## 4 Conclusions  
The results of the LWFA simulation of electrons using a 10 fs TH laser beam with a limited pulse energy of 85 mJ, which was focused using an OAP and an AXP+STC, have shown that the energy of accelerated electrons was predominantly determined by the self-focusing and ionisation injection effects of the laser beam propagating in plasma. The electrons accelerated using the OAP focused towards the focal plane \(z_{f}\) = 30 \(\mu\)m reached \(E_{max}\) = 130 MeV and 170 MeV when focused towards the focal plane \(z_{f}\) = 330 \(\mu\)m. The corresponding average energy \(E_{>0.8 max}\) of electrons, in the interval from \(E_{max}\) to 0.8 \(E_{max}\), was 100 MeV and 145 MeV, respectively. The maximum energy E\({}_{max}\) of the accelerated electron using the TH laser beam which was focused using the AXP was 6% higher--180 MeV, and, in the case of the AXP+STC, the maximal electron energy increased by 12% to 200 MeV, relative to the best OAP case. The corresponding average energy \(E_{>0.8 max}\) of electrons was 150 MeV and 170 MeV, respectively. We found that the process of the LWFA of electrons, using an OAP and AXP to focus the laser pulse with limited energy, is similar. An advantage to the energy gain and formation of a quasi-monoenergetic bunch is observed only in the AXP+STC case, and while choosing the appropriate distance of the injection zone. The initial starting values of the laser strength parameter \(a_{0}\) affect the injection mechanism of electrons. The ionisation injection starts when \(a_{0}\) > 2, and with a limited length of the ionisation injection zone \(L_{n}\) = 200 \(\mu\)m, the continuing injection within 200 \(\mu\)m for the OAP when focused onto the focal plane \(z_{f}\) = 30 \(\mu\)m forms two peaks in the electron spectra: one in the area of high energies, and the other in the area of low energies. The total charge of accelerated electrons is 30 pC. There is a shorter injection zone when the TH beam is focused using the OAP towards the focal plane of \(z_{f}\) = 330 \(\mu\)m, and using the AXP results in the formation of quasi-monoenergetic electron bunches. However, the total charge of accelerated electrons becomes smaller, down to 2.5-12 pC.  
**Author Contributions**: [PERSON] conducted the physical analysis, established the methodology, performed the FBPIC simulation, and wrote the original draft. [PERSON] carried out the physical analysis and FBPIC simulation, and wrote the original draft. M.A.-[PERSON] performed the physical analysis and FBPIC simulation, and wrote the original draft. [PERSON] was responsible for defining the methodology, supervising the research, formulating the investigation's objectives, and revising and editing the manuscript. All authors have read and agreed to the published version of the manuscript.  
**Funding:** The research leading to these results was funded by the Research Council of Lithuania under grant agreement No. S-MIP-21-3.  
**Institutional Review Board Statement**: Not applicable.  
**Informed Consent Statement**: Not applicable.  
**Data Availability Statement**: The data that supports the findings of this study are available inside the paper.  
**Conflicts of Interest**: The authors declare no conflict of interest.