The effects of neutral distribution and an external magnetic field on plasma distribution and thruster performance are numerically investigated using a particle-in-cell simulation with Monte Carlo collisions (PIC-MCC) and the direct simulation Monte Carlo (DSMC) method. The modeled thruster consists of a quartz tube 1 cm in diameter and 3 cm in length, where a double-turn rf loop antenna is wound at the center of the tube and a solenoid is placed between the loop antenna and the downstream tube exit. A xenon propellant is introduced from both the upstream and downstream sides of the thruster, and the flow rates are varied while maintaining the total gas flow rate of 30 μg/s. The PIC-MCC calculations have been conducted using the neutral distribution obtained from the DSMC calculations, which were applied with different strengths of the magnetic field. The numerical results show that both the downstream gas injection and the external magnetic field with a maximum strength near the thruster exit lead to a shift of the plasma density peak from the upstream to the downstream side. Consequently, a larger total thrust is obtained when increasing the downstream gas injection and the magnetic field strength, which qualitatively agrees with a previous experiment using a helicon plasma source.