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Basic Plasma Physics 53 3 p s + 5 p v + v p = Q n m s v s 2 . ( 3 . 5 - 3 4 ) 2 t 2sss ssss 2 The heat-exchange terms for each species Qs consists of “frictional” (denoted by superscript R) and “thermal” (denoted by superscript T) contributions: Q s = Q sR + Q sT , Q sR R s n v s , In a partially ionized gas consisting of electrons, singly charged ions, and neutrals of the same species, the frictional and thermal terms for the electrons take the form QR= (R +R ) v = Rei+Ren J e ei en e ene e (3.5-36) QT= 3nm k(T T)+ k(T T) , e eM eieeieneen where as usual M denotes the mass of the heavy species, and the temperature of the ions and neutrals is denoted by Ti and Tn , respectively. Using the steady- state electron momentum equation, in the absence of electron inertia, it is possible to write n Q sT n s s s n s n . 2m 3 kT kT n ma 2 e e (3.5-35) QR = Rei +Ren J = E+ pe J . e ene e ene e Thus Eq. (3.5-34) for the electrons becomes 3 pe+ 5pv + =Q J pe n eU 2 t 2eee eeen i (3.5-37) energy loss due to ionization, with Ui (in volts) representing the first ionization potential of the atom. In Eq. (3.5-38), the meve2 / 2 correction term has been neglected because usually in ion and Hall thrusters eUi >> meve2 / 2 . If multiple (3.5-38) where the inelastic term is expressed as e = en Ui to represent the electron = E Je n eUi ,PDF Image | Fundamentals of Electric Propulsion: Ion and Hall Thrusters
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