Fully kinetic simulations of magnetic nozzle acceleration were conducted to investigate the axial momentum gains of ions and electrons with electrostatic and Lorentz forces. The axial momentum gains per ion and electron are directly calculated from the kinetics of charged particles, indicating that electrons in the magnetic nozzle obtain the net axial momentum by the Lorentz force, even though they are decelerated by the electrostatic force. Whereas ions are also accelerated by the electrostatic force, the axial momentum gain of electrons increases significantly with increasing magnetic field strength and becomes dominant in the magnetic nozzle. In addition, it is clearly shown that the axial momentum gain of electrons is due to the electron momentum conversion from the radial to the axial direction, resulting in a significant increase in the thrust and exhaust velocity.
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