Particle-in-cell Simulations for the Effect of Magnetic Shielding and Channel Length on Cylindrical Hall Thruster

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1 Prtile-in-ell Simultions for the Effet of Mgneti Shielding nd Chnnel Length on Cylindril Hll Thruster IEPC /ISTS Presented t Joint Conferene of 3th Interntionl Symposium on Spe Tehnology nd Siene 34th Interntionl Eletri Propulsion Conferene nd 6th Nno-stellite Symposium, Hyogo-Koe, Jpn July 4 1, 215 Go Yunyun 1,Liu Hui 2, Yu Dren 3, Hung Hongyn 4, Hu Peng 5. L of Plsm Propulsion, Hrin Institute of Tehnology, (HIT), Hrin, Heilongjing, 151, Chin Astrt: The prtile-in-ell plus Monte Crlo method is used to simulte miniturized Cylindril Hll Thruster (1W of power level). In PIC-MCC model, the potentil distriution, the eletron density nd the eletron temperture in the ondition of different mgneti shield ple nd hnnel length re hieved, respetively. The results exhiit tht the mgneti shield round the entrl mgneti pole derese the mgneti field strength ner the node, whih led to the ioniztion rtio derese nd the eletron moility enhne. On the other hnd, with the extension of the hnnel length (enlrge the front eletromgneti oil region s well), the eletrons moility enhned through inresing the ion residene time in hnnel nd enhne the ioniztion. Integrting ove ftors, it s onluded tht the optimiztion effet on the hnnel length is etter thn the mgneti shield. Nomenlture CHT = Cylindril Hll Thruster wpe = Plsm Osilltion Frequeny w = Eletron Cylotron Frequeny t = Time Step Te = Simulted Initil Eletron Temperture RPA = Retrding Potentil Anlyzer I. Introdution Hll thrusters in lrge power of high thn 3W hve een pplied mturely. However, sling down the onventionl nnulr Hll thruster ring the prolem of lrge surfe-to-volume, the diffiulty of miniturized mgneti iruit, nd the signifint erosion of the wll, whih effet the performne nd lifetime severely. Cylindril Hll Thruster (CHT) derese the surfe-to-volume ompred the nnulr Hll thruster nd solve the prolem of indequte inner pole through shorten the enter mgneti pole, whih my e the suitle pproh of sling to Hll thruster 1. Cylindril Hll thrusters hve lredy een studied experimentlly nd reh the omprle performne ompred the nnulr Hll thruster 1. CHT fetures the high ioniztion rte, whih is vlidted due to more multi-hrged thn nnulr Hll thruster 2. 1 PhD ndidte, Shool of Energy Siene nd Engineering, goyunyun @163.om. 2 Leturer, Shool of Energy Siene nd Engineering, thruster@126.om. 3 Professor, Shool of Energy Siene nd Engineering, yudren@hit.edu.n. 4 Professor, Shool of Energy Siene nd Engineering. 5 PhD ndidte, Shool of Energy Siene nd Engineering, hupengemil@126.om. 1 Joint Conferene of 3th ISTS, 34th IEPC nd 6th NSAT, Koe-Hyogo, Jpn July 4 1, 215

2 Compred with the nnulr Hll thruster, the mgneti field topology nd plsm hrteristis in CHT hnge lot due to the shorten of inner mgneti pole nd mnifest the ovious two-dimensionl vries 3. The mgneti field present negtive grdient long the xil, nd the strongest mgneti field is loted ner the node. The mgneti line diretions exhiit signifint differene long the rdil: the mgneti lines loted t the hnnel enter re minly xil, while the rdil mgneti field omponent is inresed ner the wll. In this mgneti field topology, the strongest onfinement to the mgnetiztion eletrons ours ner the node. The min trnsport pth of eletrons emitted from the thode is likely long the hnnel xis s the ontriution of eletron-wll ollisions to ross-field trnsport is vlidted to e insignifint 4. While the eletrons losed to the xis is trpped y the mgneti mirror nd oune over n xil region. The plsm potentil drops shrply from the node towrd the downstrem region nd the rdil eletri field exists 