They calculated generation and propagation of electromagnetic wave in LTD stage. [PERSON] et al. [14] compared effects of two different dielectric media in induction cavity on the operational performance using the FDTD algorithm. In [15], [PERSON] et al. studied azimuthal uniformity of injection currents in induction cavity based on 3-D electromagnetic numerical model. FDTD method is simple in terms of implementation and programming and it can effectively deal with EM wave propagation problems [24]. However, its calculation accuracy is limited by the staircase approximation of the Yee-cell and numerical dispersion. [PERSON] et al. [16] used iterative FEM, circuit, and magneto-hydro-dynamic (MHD) simulations to determine the design of a pulsed power accelerator. [PERSON] et al. [17] calculated static halo currents in magnetic confinement fusion devices based on electric vector potential and geometric mixed-hybrid formulations of finite element. [PERSON] et al. [18] addressed the poloidal distributions of EM load in the vacuum vessel of COMPASS-U tokamak with ANSYS Maxwell and CarMa0 NL. [PERSON] et al. [19] analyzed geometries of nested transmission lines in the FLT driven accelerator using the RF module of FEM software COMSOL. [PERSON] et al. [20] implemented frequency domain higher-order FEM to determine the generalized scattering matrices of a long accelerator structure. FEM is suitable for modeling complex structures and media distributions [25]; nevertheless, it has low calculation speed and high memory consumption [26]. [PERSON] et al. [21] investigated and optimized the output current of a multi-brick parallel discharge driver using the PEEC method. [PERSON] et al. [22] coupled low rank approximation with the PEEC equations for efficient modeling of thermonuclear fusion facility. [PERSON] et al. [23] proposed fast and parallel modeling of the RFX-mod fusion machine with integral equation method and hybrid CPU-GPU parallelization. The PEEC method can directly embed transient EM model of the multi-conductor system into circuit model [27], but it is difficult to model materials with intricate distribution [28]. The finite integration theory (FIT) is proposed by [PERSON] [29] and then it is combined with particle-in-cell algorithm for simulating particle accelerators [30; 31; 32]. FIT starts with [PERSON]'s equations in integral form and defines integration of field quantity on the edge or facet of a grid as degree of freedom (DoF) [31]. Unlike differential variables, integral variables can be directly measured  
Figure 2: Cross-sectional view (\(r\)-\(z\) plane in cylindrical coordinate system) of the newly developed single-stage FLT. A: load cavity filled with water solution, B: insulating barrier of the load, C: load cavity top lid, D: load cavity bottom lid, E: deionized water-filled cavity, F: negative output electrode, G: positive output electrode, H: epoxy resin casings for magnetic cores, I: middle insulator, J: negative capacitor mounting bracket, K: positive capacitor mounting bracket, L: four separate rings of the magnetic core, M: top lid of FLTO cavity, N: bottom lid of FLTO cavity, O: top insulator, P: bottom insulator, Q: separate columns (24 in total), R: switch terminals, S: switch electrodes. by experiments and are continuous through the separation surface of different materials. FIT is a spatial discretization strategy to numerically solve EM field problems and can yield results in both time- and spectral-domain [32]. [PERSON] et al. [33] derived the field-circuit coupled formulations for time-domain FIT (TD-FIT) based on the concept of winding functions. [PERSON] et al. [34] used the FIT for simulating electrical resistivity tomography and verified its ability for large-scale computation. [PERSON] et al. [35], [PERSON] et al. [36], and [PERSON] et al.