A Study of High Specific Impulse Ion Thruster Optics

Transcription

1 A Study of High Specific Impulse Ion Thruster Optics Pul J. Wilur, Joshu Miller, Cody Frnell Deprtment of Mechnicl Engineering Colordo Stte University Fort Collins, CO nd Vincent K. Rwlin NASA Glenn Reserch Center Clevelnd, OH IEPC An experimentl study conducted on nineteen-hole-pir, two-grid optics sets suitle for opertion t high specific impulse is descried. Pervence nd crossover emlet current limits ove nd elow which ccelertor grid direct impingement currents rise re mesured. Accelertor grid voltges required to prevent electron ckstreming re shown to e modest. The importnce of selecting screen grid thickness to prevent ccelertor grid sputtering y ions drwn from upstrem of screen grid wes is illustrted. Experimentl results re compred to numericl results otining using the "igx"code nd shown to e in resonle greement. Results from the code suggest tht grid systems of resonle size nd with long lives cn e designed for high specific impulse missions. Nomenclture d grid hole dimeter (mm) D em dimeter (cm) e electron chrge (coul) F fltness prmeter J current (ma) l seprtion distnce (mm) m krypton ion mss (kg) m krypton flow rte (ma eq) t grid thickness (mm) V voltge (V or kv) w min. grid weing thickness (mm) ε o permittivity of free spce (f/m) η u propellnt utiliztion efficiency - normlized pervence per hole suscripts ccelertor grid emlet (i.e. per hole) B em g etween screen nd ccelertor grids i impingement per emlet N net s screen grid sh etween screen grid nd sheth T - totl Copyright 001 y the Electric Rocket Propulsion Society. All rights reserved.

2 Introduction For mny yers, electric propulsion mission emphses hve een on ner-erth pplictions, chrcterized y reltively low specific impulses nd modest power levels. Ion thruster development hs, s consequence, een focused on mximiztion of thrust density within frmework of generl improvement in thruster reliility nd lifetime. Renewed interest in the explortion of interstellr spce under the NASA Origins Progrm is ccompnied y the need for high specific impulse, high power propulsion. Ion propulsion systems re well suited to this ppliction ecuse the modifictions needed to chnge them so they cn e operted t high specific impulse nd high power rther thn low specific impulse nd more modest power re quite strightforwrd. This pper ddresses the prt of ion thruster design tht is chnged sustntilly, nmely, the design of the ion extrction optics (grids). Although the min emphsis of this work hs een experimentl, it hs een guided y numericl nlysis. Further, simple nlyticl model is used to estimte the impct of results otined from the study on typicl mission. The gol of the work hs een to generte ody of dt from which grid system geometricl nd operting prmeters could e defined to ccomplish specified mission ojective. The study will e focused round ion extrction grid design for nominl 30-kW ion propulsion module operting on krypton t specific impulse of 14,000 s for 88,000 h (10 yers) [1]. Assuming opertion t thruster propellnt utiliztion efficiency ner 80%, these power nd specific impulse vlues correspond to net ccelerting voltge of 13 kv nd n ion em current of.3 A. synthetic spphire lls tht were clmped etween sputter-shielded ssemlies ttched to the grids. These spheres would frequently glow ut they did not conduct mesurle current when voltge differences s gret s 15 kv were pplied etween them. Fig. 1 Grid System The dischrge chmer node dimeter ws 15 cm nd the lrgest dimeter of the screen grid region over which ions were extrcted on the dischrge chmer centerline ws 4.7 cm. Becuse the ion extrction region is smll frction of the plsm dimeter, it is rgued tht ll nineteen of the screen grid holes will see the sme dischrge plsm conditions. Hence, it is rgued tht the ion extrction ehvior should e out the sme for ech screen/ccelertor hole pir, nd tht mesured em nd impingement currents cn e divided y nineteen to otin per hole (emlet) vlues. Additionl verifiction tht this is the cse ws otined y using Frdy proe [3] swept through the em cm downstrem of the ccelertor grid to mesure em current density profiles. Figure shows typicl Apprtus nd Procedures Experimentl studies were conducted using two-grid, nineteen-perture-pir ssemlies tht were configured s shown in Fig. 1 nd mounted to ringcusp dischrge chmer []. Most of the dt reported here were collected with twelve different grid geometricl configurtions. The grids were mde of stinless steel nd were seprted nd isolted from ech other using three, 1.7-mm dim. Fig. Typicl Current Density Profile for nineteenhole Grid Set

