The pulse-dilation framing camera using electrostatic focusing serves as a two-dimensional diagnostic device characterized by a long drift area, an electron optical imaging system, and ultrafast temporal resolution. The spatio-temporal dispersion (STD) resulting from the space charge effect (SCE) is influenced by electrons with different initial states, which limits the improvement of spatio-temporal performance. The main parameters affecting the SCE include acceleration, drift time, number of electrons, time width, and radius of the electron pulse. The first three are static variables with a linear relationship to the STD, while the latter two are dynamic variables exhibiting a non linear relationship, influenced by the dilation pulse. Therefore, analyzing the SCE based on dynamic variables is challenging yet provides important reference values for further studies on STD in pulse-dilation framing cameras.

To investigate the dynamic SCE of the pulse-dilation framing camera, we first design the imaging system with double electrostatic lenses. We study the dynamic characteristics of electronic pulses in electrostatic focusing, including time width, transmission radius, and electron density, to analyze the pulse-dilation principle of the electron beam and simulate the trajectory of electron motion. Based on the potential distribution of the electronic pulse, we construct an analysis model of the SCE applicable to the dynamic time width and radius of the electronic pulse using the electric field force equation and mean field theory. Next, we study the characteristics of the imaging electric field distribution of the pulse-dilation framing camera by adjusting the spacing of the two electrostatic lenses. Finally, we analyze the time width and dynamic transmission radius of the electronic pulse under different electric field distributions, study the influence of electrostatic focusing on the STD of the SCE, and quantitatively evaluate using mean relative error (MRE) based on the maximum value.

Our research results include three main findings. First, we analyze the trajectory characteristics of the electron beam by coupling the electric field with the second derivative of the potential distribution [Figs. 1(b) and 1(c)]. Based on the working principle of the pulse-dilation framing camera, we first analyze the dynamic characteristics of electronic pulses, such as dynamic time width, transmission radius, and electron density (Fig. 2). Second, we study the influence of electric field distribution on dynamic radius by adjusting the spacing of the two electrostatic lenses, quantified using MRE. As the spacing increases from 70 to 370 mm, the uniformity of the electric field distribution gradually improves, balancing the focusing and diverging capabilities of the electronic pulse, leading to a gradual decrease in the dynamic radius deviation from the maximum defocus radius within the effective detection region. Third, we apply the dynamic time width and radius of the electronic pulse to the SCE model and study the STD. As the spacing between the two lenses increases, the STD decreases, particularly at spacings of 310 and 370 mm, where the temporal dispersion ranges are 0.33?0.44 ps (MRE is 10.99%) and 0.28?0.45 ps (MRE is 22.13%), respectively. The spatial dispersion ranges are 4.11?8.78 μm (MRE is 22.94%) and 2.09?6.34 μm (MRE is 43.17%). Integrating the numerical ranges of the STD and MRE reveals that the STD is smaller at 370 mm spacing, while 310 mm spacing exhibits better uniformity (Fig. 5 and Table 1).

In the electrostatic focusing pulse-dilation framing camera, the dynamic characteristics of the electronic pulse?such as time width, transmission radius, and electron density?change dramatically during transmission due to the dilation pulse and the imaging system of the electrostatic lenses. The STD and uniformity of the SCE are significantly affected by the defocusing of the electronic pulse and fluctuations in radius caused by the electric field distribution. Our results determine the optimal electric field distribution of the pulse-dilation framing camera with the double electrostatic lenses by adjusting the spacing of the lenses, providing a basis for electrostatic focusing in the camera. Additionally, this research offers a theoretical foundation for analyzing the influence of STD and its uniformity of the SCE. In future studies, we aim to systematically investigate the STD of the SCE across different types of electrostatic focusing imaging systems to support the realization of faster temporal resolution in pulse-dilation framing cameras.