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412 Chapter 8 8.4.1 Momentum of the Plume Particles Just as with chemical thrusters, when electric thruster plumes impact spacecraft surfaces, they exert a force, which causes a torque on the spacecraft. The force is easily calculated as the difference in momentum between the plume particles that impact the surface and the momentum of particles that leave the surface. The momentum of the plume particles is the sum of the ion and neutral atom fluxes. Since the plume consists primarily of ions, and the velocity of the ionized particles is much greater than the neutral atoms, the neutral component can usually be neglected. The ion momentum is pi = ni M Xe vi , In one extreme, an ion that impacts a surface may scatter elastically and leave the surface with its kinetic energy unchained, but its velocity component normal to the surface is reversed: pelastic n= 2p n. (8.4-4) surface plume In the other extreme, the incident xenon ion resides on the surface long enough to transfer its momentum and energy to the surface, and the particle leaves the surface with a velocity distribution corresponding to the surface temperature. This process is called accommodation, and the fraction of particles that undergo this process is called the accommodation coefficient. Since spacecraft surfaces are typically less than a few hundred degrees kelvin, the velocities of accommodated atoms are orders of magnitude less than energetic thruster ions. For example, the speed of a xenon atom leaving a 300-K surface is vi(300K)= kT =137[m/s], (8.4-5) M while the speed of a beam ion from a 300-V Hall thruster is and the neutral momentum is so that the total plume momentum is (8.4-1) (8.4-2) (8.4-3) po = no M Xe vo , pplume = pi + po pi .PDF Image | Fundamentals of Electric Propulsion: Ion and Hall Thrusters
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