5. 522, Space Propulsic Prof. manuel martinez-sanchez Lecture 15: Thrust Calculation(Single Grid, Single Potential) d xx 十 a=Pche x= so dx er dx xx0 ch 十 十 十 d d E 3 d A 9 8 Alternative F d2 Child-Langmuir 16.522, Space P pessan Lecture Prof. Manuel martinez Page 1 of16.522, Space Propulsion Lecture 15 Prof. Manuel Martinez-Sanchez Page 1 of 11 16.522, Space Propulsion Prof. Manuel Martinez-Sanchez Lecture 15: Thrust Calculation (Single Grid, Single Potential) 2 x d 1 E dx 2 ⎛ ⎞ ⎜ ⎟ ⎝ ⎠ d d d 2 x x 0 x ch x 0 x 0 0 0 F dE E = E dx = E dx = A dx 2 ε ρ ε ∫ ∫ 4 3 a x = -V d ⎛ ⎞ φ ⎜ ⎟ ⎝ ⎠ 1 3 a x V 4 x E = d3 d ⎛ ⎞ ⎜ ⎟ ⎝ ⎠ x 0 E =0 a x d 4 V E = 3 d 2 2 x 0a a 2 2 0 F 16 8 V V = = A 29 9 d d ⎡ ε ⎤ ⎢ ε ⎥ ⎣ ⎦ Alternative: 3 3 2 2 xi i aa a 0 0 2 2 i i Fm m 42 e 8 V 2eV V = jc = = A e e9 m m 9 d d ε ε m i j from Child-Langmuir