In the Reply, we suppose that although the higher order correction terms of the combined field with a tightly focused Gaussian laser pulse and an external uniform magnetic field have certain influence on the dynamics and radiation spectrum of the electron, it does not affect the issues and concerns studied in our paper [EPL, 139 (2022) 14001]. Therefore, it is feasible for us to adopt the lowest order approximation for the tightly focused Gaussian laser pulse and it does not affect the main ideas and conclusions of our paper.

In a recent Comment, Chang et al. [Phys. Plasmas 29, 114703 (2022)] have studied the electron dynamics for an electron accelerating in a tightly focused Gaussian laser pulse with the higher order correction terms, and it is found that the initial position of the electron is the reason why the electron is pushed to the − z axis at the end. In this Reply, the electron dynamics and its nonlinear Thomson backscattering in a tightly focused Gaussian laser pulse with the higher order correction terms are presented, and it is found that the result is consistent with the lowest order approximation case in our paper [Hong et al., Phys. Plasmas 29, 043102 (2022)]. Meanwhile, it is also found that when the longitudinal deceleration effect of the ponderomotive force on the electron introduced by the falling part of the tightly focused laser pulse is greater than the longitudinal acceleration effect of the rising part, the electron that is initially stationary will be slightly pushed to the − z axis at the end, which can well explain the “return” phenomenon of the electron in the longitudinal direction both in our paper and in the Comment.