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Hall Thrusters 367 J =μ enE + pe μe J , e e x μei i and the electron mobility due only to electron–ion collisions is given by μei = e . m ei (7.4-4) (7.4-5) Usually, the ion flux term in Eq. (7.4-4) is neglected and an effective electric field is used such that the electron flux is expressed as J =enμ E , e e where the effective electric field is E = E +1 pe . en x The effective perpendicular electron mobility in Eq. (7.4-4) is μe = e 1 = μe , m m1+ c2 m2 1+ 2e (7.4-6) (7.4-7) (7.4-8) where 2e is the electron Hall parameter, and the momentum-transferring collisionfrequency m isdescribed,asinChapter3,by m = ei + en . (7.4-9) This expression for the transverse electron mobility then accounts for both electron–ion and electron–neutral collisions in the partially ionized plasma. Since the electrons are well magnetized in the plasma near the exit of the channel where the magnetic field strength is the highest, the electron Hall parameter is much greater than unity and the transverse electron mobility across the field lines is found to be small. In fact, calculations of the electron collision frequency based on the classical collision terms in Eq. (7.4-9) are unable to provide sufficient cross-field transport to support the discharge current passing through the thruster [54,57,59]. In addition, the neutral density in the plume of the Hall thruster is low due to the high mass utilization efficiency, which reduces the effective collision frequency in Eq. (7.4-9) and again leads to problems in providing sufficient transport of the electrons from the externalPDF Image | Fundamentals of Electric Propulsion: Ion and Hall Thrusters
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