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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Basic Plasma Physics 87 If there is no net current to the boundary, the ion and electron currents must be equal. The Bohm current of ions through the sheath is given by the current density in Eq. (3.7-50) times the wall area A: Ii=1nie kTeA. (3.7-51) 2M The electron current through the sheath is the random electron flux times the Boltzmann factor: I=1 8kTeneAexp–e, (3.7-52) e 4 m e kTe where the potential is by convention a positive number in this formulation. Equating the total ion and electron currents ( Ii = Ie ), assuming quasi-neutrality in the plasma ( ni = ne ), and solving for the potential gives =kTeln 2M. (3.7-53) e m This is the potential at which the plasma will self-bias in order to have zero net current to the walls and thereby conserve charge and is often called the floating potential. Note that the floating potential is negative relative to the plasma potential. For sheath potentials less than the electron temperature, the sheath thickness is given by the Debye length: D = okTe . (3.7-54) noe2 For sheath potentials greater than the electron temperature ( e > kTe ), a pre- sheath forms to accelerate the ions into the sheath to avoid any inflection in the potential at the sheath edge. The collisionless pre-sheath has a potential difference from the center of the plasma to the sheath edge of Te / 2 and a density decrease from the center of the plasma to the sheath edge of 0.61 no . The Te / 2 potential difference accelerates the ions to the Bohm velocity: vBohm = vB = kTe . (3.7-55) M

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