We have, so far, regarded the efficiency n as a constant independent of the choice of specific impulse. This is not, in general, a good assumption for electric thrusters where the physics of the gas acceleration process can change significantly as the cower loading(hence the jet velocity)is increased. For each thruster family can typically establish a connection between n and c alone. Thus, as we will see in detail later, n increases with c in both ion and MPD thrusters, whereas it typically decays with c for arcjets(beyond a certain c). In general, then one needs to return is instructive to consider in some detail the particular case of the ion engine, both e to Equation(5)with n=n(c) in order to discover the best choice of c in each case because of its own importance and because relatively simple and accurate laws can be obtained in that case Ion engine losses can be fairly well characterized by a constant voltage drop per accelerated ion. If this is called A o, and singly charged ions are assumed, the energy spent per ion is 1/2mc2+△中(m= Ion mass, e= electron charge), of which only 1/2m, c2 is useful The efficiency is the n- We should also include a factor of n z1 to account for power processing and other losses. We then have 16.522, Space Propulsion Prof. Manuel Martinez-Sanchez Page 3 of 1916.522, Space Propulsion Lecture 2 Prof. Manuel Martinez-Sanchez Page 3 of 19 We have, so far, regarded the efficiency η as a constant, independent of the choice of specific impulse. This is not, in general, a good assumption for electric thrusters where the physics of the gas acceleration process can change significantly as the power loading (hence the jet velocity) is increased. For each thruster family (resistojets, arcjets, ion engines, MPD thrusters) and for each fuel and design, one can typically establish a connection between η and c alone. Thus, as we will see in detail later, η increases with c in both ion and MPD thrusters, whereas it typically decays with c for arcjets (beyond a certain c). In general, then, one needs to return to Equation (5) with η η = c( ) in order to discover the best choice of c in each case. It is instructive to consider in some detail the particular case of the ion engine, both because of its own importance and because relatively simple and accurate laws can be obtained in that case. Ion engine losses can be fairly well characterized by a constant voltage drop per accelerated ion. If this is called ∆ φ , and singly charged ions are assumed, the energy spent per ion is ( ) 2 1 2m c + m = ion mass; e = electron charge i i ∆ φ , of which only 2 1 2m ci is useful. The efficiency is then 2 2 i c = 2e c + m η ∆φ (8) We should also include a factor of η0 ∠ 1to account for power processing and other losses. We then have 2 0 2 2 L c = c +v η η (9)