## 2 Theory and Simulation of XS Anode
### Anode Theoretical Model  
Using the comsol 6.1 simulation software, we studied the model of the interaction between the charge cloud and the XS anode, and the equivalent diagram of the XS anode model is shown in Figure 2. The solid line represents the capacitance between adjacent strips, and the dashed line represents the coupling capacitance between all strips. When simulating the XS anode, some simplifications and assumptions were made to the model. The first is the number of strips. There are 32 horizontal strips and 32 vertical strips, respectively, since the simulation of 64 strips requires a large amount of computation and complicated grid division, the calculation requirements for creating a sufficiently detailed grid are very high. We simulated using five horizontal electrodes and five vertical electrodes so that the footprint of the electron cloud can be covered and any electric field effect or charge effect during the electron movement can be observed.  
The photons incident on the MCP are converted into photoelectrons by the photo-cathode. Under the action of high voltage, the photoelectrons are multiplied by the MCP to form an electron cloud. The multiplied electron cloud passes a certain distance and is received by the XS anode. The electron cloud roughly satisfies the Gaussian distribution. The charge density of the electron cloud can be approximated [23] as  
\[\sigma(x,y)=\frac{q}{\pi r_{i}^{2}}exp(\frac{-(x^{2}+y^{2})}{r_{i}^{2}}) \tag{2}\]  
A traditional cross-strip anode consists of two layers: one for the X dimension and one for the Y dimension. The geometry designed in this article uses a single layer of strip XS anode with the strip array located on the front side of a thin PCB. The anode is divided into transverse electrodes and longitudinal electrodes, which are used for the position encoding  
Figure 1: Electronic collection model.  
Figure 2: Equivalent diagram of XS anode model.  
of two sets of events. The anode converts the received electrons into charges, which are transmitted to 32 horizontal strips and 32 vertical strips, respectively. The model diagram of the XS anode is shown in Figure 3a. And, Figure 3b is the smallest unit of the designed single anode shape, which is composed of horizontal strips and 32 vertical strips. The horizontal electrodes are strip-shaped and the shape of the vertical electrode is a hexagonal pad, and the horizontal and vertical receiving areas are 1:1 to ensure that the signal pickup amplitude on each layer is almost equal. This is designed to improve the ability to resolve \"multiple hit\" events. For pulsed sources or high-rate operation, it is beneficial to increase the count rate.  
The charge value at each strip is determined by the numerical integration of the charge density over the strip area. The XS anode scheme uses the charge detected on each strip to determine the charge cloud centroid for each strip. The size of the charge cloud should be optimized so that it covers multiple strips to obtain the best spatial resolution. The charges collected on the strips are sensed by charge-sensitive amplifiers connected individually to each strip. The preamplified signal from each strip is then digitized using two 32-channels and interfaced to a PC. Each recorded photon is represented by a set of digitized strip signal amplitudes Qi. Two MCPs which produce a 'chevron' stack were placed a distance d above the XS anode, and a potential of 200 V was applied between the MCP output and the XS anode to provide an accelerating electric field. Through this model, we can more fully understand the specific movement process of electrons on the anode.