The lines kT and mr v. must F ↓.1-↓ Supersonic cross at v kTe here their sum is minimum kTe Ii m So, no solution at Ions accelerate to vi = ve in the quasineutral plasma. Beyond that, becomes very strong, and ions just free-fall to wall (in the sheath)so, entering How big is the sheath? sheath Pre-sheath ne ni In sheath, say n =0 Child-Langmu 42 But also J=en 16.522, Space P pessan Lecture Prof. Manuel martinez Page 3 of 1116.522, Space Propulsion Lecture 15 Prof. Manuel Martinez-Sanchez Page 3 of 11 The lines i e i kT v Γ and m v iii Γ must cross at e i i kT v m = , where their sum is minimum. So, no solution at e i B i kT v > =v m Ions accelerate to v =v i B in the quasineutral plasma. Beyond that, n << n , E e ix becomes very strong, and ions just free-fall to wall (in the sheath) so, entering sheath, v =v i B . How big is the sheath? In sheath, say n 0 e  Child-Langmuir: 3 2 s i ii 0 2 i 42 e V j = en v = 9 m ε δ But also sh e i e i kT j en m  sh 3 2 s e 0 e 2 i i 42 e V kT en 9m m ε δ