## 3 Results
### Polar Distribution of NITS Temporal Intensity  
To further explore the temporal structure of NITS spatial radiation, the joint distribution of radiation power in time and polar angle is analyzed in in this section. For each set of parameter \(a_{0}\) and \(\gamma_{0}\), the azimuth angle is fixed in the direction corresponding to the power peak, that is, to explore the temporal intensity of radiation across the radiation ring in Figure 2. The results are illustrated in Figure 5. The analysis of the joint distribution of radiation power in time and azimuth angle will be in the next section. Figure 5: The joint distribution of NITS radiation temporal power and polar angle \(\theta\), in which the electron’s normalized initial energy \(\gamma_{0}\) and the normalized laser field intensity \(a_{0}\) have been marked, and \(\phi\) is fixed as the direction of its radiation power peak. It is worth noting that the scales of different rows are different. The parameters of Video S3 correspond to (**e**). When the \(\theta\) and \(\phi\) are fixed, Video S3 can be obtained by changing the initial phase \(\psi_{0}\) of the laser from \(0^{\circ}\) to \(360^{\circ}\). In Figure 5, we can easily tell that the radiated pulses are clearly symmetrical not only with respect to time, but also the polar angle. From the perspective of time, the NITS radiation pulses are symmetrical about its main radiation peak, whose time of appearance \(t=t_{peak}\). Enlarging the cross-section of the main radiation peak in Figure 5g-i, we can obtain Figure 6, and the above time symmetry is more intuitive. The main peak of radiation always has the maximum power and minimum pulse width compared with other peaks, from which a consensus can be clarified that study of the main peak deserves attention. From the perspective of polar angle distribution, we find the NITS radiation temporal intensity is quasi-axisymmetric about \(\theta=180^{\circ}\). To demonstrate the spatiotemporal structure of the NITS radiation pulse more specifically, we enlarge Figure 5e to Figure 7a, and Figure 7b shows the logarithm projection of the radiation pulses in this case. On one side of \(\theta=180^{\circ}\), we can observe a single main peak with stronger power, while on the other side, two double main peaks with weaker power appear symmetrically. This is actually the impact of the laser's initial phase \(\psi_{0}\), which is clearly shown in Video S3 when the azimuth angle is fixed. However, some more interesting phenomena are shown in Figure 7b. The distribution of one single pulse peak on the polar angle is an extremely thin line, and the power decreases; also, the pulse width increases, as \(\theta\) leaves its radiation peak. This is why the middle of the radiation ring in Figure 3 is the brightest. If we connect the radiation peaks on both sides of \(\theta=180^{\circ}\) separately, we will obtain the bracket-shaped dash-line in Figure 7b. The strongest and shortest pulses will appear farthest from \(\theta=180^{\circ}\), and this happens to be the moment when the transverse ponderomotive force exerted on the electron reaches its maximum, and also its transverse velocity. Pulses that precede or follow the main peak of radiation are responsible for the appearance of radiation vortices. Figure 6: The NITS temporal power distribution at the radiation main peak when \(\gamma_{0}=100\), where the green line shows the pulse interval, and the red line shows its FWHM. The laser intensity \(a_{0}\) gradually increases in the longitudinal direction between subplots, which is achieved primarily by adjusting the gain factor of the laser generator. Furthermore, we find the time-compression effect of NITS radiation from Figure 7b that the radiated pules when \(\theta=180^{\circ}\) are tightly compressed in time, and when the polar angle \(\theta\) deviates from \(180^{\circ}\), the pulses come earlier than \(t=t_{peak}\) will advance, and the pulses come later than \(t=t_{peak}\) will lag. And, as \(\theta\) moves away from \(180^{\circ}\), this advance-lag extent will increase.