3 profile mesured when the proe ws swept on n rc through the thruster centerline. It shows pek for ech of the five emlets tht differ y only out 10%. It is elieved tht the pek current densities would e more nerly equl if the proe could hve een swept long the line on which the holes re locted rther thn on n rc tht pssed over the centerlines of some holes nd the edges of others. It is noted tht the current sensor dimeter is 5. mm nd tht numericl results suggest tht the ulk of the em current from ech hole is concentrted in much smller dimeter. Hence, it does not sense the structure of the emlets precisely nd the em current determined y integrting Fig. is, s result, greter thn the mesured current. Ion em neutrliztion ws generlly ccomplished using two tungsten wires tht pssed through the em. A 3.-mm dim., krypton hollow cthode neutrlizer equipped with 0.-mm dim. orifice ws used in some tests nd it ws demonstrted tht results otined using the filment nd hollow cthodes were the sme. Results Screen Grid Sheth Effects The initil design of the 19-hole screen grid to e used in these tests ws thin (0.5 mm) compred to the screen grid hole dimeter (7 mm). A thin grid ws used ecuse it ws rgued it would produce sheth tht would e sustntilly upstrem of the screen grid. In this loction it ws elieved the sheth would e le to extrct most of the ions incident upon it through the screen grid therey reducing screen grid erosion nd improving dischrge chmer performnce. Initil tests mde the drwcks of such design ovious. Figure 3 shows typicl erosion ptterns produced on T foils covering 3-mm dimeter ccelertor grid holes fter out n hour of opertion. For out minute, the foil t n erosion site would e white-hot nd the impingement current would e high nd then the foil would cool s the impingement current dropped to ner norml for the rest of the test. Tests were conducted in 45-cm dim. vcuum ell jr test fcility. Pre-test pressures in the chmer were out 3x10-6 Torr, ut they vried through the rnge from 5x10-5 to 1.8x10-4 Torr s totl flow rte ws vried from 60 to 150 ma eq. Kr. After the estlishment of stle flow nd operting conditions, the tests generlly involved mesurement of em current nd ccelertor grid impingement current s dischrge power, screen grid voltge or ccelertor grid voltge were vried. On some occsions, however, the emlet cross section ws mesured y sputter eroding through mm thick T foil spot-welded to the upstrem side of the ccelertor grid. Although tests were conducted t net ccelerting voltges of 10 nd 13 kv using grids with screen hole dimeters of 7-mm nd 9-mm emphsis will e given, to dt otined using the screen grid with 9-mm holes operting t 13-kV in this pper. 3 Fig. 3 Bemlet Current Ptterns t Accelertor Grid The sketch in the upper right hnd corner of Fig. 3 shows the grid-hole sets, s they would e viewed from the dischrge chmer. Figure 3 shows the str pttern

