Excitation of Ion Acoustic Waves in Plasmas with Electron Emission from Walls

Transcription

1 Excitatio of Io Acoustic Waves i Plasmas with Electro Emissio from Walls IEPC /ISTS Preseted at Joit Coferece of 30th Iteratioal Symposium o Space Techology ad Sciece 34th Iteratioal Electric Propulsio Coferece ad 6th Nao-satellite Symposium, Hyogo-Koe, Japa Alexader V. Khrarov 1, Igor D. Kagaovich, ad Yevgey Raitses 3 Priceto Plasma Physics Laoratory, Priceto, 08543, NJ, USA Dmytro Sydoreko 4 Uiversity of Alerta, Edmoto, T6G G7, Caada ad Adrei Smolyakov 5 Uiversity of Saskatchewa, Saskatchewa, Saskatoo, S7EN 5E, Caada Astract: Various plasma propulsio devices exhiit strog electro emissio from walls, either as a result of secodary processes or due to thermioic emissio. To uderstad the details of electro kietics i plasmas with strog emissio, we have performed particle simulatios of such plasmas usig the EDIPIC code. We show that excitatio of io-acoustic waves is a uiquitous pheomeo i may differet plasma cofiguratios with strog electro emissio from oudig surfaces. Io-acoustic waves were oserved to e geerated i the viciity of strogly emittig walls. B E v = magetic field = electric field = frequecy of oscillatios = electro-electro emissio yield = electro desity = wave propagatio speed Nomeclature I. Itroductio lasmas i cross-field discharge devices exhiit complex oliear ehavior resultig i a variety of turulet P fluctuatios ad structures that critically affect operatio ad performace of these devices. Recet experimets with Hall thrusters ad Peig discharges demostrated that low-frequecy (1-10 s khz) spoke oscillatios are resposile for aomalous electro cross-field trasport that limits the maximum achievale electric field ad 1 Research Associate, Plasma Sciece ad Techology Departmet, akhrarov@pppl.gov. Pricipal Research Physicist, Plasma Sciece ad Techology Departmet, ikagaov@pppl.gov. 3 Pricipal Research Physicist, Plasma Sciece ad Techology Departmet, yraitses@pppl.gov. 4 Research Physicist, Departmet of Physics, sydorek@ualerta.ca. 5 Professor, Departmet of Physics ad Egieerig Physics, adrei.smolyakov@usask.ca. 1 Joit Coferece of 30th ISTS, 34th IEPC ad 6th NSAT, Koe-Hyogo, Japa

2 icreases power losses i these devices. Our recet measuremets i cylidrical Hall thruster 1 ad Peig discharge revealed a strog depedece of spoke oscillatios o the cotrol parameters of the discharge, icludig the type of gas, the gas pressure, the magetic field, ad the electro ijectio from the cathode. I this paper we focus o the effects of electro ijectio or emissio from oudig surfaces upo possile excitatio of ioacoustic waves. II. Oservatio of Io Acoustic Waves i Particle-i-Cell Simulatios Recetly, we have performed extesive studies of Hall thruster plasma usig the EDIPIC particle-i-cell code. For example, i Ref. 3 we ivestigated the effect of asymmetric secodary emissio i ouded low-collisioal E x B plasma o the sheath ad plasma properties. We also oserved a ew regime i which all of the plasma electros escape ad are sustituted y secodary electros 4. I this regime, there is practically o electric field i the plasma or i the sheath, so that the ios are ot draw towards the wall, the plasma electros are ot cofied ad the plasma potetial is egative. The sheath i those simulatios was oserved to exist i three differet regimes: (1) regular sheath with a egative wall charge, ad a positive space charge i the sheath, whe the emissio is t strog; () space-charge-limited sheath with a positive wall charge, ad oth positive ad egative space charge regios preset i the sheath, whe the emissio is stroger; (3) iverse sheath with a positive wall charge, ad a egative space charge i the sheath, whe the emissio is very strog. The first regime occurs for most cases if the electric field ad the electro heatig do ot exceed critical values. The critical values are determied y the coditio that the secodary electros emitted from the wall ca acquire eough eergy to emit more tha oe secodary electro whe impactig the opposite wall; that is, the averaged secodary electro emissio (SEE) coefficiet for these eam electros satisfies 1 1. (1) I the latter case, a positive charge egis to accumulate at a floatig wall ad to pull ack fractio of emitted electros, to equate the icidet ad outgoig electro fluxes. Thus a positive space charge will always form if the criterio i Eq.(1) is satisfied. The sheath ca e either space-charge-limited, or a iverse kid, depedig o the iitial state ad temporal evolutio of the system. The trasitio etwee regular space-charge-limited sheath ad iverse sheath was oserved i our simulatios ad, e.g., i Ref. 5. If the ios are accelerated to soic velocity efore a trasitio to the Figure 1. Desity profile i the simulated Hall thruster chael. The plasma parameters are give i the text. regime 1 takes place, the space-charge-limited sheath occurs iitially, ad the trasforms ito a iverse sheath. I the parameter rage where the emissio is strog eough to produce SEE eams with the desity comparale to that of the plasma we oserve excitatio of io acoustic waves. Joit Coferece of 30th ISTS, 34th IEPC ad 6th NSAT, Koe-Hyogo, Japa

