## 3 Results
### Spatial Radiation Features of NITS Radiation  
To explore the spatial radiation properties of NITS, the peak power of NITS radiation pulses at each angle in space are recorded and shown in the angular plane, as is shown in Figure 3. A plane projection of the spatial radiation power is added on the top of each figure for clearer observation and analysis. The NITS radiation is almost uniform and continuous with a period of \(2\pi\) on the azimuth angle \(\phi\), which can be seen in Figure 3. The angular distribution of NITS radiation power is a shape of a ring, and the polar distribution of the ring-shaped radiation occurs only within a narrow range of polar angles. Although the radiation ring appears to be uniform, there is one single maximum on the ring for each set of parameters, whose power is known as the NITS power peak. In Figure 4, we further calculated the changes in radiation peak power and deviation angle when the normalized laser intensity \(a_{0}\) increases from 0.1 to 10 and the electron's initial energy increases from 1 to 100. As the \(a_{0}\) increases, the radiation peak power increases exponentially [Figure 4a]. In terms of radiation direction, the deviation angle increases linearly [Figure 4b], which is shown in Figure 3 as an increase in the ring-shaped radiation radius. It is worth noting that the radiation vortex gradually becomes significant as \(a_{0}\) increases, which can be seen clearly in Video S1. In fact, when the laser intensity increases, a much greater transverse ponderomotive force is exerted on the electron in average, while the rising edge of the laser also decelerates the electron more violently, so the transverse  
Figure 2: An illustration of spatial NITS radiation power normalized by its maximum value in the angular plane. The radiation components \(\theta\) and \(\phi\) are shown as a red circle and a blue line, respectively. component of the electron's average velocity increases at the laser focus. Therefore, the radiation direction changes from backward to sideways, and this kind of change is linear, while the collimation of the radiation decreases at the same time. When the electron is relatively far away from the laser focus, the instantaneous laser intensity is not that high, so the electron still has weak backward radiation, which is also the cause of the radiation vortex in Figure 3.  
Figure 4: With different laser intensities and different electron initial energies, the peak power of NITS radiation (**a**) and the deviation angle (**b**) in the direction of radiation peak. Figure 3: The angular distribution of the NITS radiation pulses, in which the initial electron energy \(\gamma_{0}\) and the normalized laser intensity \(a_{0}\) are marked. It is worth noting that the scales of different rows are different. The radiation vortex becomes more obvious when \(a_{0}\) increases (see Video S1), and the collimation becomes better with \(\gamma_{0}\) increasing (see Video S2). On the other hand, the peak power of NITS radiation also increases exponentially as \(\gamma_{0}\) increases [Figure 4a], which is achieved by adjusting the force exerted by the electron accelerator on the electrons so that the electrons obtain a higher initial velocity when they leave (\(\gamma_{0}=1/\sqrt{1-v^{2}/c^{2}}\)). The ultra-intense NITS radiation power reaches \(6.4\times 10^{15}\big{(}e^{2}\omega_{0}^{2}/4\pi c\big{)}\) when \(a_{0}=10\) (i.e., \(I=1.384\times 10^{20}\)\(W/\)cm\({}^{2}\)) and \(\gamma_{0}=100\) (i.e., \(\Gamma=51.1\) MeV). However, the deviation angle becomes exponentially smaller, and the radiation is concentrated backward with higher collimation [Video S2, Figure 4b]. The initial velocity of the electron is higher owing to the higher initial energy; thus, the time that the electron interacts with the laser is shorter, and the effects of the transverse ponderomotive force on average are less, even if in an ultra-intense laser.