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Hollow Cathodes 267 cathode is fixed, then the number of ions flowing to the insert ( Ii in the denominator) is proportional to this ionization rate per unit volume. Therefore, the value of alpha will be constant for varying operating conditions of a given size of cathode. This behavior is illustrated in Fig. 6-14, where the density profile for an NSTAR-sized cathode with two different orifice sizes operating at the same discharge current and gas flow is shown. For the larger orifice cathode, the internal pressure at the constant gas flow is lower, and the penetration of the 2-D effects associated with the downstream boundary condition and the electron current funneling into the orifice extends deeper into the insert region. However, once the collisionality establishes a diffusion- limited plasma flow to the insert upstream of the orifice, then Eq. (6.4-23) is again valid and the value of alpha in the cathode is seen to be essentially constant. It should be noted that the e-folding distance for the plasma density measured inside the NSTAR cathode in Fig. 6-13 is 1/ = 1.7 mm. Therefore, the plasma in the small orifice case is only in significant contact with the insert for a few e-foldings, which is less than 1 cm. This rapid plasma density decrease away from the orifice is the result of the very high pressure in the NSTAR cathode [5,6,] and also occurs in most neutralizer cathodes. For high-pressure cathodes like this, utilizing inserts significantly longer than 1 to 1.5 cm in length is not very useful because there is little plasma left beyond this distance to accept the thermionic emission from the insert. Fig. 6-14. Plasma density measured on axis in the insert region for an NSTAR-sized cathode operating at TH15 with two different orifice sizes.PDF Image | Fundamentals of Electric Propulsion: Ion and Hall Thrusters
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