5, 6. The slow ions onentrted in downstrem of hnnel enter 5. From the ove nlysis, the min onfined region of the eletrons is loted in the upstrem losed to the xis nd the position of min potentil drop is lso loted in upstrem due to the mgneti field. But if the min potentil drop is lose to the node exessively, it is likely to mke the min voltge lod to the eletrons nd prevent the formtion of stle ioniztion nd elertion region. In order to mke the min potentil drop move towrds the exit, it is neessry to inrese the eletron trnsport in the viinity of node, while eletron moility is minly ssoited with the mgneti field strength nd the ross setion of eletrons nd hevy prtiles. In this pper, two wys is proposed to inrese the eletrons ross-field trnsit ner the node s following: 1. mounting the mgneti shield round the node to derese the mgneti field; 2.extending the hnnel length to improve the ollide frequeny. Jongsu Lee et l. hve studied the effet of hnnel length on thruster y experiment 7 nd the results shown tht the ion urrent nd the totl ion energy were enhned with the inrese of hnnel length, whih ws interpreted tht the inrese of hnnel length proly inrese the ions residing time nd enhne the multihrged ions, ultimtely mke the ioniztion region extend towrds the node so tht the ioniztion region nd elertion region seprte lerer. However, their explntion out the link etween the inresed ions residene time nd the extension of the ioniztion lotion is undefined, whether the extension of the ioniztion region towrds the node ffet the eletri potentil distriution is lso fint. This pper emphsizes to reserh the plsm hrteristis nd revel the inner physil mehnism, so we minly employ the PIC-MCC simultion model 8, whih is uilt y HIT nd hieved the pplition mturely in SPT 9 nd HEMPT 1, 11. While the experiment ply the role of vlidting the model resonility nd ws exhiit s supplement. In this pper, we orgnize s follow: in setion II, the lortory CHT prototype nd their opertion ondition is exhiit. In setion III, the PIC-MCC simultion model of CHT is introdued in detil. In setion IV, the simultion result nd the relted nlysis on the effet of hnging the mgneti shield length nd hnnel length is hieved, inluding eletron density spe distriution, eletri potentil distriution, eletron temperture distriution nd so on. In setion V, the omprison nd nlysis of simultion nd experiment result. At lst, there re severl onlusions nd prospetions. II. The opertion of lortory CHT prototypes. The lortory CHT prototypes pplied in PIC model is introdued s following: Three lortory CHT prototypes re designed s Fig. 1, they re nmed s C1, C2 nd C3, respetively. In C1, the hnnel length is 15mm nd the enter mgneti shield wsn t mounted. In C2, the hnnel length is 15mm nd the enter mgneti shield ws mounted, it ws mde of pure iron. In C3, the hnnel length is 25mm nd the enter mgneti shield wsn t mounted. They ll onsist of ylindril hnnel, ring-shped node, whih lso serve gs distriutor, mgneti ore nd mgnetized soures. The dimeter of these thrusters re ll 3m. The urrent diretion in the two oils re in sme diretion to produe the diret onfigurtion nd the front nd k oil urrent re 2A nd 5A, respetively. In our experiment, the thode ws loted 4m rdilly from thruster enterline, nd 2.m downstrem of the thruster exit plne. The thode Xe flow rte ws 2sm. The node voltge nd Xe flow rte were fixed t 3V nd 4sm, respetively. The thrusters were pled in vuum hmer of 4m long nd 1.2m dimeter, nd the gs pressure kept in P. The Frdy proe ws used for mesuring ion urrent whih ws mounted on rottionl stge with the distne of 3m from the pivot t ngles of up to 8 from the thruster xis. The ion olleting re of Frdy proe ws.75m 2, oth the proe olletor nd gurd ring were ised to -24V. The RPA ws used to mesure ion energy distriution nd loted t 4 m downstrem from the hnnel exit on the 2 Joint Conferene of 3th ISTS, 34th IEPC nd 6th NSAT, Koe-Hyogo, Jpn July 4 1, 215

