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Ion and Hall Thruster Plumes 421 with the same effective cone angle . The radius of the beam and neutral plumes as a function of the distance z from the thruster is then R = Ro + z tan , (8.5-2) where Ro is the initial radius. Assuming a quasi-neutral beam, the ion and electron densities are ne=ni= Ib 2. e vi R (8.5-3) (8.5-4) The neutral density is given by n = Ib 1 m . o evn R2 m Emission from the neutral gas is proportional to the product of the electron density, the neutral gas density, the electron velocity, and the Maxwellian- averaged excitation cross section: Pemission= nenove excite eEemissiondV 2 = 0 ne no ve excite e Eemission 2 R dz (8.5-5) 2 R2 = nenove excite eEemission dR, Ro tan where the temperature-averaged excitation cross section, excite , is from [20]: excite(TeV)= 19.3exp( 11.6/TeV) 10 20 m2 . (8.5-6) TeV For example, at 2 eV, the value of excite is about 0.8 10–20 m2. Integrating over the plume volume, assuming that Eemission is 10 eV (approximately the energy of the lowest-lying excited state of xenon), and that the neutral temperature is 500 deg C, the total radiated power in the NSTAR thruster plume at the full power point ( Ibeam 1.76 A, Vbeam = 1100 V) isPDF Image | Fundamentals of Electric Propulsion: Ion and Hall Thrusters
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