4 eroded in the foil over the "A" hole identified in the sketch. Six holes nd six wes surround this hole nd the str hs six points. The erosion pttern for hole "B" from the sketch, which is shown in Fig. 3, is surrounded y four holes nd three wes nd hs three shrp points. Similrly, hole "C", which is surrounded y three holes nd two wes, hs two shrp points. On the sis of these oservtions it is concluded tht the points re ssocited with the wes. The lignment of the points reltive to the wes suggests tht the erosion of the points is eing produced y ions drwn from the region upstrem of the screen-grid we nd ccelerted digonlly cross the hole-pir xis nd into the upstrem side of the ccelertor grid. The pth of ions tht erode the peks is suggested y the rrows in the sketches to the right of Figs. 3 nd 3c. It is noted tht the right spots on the left sides of Figs. 3 nd 3 re cused y reflections from smll wrinkles in the foils. The effect of emlet current nd screen grid thickness on the pttern of n ccelertor hole surrounded y six other holes is illustrted in Fig. 4. All of the operting nd geometricl prmeters except the emlet current were the sme for the two ptterns shown in Fig. 3 nd 3 ut the 1.05 ma pttern ws run for shorter time to hold the totl ion dose out the sme. Comprison of the photogrphs suggests greter concentrtion of current ner the hole center nd shorter points for the greter emlet current. This is consistent with the fct tht the sheth to screen grid seprtion would e less t the higher em current. Comprison of Figs. 4 nd 4c shows the drmtic effect of n increse in screen grid thickness on the erosion pttern otined with n otherwise identicl geometry t emlet current of 0.58 ma. With the thicker screen grid, it is rgued tht the edge of the sheth does not extend sustntilly upstrem of the upstrem edge of screen grid hole. As result interction etween the sheths t djcent holes is minimized, ions re not drwn from upstrem of the screen grid wes nd the shrp points in the foil re not produced. Bckstreming Limittions The mgnitude of the negtive voltge tht must e pplied to the ccelertor grid to prevent electron ckstreming ws mesured t ech emlet current nd grid geometry condition investigted. The 5 mm ) Thin Screen Grid (0.5 mm), 0.58 ma Bemlet ) Thin Screen Grid (0.5mm), 1.05 ma Bemlet c) Thick Screen Grid (1.5 mm), 0.58 ma Bemlet Fig. 4 Effect of Screen Grid Thickness nd Current on Bemlet Pttern mgnitude of this voltge could e mjor design driver for high specific impulse grids if it incresed long with net ccelerting voltge. If this did occur, then chrge-exchnge ion sputtering dmge could e expected to increse nd this would shorten ccelertor grid lifetimes. A typicl curve showing the sudden increse in pprent emlet current tht occurs when the mgnitude of this voltge is insufficient to prevent ckstreming is given in Fig. 5. The ordinte in this plot is the rtio of emlet currents t V nd t voltge significntly greter thn the ckstreming limit, nmely V = 500 V. At the ckstreming limit electrons drwn upstrem from the em into the dischrge chmer cuse the increse in pprent 4

5 Fig. 5 Effect of Accelertor Grid Voltge on Electron Bckstreming emlet current. Bckstreming limits like the one identified shown in Fig. 5 were determined s function of emlet current nd grid geometricl chnges. The results otined in this wy re plotted in Fig. 6 for vrious grid spcings nd for n ccelertor hole dimeter of 4.5 mm. A full-sized thruster operting t emlet currents over the full rnge etween the mximum nd minimum vlues ssocited with ech of the curves in Fig. 6 would hve to operte with the ccelertor grid ised to the mximum limit (identified s the grid limit for the upper curve). Adding 30-V mrgin ginst ckstreming to these mxim nd plotting the results s function of ccelertor hole dimeter with grid seprtion s prmeter, one otins the results shown y the solid symols nd finer lines in Fig. 7. The dt identified y the open symols nd hevier lines re vlues predicted y the "igx" code pplying the sme mrgin [4]. Both sets of dt exhiit similr trends lthough the numericl results re 50 to 100 V greter thn the mesured vlues. All of the dt generlly show tht the ccelertor grid voltge mgnitude required to prevent ckstreming increses s the grid seprtion is reduced or the ccelertor hole dimeter is incresed. These trends re consistent with theory nd dt otined on low specific impulse thrusters. It is importnt to note tht the voltges required to limit ckstreming through ccelertor grids tht re given in Fig. 7 for high specific impulse grids do not differ much from those required for low specific impulse grids. This reflects the fct tht the ckstreming limit depends mostly on the intrgrid electric field rther thn the net ccelerting voltge. Fig. 6 Effects of Grid Seprtion nd Bemlet Current on Bckstreming There is ovious sctter in these dt, ut ll pper to follow the sme generl trend in which the pek ckstreming limit is oserved t current intermedite etween typicl mximum nd minimum vlues ssocited with ech grid spcing. The intermedite current t which these curves pek corresponds to the emlet focusing condition where positive spce chrge is most conducive to electron ckstreming. 5 Fig. 7 Effects of Accelertor Grid Hole Dimeter nd Grid Seprtion on Bckstreming

