cut with a truncated pulsed water jet. To further enhance the original ability of the jet by mechanical cutting, a miniature hydraulic cutting disk was set in the exploratory well bit to generate a PWJ, thereby effectively improving the drilling ability of the bit [31]. In addition, [PERSON] et al. [32] studied the pressure fluctuation characteristics of a self-excited oscillating pulsed jet and concluded that a stable fluid flowing through the constriction generates self-excited pulsation when it collides with the opposite inner wall,which then feeds back to the resonant cavity and creates pressure oscillation. [PERSON] et al. [33] studied the influence of air content on pulse frequency; [PERSON] et al. [34] added abrasive particles to the oscillation cavity; and [PERSON] et al. [35; 36] studied the influence of feed pipe diameter and nozzle inlet discontinuity on the characteristics of a self-excited oscillating jet. Furthermore, [PERSON] et al. [37] studied the influence of the main structural parameters on jet dynamics through orthogonal experiments. The aforementioned research results have played a key role in the development of PWJs. Although several studies have been conducted on the MPWJ, there are few studies on the APWJ and its rock erosion characteristics. [PERSON] [38] conducted a theoretical and experimental study on a supersonic PWJ produced by an impact pipe. The study showed that a strong radial burst occurred when the jet was sprayed under the influence of the pressure wave formed by impact piston extrusion. [PERSON] et al. [39] calculated a high-speed pulsed jet generated by the piston impact caused by combustion chamber expansion. [PERSON] [40] evaluated the influence of fluid compressibility on the performance of a pulse water cannon. Additionally, [PERSON] et al. [41] used electromagnetic braking to generate a high-speed pulsed jet. However, these studies were mainly focused on the flow field characteristics of the impact PWJ and less on the rock-breaking performance of the variable cross-section squeezed pulsed water jet (SPWJ).