High-order correction terms to the expression of the field of circularly polarized Gaussian laser are derived. Terms up to seventh order in the small dimensionless spatial parameter are explicitly presented. Using the test particle simulation programs, the CAS (Capture & Acceleration Scenario) phenomenon in the circularly polarized field has been proved, and the difference efficiency of CAS scheme between the circularly polarized field and linearly polarized field has been investigated, further more the electron dynamics obtained by the paraxial approximation, the fifth-order correction, and the seventh-order correction are compared in detail. The numerical calculations show that the results of three corrected models coincide with each other very well for $kw_{0}> 60$, and the difference of the three corrected models is very conspicuously for $kw_{0}\leq 50$. Then the ranges of the electron incident momentum for the CAS scheme in circularly polarized field to emerge are examined. This study is of significance in designing experimental setup to test CAS and helpful in understanding the basic physics of CAS.