Fully Kinetic Simultions of Ion Bem Neutrliztion Joseph Wng University of Southern Cliforni Hideyuki Usui Kyoto University E-mil: josephjw@usc.edu; usui@rish.kyoto-u.c.jp 1. Introduction Ion em emission/neutrliztion is one of the most fundmentl prolems in spcecrft plsm interctions nd electric propulsion. It is well known tht, in order to trnsmit current exceeding the spce chrge limit from spcecrft to the mient, the em must e dequtely neutrlized or the trnsmission would e locked y virtul node formtion in the em 1 nd spcecrft chrging. Hence, the opertion of n electric thruster or ny other lrge current ion emitting source from spcecrft requires neutrlizer to neutrlize the ion em. In such systems, the ions re typiclly emitted s cold em while the electrons re typiclly emitted s sttionry therml electrons from the neutrlizer. The emission is such tht v te >>v em >>v ti, where v te, v em, v ti re the electron therml velocity, em drifting velocity, nd ion therml velocity, respectively, nd the electron current emitted equls the ion current emitted. One notes tht the plsm emitted is strongly non-neutrl ner the source regrdless of the neutrlizer loction or the emitting surfce re. Even for hypotheticl sitution where the electrons nd ions were emitted from exctly the sme loction nd sme surfce re, the initil em would still e strongly non-neutrl due to the difference in electron nd ion emitting velocity. The ion em neutrliztion process not only is n interesting physics prolem ut lso hs importnt prcticl implictions. For instnce, such knowledge is importnt in the neutrliztion design for electric thruster clusters. It is oviously lso of criticl importnce in ny modeling studies involving plsm emission. Ion em neutrliztion is one of the first prolems studied during electric propulsion development. Although ion em neutrliztion is redily chieved in experiments, the understnding of the underlying physicl process remins t rther primitive level. No theoreticl or simultion models hve convincingly explined the detiled neutrliztion mechnism. Erlier theoreticl nd simultions models hve considered the neutrliztion of infinitively lrge uniform ion em 2-6. More recent models hve considered more relistic setting for finite size ion em emission 7-9. These previous studies suggest tht wve-prticle interction nd plsm instility my e the driving neutrliztion mechnism. However, no conclusions hve een reched. Prt of the reson for the lck of good understnding of the neutrliztion process is ecuse prticle simultion of em neutrliztion is n extremely chllenge prolem due to computtionl constrints. This is ecuse, in order to simulte the physics correctly, such simultions must e crried out using the relistic ion to electron mss rtio so the correct mesotherml velocity order for ions nd electrons, v te >>v em >>v ti cn e mintined. Additionlly one must lso use very lrge simultion domin in order to minimize the effects of the simultion domin oundry. This pper presents fully kinetic simultion of ion em neutrliztion nd plsm em propgtion. The focus is on the physics of electron-ion coupling nd the resulting propgtion of the mesotherml plsm. Section 71
JAXA-SP-08-018 representing the electrons s sttionry Mxwellin distriution. In order to mintin the relistic reltive velocity rtio etween the em velocity, nd electron nd ion therml velocities in the simultion, the simultions re performed using relistic mss rtio of mi/me=1836. Figure 1: Simultion setup 2 presents the simultion model. Section 3 discusses the simultion result. Section 4 contins summry nd conclusions. 2. Simultion Model The ion em neutrliztion process involves the following spects: initil mixing of electrons nd ions, electron-ion coupling, nd em propgtion. The initil electron-ion mixing, to lrge extent, is determined y device design nd hence, the mixing process vries for different systems. In this pper, we will focus on the electron-ion coupling nd em propgtion spects. The prolem is studied using full prticle PIC simultion. In this model, oth the electrons nd ions re modeled s mcro-prticles. The prticle dynmics, spce chrge, nd electric field re solved self-consistently. In order to reduce the computtion, the 3-D PIC code is pplied to 2-D configurtion. The simultion setup is shown in Figure 1. We consider tht the electrons nd ions re emitted from the sme surfce re ut with different velocity distriution functions. At every time step, Mcro-prticles representing the ions re emitted into the simultion domin s drifting Mxwellin distriution nd those Compring to v te, v em nd v ti re v em =0.1 v te nd v ti = 0.0023 v te, respectively. These reltive vlues re similr to typicl ion thruster prmeters. The emitted electron nd ion currents re kept the sme. For cold em ions nd therml electrons, the electron nd ion current density t the emitting surfce re J eo =n eo < v te > nd J io =n io v em, respectively, where ne0 nd ni0 denote the electron nd ion density outside the emitting surfce, respectively. For the v te nd v em considered here, n eo ~ 0.2n io. Hence, if the electrons nd ions were uncoupled, such n emission would led to very non-neutrl em, s illustrted in Figure 2. In the simultion, the cell size equls the Deye length clculted using n io nd the electron termperture Te t the emitting surfce. We consider spcecrft with size 50X50. The em emission width is R T =20. The simultion domin is tken to e 600X400, or 30R T X20R T. The potentil t spcecrft ody is fixed nd while the potentil t domin oundry is floting. The numer of mcro-prticles ner the emitting source is ~850/cell for ech popultion nd the totl numer of mrco-prticles used t end of run is typiclly round 7 million. Simultions were run using time step resolution of dt pe ~0.1, where dt nd pe denote the time step nd the electron plsm frequency, respectively. 3 Results nd Discussions 72
