The Hall thruster has the advantages of high specific impulse, long life, compact structure, small volume and less pollution.^[1–5] Therefore, it has been gradually noticed and favored in the aerospace field. It has been widely used in satellite station keeping, attitude adjustment, orbit transfer, drag compensation and many interplanetary missions. Hall thruster has an annular channel. The radial magnetic field is formed in the channel due to the inside and outside electric coils and permanent magnet structure. The axial electric field is formed by the potential difference between the anode and the cathode. The electrons are bound by the magnetic field, and the electrons drift along the axis under the orthogonal electromagnetic field. The propellant (usually xenon) is ionized into plasma by electrons, and ions are accelerated to form thrust as shown in Fig. 1.^[6] According to the structure and composition, Hall thruster can be divided into two types. One is stationary plasma thruster, its anode area is shorter, the channel structure is longer, the channel wall material is general boron nitride ceramic and other insulation materials; the other is the anode layer Hall thruster, its anode area is longer, the channel is relatively short. The main material for the channel wall of the anode layer Hall thruster is graphite. In experiments, the metal materials such as stainless steel, copper and molybdenum are generally used, and the structure is shown in Fig. 1. Due to the short length of the anode layer Hall thruster channel, the collision between the ions and the wall can be reduced and the life of the thrusters can increase. Therefore, the anode layer thrusters can be used for long-time missions. At present, many researchers have investigated the life of the anode layer Hall thruster, and the main methods of increasing the life are magnetic shielding technology, etc. Compared with stationary plasma thrusters (such as SPT100), the anode layer Hall thruster has a hollow anode structure as shown in Fig. 1. Due to the hollow anode structure, the thruster discharge oscillation can be effectively reduced.^[7,8]

Fig. 1.

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	Fig. 1. Anode layer Hall thruster structure diagram.[6]

Channel wall is an important part of Hall thruster. The change of the channel length has a significant effect on the ionization process and the interaction between particles and wall.^[9] And some researches have shown that choosing proper channel length matched with the magnetic field can effectively constrain the neutral gas, improve the utilization of working fluid, make full use of the energy generated by ionization acceleration, improve the ionization and acceleration characteristic, and enhance the thruster performance.^[10] Therefore, the research on the influence of the channel length on Hall thruster has an important research value.

Aiming at the influence of anode layer Hall thruster channel length on thruster performance, some researchers have carried out relevant work at present, mainly based on experimental methods. Seiro Yuge et al. conducted an experimental study on the influence of the channel length variation and compared the thrust and specific impulse parameters under the conditions of 3 mm and 4 mm in channel length. The results show that the shorter channel length results in lower thrust efficiency and specific impulse.^[11] Kimiya Komurasaki et al. studied the influence of the channel length on thruster performance under different working conditions. The results show that the acceleration efficiency of ions is the highest when the channel length is 4 mm in Ar environment.^[9] Their research focuses on the effect of the channel length on the performance of the thruster. Due to the limitation of experimental measurement, the distribution of the parameters in the channel cannot be obtained. Therefore, the influence of the channel length on the parameters of the anode layer Hall thruster needs to be studied by simulation. For the simulation of the anode layer Hall thruster, the research focuses on the interior of the hollow anode at present. The internal parameter distribution of the hollow anode is adjusted by changing the magnetic field and discharge parameters to try to reduce the effect of the discharge oscillation on the thruster work.^[12–16] In previous simulation work, the parameter characteristics in the discharge channel and the hollow anode were described. However, the effect of the channel length on the performance of the thruster was not studied thoroughly.

In this paper, the particle-in-cell simulation method (PIC) is mainly used to simulate and analyze the effect of the channel length on the distribution of parameters. The rest of the paper is organized as follows. In Section 2, a model and magnetic field selection are introduced. In Section 3 the results of numerical simulation results are discussed. Finally, in Section 4 some conclusions are drawn from the present study.

