For the case of the usual linear polarization laser field, the first ionized electron carries higher energy back to recollide with the parent ion, which leads to the ionization of the second electron. However, ionized electrons in the co-rotating TCCP laser field will be far away from the parent ion, and the chance of electrons returning to the nucleus is small. The probability of the direct ionization of molecular ions in the co-rotating TCCP field is also small. Thereby, for different amplitude ratios of the co-rotating TCCP laser, the single ionization probability is close to 1, but the probability of the double ionization is only 10
−3. The ionization probability of the first ionized electron in the double ionization has an important influence on the probability of the subsequent double ionization. So, we calculated the probability of the ionization time of the first ionized electron in NSDI and SDI for three amplitude ratios
γE = 1.8, 3 and 6. In figure
5(
a1)
γE = 1.8, 5(
a2)
γE = 3, 5(
a3)
γE = 6, the solid and dashed lines are the probability of the ionization time of the first ionized electron in SDI and NSDI, respectively. It can be seen from figure
5(a) that the probability of the ionization time of the first ionized electron is quite different for three amplitude ratios in the case of SDI. For peak B, the ionization probability enhances with the increase of the amplitude ratio. But peak D is just the opposite, it decreases with the increase of the amplitude ratio, when the amplitude ratio
γE = 6, the ionization only occurs at peak B. For the case of NSDI, the probability of the ionization time of the first ionized electron is mainly located at peaks A and C. For peak A, the ionization probability also increases with the amplitude ratio. But for peak C, with the increase of the amplitude ratio, the ionization probability is small at
γE = 1.8, and increases at
γE = 3, finally disappears at
γE = 6. In addition, the single ionization yield in SDI and NSDI has a strong dependence on the laser field amplitude. Figure
5(b) presents laser field amplitudes for three amplitude ratios
γE = 1.8, 3 and 6. It can be seen that the amplitudes of co-rotating TCCP lasers are the same at integer optical cycles for different amplitude ratios; however, at non-integer optical cycles, the amplitude is gradually enhanced with the increase of
γE. We marked the corresponding peaks A, B, C, and D in figure
5(b) and found that the variation of the peaks A and B with the amplitude ratio is consistent with the change of the laser amplitude, but the variation of peaks C and D with the amplitude ratio is different from the change of the laser amplitude. When bound electrons of the system are not exhausted, the field strength at the first electron ionization time increases with the amplitude ratio and the ionization yield should be increased with the amplitude ratio. Figure
5(c) shows total single ionization probabilities in the three amplitude ratios. For the case of
γE = 1.8, bound electrons of the system are almost ionized when the ionization time is larger than 3 o.c.. With the amplitude ratio increases (
γE = 3), bound electrons of the system are exhausted rapidly, and the ionization probability of the SDI decreases (peak D), thus the proportion of the nonsequential ionization in the total double ionization increases (
γE = 3). With the amplitude ratio further increasing (
γE = 6), the ground state of the system is depleted at about ionization time C, and peak C contributes to NSDI. Thereby, the proportion of NSDI decreases by raising the amplitude ratio. According to the above analysis, due to the difference of laser amplitudes at the ionization time of the first ionized electrons in SDI and NSDI and the single ionization saturation effect, yields of NSDI and SDI can be effectively controlled by changing the amplitude ratio of the co-rotating TCCP laser field.