Typicl simultion results re presented in Figs. 3 through 8. Fig.3 shows potentil contour t t pe =1600 (t pi =37.3 where pi denotes the ion plsm frequency ). Fig.4 shows electron nd ion positions, electron density contour, ion density contour, nd totl chrge density contour t t pe =1600 (t pi =37.3). These results show tht, while the em is strongly non-neutrl ner the emitting source, the electron-ion coupling occurs immeditely t the downstrem of the emitting source nd qusi-neutrl plsm em quickly forms. The therml electrons follow the motion of the cold em ions, nd the electron density closely mtches the ion density inside the em. For this prticulr cse, the potentil inside the Figure 2: Illustrtion of hypotheticl non-neutrl em generted y the emission of cold em ions nd therml electrons. ) electron (lue) nd ion (red) positions; ) totl chrge density contour. Figure 3: Simultion results: potentil contour t t pe=1600 (t pi=37.3) em t the downstrem of the em exit surfce is only few Te. To investigte the process of electron nd ion coupling, Figs. 5 through 7 show the time evolution of the phse plots, potentil profiles, nd electron nd ion density profiles long the em direction. In these plots, we compre the snpshots tken t t pe =40 (t pi =0.93) with tht t t pe =1600 (t pi =37.3). The initil electron expnsion long the em direction follows the sme physicl process studied in 1-D expnsion of mesotherml plsm into vcuum. It is well understood tht such expnsion estlishes n ion-coustic like em front propgtion. As the electron therml velocity is much lrger thn the ion em velocity, the region ehind the em front will hve slightly positive potentil with respect to the mient. Hence, the region etween the em source nd the em front grdully trps the electrons. It is the interction etween the trpped electrons nd the potentil well tht leds to electron-ion coupling nd em neutrliztion. Further frequency nd wve numer spectrum nlysis (not shown here) lso show tht no em plsm instilities were present. We lso performed the liner dispersion nlysis using the plsm prmeters such s the electron nd ion velocities nd densities oserved in the potentil well. However, the otined 73
JAXA-SP-08-018 c Figure 5: Phse plots for electrons (lue) nd ions (red). ) t pe=40 (t pi=0.93) ) t pe=1600 (t pi=37.3) grow. Therefore, in the current cse, we find tht ion em neutrliztion is not through plsm micro-instility, s previous studies suggested. d Figure 4: Simultion results: ) electron (lue) nd ion (red) positions. ) electron density contour; c) ion density contour; d) totl chrge density contour t t pe=1600 (t pi=37.3). growth rte of the em instility is too smll to As the em front propgtes forwrd, the electrons nd ions develop similr density profile long the em direction, s shown in Fig. 8. Once the qusi-neutrl em is estlished, n expnsion wve is generted outside the em (Fig. 4c nd 4d). The expnsion in the trnsverse direction is similr to tht ssocited with the self-similr expnsion of mesotherml plsm into vcuum. 4. Summry nd Conclusions In summry, we hve developed full prticle PIC simultion model to simulte the ion em neutrliztion process. We find tht em neutrliztion nd propgtion re two closely 74
Figure 6: Potentil profiles long the em direction ) t pe=40 (t pi=0.93) ) t pe=1600 (t pi=37.3) Figure 7: Totl chrge density profile long the center xis ) t pe=40 (t pi=0.93) ) t pe=1600 (t pi=37.3) coupled processes. The initil expnsion of therml electrons over cold em ions estlishes ion-ccoustic-like em front propgtion. Susequently, the emitted electrons re trpped in the region etween the forwrd propgting em front nd the emitting source. Electron-ion coupling is chieved through the interctions etween the trpped electrons nd the potentil well long the em direction. Bem neutrliztion is not through plsm instilities s previous studies suggested. Self-similr expnsion of ion coustic wves similr to tht ssocited with plsm expnsion into vcuum lso occurs in the trnsverse direction outside the em. Becuse of electron trpping in the em direction nd the interctions etween the trpped electrons nd the electric field, the electron Figure 8: Ion density profile () nd electron density profile () long the center xis t t pe=1600 (t pi=37.3) 75
JAXA-SP-08-018 distriution is highly non-mxwellin long the em direction. Hence, the commonly used Boltzmnn ssumption for electron density in spcecrft plsm interction models in generl is not vlid for interctions concerning plsm em emission. Reference [1] Wng, J. nd Li, S., Virtul Anode in Ion Bem Emissions in Spce: Numericl Simultions, J. Spcecrft Rockets, 34(6), 1997, p829-836. [2] Bunemn, O. nd Kooyers, G., Computer Simultion of the Electron Mixing Mechnism in Ion Propulsion, AIAA J. 1(11), 1963, p2525-2528. [3] Wdhw, R., Bunemn, O., Bruch, D., Two-Dimensionl Computer Experiments on Ion Bem Neutrliztion, AIAA J., 3(6), 1965, p1076-1081. [4] Dunn, D. nd Ho, T., Longitudinl Instilities in n Electrosttic Propulsion Bem with Injected Current Neutrlity, AIAA Preprint 63041, 1963. [5] Derfler, H., Nonexistence of Quiescent Plsm Sttes in Ion Propulsion, Physics of Fluids 7(10), 1964, p1625-1637. [6] Bunemn, O., Mintennce of Equilirium y Instilities, J. Nucl. Energy C, V2, 1961, p119-134. [7] Wheelock, A., Cooke, D., nd Gtsonis, N., Ion Bem Neutrliztion Processes for Electric Micropropulsion Applictions, AIAA 2003-5148, 2003. [8] Bried, L., nd Wng, J., Modeling Ion Thruster Bem Neutrliztion Using Fully Kinetic ES-PIC Code, AIAA 2005-4045, 2005. [9] Co, Y. nd Wng, J., Modeling Ion Bem Neutrliztion, IEPC 2007-241, 2007. 76