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260 Chapter 6 The resistivity of the plasma is given from Eq. (3.6-21) by = 1 , (6.4-10) o e 2p where the collision time, e , for electrons, accounting for both electron-ion and electron-neutral collisions, is given by e = 1 , (6.4-11) ei + en where ei is the electron-ion collision frequency given in Eq. (3.6-14) and en is the electron-neutral collision frequency given in Eq. (3.6-12) from [29]. At the insert, power balance gives + TeV T H(T)+It wf=Ii U + s+ 2 wf +(2TeV+ wf)Ire s eV, (6.4-12) where H (T ) is the total heat lost by the insert due to radiation and conduction and wf is the cathode work function. Particle conservation in the discharge dictates that Ie = It + Ii Ire s TeV . (6.4-13) The random electron flux within a collision length of the sheath edge is given by 1 8kTe 1/2 I r = 4 m n e e A , ( 6 . 4 - 1 4 ) where the plasma density, ne , is evaluated at the sheath edge. The ion current is given by the Bohm current in Eq. (3.7-29), where the ion density is again evaluated within one collision length of the sheath edge. Equations (6.4-12), (6.4-13), and (6.4-14) can be combined to eliminate the ion current term, which gives 2 5 + 2M 1/2 T R I e + I e s + 2 T e V H(T)+I ewf = U + s + 2 T e V m e s e V 1/2 . (6.4-15) U++ +TeV+2T 2M e T s 2 eV m s eVPDF Image | Fundamentals of Electric Propulsion: Ion and Hall Thrusters
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