## 2 Simulation Model and Methods  
Figure 1 is a schematic diagram of a typical negative hydrogen ion source structure. It is mainly divided into three parts: the driver, the expansion region, and the extraction region. The driver generates hydrogen or deuterium plasma through RF power coupling (up to 100 kW at 1 MHz) with an electron temperature greater than 10 eV and an electron density greater than \(10^{18}\) m\({}^{-3}\). As the plasma diffuses into the expansion region, the electron temperature is cooled below 2 eV by the magnetic filter field [21]. The extraction region mainly includes a bias plate (BP) and three grids (a plasma grid PG, an extraction grid EG, and a grounded grid GG). There is usually a positive bias voltage of about 15 V between BP and PG. The purpose of this paper is to study the mechanism of the magnetic filter field on \"hot\" electrons, so the simulation domain selects the expansion region, which contains a long-range weak magnetic filter field. The surface production process and the extraction and acceleration processes of \(H^{-}\) ions are not considered, so the model we built only simulates the expansion region of the front end of BP shown in Figure 2. Since BP is connected to the source body, the expansion region can be considered to be equipotential. The main generation method for \(H^{-}\) ions in the expansion region is volume production, that is, \(H_{2}\) achieves an excited state after colliding with fast electrons (\(T_{e}\geq 5\) eV) and then dissociates and adsorbs with low-temperature electrons to generate \(H^{-}\). Figure 2 is the schematic diagram of the X\(-\)Z cross section of the negative hydrogen ion source expansion region model. The simulation domain is 18 cm \(\times\) 60 cm \(\times\) 30 cm. The black frame represents the metal conductor; the yellow lines represent the ends of the emission surface of the electron beam and the BP, which are all metal conductor materials; the green dashed line represents the ends of the extraction surface; and the grey area represents the plasma. Samarium-cobalt permanent magnets are attached on both sides of the chamber. When electrons reach the simulation boundary (the surface of a metal conductor), they are destroyed. This paper approximates the process of generating plasma by an RF power coupling in the driver as follows: electron beams are emitted from a perfect conductor surface, colliding with the background gas to generate plasma, and the emitting surface is circular, with a radius of 12 cm. The electron beam temperature is set at 10 eV, and the electron velocity distribution follows the Gaussian distribution. The initial electron density is \(5\times 10^{18}\) m\({}^{-3}\), and the background hydrogen has a pressure of 0.6 Pa and a temperature of 1200 K. Due to the extremely high initial density of electrons, affected by the space-charge-limited current, the generated reverse electric field force leads to most of the electrons being unable to be successfully emitted and thus accumulating on the emitting surface. Therefore, the model ignores the interactions between particles and adopts the electrostatic simulation method. Figure 1: Schematic view of negative hydrogen ion source. Figure 2: The schematic diagram of the X\(-\)Z cross section of the negative hydrogen ion source expansion region model. The simulation parameters are set as shown in Table 1[32; 33; 34]. The main collision reactions considered in the expansion region are shown in Table 2[32; 35; 36]. The magnetic filter field is calculated by the scalar magnetic potential finite-difference method (SMPM)[26; 37]. Magnetic boxes are located on both sides of the source body, and there are 4 magnetic boxes in total. Each magnetic box could hold \(~{}2\times 4\) samarium-cobalt magnets; that is, CoSm magnets are superimposed, and 2 CoSm magnets are placed on each layer for a total of 4 layers.