6 Direct Ion Impingement Limittions A common wy to ssure tht direct erosion of the ccelertor grid y em ions is not occurring in grid set is to hold em current constnt nd mesure impingement current s function of net ccelerting voltge [5]. This usully yields limit on screen grid voltge, elow which the impingement current rises. When this ws done in the course of the present study, dt like those shown in Fig. 8 were otined. Under high net ccelerting voltge test conditions this figure shows tht oth pervence (lower) limit nd crossover (higher) limit were oserved. The higher limit ws neither s ovious nor s importnt t lower screen voltge (i.e. specific impulse) levels. The pervence nd crossover current limits identified in Fig. 8 correspond, to current conditions t which emlet ions impct directly on the ccelertor grid. At the pervence limit they follow trjectories tht re stright nd they re drwn from fltter sheth s the inset sketch suggests. At the crossover current limit, the sheth is more concve nd some trjectories cross. In etween these two limits, the impingement current is t low (seline) level fixed y the mission, it is more useful to vry em current while holding net ccelertion voltge constnt nd to plot impingement-to-emlet current rtio ginst emlet current to identify the pervence nd crossover limits. Figure 9 shows dt otined following this procedure for cses where the grid seprtion (l g ) ws vried from 7 to 11.5 mm. Curves through these dt lso show tht there re indeed emlet currents t which impingement currents egin to chnge rther suddenly. However, these curves differ from those in Fig. 8 in the following wys: The seline impingement-to-em current rtio is sustntilly greter in Fig. 9 thn it is in Fig. 8. This difference is due to the greter Kr flow required to chieve the highest emlet current (~4 ma). This results in sustntilly greter chrge exchnge (CE) ion production, which yields greter impingement currents for the Fig. 9 dt. The Fig. 9 dt exhiit seline impingementto-emlet current rtio tht increses s emlet current is reduced while the one in Fig. 8 otined t constnt emlet current ws quite flt. This difference is lso relted to the greter flow rte nd to the fct tht the unionized propellnt loss rte nd, therefore, the impingement current increse s emlet current is reduced. If flow rte is reduced long with emlet current, selines for dt like those in Fig. 9 ecome more nerly horizontl. Fig. 8 Effect of Screen Grid Voltge on Accelertor Grid Impingement where ccelertor grid opertion in thruster could e sustined over long time with low direct ion erosion levels on the ccelertor grid. It is noted tht the emlet current (J ) cited on Fig. 8 is nineteenth of the em current ctully mesured during the test. For this study, where the net ccelertion voltge is Fig. 9 Typicl Effect of Bemlet Current nd Grid Spcing on Impingement Current In order to determine the crossover nd pervence limits on emlet current from experimentl dt like those from Fig. 9, the pproch suggested y Fig. 10 6

7 ws used. Specificlly, it ws determined tht the dt generlly fell into three groupings tht could ech e fit using liner lest-squres nlysis. The intersections of these three lines defined the limits suggested in the figure. When the emlet current limits from plots like those in Fig. 9 ssocited with direct interception of ion trjectories on the ccelertor grid (i.e. the pervence limit) were interpreted s shown in Fig. 10, results identified y the solid symols nd light lines in Fig 11 were otined. Also identified in this figure y the open symols nd hevier lines re corresponding numericl results otined using the "igx" code. The greement etween these dt is resonly good for the closer grid seprtions nd lrger ccelertor holes ut greement is poorer for greter seprtion. As expected the pervence limited emlet current increses s ccelertor grid hole dimeter is incresed or grid seprtion is reduced. temperture. Fig. 11 Effect of Grid Spcing nd Accelertor Hole Dimeter on Pervence Limit Fig. 1 Effect of Grid Spcing nd Accelertor Hole Dimeter on Crossover Limit Fig. 10 Determintion of Crossover nd Pervence Limited Bemlet Currents When crossover limited emlet current experimentl nd numericl dt re plotted s function of the grid prmeters eing investigted, the results of Fig. 1 re otined. These two sets of dt generlly show similr trends, ut the experimentl dt re out 0.5 ma/hole less thn the numericl dt. This suggests numericlly predicted sheth shpes re ffected less y emlet current thn re the experimentl ones. There is experimentl evidence which suggests flow rte effect my e the source of this difference, possily ecuse it influences the sheth through the dischrge chmer electron 7 All of the dt in Fig. 1 show tht greter grid seprtion results in lower crossover limit. This my occur ecuse sheth distortion dimensions ecome smller frctions of the effective ccelertion length, which ppers in the expression for pervence, s the grid seprtion is incresed. Discussion Generliztion of Results It is desirle to correlte emlet current limits like those given in Figs. 11 nd 1 using n pproprite physicl model. For these dt, tht model would e sed on the Child-Lngmuir Lw [6] nd the limits

