If holes much bigger than 8 If much smaller, ions lost plasma would escape to grid Space charge effects in the accel-decel gap For o< x<d d 2 dx Note: Slope here not necessarily zero Change integration variable 2 Xdv V=C m ceo 2 16.522, Space Propulsion Lecture 15 Prof. Manuel martinez-s Page 5 of 1116.522, Space Propulsion Lecture 15 Prof. Manuel Martinez-Sanchez Page 5 of 11 If holes much bigger than δ, If much smaller, ions lost plasma would escape to grid Space charge effects in the accel-decel gap For 0 x<dd < , 2 i 2 0 0i 2 0 0 i d jj en =- =- =- dx v 2e v - m φ ε ε φ ε 2 0 0 2 0 i 1d j d =- +c 2 dx 2e v - m φ ⎛ ⎞ φ φ ⎜ ⎟ ⎝ ⎠ ε φ ∫ Note: Slope here not necessarily zero. Change integration variable : 2 0 i 2e v= v - m φ ( ) i 2 2 0 m = v -v 2e φ mi d = - vdv e φ ( ) 0 i 2 v i i 2 0 00 0 00 v m- vdv 1 d j j j 2e e m m =c- =c- v -v =c- v - v - 2 dx v e e m φ φ ⎛ ⎞ ⎛ ⎞ ⎜ ⎟ ⎜ ⎟ ⎝ ⎠ εεε ⎝ ⎠ ∫