## 1 Introduction  
Chirped pulse is a special form of laser pulse whose frequency varies with time. Chirped pulses usually are characterized by linear frequency modulation, that is, the frequency at which the pulse begins is different from the frequency at which it ends, resulting in a broadband spectrum. One of the characteristics of a chirped pulse is that its phase changes linearly with time, and this change results in a change in frequency. Chirped pulse has a characteristic of large bandwidth and short duration in spectrum, which makes it widely used in ultrafast spectroscopy and laser spectroscopy. In a chirped pulse, the rate of frequency change is called the Chirp Rate parameter and is usually expressed as the absolute value of the rate of frequency change. The chirp rate of a chirped pulse can be positive (gradually increasing in frequency) or negative (gradually decreasing in frequency), depending on how the pulse is modulated [1, 2, 3, 4, 5]. First proposed in the 1990s, chirped pulses have significant application potential in ultrafast laser spectroscopy, optical coherence tomography (OCT) [6], fiber optic communication [7, 8] and other fields. Since 1992, when optical parametric amplification proved the principle of effectively amplifying chirped laser pulses, optical parameter chirped pulse amplification (OPCPA) has become the most promising method for broadband optical pulse amplification. At the same time, we are witnessing exciting progress in the development of powerful ultrashort-pulse laser systems with chirped-pulse parametric amplifiers. The output power and pulse duration of these systems range from a few gigawatts to hundreds of terawatts, with potential power levels reaching tens of petawatts [9]. They are capable of providing broader spectrum coverage than conventional pulses, thus performing exceptionally well in applications requiring high resolution and sensitivity. For example, [PERSON] et al. [10] proved that the bandwidth and duration of the incident pulsed beam play an important role in the correction of nonlinear images of amplitude-type scatterers. At the same time, chirped pulses also have a significant demand for high-power, high-intensity laser pulses in areas such as particle laser acceleration. [PERSON], [PERSON] [11; 12; 13; 14; 15] et al. pointed out that high-intensity pulses play an important role in electronic trajectory control and state change. The chirped-pulse amplification technology also has great advantages in the generation of high-power and high-intensity pulses and electronic control at the nanoscale, and the effect is better than that of traditional large instruments [16; 17; 18]. The spatial radiation characteristics of pulses can be divided into linear polarization, circular polarization, and elliptic polarization based on the state of space radiation. Due to the complexity of chirped laser pulse analysis, most studies are conducted under the condition of online polarization or the chirped amplification effect using different crystal materials. For example, [PERSON] et al. [1; 19] qualitatively analyzed the influence of linear polarization on chirped-laser-pulse single-electron acceleration and its related effects on electron dynamics. [PERSON] et al. [20] studied the dynamics of single electrons directly accelerated by linearly polarized chirped laser pulses in an inhomogeneous cylindrical plasma channel. [PERSON] et al. [21] studied the ionization dynamics of atoms with chirped-attosecond pulses. [PERSON] et al. [22] studied the high-order harmonic generation cutoff extension of strongly few-cycle linearly chirped laser pulses. [PERSON] et al. [23] mainly studied optical parametric chirped-pulse amplification based on photonic crystal fiber. Due to the axisymmetric nature of the circularly polarized laser field, it provides a better acceleration effect.