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In this paper, we mainly consider a kind of discrete second-order boundary value problem with fully nonlinear term. By using the fixed-point index theory, we obtain some existence results of positive solutions of this kind of problems. Instead of the upper and lower limits condition on f, we may only impose some weaker conditions on f. [ABSTRACT FROM AUTHOR]

The wall-less Hall thruster is expected to overcome the issue of wall erosion in miniaturized Hall thrusters. A unique structure of negative gradient magnetic field is used to constrain the plasma behavior. In this paper, permanent magnet rings with different thicknesses were used to adjust the magnetic field strength, and its effect on discharge characteristics and thrust performance was experimentally investigated. The experiment results show that increasing the magnetic field strength can reduce the current oscillation and increase the maximum operating voltage. Within a limited range, increasing the magnetic field strength can significantly improve thrust performance. However, excessive magnetic field strength leads to a decrease in anode efficiency. The optimal magnetic field strength appears at 121 mT, with a thrust of 5.5 mN, a specific impulse of 935 s, a thrust power ratio of 51 mN/kW, and an anode efficiency of 23.1 %. Based on the analysis of different efficiency parameters and plume images, under excessively high magnetic field strength, the shortening of the ionization region may lead to intensified leakage of neutral atoms, which may be the primary reason for the reduction in propellant utilization and anode efficiency. • The effect of magnetic field strength on discharge characteristics and thrust performance was experimentally studied. • Increasing the magnetic field strength can suppress the anode current oscillation and enhance the maximum operating voltage. • There is an optimal magnetic field strength to maximize the thrust performance. • The reduced propellant utilization under high magnetic field strength is the main reason for the decrease in performance. [ABSTRACT FROM AUTHOR]

The external discharge plasma thruster removes the annular channel of the traditional Hall thruster, allowing the ionization region to appear outside the thruster, which is expected to reduce the plasma-wall interaction and extend the thruster lifetime. Due to its simpler structure and lighter weight, the external discharge plasma thruster is expected to be scaled down to lower power levels. In this work, the effect of radial scaling down on the performance of low-power external discharge plasma thrusters was experimentally investigated by comparing the discharge characteristics, thrust performance, beam characteristics, and spectral characteristics of thrusters with two different anode diameters of 15 and 30 mm. The 30 mm thruster has thrust of 78–235 mN, specific impulse of 566–1071 s, and anode efficiency of 11.8–23.4% at 78–235 W anode power. Compared with the 30 mm thruster, the anode power and thrust of the 15 mm thruster were decreased by approximately half. Plume diagnostic results show that the 15 mm thruster had a higher current utilization, higher ion peak energy and more active ionization due to better electron confinement. However, the propellant utilization of the 15 mm thruster was lower because of the shortened ionization region length. • The manuscript's highlights are as follows: • The performance of external discharge plasma thrusters with anode diameters of 15 and 30 mm were experimentally compared. • The 15 mm thruster had a higher current utilization, higher ion peak energy and more active ionization. • The shortened ionization region length leads to a lower propellant utilization. • The external discharge plasma thruster has an advantage in thrust density. [ABSTRACT FROM AUTHOR]