Fundamentals of Electric Propulsion: Ion and Hall Thrusters

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Fundamentals of Electric Propulsion: Ion and Hall Thrusters ( fundamentals-electric-propulsion-ion-and-hall-thrusters )

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Ion Thruster Plasma Generators 153 and the second current fraction is likewise: I*=2no *ve V. (4.5-9) Ib kTe AsTs M The screen current-to-beam current ratio is given in Eq. (4.3-57) as (1 – Ts ) / Ts . The ion current that goes to the wall is the Bohm current to the wall area Aw reduced by radial confinement provided by any applied or induced magnetic fields. The fourth current ratio is then 1 nivaAw fc Iw = 2 = Aw fc , (4.5-10) I b 12 n i v a A s T s A s T s where fc is again a confinement factor for the reduction in the Bohm velocity due to ambipolar effects in the ion and electron flows to the wall. Since there are no applied DC potentials in the discharge chamber and all the walls float, the electron current out is the same as the ion current out: Ia = Is + Iw + Ib . (4.5-11) Plasma potential in the expression for the discharge loss [Eq. (4.5-7)] can be evaluated by equating the total ion and electron currents exiting the plasma: ni kTe (Aw fc + As)= ne 8kTe [Aw +(1–Ts)As]exp–e/kTe . (4.5-12) 2M 4m Solving for the plasma potential gives = kTe lnAw +(1–Ts)As 2M . (4.5-13) eAwfc+As m If the wall area is large compared to the screen area, or the grid transparency is small compared to 1, this turns into the normal equation for floating potential: =kTeln 2M, (4.5-14) e m

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