limited roughly to the Alfven critical speed of the gas used (if exit arcs are to be For various gases, assuming V= 2V, we find Hydrogen Nitrogen argon Lithium (3)(s)512014208701220 M Expressing m=n(Na=Avogadro's number), and using kA for I and g/s for m Equation(28) can also be rewritten as PM(kA?(g/mol =154 (30) volts For Argon at 6 g/s and W/H=4, this predicts an "onset current"I= 18kA Experimental values tend to cluster around r-20-23 ka, in reasonable agreement. Much of the difference is simply due to the geometry(coaxial vs rectangular ).The scaling of I with m and with M /2 is also well documented experimentally Efficiency Accounting only for the power lost to ohmic dissipation and to near-electrode voltage drops(△V=△V cathod+△V 10-20 Volts ) we have 1 u 2 muz +d+IAv From the equations derived before 212w 1Hs2+4(H 22 9 2I△V 1+ 1HHoI' 3.05 16.522, Space P pessan Lecture 22 Prof. Manuel martinez Page 7 of 816.522, Space Propulsion Lecture 22 Prof. Manuel Martinez-Sanchez Page 7 of 8 limited roughly to the Alfvèn critical speed of the gas used (if exit arcs are to be avoided). For various gases, assuming i i ' V = 2V , we find Gas Hydrogen Nitrogen Argon Lithium Mi (g/mol) 1 14 40 7 Vi (volts) 13.6 14.6 15.8 5.4 (Isp)MAX (s) 5,120 1,420 870 1,220 Expressing i a M m = N (Na=Avogadro’s number), and using kA for I and g/s for m i , Equation (28) can also be rewritten as ( )1 2 2 2 i ' IM w kA g/mol 15.4 V g/s H m ⎛ ⎞ ⎜ ⎟ ⎜ ⎟ ⎝ ⎠ i  (30) volts For Argon at 6 g/s and w/H=4, this predicts an “onset current” * I 18kA  . Experimental values tend to cluster around * I 20 - 23 kA ∼ , in reasonable agreement. Much of the difference is simply due to the geometry (coaxial vs. rectangular). The scaling of * I with 1 2 m i and with -1 Μ 2 is also well documented experimentally. Efficiency Accounting only for the power lost to ohmic dissipation and to near-electrode voltage drops ( ∆∆ ∆ V = V + V 10 - 20 Volts cathode anode ∼ ), we have 2 e 2 e 1 mu = 2 1 mu +D+I V 2 η ∆ i i (31) From the equations derived before, 2 2 0 1 = 32 2I V 1+ + 9 3 1 H I m 2 w m η ∆ ⎛ ⎞ µ ⎜ ⎟ ⎜ ⎟ ⎝ ⎠ i i 3.05 2 2 0 2 2 24 2 0 0 1 1H I m 2 2w = m 1 1H 4 H I I m + +I V 2 2w w m m 9 3 ⎛ ⎞ µ ⎜ ⎟ ⎜ ⎟ ⎝ ⎠ η ⎛ ⎞ µ µ ⎛ ⎞ ⎜ ⎟ ⎜ ⎟ ∆ ⎜ ⎟ ⎝ ⎠ ⎝ ⎠ i i i i i