8 would e expressed in terms of new normlized pervence/hole given y the expression: J = 3 V T / l d e s 9 πε o m e. (1) In this expression, the effective ccelertion length (l e ) cn e pproximted using e g s sh + l = ( l + t + l ) d 4 () For the cse of the pervence limited emlet current where the sheth could e expected to e ner the upstrem side of the screen grid the sheth-screen grid seprtion (l sh ) could e ssumed to e zero. Pervences ssocited with ll of the experimentl pervence limited emlet current dt from Fig. 11 were clculted under this ssumption using Eqs. (1) nd (). Men vlues of these results re plotted ginst normlized ccelertor grid perture dimeter s the solid squres nd fine line in Fig. 13. Fig. 13 Correltion of Pervence nd Crossover Limit Dt As the error rs through these symols suggest, the ssocited stndrd devitions re not too lrge nd this indictes tht the sheth nd pervence model ssumptions re resonle. In order to develop similr curve for the crossover limited emlet current dt of Fig. 1, it ws necessry to model the sheth seprtion from the screen grid we surfce (l sh ). This ws done y s 8 selecting sheth seprtions for ech dt point tht yielded the est lest-squres-regression fit of the Child-Lngmuir model. The vlues of l sh rnged from 0.09 mm t grid seprtion of 7 mm to out 0.19 mm t grid seprtion of 11.5 mm. The resulting men nd stndrd devition results re represented y the solid dimonds nd error rs in Fig. 13. Agin, their reltively smll size suggests the collective dt re modeled resonly well. Pervence vlues ssocited with the pervence nd crossover limited emlet currents were lso clculted using the "igx" code. Men vlues nd stndrd devitions were gin determined for ll grid seprtions studied nd the results re represented in Fig. 13 y the open symols nd hevy lines. In doing these clcultions, the ctul screen-surfce-to-sheth seprtion distnces determined y the code were used in Eq. (). Figure 13 shows similr trends for oth the experimentl nd numericl results. As expected, increses in ccelertor grid hole dimeter widen the operting mrgin etween the pervence nd crossover limits. It is noted tht experimentl dt collected t net ccelerting voltge of 10 kv gve essentilly identicl results s those for the 13 kv tht re shown in Fig.13. Thruster Design Implictions It is of interest to investigte the impct of the findings of this study on typicl high specific impulse mission. This will e done here y pplying typicl results from the simple model descried in the Appendix of this pper to exmine the Interstellr Precursor (ISP) Mission [1]. Input to the nlyses will e drwn from "igx" code results ecuse the code yields seline (i.e. chrge-exchnge) impingement currents tht re more pproprite for spce ppliction thn re the experimentl results. The code results lso yield ckstreming voltge limits of greter mgnitude which re, therefore, more conservtive. The em fltness prmeter (F B ) t which thruster would operte if emlets were t the pervence limit on the em centerline nd t the crossover limit on the em edge re clculted using Eq. (A4). This is the minimum fltness prmeter t which thruster hving prescried grid geometry could e operted with low (seline) impingement currents cross the grids. Of course, the grids could e operted with greter fltness

