cn is seen to be the energy per ion created if no primary electrons were to escape (E,+o). The expression for ep(neglecting ion capture by the screen, fia=0, and heating power, V=o)was 1 Eo=U++U nuPlEx(o) and this does depend on Te and"(Te). Substituting the expression for pfound above, and simplifying, we obtain NOTE: An intermediate expression for En(still containing -p), which will be useful later, is n Calculation of utilization efficienc d Ceo, r JB=fBJ e D/+n ↑m(1-n) 4 v(np2,)+na)4-n)=2m But also n,=nm+np and JB=en, 0.61DB A, i 16.522, Space Propulsion Lecture 16 Prof. Manuel Martinez-Sanchez Page 6 of 8ε * is seen to be the energy per ion created if no primary electrons were to escape p * (ε o → ∞). The expression for ε (neglecting ion capture by the screen, f p ia = o , and heating power, Vc = o ) was pε * = D m mo V − + ε εε 1 ; oε = U+ + p exc J J U exc or ε o = + U + U exc ( ) ( ) + + + υ σ υ σ Dp p Dexc p p Vn Vn σ + σ e m exce m c n c n and this does depend on Te and ( ) e m p T n n . Substituting the expression for m p n n found above, and simplifying, we obtain * σ (V σ + (U + + ε m ) + σ excUexc ε p = V T D D ) [σ σ (V ) − σ (V )σ ]U + σ σ T (V )(V − ε m ) exc + B exc D + exc + D D n * p NOTE: An intermediate expression for ε p (still containing ), which will be useful nm later, is ⎛σ T ⎞ ⎜ ⎟ * VD ⎝ ⎜ σ + ⎠ ⎟ ε p = nm ce σ + 1 + n υ σ (VD ) p p + Calculation of utilization efficiency  Jp = ( n Vd υ σ (V ) + c n eσ + )n JB = J f = e )( p p + D m n p B η um e mi ↑ m (1 − η ) 4 u cnφAgmi ( η u V(n υ σ (V ) + c n eσ + ) 1 4 − η u ) p p + D m = cnφAg fB But also n+ = nm + np and JB = n e + 61.0 υ A φi g B 16.522, Space Propulsion Lecture 16 Prof. Manuel Martinez-Sanchez Page 6 of 8