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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198 Chapter 5 Jmax =4.75109 VT3/2 . (5.2-4) 2e The units of the current density in the Child–Langmuir equations are amperes divided by the dimension used for the sheath thickness, e , squared. The maximum thrust per unit area possible from an ion thruster can also be found. Thrust was defined in Chapter 2 for electric thrusters as T = d ( m v ) = m i v i . dt Assuming the ions start at rest, the ion velocity leaving the accelerator is vi = 2eVb , M ( 5 . 2 - 5 ) (5.2-6) where eVb is the net beam energy. Using Eq. (2.2-3) for the time rate of change of the mass, the thrust per unit area of the grids becomes T = Jmax TsMvi , (5.2-7) Ag e where Ag is the active grid area (with extraction apertures) and Ts is the grid transparency defined in Eq.(5.2-1). The effective electric field in the acceleration gap is E=VT , (5.2-8) e where VT is the total voltage across the accelerator gap (the sum of the screen and accel voltages): VT =Vs+Va =Vb, (5.2-9) R and R is the ratio of the net beam voltage to the total voltage. Using Eq. (5.2-2) for the space-charge-limited current density and the electric field from Eq. (5.2-8), the maximum achievable thrust density is

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