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Hollow Cathodes 263 Fig. 6-11. Peak plasma density calculation for the NSTAR cathode operating at a constant gas flow of 3.7 sccm. current is predicted by the model and shown experimentally. While the simple 0-D cathode model requires insert heat loss from a cathode thermal model and on-axis potentials from probe measurements or 2-D code runs, it provides reasonable agreement with the data and illustrates the dependence of the insert plasma density and temperature on the geometry and the plasma conditions inside the cathode. The 0-D model also illuminates the heating mechanism in the hollow cathode. The ion heating to the insert is found in Eq. (6.4-12): Power =I U++ +TeV , (6.4-20) ions i s 2 wf where the ion current is given by the Bohm current at the sheath edge. Using the above parameters for the Type B NSTAR discharge cathode shown in Fig. 6-5 at the full-power TH15 operating point of 13 A and 3.7 sccm (U+ =12.1 eV, s =3.6 eV, Te =1.36 eV, wt =2.06 V, axis =8.5 V, and ni 1.5 1021 m–3), the ion heating power from Eq. (6.4-20) is only 4.7 W. The electron heating of the insert is also found in Eq. (6.4-12): Powerelectrons = (2TeV + wf )Ire s TeV , (6.4-21) where the random electron flux is again evaluated at the sheath edge. For the same parameters for the Type B NSTAR cathode given in the paragraph above, the electron heating of the insert is found to be about 45 W. This Type BPDF Image | Fundamentals of Electric Propulsion: Ion and Hall Thrusters
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