3 xis. A ommeril digitl single-lens reflex mer ws mounted in side window of the vuum hmer to otin the plume dishrge imge. Fig.1 Three onfigurtions of CHT:. C1: 15mm hnnel length nd without enter mgneti shield;.c2: 15mm hnnel length nd with enter mgneti shield;. C3: 25mm hnnel length nd without enter mgneti shield Fig. 2 plume dishrge photogrphs for three onfigurtion CHTs t the node flow 4sm nd node voltge 3V the plume ngles (shown in the ottom right orner) ontin 9% of totl ion urrent I d.2 C1 C2 C Current/A.6.5 I i IEDF onfigurtion vry I e Ion Energy (ev) Fig.3 : omponent of the dishrge urrent, : IEDF in z=37m of xis: C1, C2 nd C3. The plume dishrge photogrphs of different strutures re shown in Fig 2, nd the plume in C3 emitted the stle lue light nd the intensity is oviously stronger thn C1 nd C2. While the light intensity in C2 is slightly 3 Joint Conferene of 3th ISTS, 34th IEPC nd 6th NSAT, Koe-Hyogo, Jpn July 4 1, 215

4 stronger thn C1, from whih we find tht the plume plsm energy in C3 is highest in three thrusters. While the plume ngle of C1, C2, C3 re 58, 55.3, The ion urrent, eletron urrent nd totl dishrge urrent in plume re shown in fig 3. The eletron urrent nd totl dishrge urrent in C2 is lrgest in three strutures, while the ion urrent is smllest. The ion urrent in C3 is lrgest in three strutures, its totl urrent is lrger thn C1 nd the eletron urrent is lmost onstnt orresponding to C1. The ion energy distriution funtion in plume re shown in fig 3. The pek energy in C3 is lrgest, nd its full width t hlf mximum (FWHM) is nrrowest. While the pek energy in C2 is lrger thn C1 nd its FWHM is nrrower thn C1. As FWHM of ion energy n reflet the reltive distne of ioniztion region nd elertion region. We suggest tht the ioniztion nd elertion region in C3 seprte most lerly in three strutures nd the C2 is inferior. From the ove mesurement results, we n onlude s following: with the mounting of enter mgneti shield, the inrese inrement of eletron urrent ws muh lrger thn ion urrent, the plume ion energy enhned slightly nd the ion em is more onvergene. With the extension of hnnel length, the ion urrent inresed sustntilly nd eletron urrent lmost kept onstnt, the ion energy lso enhned signifintly, ut the ion em is more divergene. In order to explin the ove phenomenon nd revel the physil mehnism with the mounting of enter mgneti shield nd the extension of hnnel length, the PIC-MCC model is uilt s following: III. Simultion model Aording to the struturl fetures of CHT in different onfigurtions mentioned ove, three PIC-MCC models re pplied respetively, whih xil symmetry is ssumed nd ll zimuthl vritions re negleted. In these models, eletrons, ions nd neutrl toms re solved s Super-Prtiles ( super simulted prtile represent 1 6 rel prtiles) in order to sve the omputtionl ost 8, 9. The initil eletron nd neutrl tom distriution re solved s the hlf Mxwell distriution. The mgneti field distriution hieved y FEMM softwre is import into the simultion progrm nd ssumed onstnt (self-indued mgneti field is ignored). The Poisson eqution whih is solved y Alternting Diretion Impliit (DADI) method is pplied to hieve the self-indued eletri field. The stndrd lepfrog method is pplied to push the prtiles forwrd nd solve the prtile movement. As to the eletron ross-field trnsport, Monte Crlo model is developed to revel the mehnism of the eletron trnsport perpendiulr to the mgneti field, whih ounts for eletron-tom ollisions, eletron-wll ollisions nd Bohm diffusion. The Bohm oeffiient equls 1/64. While