## 1 Introduction  
Compared with other multi-type ion sources, the radio frequency (RF) negative hydrogen ion source has a relatively simple structure, reliable performance, long life, and is almost maintenance-free [1]. It has its unique advantages and characteristics. Therefore, the RF negative hydrogen ion source is favored by many researchers. In 2007, the RF negative hydrogen ion source was established as the reference scheme for plasma generation in the International Thermonuclear Experimental Reactor (ITER) neutral beam injection system [2; 3; 4; 5]. With the development and testing of the ITER neutral beam test facility located in Padova, Italy, countries are experiencing a research boom with respect to negative hydrogen ion sources [6; 7; 8; 9]. At present, the Max-Planck-Institute fur Plasma Physik (IPP) in Germany is one of the leading institutions in the research of RF negative hydrogen ion sources [10; 11]. Some experimental parameters obtained by the BATMAN, BATMAN upgrade, MANITU, ELISE, and RADI experimental devices [12; 13; 14] have reached or exceeded the requirements of the ITER project. Based on the BATMAN testbed, India has developed an ion source device, ROBIN [15], similar to the BATMAN structure. China has also successively developed a single-exciter experimental device, HUST [16], a RF negative ion source device, HUNTER [17], and so on. At the same time, a large number of numerical simulation studies have also been carried out on negative hydrogen ion source devices, mainly using the two-dimensional or three-dimensional Particle-In-Cell/Monte Carlo Collision (PIC/MCC) method to perform a lot of work on \(H^{-}\) volume generation, surface generation processes, and extraction processes [18; 19; 20]. The factors affecting the beam quality have been studied in an attempt to clarify the physical mechanism in the source and to improve the performance of the device.  
Many examples in the existing literature show that the negative hydrogen ion source needs to add a magnetic filter field near the extraction region to filter the \"hot\" electrons (\(T_{e}\geq 10\) eV), so as to reduce the electron temperature and reduce the stripping loss of negative hydrogen ions [21; 22; 23; 24]. The design of the magnetic filter field is strongly dependent on experiments [23]. In addition to the effect of \"reducing the temperature of electrons\", which is widely understood by researchers, the mechanism behind it also needs to be studied by means of numerical calculation. Based on the three-dimensional PIC/MCC method [25] and using the CHIPIC code [26; 27; 28], this paper studies the transport mechanism of \"hot\" electrons passing through the magnetic filter field system in the expansion region and the influence of different collision types on \"hot\" electron filtering. Results from modelling [29; 30] show that a gradient drift occurs in the IPP prototype source. Likewise, the vertical drift of electrons due to gradient drift is observed in this paper. The temperature of the initial electrons is reduced from 10 eV to about 3.2 eV through the magnetic filter field system, which is consistent with the 3 eV of a reference [31] with the same magnetic field structure. However, numerical results show that the magnetic filter field filters both \"hot\" and \"cold\" electrons (energy \(\varepsilon\leq 2\) eV), which is different from the descriptions in the literature. The filtering, reflection, and drift phenomena of electrons in the numerical results are presented and discussed to understand the complex behavior of electrons on the magnetic filter field. The research in this paper helps elucidate the particle transport process under the magnetic filter field system, the formation process of cold electrons on the extraction surface, and the objective role of the magnetic filter field system in negative hydrogen ion source devices.