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Hall Thrusters 339 where Vb represents, in this case, the average potential across which the ions are accelerated. The actual spread in the beam energy can be significant [27,28] and must be measured by plasma diagnostics. The beam from the Hall thruster is charge neutral (equal ion and electron currents). As in ion thrusters, the thruster floats with respect to either spacecraft common in space or vacuum-chamber common on the ground. The common potential normally floats between the cathode and the beam potentials and can be controlled on a spacecraft by a resistor between the spacecraft common and the cathode common. The actual beam energy cannot be measured directly across the power supplies because the potential difference between the beam and ground or spacecraft common is unknown and must be measured by probes or energy analyzers. The coupling voltage is typically on the order of 20 V in order to operate the cathode discharge properly, which usually ranges from 5% to 10% of the discharge voltage for Hall thrusters with moderate Isp. In a Hall thruster, the measured discharge current is the net current flowing through the discharge supply. The current flowing in the connection between the anode and the power supply in Fig. 7-7 is the electron and ion current arriving to the anode: Id = Iea Iia. (7.2-24) The ion current is typically small due to its higher mass, and so the discharge current is essentially the electron current collected by the anode. Likewise, the current flowing in the cathode leg (neglecting any keeper current) is Id =Ie+Iic, (7.2-25) where Ie is the emitted current and Iic is the ion current flowing back to the cathode. As with the anode, the ion current to the cathode is typically small, and so the discharge current is essentially just the cathode electron emission current. Therefore, the discharge current is approximately Id Ie Iea. (7.2-26) Figure 7-8 shows a simplified picture of the currents flowing through the plasma, where the ion currents to the anode and cathode are neglected as small and the ion and electron currents to the dielectric walls are equal and are not shown. Ions are produced in the plasma by ionization events. The secondary electrons from the ionization events, Iei, go to the anode, along with the primary electrons from the cathode, Iec . Primary electrons either ionize neutrals or contribute energy to the plasma electrons so that the energeticPDF Image | Fundamentals of Electric Propulsion: Ion and Hall Thrusters
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