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Hall Thrusters 359 The peak electron temperature is found by equating the input power to the plasma in Eq. (7.3-51) with the sum of the various loss terms described above, and then iterating to find a solution. For example, the SPT-100 Hall thruster has a channel outside diameter of 10 cm, a channel inside diameter of 7 cm, and runs nominally at a discharge of 300 V at 4.5 A with a current utilization efficiency of 0.7 and a voltage utilization efficiency of 0.95 [6]. From Eq. (7.3-55), the plasma density at the thruster exit is about 1.6 1017m–3. The power into the plasma, from Eq. (7.3-51), is about 433 W. Taking the electron temperature at the anode to be 5 eV and the hot-plasma thickness L to be about 1 cm, the power balance equation is satisfied if the electron temperature in the channel plasma is about 25 eV. It is a common rule-of-thumb in Hall thrusters to find that the electron temperature is about one-tenth the beam voltage [35]. The result in the example above of Te 0.08 Vd is consistent with that observation. It is also important to note that nearly 70% of the power deposited into the plasma goes to the dielectric channel walls in the form of electron heating, and that the radiation losses predicted by Eq. (7.3-54) are negligible for this case because the electron temperature is so high. Finally, the ion current to the wall for this example from the solution to Eq. (7.3-28) is 0.52 A, which is about 12% of the discharge current and 8% of the beam current in this thruster. This amount agrees well with the 10% of the ion current going to the wall calculated by Baranov [40] in analyzing Hall thruster channel wear. 7.3.5 Hall Thruster Efficiency (Dielectric Walls) The efficiency of a Hall thruster with a dielectric wall can be estimated by evaluating the terms in the thruster efficiency given by Eq. (2.5-7), which requires evaluating the total power-loss terms in Eq. (7.3-27) to obtain a value for the effective electrical efficiency. This also illustrates the dominant loss mechanisms in the thruster. The first term in Eq. (7.3-27), the beam power due to the accelerated ions, Pb , is just IbVb , where the effective beam voltage will be used. The power loss to the dielectric wall will be estimated for the SPT-100 Hall thruster [4–6] using the analysis of Hobbs and Wesson [39] described in Section 7.3.3. The heat flux to the wall was given by Eq. (7.3-46): 2M 1/2 e /kT kTe P w = I i w m e s e e + ( E s ) , ( 7 . 3 - 5 7 )PDF Image | Fundamentals of Electric Propulsion: Ion and Hall Thrusters
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