lecture16

lecture16 - 16.522, Space Propulsion Prof. Manuel...

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Unformatted text preview: 16.522, Space Propulsion Prof. Manuel Martinez-Sanchez Lecture 16: Ion Engine Performance. Brophy’s Theory DEFINITIONS: J B =Beam ion (and neutralizer electron current) J E =cathode emitted current J c = i o n c u r r e n t t o c a t h o d e- potential surfaces J D =current through disch. power supply J P =total ion production rate J ia =Ion current to anode J acc =Ion current intercepted by accel. grid Current Balances: J D = J E + J c + J B + J acc and also J D = J P + J E − J ia J P = J B + J C + J ia + J acc (ion balance) B ( Useful Power = V J + V D ) B ' Total Power = V J + V J acc B B D D + V J B + P Heaters Energy cost ' B ) P. Total - P. Useful ( J D − V J D + J acc V B + P H per beam ion ε B = = J B J B P H = V J c E J D − J B = J E + J c + J acc ' ε B = ⎜ ⎜ D E + P H ⎞ ⎟ ⎟ J P V J D + J acc ( V + V D ) ⎛ V J + c B ⎝ J P ⎠ J B J B ε p ε ' ε B = p + f c V D + f acc ( V + V D ) (plasma ion cost) f B f B f B B 16.522, Space Propulsion Lecture 16 Prof. Manuel Martinez-Sanchez Page 1 of 8 V J + P H where f B = J B , f c = J c , f acc = J acc and ε p = D E J J J J p p p p More definitions: U + = ionization energy per ion U j = excitation energy of level j J j = excitation rate (total) J LP = loss rate of primary electrons ε m = mean energy of Maxwellian electron group Discharge Energy Balance U + j + ∑ j J P j J U + P D Lp J V J m + ε ( p J + E J P ia J J − − ) Lp J = p D E J V J = p ε − p H J P Define o ε = U + j + ∑ j J p j J U . Then − P H J P p + ε = o ε m + ε + ( D V ) m − ε E Lp J J p E J J − p ia J J m ε p m ⎜ ⎜ ⎝ ⎛ + ε ε D H V P − / p J ⎟ ⎟ ⎠ ⎞ Use p ε D H V P − P J / p ⎢ ⎢ ⎣ ⎡ ε 1 − D m D V V − ε E Lp J J − D m V ε ⎥ ⎥ ⎦ ⎤ = o ε m + ε − ( D V ) m − ε E Lp J J D p H V J P − p ia J J m ε m − ε D p H V J P + D p H V J P + p H J P 1 − E Lp J J − D m V ε ⎜ ⎜ ⎝ ⎛ 1 − E Lp J J ⎟ ⎟ ⎠ ⎞ 1 − ⎜ ⎜ ⎝ ⎛ 1 − E Lp J J ⎜ ⎜ ⎝ ⎛ ⎟ ⎟ ⎠ ⎞ 1 − D m V ε ⎟ ⎟ ⎠ ⎞ 16.522, Space Propulsion Lecture 16 Prof. Manuel Martinez-Sanchez Page 2 of 8 1 J Lp ε m − J Lp ε m + ⎛ ⎜ ⎜ ⎞ ⎟ ⎟ ⎠ ⎛ ⎜ ⎜ ⎞ ⎟ ⎟ ε m − ⎛ ⎜ ⎜ ⎝ ⎞ ⎟ ⎟...
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This note was uploaded on 11/07/2011 for the course AERO 16.512 taught by Professor Manuelmartinez-sanchez during the Fall '05 term at MIT.

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lecture16 - 16.522, Space Propulsion Prof. Manuel...

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