Various configurations of the thruster have been tested so far and the thruster efficiency has been gradually increased and approaches twenty percent in recent years. The direct measurement of the force exerted to the magnetic field has demonstrated a thrust enhancement by the magnetic nozzle, where a Lorentz force arising from an azimuthal electron diamagnetic current and a radial magnetic field is exerted to the magnetic field, being equivalent to an electron pressure force to the expanding magnetic field. However, the generation of the collimated ion beam would be beneficial for the thruster since the accelerated ions can be detached from the magnetic field lines, where the electron detachment from the magnetic nozzle is still an open question. The above-mentioned electrostatic ion acceleration does not increase the thrust due to the absences of both any external energy source and the vector conversion of the momentum. Thrusts imparted by magnetic nozzle rf plasma thrusters have been assessed for the last decade by using thrust balances, where the thrust is the reaction force of the momentum exhausted from the system per unit time. Actually, the increases in both the ion beam energy and the electron temperature with a decrease in the operating gas pressure have been detected so far. Since the energy source of the potential drop is considered to be the electron energy as discussed in, the electron energy distribution significantly affects the ion acceleration energy. Measurement of an electron energy probability function (eepf) in the magnetically expanding rf plasma has identified the presence of the two species of electrons: trapped and free electrons, where the high energy (but low temperature population) electrons overcome the potential drop and neutralize the accelerated ion beam. The magnetic field configuration and strength are key parameters in the spontaneous ion acceleration phenomenon as demonstrated before, where the ion beam is generated when the Larmor radius of the ions becomes smaller than the source radius. Measurements of ion energy distributions by using a retarding field energy analyzer and a laser-induced fluorescence method have shown a generation of a supersonic ion beam at the low-potential side, where the number of the beam ions decays along the axis due to a charge exchange process. A number of subsequent experiments have also shown the similar structure or a broader (but still narrower than the scale of the magnetic field gradient) potential drop over about 10 cm in the expanding magnetic fields. Charles and Boswell have discovered a formation of a current-free electric double layer, which has a potential drop over a narrow region of about a few tens of Debye length, in the magnetically expanding radiofrequency (rf) plasmas. When a plasma density decays due to a volume expansion, an axial electric field accelerating the ions and confining the electrons develops in the plasmas. Especially, unmagnetized ions having a mass much heavier than the electrons are significantly affected by electric fields rather than magnetic fields hence the potential structure plays an important role in the ion acceleration processes in weakly magnetized plasmas. Spontaneous accelerations of charged particles can be frequently observed in space, astrophysical, and laboratory plasmas. When increasing the rf power up to 500 W, discontinuous changes in the source plasma density, the imparted thrust, and the signal intensity of the ion beam downstream of the thruster are observed, indicating effects of the discharge mode on the thruster performance and the ion energy distribution. The reproducibility of the impedance matching and the stability of the net rf power are assessed, showing the fast impedance matching within about 10 msec and the long and stable delivery of the rf power to the thruster. The frequency and the output power are controlled so as to minimize the reflection coefficient and to maintain the net power corresponding to the forward minus reflected powers at a constant level.
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