here 2ev 2j m T 2c-2jm 2ev. 2e(V-o) d C, then all profiles follows 2jm|2ev2e(v-ψ Ege[y m, In the limit when the second gap becomes choked as well,(as in the case with no decel grid, in which case dd is the downstream sheath thickness) 0→c= jm,/2ev 2eVN Then d 2m|2e(W-9) spev m Change again variable 16.522, Space P pessan Lecture Prof. Manuel martinez Page 6 of 1116.522, Space Propulsion Lecture 15 Prof. Manuel Martinez-Sanchez Page 6 of 11 where 2 T 0 i 2eV v = m ( ) 2 i T T 0i i 1 d 2j m 2eV 2e V - = 2c - - 2 dx e m m ⎛ ⎞ φ ⎛ ⎞ φ ⎜ ⎟ ⎜ ⎟ ⎝ ⎠ ε ⎝ ⎠ ( ) i T T 0i i d dx = 2jm 2eV 2e V - 2c - - em m φ ⎛ ⎞ φ ⎜ ⎟ ε ⎝ ⎠ ( ) =V -V T N d 0 i T T 0i v d d = c, 2jm 2eV 2e V - 2c - - em m φ φ ⇒ ⎛ ⎞ φ ⎜ ⎟ ε ⎝ ⎠ ∫ then all profiles follows. In the limit when the second gap becomes choked as well, (as in the case with no decel grid, in which case dd is the downstream sheath thickness) d iT N x=d 0i i d jm 2eV 2eV =0 c= - dx e m m ⎛ ⎞ ⎛ ⎞ φ ⇒ ⎜ ⎟ ⎜ ⎟ ⎝ ⎠ ε ⎝ ⎠ ( ) =V -V T N φ Then ( ) V -V T N d 0 i N T 0ii d d = 2jm 2eV 2e V - - em m φ ⎛ ⎞ φ ⎜ ⎟ ε ⎝ ⎠ ∫ Change again variable: mi d = - vdv e φ ( ) T i 2e V - = v m φ