Fully kinetic analysis of radio frequency plasma generation
and acceleration in magnetic nozzle thrusters
Kazuma Emoto
March 2022

Fully kinetic analyses were conducted to evaluate the kinetics of plasma generation and acceleration inmagnetic nozzle thrusters. The momentum conversion and energy transport in the magnetic nozzle were also
clarified through simulations. The main topics of this study are high-energy electron transport, internal plasma
currents, axial momentum gains, and energy losses in magnetic nozzle thrusters. To perform fully kinetic
simulations, a two-dimensional and symmetric calculation model was employed, including both the plasma
source and diffusion region in the magnetic nozzle.
Electron heating and density profile transitions were evaluated by changing the intensity of the magnetic
field. The bimodal plasma profile observed in the previous experiments was reproduced in the simulations.
The density profile transition is discussed with respect to the ionization, electron temperature, and high-energy
electron number density. It is shown that high-energy electrons are transported by an elastic collision acrossthe magnetic field lines and generate a bimodal density profile in the strong magnetic nozzle, implying a longer
existing time for high-energy electrons that move radially inward away from the rf antenna.
The internal plasma currents in the magnetic nozzle were numerically obtained in the simulations andwere found to be diamagnetic and 𝑬 × 𝑩 drift effects in addition to other drift components. The diamagnetic
drift current increases and becomes dominant in a strong magnetic nozzle, whereas the 𝑬 × 𝑩 drift current
decreases with increasing magnetic field strength, which is consistent with previous experimental results. The
electromagnetic thrust induced by the internal plasma currents was also calculated, indicating an increase in theelectromagnetic thrust with increasing magnetic field intensity.
The electrostatic and Lorentz forces in the magnetic nozzle were obtained in the simulations, and theaxial ion and electron momentum gains from these forces were calculated. The simulation results show that
the Lorentz force in the magnetic nozzle exceeds the electrostatic force with a strong magnetic field. In thissituation, the axial electron momentum gain due to the Lorentz force also exceeds the axial ion momentum gain,
implying that the axial electron momentum gain becomes dominant in the magnetic nozzle. Additionally, it
was confirmed that the electron momentum gain was due to the momentum conversion from the radial to axialdirections.
The energy losses in the magnetic nozzle were calculated to further improve the thruster efficiency. The
major energy loss in a weak magnetic field is the energy loss to the dielectric wall. As the magnetic fieldstrength increased, the energy loss to the dielectric was suppressed, and the plasma beam energy contributing
to thrust generation increased. Although there is essential energy loss due to electron-neutral collisions and thedivergent ion beam, it is indicated that the thruster efficiency in the magnetic nozzle could be further improvedby increasing the intensity of the magnetic field.

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