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Hall Thrusters 333 L LE IH =nee 0 vE dz w=nee 0 Bdz w, (7.2-5) where w is the plasma width (shown in Fig. 7-5) that essentially fills the channel. The axial electric field in the plasma channel is, approximately, the discharge voltage divided by the plasma thickness, so the Hall current is IH neew Vd . (7.2-6) B Equation (7.2-6) shows that the Hall current increases with the applied discharge voltage and with the channel width provided that the magnetic field is unchanged. Hofer [10] showed that in Hall thrusters optimized for high efficiency, the optimal magnetic field was proportional to the discharge voltage. This implies that the Hall current is approximately constant for a given plasma density or beam current in high-efficiency Hall thrusters. The ion current leaving the plasma to form the beam through the area Ae is approximately Ii = nievi Ae nie 2eVd 2 Rw , (7.2-7) M where R is the average radius of the plasma channel. Since the plasma is quasi- neutral ( ni ne ), even in the magnetized region, the Hall current can be expressed using Eq. (7.2-7) as IH Ii MVd . (7.2-8) 2 RB 2e Increasing the beam current in a fixed thruster design will increase the circulating Hall current for a given magnetic field and discharge voltage. From Chapter 2, the total thrust produced by a Hall thruster is MV T= (JH B)dA=IHB Ii d. (7.2-9) 2e This expression for the thrust has the same form as Eq. (2.3-8) derived in Chapter 2, where the force is coupled magnetically to the Hall thruster body instead of electrostatically to the ion thruster grids.PDF Image | Fundamentals of Electric Propulsion: Ion and Hall Thrusters
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