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Hall Thrusters 357 P =2T Ib . (7.3-49) a eV b In well-designed Hall thrusters, b ranges typically from 0.6 to 0.8. Therefore, the power loss to the anode is 3 to 4 times the product of the electron temperature in the near-anode region and the beam current. This is the most significant power loss mechanism in TAL thrusters. 7.3.4 Plasma Electron Temperature The electron temperature in the channel must be known to evaluate the power loss mechanisms described above. The peak electron temperature in the plasma channel can be found using power balance, described by Eq. (7.3-27). This method provides reasonable estimates because the power loss in the thruster will be shown to be a strong function of the electron temperature. Even though the plasma density and electron temperature peak in different locations along the channel associated with the different ionization and acceleration regions, the strong axial electron temperature profile in Hall thrusters causes the majority of the power loss to occur in the region of the highest electron temperature. This occurs near the channel exit where the magnetic field across the channel is the strongest. Evaluating the plasma parameters and loss terms in this region, which is bounded by the channel width and magnetic axial field extent in the channel, establishes the electron temperature that is required to satisfy the power balance in the plasma for a given thruster current and voltage. The individual terms in Eq. (7.3-27) will now be evaluated. The input power to the thruster is the discharge current times the discharge voltage ( Pd = IdVd ). The power in the beam, using Eq. (7.3-48), is Pb = b vIdVd = vIbVd, (7.3-50) where the current utilization and voltage utilization efficiencies have to be known or evaluated by some means. The difference between the beam power and the discharge power is the power remaining in the plasma channel to produce the plasma and offset the losses: Pp =(1 b)IdVd =IecVd, (7.3-51) where Pp is the power into the plasma. The plasma is produced and heated essentially by the collisional transport of the electrons flowing from the cathode plasma in the near-plume region to the anode inside the thruster. The power into channel walls, from Eq. (7.3-45), can be written asPDF Image | Fundamentals of Electric Propulsion: Ion and Hall Thrusters
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