allow more holes per unit area(if the hole spacing varies in proportion to their size), hence more current per unit grid area. Due to this circumstance Ref. 7 recommends low R designs. (5) The perveance generally increases as Da/Ds increases, with the exception of cases with R near unity when an intermediate D,/D=0.8 is optimum (6)Increasing Vo/VT, which increases the plasma density appears to flatten th contour of the hole sheath( 8), which reduces the focusing of the beam. this results in direct impingement on the screen, and, in turn forces a reduction of the beam current Some appreciation for the degree to which Child-Langmuir's law departs from the observed current extraction capacity of real devices can be obtained from the data for the 30 cm. J-series thruster, as reported for example in Ref.( 9). In this case,we have d=0.5 mm ta=ts=0. 38 mm, Ds=1.9 mm, Da=1. 14 mm, and a total of 14860 holes. We will refer to data in Xe, for VNET/V=0.7 and Vo=31.2 Volts. VBeam=1200 V. Table Ill of Ref (9)then gives a beam current ]8=4.06 A. The correlation given in the same reference for various propellants is aM+25%6 (15) here a is a double-ion correction factor, given as 0.934 for this case, and M is the molecular mass in a. m u. The power of 2.2 instead of 1.5 for the effect of extractio oltage is to be noticed. This correlation yields for our case Ib=5.4 A, on the outer boundary of the error band For these data, if we apply the Child-Langmuir law(Equation 13)to each hole (diameter Ds), and use directly the spacing d=0.5 mm, we obtain a hole current of 3.83 mA, or, in total IB=57.1 A, i.e. 14 times too high. an approximate 3-D correction(Ref. s 10a, b)is to replace d by (d+t 2+D2/4 in Child-Langmuir's equation this gives now IB=8.4 A, still twice the experimental value. It is of interest to see how well the data of Rovang and Wilbur(ref. 7) can be extrapolated to the J thruster. We first use the data in Fig. 6a of Ref (7), which are for Ds=2mm ,R=0. 8 Da/Ds=0.66(lowest value measured), and VD/V=0. 1. Corrections for the actual Da/Ds=0.6 and Vo/VT=0.018 can be approximated from Fig. ' s 5 and (6a) of the same reference. The effects of R=0.7 instead of 0.8, as well as of the slightly different Ds should be small, according to Ref. 7. We obtain in this manner IB=5.2 A which is indeed as accurate as the correlation of Equation(15) Additional data on grid perveance are shown and assessed Ref.(10c)in the context of ion engine scaling To complete this discussion two limiting conditions should be mentioned he (a)Direct ion impingement on screen: At low beam current, the screen collects a very small stray current, which is due to charge-exchange ion-neutral collisions in the accelerating gap: after one such collision, the newly formed low speed ion is easily accelerated into the screen. The screen current takes however, a strong upwards swing when the beam current increases beyond some well defined limit. This is due to interception of the beam edges and 16.522, Space Propulsion Lecture 13-14 Prof. Manuel martinez-Sanchez Page 8 of 2516.522, Space Propulsion Lecture 13-14 Prof. Manuel Martinez-Sanchez Page 8 of 25 allow more holes per unit area (if the hole spacing varies in proportion to their size), hence more current per unit grid area. Due to this circumstance, Ref. 7 recommends low R designs. (5) The perveance generally increases as Da/Ds increases, with the exception of cases with R near unity, when an intermediate D /D 0.8 a s ≈ is optimum. (6) Increasing VD/VT, which increases the plasma density, appears to flatten the contour of the hole sheath(8), which reduces the focusing of the beam. This results in direct impingement on the screen, and, in turn, forces a reduction of the beam current. Some appreciation for the degree to which Child-Langmuir’s law departs from the observed current extraction capacity of real devices can be obtained from the data for the 30 cm. J-series thruster, as reported for example in Ref. (9). In this case, we have d=0.5 mm, ta=ts=0.38 mm, Ds=1.9 mm, Da=1.14 mm, and a total of 14860 holes. We will refer to data in Xe, for VNET/VT=0.7 and VD=31.2 Volts. VBeam=1200 v. Table III of Ref. (9) then gives a beam current JB=4.06 A. The correlation given in the same reference for various propellants is ( )2.2 T B 17.5 V 1000 J = + -25% α M (15) where α is a double-ion correction factor, given as 0.934 for this case, and M is the molecular mass in a.m.u.. The power of 2.2 instead of 1.5 for the effect of extraction voltage is to be noticed. This correlation yields for our case IB=5.4 A, on the outer boundary of the error band. For these data, if we apply the Child-Langmuir law (Equation 13) to each hole (diameter Ds), and use directly the spacing d=0.5 mm, we obtain a hole current of 3.83 mA, or, in total IB=57.1 A, i.e., 14 times too high. An approximate 3-D correction (Ref.’s 10a, b) is to replace d2 by 2 2 s s (d + t ) + D /4 in Child-Langmuir’s equation. This gives now IB=8.4 A, still twice the experimental value. It is of interest to see how well the data of Rovang and Wilbur (Ref. 7) can be extrapolated to the J￾thruster. We first use the data in Fig. 6a of Ref. (7), which are for Ds=2mm., R=0.8 Da/Ds=0.66 (lowest value measured), and VD/VT=0.1. Corrections for the actual Da/Ds=0.6 and VD/VT=0.018 can be approximated from Fig.’s 5 and (6a) of the same reference. The effects of R=0.7 instead of 0.8, as well as of the slightly different Ds, should be small, according to Ref. 7. We obtain in this manner IB=5.2 A., which is indeed as accurate as the correlation of Equation (15). Additional data on grid perveance are shown and assessed Ref. (10c) in the context of ion engine scaling. To complete this discussion, two limiting conditions should be mentioned here: (a) Direct ion impingement on screen: At low beam current, the screen collects a very small stray current, which is due to charge-exchange ion-neutral collisions in the accelerating gap: after one such collision, the newly formed low speed ion is easily accelerated into the screen. The screen current takes, however, a strong upwards swing when the beam current increases beyond some well defined limit. This is due to interception of the beam edges, and