the DSMC method is used to solve the ollision mong the toms. With respet to the grid size nd time step in the ompute region, it s required tht the grid size should smller thn the Deye length in order to th the plsm osilltion nd the time step should stisfy tht. To elerte the onvergene of the ompute region, the vuum permittivity is inresed y 16 times 9. Fig.3 the simulted zone, oundry ondition nd mgneti field lines in the PIC-MCC model With respet to the rrngement of oundry ondition nd simulted regions, s shown in Fig. 3, the xil oordinte of simulted region vries from m to.3 m, nd the rdil oordinte vries from.2 m to.45 m. The left lterl oundry is the node (.275m r.35m) nd dieletri ermi (.2m z.275m) nd the former s length equls the ltter, while the lower nd upper oundries re the symmetri xis nd dieletri ermi wll. The plume is lso onsidered in the model, the left oundry of the plume zone is dieletri ermi nd the upper oundry is thode. 4 Joint Conferene of 3th ISTS, 34th IEPC nd 6th NSAT, Koe-Hyogo, Jpn July 4 1, 215

5 18 6 IV. Simultion results nd disussion We performed lultions for given set of oil urrents I front=2a, I k=5a, for node mss flows of 4sm, the dishrge voltge is 3V, whih re onsistent with the experiments. The effets of enter mgneti shield on the plsm hrteristis re shown in setion A, whih inlude the eletron density distriution, the eletri field distriution nd the eletron temperture. In setion B, the effets of the hnnel length on the plsm ehviors re presented. eletron density: 1E+17 2E+17 3E+17 4E+17 5E+17 6E+17 7E+17 8E+17 eletron density: 1E+17 2E+17 3E+17 4E+17 5E+17 6E+17 7E+17 8E potentil/v: potentil/v: d Te/eV: Te/eV: e.45.4 f Fig.4 the plsm hrteristis distriutions:,, e indite the eletron density, potentil nd eletron temperture in C1, respetively, the orresponding distriutions of C2 re shown in, d, f. A.the effet of enter mgneti shield on the plsm hrteristis Compring the mgneti field topology hnge with the different mgneti shield struture shown in Fig. 1() (), it is ler tht the mgneti field strength is deresed generlly, the redution ner the node is most ovious. As shown in Fig. 5, the mgneti field strength in r=.3m, z=m (the lotion of node) dereses from 5G to 3G, nd the node surrounding re hs lso oviously redution, while the mgneti field ner the hnnel xis vried slightly. Fig. 4() nd () show the simultion results of the eletron density distriutions for C1 nd C2, respetively. It is ler tht the eletron density ner the node in onfigurtion 2 redues ompred with onfigurtion1, whih n e due to the mgneti field hnge: the mgneti field ner the node is weken y the mgneti shield ring, nd the eletron ross-field trnsport is enhned, thus the eletron density ws redued in the dishrge hnnel. 5 Joint Conferene of 3th ISTS, 34th IEPC nd 6th NSAT, Koe-Hyogo, Jpn July 4 1, 215

6 3 Fig. 4() (d) show the simultion results of potentil distriution for C1 nd C2, respetively. It is ler tht the min potentil drop region move towrds downstrem ompred when the mgneti shield ring is mounted in C2, it n e explined tht the enhned eletron ross-field trnsport led to the deese of potentil drop ner the node, s the pplied voltge is fixed, the potentil drop should move towrd downstrem long the xis. As shown in Fig. 4(e) (f), the high eletron temperture zone extends to the midstrem long the xil diretion, whih n e due to two ftors: the enhned eletron trnsport led to the redution of ioniztion rte in midstrem, t the sme time, the eletri field strength in this region is inresed. Therefore, the eletrons n otin more energy from the eletri field with less onsume. mgneti field strength/g mgneti field strength/g mgneti field strength/g Fig. 5 the mgneti field strength long the xil