9 prmeters provided chmer could e uilt to produce sufficiently uniform dischrge plsm. The mximum fltness prmeter would e unity nd grids could e operted t this limit t ny emlet current etween the pervence nd crossover limits. Figure 14 shows the effect of ccelertor grid hole dimeter nd grid spcing on the minimum fltness prmeter t which the grids could e operted s determined from the dt of Figs. 11 nd 1. Fig. 14 Limiting Bem Fltness Prmeter Limits Using the fltness prmeter results, one cn compute the em dimeter required to produce the.3-a em needed for the 30-kW ISP thruster module. Figure 15 shows the effect of grid spcing on this dimeter for the three limiting cses (minimum em fltness nd mximum em fltness t the crossover nd pervence emlet current limits) for typicl ccelertor hole dimeter (d = 4.5 mm). These dt show the required dimeter rnges from out 5 cm for the closest grid spcing with mximum fltness (unity) t the pervence limit to over 50 cm for the gretest grid spcing with mximum fltness t the crossover limit. Dischrge chmer opertion t the minimum fltness condition yields intermedite dimeters s the figure shows. Of course opertion t emlet currents etween the crossover nd pervence limits lso gives intermedite em dimeters. If greter ccelertor hole dimeter is used, the rnge of em dimeters t given grid spcing is lso greter. Using these results long with similr ones for the other ccelertor hole dimeters investigted yields the ccelertor grid sputter erosion lifetime dt shown in Fig. 16. As the legend suggests, they were determined using titnium sputtering dt nd ssuming end-of-life (EOL) when 10% of the ccelertor grid mss ssocited with the most severely eroded hole hd een lost to sputter erosion. This numer is only pproximte nd the dt of Fig. 16 re, therefore, most useful s indictors of trends. It is noted tht more ccurte exmintion of lifetime would hve to consider effects such s those ssocited redeposition nd resputtering which could e importnt for the thick ccelertor grids eing considered here. Fig. 16 Accelertor Grid Lifetime Trends Fig. 15 Bem Dimeters Required for.3a Bem Current 9 Lives for the cses of minimum em fltness nd unity em fltness t the pervence limit re represented y the sme lines in Fig. 16. These lines fll on top of ech other ecuse the life limiting holes re operting t the pervence limit nd ccelertor grid voltges re not very different for these two cses. These dt show greter lifetimes s grid spcing is incresed ecuse em dimeter increses nd more ccelertor grid mteril is ville to e sputtered. They lso show

10 greter lifetimes s ccelertor hole dimeter is reduced, gin ecuse more grid mteril is ville to e sputtered. The gretest lifetimes re relized for opertion with unity em fltness t the crossover limit. Lifetimes ecome very long t this condition not only ecuse the mount of ville grid mteril is gretest, ut lso ecuse the ckstreming voltge t which the ccelertor grid must e operted is lowest nd sputter yields re, therefore, lso t their lowest vlues. Once gin it should e noted tht opertion could occur etween ny of the corresponding dshed nd solid lines (i.e. etween the pervence nd crossover limits) with the sme symols (e.g. circles). Conclusions The rnge of low ccelertor-grid impingement currents in high specific impulse grids is ounded y pervence nd crossover limits t high nd low emlet currents, respectively. The crossover limit seems to e more pprent with high specific grids thn it ws with low specific impulse ones. These limits re strong functions of grid seprtion nd ccelertor grid hole dimeter. The ccelertor grid voltges tht must e pplied to stop electron ckstreming in high specific impulse grids re not mrkedly different thn those required t low specific impulse. If screen grid is too thin the dischrge chmer plsm sheth my e locted sustntilly upstrem of the grid surfce. Under these conditions sustntil current of ions will e drwn from the region upstrem of the screen-grid we, ccelerted digonlly cross the screen hole xis nd onto the upstrem side of the ccelertor grid Numericl nlysis tht ppers to e consistent with experimentl oservtions shows tht two-grid ion optics set cn e designed tht will e resonle in size nd suitle for long durtion missions. Acknowledgement Finncil support under Reserch Grnt NAG through the NASA Glenn Reserch Center is grtefully cknowledged. References [1] Ptterson, M.J., R.F. Romn, nd J.E. Foster, "Ion Engine Development for Interstellr Precursor Missions," AIAA Pper , Joint Propulsion Conference, Huntsville, AL, July 000. [] Wilur, P.J. nd B.W. Buchholtz, "Surfce Engineering using Ion Thruster Technology," AIAA Pper , p., 30 th Joint Propulsion Conference, Indinpolis, IN [3] Wilur, P.J. nd L.O. Dniels, "The development nd ppliction of n ion implnter sed on ion thruster technology," Vcuum, v. 36, p 4, [4] Nkym, Y., nd P.J. Wilur, "Numericl Simultion of Ion Bem Optics for Mny-grid Systems," AIAA Pper , 37 th Joint Propulsion Conference, Slt Lke City, UT, 001. [5] Souls, G.C., J.E. Foster, nd M.J. Ptterson, "Performnce of Titnium Optics on NASA 30 cm Ion Thruster," AIAA Pper , 36 th Joint Propulsion Conference, Huntsville, AL, 000. [6] Child, C.D., "Dischrge from Hot CO," Physics Review, v. 3, pp , [7] Wehner, G.K., "Sputter Yield Dt in the ev Energy Rnge," Generl Mills Report 309, July 15, 196. [8] Bohdnsky, J., J. Roth nd H.L. By, "An nlyticl formul nd importnt prmeters for lowenergy ion sputtering," J. Appl. Phys. 51, pp , My [9] Anderson, J.R., J.E. Polk nd J.R. Brophy, "Service Life Assessment for Ion Engines," 5 th Interntionl Electric Propulsion Conference Pper , Clevelnd, OH Appendix A Model of Thruster Accelertor Grid Erosion Since much of the ppendix nomenclture is not used in the ody of this pper, new nomenclture will e 10

