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Thruster Principles 21 Using quasi-neutrality and the definition of the Hall current density, JHall = –eneve , the force on the ions is shown to be equal to Lorentz forces on the electrons: Fi = 2 qni E rdrdz +2 JHall B rdrdz=0. (2.2-13) Solving Eq. (2.2-13), the force on the ions is then Fi =JHall B (2.2-14) By Newton’s second law, the Hall current force on the magnets is equal and opposite to the Hall current force on the electrons and, therefore, is also equal and opposite to the force on the ions: T = J H a l l B = Fi . ( 2 . 2 - 1 5 ) In Hall thrusters the thrust is transferred from the ions to the thruster body through the electromagnetic Lorentz force. These thrusters are sometimes called electromagnetic thrusters because the force is transferred through the magnetic field. However, since the ion acceleration mechanism is by the electrostatic field, we will choose to call them electrostatic thrusters. 2.3 Thrust Thrust is the force supplied by the engine to the spacecraft. Since the spacecraft mass changes with time due to the propellant consumption, the thrust is given by the time rate of change of the momentum, which can be written as d dmp T=dt(mpvex)= dt vex=m pvex (2.3-1) where m ̇ p is the propellant mass flow rate in kg/s. The propellant mass flow rate is m p = Q M , ( 2 . 3 - 2 ) where Q is the propellant particle flow rate (in particles/s) and M is the particle mass. The kinetic thrust power of the beam, called the jet power, is defined as P =1m v2. (2.3-3) jet 2 p exPDF Image | Fundamentals of Electric Propulsion: Ion and Hall Thrusters
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