diretion:. r=.2m,. r=.25m,. r=.3m (red line demonstrtes onfigurtion1, lue line demonstrtes onfigurtion2) B. The effet of hnnel length on plsm hrteristi eletron density: 1E+17 2E+17 3E+17 4E+17 5E+17 6E+17 7E+17 8E+17 eletron density: 1E+17 2E+17 3E+17 4E+17 5E+17 6E+17 7E+17 8E potentil/v: potentil/v: d Te/eV: Te/eV: e.4 f Fig. 6 the plsm hrteristis distriutions:,, e indite the eletron density, potentil nd eletron temperture in C1, respetively, the orresponding distriutions of C3 re shown in, d, f. 6 Joint Conferene of 3th ISTS, 34th IEPC nd 6th NSAT, Koe-Hyogo, Jpn July 4 1, 215

7 mgneti field strength/g mgneti field strength/g mgneti field strength/g Fig. 7 the mgneti field strength long the xil diretion: r=.2m; r=.25m; r=.3m Fig. 6() () (e) shown the eletron density, potentil nd eletron temperture in C1, respetively: the min potentil drop nd high eletron temperture fous on the viinity of the node, while the most rowded eletron density is pled on the xis losed to z=.5m. The lrgest Ne zone is fter the min potentil drop zone nd this distriution mkes the pplied voltge minly lod to the eletron nd my not form the optimized ioniztion zone nd elertion zone. While Fig. 6() (d) (f) shows the orresponding plsm hrteristis in CHT of 25mm hnnel length, the distriution region of min potentil drop nd high eletron temperture move wy the node ompred the former nd is pled on the xis losed to z=.1m, while the eletron density Ne is rowded round the node. The lrgest Ne zone is loser to the node ompred the min potentil drop, whih is helpful for the ler seprtion of ioniztion zone nd elertion zone. As to wht redued the signifint hnge of the plsm ehviors with the extension of hnnel length, it n e explined s following: With respet to the region z.15m, the hnge of mgneti field is negleted s fig.7, the mgnetiztion level of eletrons is lmost onstnt. With respet to the region.15m z.25m, the originl plume zone eome the downstrem of hnnel nd the mgneti field intensity in this extend region is lso inresed, whih result in the residene time of slow ions inresed nd the mgnetiztion level of eletrons in this region. So the ioniztion rte is enhned nd the more seond eletrons is indued. When the inresed seond eletrons move to upstrem, the ioniztion rte is inresed further nd the eletrons trnsport is enhned, so the ioniztion zone move towrds the node, while the potentil fll is deresed ner the node, whih results in the min potentil drop move towrds the exit side nd t eletron temperture in hnnel middle enhne, thus the eletrons through this pth is elerted further nd the ioniztion rte ner the node is enhned one gin, this positive feedk mke the min potentil drop move signifint distne towrds right side finlly. In ddition, we find tht the potentil drop ner the outer wll hnge slightly with the extend of the hnnel length from Fig. 6() (d), the most possile use is tht the eletrons min trnsport pth is not the outer wll ut the hnnel enter, nd the ontriution of eletron-wll intertion to ross-trnsport trnsport is insignifint. V. Anlysis the physil mehnism omining the simultion nd experimentl results From the simultion result of dding the mgneti shield, we know tht firstly redue the mgneti field ner the node, whih mke the eletrons ross-field trnsit esier, nd the eletrons trnsport urrent inresed; t the sme time, the ioniztion rte redued, whih mkes the ion density derese in plume, while the right movement of the min potentil drop enhned the ion veloity in plume, s the redution of ioniztion rte led to the potentil drop distriution hnge, the derese inrement of ion density is lrger thn the inrese inrement of ion veloity, this my e the use tht ion urrent deresed slightly; With respet to the ion energy t xis, the weight of ion