## 1 Introduction  
In the 1980s, the introduction of chirped pulse amplification technology significantly reduced the width of laser pulses and enormously enhanced the output power of intense lasers [1]. This technological breakthrough offered robust support for research on the interaction between intense lasers and microscopic substances. In the domain of ultrafast physics, for studies at the molecular and atomic scales, shorter laser pulses can effectively enhance temporal resolution. Furthermore, in biomedical and atomic physics research, stable and high-quality X-ray sources are indispensable tools. Through the relativistic nonlinear Thomson inverse scattering process of the interaction between the intense laser and the high-energy electron, high-order harmonics can be generated, thereby generating X-ray radiation that fulfills the aforementioned requirements [2; 3; 4]. The movement of high-energy electrons within a powerful laser field demonstrates characteristics associated with relativistic effects [5]. Numerous scholars have carried out in-depth studies on nonlinear Thomson scattering under relativistic conditions [6]. [PERSON] et al. investigated the quasi-monochromatic X-ray spectra resulting from the collision of lasers with low-energy electrons [7, 8]. [PERSON] et al. studied the interaction between intense laser and electrons, which produced ultra-high-power gamma rays [9]. [PERSON] et al. examined the impact of laser intensity on the spatial radiation of high-energy electrons [10]. However, previous studies have predominantly centered on nonlinear inverse Thomson scattering [11, 12, 13]. Despite the fact that inverse axial collisions can give rise to radiation, they possess certain limitations. Specifically, the axial radiation generated by nonlinear inverse Thomson scattering may cause damage to the observation equipment and enhance the difficulty of measuring the intensity and distribution of the radiation [14, 15]. Nevertheless, in contrast to this conventional method of generating X-rays through collisions, cross-collision represents a relatively more feasible and potentially promising theoretical solution. To overcome the observation difficulties and other issues associated with head-on collisions, in this paper, through numerical simulation, radiation is generated by the cross-collision of a strong laser and a high-energy electron, thereby enhancing the practical feasibility and safety of the research approach. Additionally, the majority of previous studies have centered on circularly polarized lasers, while research on the interaction of a linearly polarized laser with an electron in a 3D space is relatively scarce. To date, there have been scarcely any actual experiments on cross-collision. In this paper, through numerical simulation experiments in a 3D space, the feasibility of generating stable and efficient X-ray radiation through the cross-collision of the linearly polarized laser and the high-energy electron is explored, with the aim of drawing the attention of relevant scholars to this blank field and facilitating its development. Meanwhile, the simulation results derived in this article can offer certain references for experimental scholars. In this paper, we employed the electrodynamics formula for derivation and investigated the impact of laser amplitude on the electron trajectory, spatial radiation power angular distribution, temporal spectrum and radiation spectrum of the cross-collision between the tightly focused linearly polarized laser pulse and the high-energy electron through numerical simulation. The experimental results indicate that the increase in laser amplitude can conspicuously elongate the length of the electron trajectory in the positive z-axis direction. When the laser amplitude is extremely small, the spatial radiation angular distribution of the electron exhibits a shape with a protrusion in the middle. As the laser amplitude increases, the radiation peak of the electron spatial radiation angular distribution graph approaches the z-axis, presenting a comet-like shape.