16.522, Space Propulsion Prof. Manuel martinez-sanchez Lecture 16: Ion Engine performance. Brophy's Theory DEFINITIONS: JB=Beam ion(and neutralizer electron current) Je=cathode emitted current ]=ion current to cathode- otential surfaces D=current through disch power supply Op=total ion production rate Jia=lon current to anode Jacc=lon current intercepted by accel. grid Current balances JD=JE+Jc+JB+J and also JD=P+JE -, Jp=JB +Jc +Jia Jacc(ion balance) Useful Power JB(VB+vD) Total Power JBVB+JDVD +JaccvB+ heaters Energy cost r beam i Total P - P. p-JB Vo Jace vB+ PH PH =JEVO JD-JB=JE +Jc+Ja JEVD+PHp JVo+J f Tac lvB+ vo)(plasma ion cost) Lecture 16 Prof. manuel martinez- Sanchez16.522, Space Propulsion Prof. Manuel Martinez-Sanchez Lecture 16: Ion Engine Performance. Brophy’s Theory DEFINITIONS: JB=Beam ion (and neutralizer electron current) JE=cathode emitted current Jc=ion current to cathode- potential surfaces JD=current through disch. power supply JP=total ion production rate Jia=Ion current to anode Jacc=Ion current intercepted by accel. grid Current Balances: JD = JE + Jc + JB + Jacc and also JD = JP + JE − Jia JP = JB + JC + Jia + Jacc (ion balance) B Useful Power = (V J + VD ) B ' Total Power = V J + V J B B D D + accV J B + PHeaters Energy cost ' B P. Total - P. Useful (JD − )V J D + JaccVB + PH per beam ion ε B = = JB JB PH = V J E c JD − JB = JE + Jc + Jacc ' ε B = ⎜ ⎜ D E + PH ⎞ ⎟ ⎟ JP V J D + Jacc (V + VD ⎛ V J ) + c B ⎝ JP ⎠ JB JB ε p ε ' ε B = p + fc VD + facc (V + VD ) (plasma ion cost) fB fB fB B 16.522, Space Propulsion Lecture 16 Prof. Manuel Martinez-Sanchez Page 1 of 8