veloity is lrger thn ion density, it is shown tht the totl energy enhned slightly, while the right movement of the min potentil drop indue the elertion zone extend towrds downstrem, whih mke the reltive distne of ioniztion zone nd elertion zone seprte lerly, so the FWHM of ion energy deresed. From the simultion results of extending the hnnel length, we know tht firstly inresed the residene time of slow ions, whih enhned the ioniztion rte nd the ioniztion zone extend towrds the node, the min potentil drop move towrds the exit side, so the ion urrent nd ion energy inresed, t the sme time, the extension of ioniztion region towrds node mke the ioniztion region nd elertion region seprte more lerly, whih my e ritil ftor for derese of FWHM; with respet to eletron urrent, lthough the eletron trnsport enhned, the inrese of ioniztion rte onsume the eletron energy t the sme time, it my e signifint use for the hrdly onstnt eletron urrent. While the inrese of plume ngle my e relted with the enhnement of rdil omponent of eletri field. 7 Joint Conferene of 3th ISTS, 34th IEPC nd 6th NSAT, Koe-Hyogo, Jpn July 4 1, 215

8 VI. Conlusion Comprison the results of dding the mgneti shield nd extending the hnnel length, there re some ommon points: the eletron ross-field trnsport ner the node enhned nd the elertion zone move towrds the exit side, whih led to totl dishrge urrent inrese nd FWHM of ion energy derese. ut they hve virtul differene for the use of eletron moility enhned: the former improve the eletrons moility through deresing the mgneti field ner the node, whih led to the ioniztion rtio derese, so the inrese inrement of eletron urrent is muh lrger thn ion urrent; while the lter improve the eletrons moility through inresing the ion residene time in hnnel nd enhne the ioniztion, whih led to the ioniztion rtio enhne finlly, so the ion urrent oost signifintly ut the eletron urrent vried slightly. Integrting ove ftors, it s onluded tht the optimiztion effet on the hnnel length is etter thn the mgneti shield. Aknowledgments The uthors would like to knowledge the Foundtion for Innovtive Reserh Groups of the Ntionl Nturl Siene Foundtion of Chin (Grnt No ) nd Ntionl Nturl Siene Foundtion of Chin (Grnt No nd ). Referenes 1 Ritses Y, Smirnov A, Fish N. Cylindril Hll Thrusters. AIAA Kim H, Lim Y, Choe W, Seon J. Effet of multiply hrged ions on the performne nd em hrteristis in nnulr nd ylindril type Hll thruster plsms. Applied Physis Letters 214; 15(14): Smirnov A, Ritses Y, Fish NJ. The effet of mgneti field on the performne of low-power ylindril Hll thrusters. IEPC pper 25; Smirnov A, Ritses Y, Fish NJ. Eletron ross-field trnsport in low power ylindril Hll thruster. Physis of Plsms 24; 11(11): Artem N. Smirnov SM, IEEE, Yevgeny Ritses, nd Nthniel J. Fish. Eletron Cross-Field Trnsport in Miniturized Cylindril Hll Thruster. IEEE Lurent Grrigues GJMH, Jen Pierre Boeuf, Yevgeny Ritses, Artem Smirnov, nd Nthniel J. Fish. Simultions of Miniturized Cylindril Hll Thruster. IEEE 28; Lee J, Seo M, Seon J, Lee HJ, Choe W. Performne hrteristis ording to the hnnel length nd mgneti fields of ylindril Hll thrusters. Applied Physis Letters 211; 99(13): Liu H, Yu DR, Yn GJ, Liu JY. Investigtion of the Strt Trnsient in Hll Thruster. Contriutions to Plsm Physis 28; 48(9-1): Liu H, Wu B, Yu D, Co Y, Dun P. Prtile-in-ell simultion of Hll thruster. Journl of Physis D: Applied Physis 21; 43(16): Zho Y, 1, HL, et l. Prtile-in-Cell Simultions for vrile mgnet length in Cusped-Field thruster. IEPC Hui Liu Hun Wu YZ, Dren Yu,Chengyu M,Di Wng nd Hoyu Wei. Study of the eletri field formtion in multiusped mgneti field. physis of Plsms, Joint Conferene of 3th ISTS, 34th IEPC nd 6th NSAT, Koe-Hyogo, Jpn July 4 1, 215