11 defined s it is used herein. Previously defined nomenclture will lso e used. The ion em fltness prmeter (F B ) for thruster is defined s the rtio of verge emlet current (<J >) to pek emlet current (J ') i.e. F B ' = J J. (A1) The verge current density cn e determined y integrting emlet currents from the thruster centerline to the em edge t rdius r e = D B / i.e. J = r e 0 J π r dr π r e. (A) If it is ssumed tht the current density profile hs cosine shpe then ' π r J = J cos (A3) rr where r r is reference rdius tht is greter thn r e. Sustituting Eq. (A3) into Eq. (A) nd integrting gives the result = 1 F B { cos α -1} + α α α sin (A4) π re where α =. r r For the cse of thruster operting t minimum F B the centerline emlet current would e t the pervence limit nd the grid-edge emlet current (i.e. t r = r e ) would e t the crossover limit. Using these limits in Eq. (A3) one otins vlue for α which cn then e used in Eq. (A4) to otin the fltness prmeter. The numer of screen/ccelertor hole pirs with verge emlet current <J > tht re required for em current J B is J B n =. (A5) J The hexgonl re occupied y screen hole nd its ssocited weing cn e expressed in terms of the screen hole dimeter (d s ) nd the minimum weing thickness (w s ). Dividing this re into the re of the thruster em ( π D B 4 ) lso yields the numer of holes. Comining these results with Eq. (A1) nd solving for the em current one otins: J B πf = B J 3 ' D B ds w + s. (A6) When em current is specified (s it is in the present cse) this eqution cn e rerrnged nd solved for the em dimeter. The estimte of ccelertor grid lifetime used for this study ws otined y ssuming end of life ws reched when specified frction of the initil mss ssocited with the most severely eroded hole hd een lost. The initil mss of the hexgonl region of re A ssocited with ech ccelertor hole emlet is given y m = A t (1- φ ) ρ (A7) where t, φ nd ρ re the thickness, trnsprency nd mss density of the ccelertor grid, respectively. The mss loss per ccelertor grid emlet induced y sputtering over time τ is given y Ji Y M τ m = (A8) e where J i is the impingement current per emlet, Y is the sputter yield for Kr ions on the ccelertor grid mteril, M is the mss of grid mteril tom nd e is the electron chrge. If it is ssumed tht grid filure occurs when the ccelertor grid mss-loss frction ssocited with the emlet operting t the gretest impingement current reches prescried vlue (f f ) one hs 11

12 m = f m. (A9) f The eqution for the yield tht is required in Eq. (A8) ws otined y fitting experimentl dt [7] to n empiricl expression [8]. The result otined for krypton ions impcting titnium is 1/ E 68 Y = (A10) 68 E If it is ssumed tht most of the impinging ions re produced ner the ccelertor grid, the energy (E) tht is needed in this eqution cn e estimted. It hs een suggested tht it hs mgnitude equl to the ccelertor grid voltge reltive to spcecrft ground plus the voltge difference etween spcecrft ground nd the men em plsm potentil t which chrgeexchnge ions re produced. This voltge difference hs een estimted to e ~0 V for the NSTAR thruster [9]. Using this vlue E = V + 0. (A11) Comining Eqs. (A7), (A8) nd (A9) nd solving for grid lifetime one otins π ff t ρ τ = 4 Y M J e 3 ( ds + w s ) π (A1) i d where J i is the mximum impingement current per emlet encountered over the entire ccelertor grid. For the results presented in this pper, the impingement currents re ssocited only with thruster generted chrge-exchnge ions. Becuse chrge exchnge ion production ssocited with test fcility effects re not included, the currents re considered to e representtive of the spce environment. These currents were determined using the "igx" computer code. 1