As the thruster is an axisymmetric structure, in this paper we use a two-dimensional (2D) simulation. The simulation area includes the anode, channel, near-field plume area. In the simulation we use the particle-in-cell (PIC) simulation method, which simulates the movement of atoms, electrons and ions. The Monte Carlo method (MCC) is used to simulate the collision between particles. The Poisson equation is used to solve the electric field. The magnetic field generated by plasma is much smaller than the applied magnetic field generated by the coils. So the magnetic field generated by plasma is neglected. This model has been used to study hall thruster,^[17,18] high efficiency multistage plasma thrusters,^[19] near-wall conductivity,^[20] power deposition on the wall and erosion.^[21] In the simulation, different boundary conditions need to be considered and different treatment methods are selected for different boundary conditions. The boundary conditions are shown in Fig. 2. The magnetic field used in the simulation is obtained by FEEM software. The design of the general magnetic field is chosen to obtain the peak value of the magnetic field at the channel outlet as shown in Fig. 2.

Fig. 2.

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	Fig. 2. (color online) Magnetic field distribution and calculation area, including the anode area, channel, near field plume area. Boundary conditions include dielectric, metal, cathode, free space boundary, symmetry axis, metal, dielectric, and anode.

The related parameters are shown in Table 1.

Table 1.

Table 1.

Table 1. Simulation area parameters. . Parameter name Parameter value Inner channel radius R1/mm 21.5 Hollow anode inner diameter R2/mm 24 Hollow anode outer diameter R3/mm 31 Outer channel radius R4/mm 33.5 Simulation area radius R5/mm 50 Hollow anode length L1/mm 25 Channel length (L2–L1)/mm 2.5 ∼ 7.0 Simulation area length L3/mm 50 Anode potential/V 300

Table 1. Simulation area parameters. .

The orthogonal grid is used. The size of the grid length is 0.5 mm, which is about 0.5 times the Debye length. The time step Δt equals a smaller value of 0.1 and 0.35 , where ω_pe is the electron oscillation frequency and ω_c is the electron cyclotron frequency. Because the electron oscillation is smaller and the value is about 10¹¹ Hz, the time step Δt is taken as 10⁻¹² s. In order to reduce the computational complexity of the simulation and accelerate the convergence, many researchers have proposed different simulation simplification methods at present.^[22–24] In this paper, a simplified model given by Szabo is selected, which increases vacuum permittivity and reduces the ion mass.^[25] And the vacuum permittivity is increased by a factor of γ² = 1600, in order to reduce the number of grids and the plasma oscillation frequency. The ion mass is reduced by a factor 1/f = 100 so that the velocity of the ions increases by times to reduce the time scale by the same amount, and the collision cross-section needs to increase by times to preserve the density of plasma in the discharge channel. The feasibility of this method has already been proved in our recent simulation work.^[26,27] The simulation is calculated by using a personal computer with the above simplified model. After about a three-day calculation, convergent results are obtained successfully.

The change of the channel length is essentially the change of the axial distance between the hollow anode outlet and the channel outlet as shown in Fig. 3. In order to fully consider the effect of the channel length on the performance and parameters of the thruster, the values of channel length L are chosen to be 2.5 mm, 4mmm, 5 mm, 6 mm, and 7 mm, respectively, in this paper.

Fig. 3.

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	Fig. 3. (color online) Selection of the channel length, L = 7.0 mm as an example.

In this paper, we simulate and analyze the effect of the channel length on the distribution of the parameters in the anode layer Hall thruster channel and near field plume area by PIC simulation method. Through the analysis of the electric potential, the potential gradient and the potential drop in the channel are maximum in the case of 5 mm in channel length, which shows that the performance of the thruster is optimal at this length.

By comparison with the distribution of ion density, the hollow anode structure can effectively confine the ionization zone near the anode outlet. And with the shortening of the channel length, the ionization zone shifts towards the channel outlet. As the channel becomes longer, the ion loss increases obviously, and the ion density at the outlet position is low. As the channel becomes shorter, the ions cannot be fully accelerated, the ion density peak significantly decreases, and the performance of the thruster decreases significantly. By analyzing the ion flux and ion energy deposition on the wall, the total influence of ions on the wall is stronger under the longer channel conditions, which has a negative effect on the life of the thruster. Appropriately, shortening the channel length increases the life of the thruster.

In summary, the channel length has a significant effect on the discharge process of the anode layer Hall thruster, and the comparison results show that there is an optimal channel length to achieve the best performance. Under this condition discussed in this paper, the thruster performance is optimal when the channel length is 5 mm.