3 Figure. Zoom-i of the io desity profile ext to the left oudary at three differet momets 386 s, 394 s, 40 s after evolutio of a uiform iitial profile. Oserved excitatio of strog ioacoustic waves is show i Figs The simulatio parameters are as follows: axial electric field E=00 V/cm, magetic field B=100 G, chael width.5 cm, Xe gas with desity 10 1 cm -3, effective turulet collisio frequecy s -1 ; the iitial desity profile is uiform at cm -3. A detailed descriptio of the simulatios ca e foud i Ref. 6. Fig. 1 clearly shows the presece of io-acoustic waves i the io desity profile. The sigature of io-acoustic waves ca also e clearly see i Figs. ad 3. I Fig., where a zoom-i of the desity profile is show ear the left oudary, oe ca see that the desity perturatio moves aout 0.3 mm i aout 00 s; this gives the propagatio velocity of perturatio v = 0.3 mm/00 s = cm/s. Fig. 3 shows the phase-space maps of electros ad ios. There are two io populatios: oe of the ios accelerated to supersoic velocities, ad the secod slow diffuse populatio, made up of the ios geerated closer to the walls. The io-soud velocity for the typical electro temperature i x-directio of 5 ev is 10 5 cm/s, whereas the fast io velocity ca e as high as cm/s, see Fig.3. If the wave propagates with the soud velocity relative to the fast supersoic ios, its velocity i the la frame is (3.5 ) 10 5 cm/s = cm/s. This is i agreemet with what is oserved i Fig.. Figure 3. Phase maps for the ios (mapped i red, scale o left) ad electros (scale o right). Secodary electros emitted from the left are mapped i gree ad those from the right are mapped i lue. Time t=394 s. Figs. 4 ad 5 show the electro x- velocity distriutio fuctios (EVDF) i the ceter ad i the regio close to the left oudary. The itese eams geerated y SEE make the EVDF omootoic. As studied i Ref. 6, such EVDF may produce a two-stream electro istaility ad drive electro plasma waves ear the ceter of the plasma. Modulatio istaility ca trasfer eergy from the electro plasma waves to io-acoustic waves. The role of the modulatio istaility is clearly see i a simulatio of a dc plasma where the dc voltage is 800 V ad the flux of electro emissio from the cathode is m - s -1. The iitial plasma desity was uiform ad equal to m -3. The io mass selected was 10 amu. The cathode emissio was tured o with a delay of 10 μs whe the desity acquired a smooth profile decayig towards the walls; the time couter was set to zero whe the emissio started. The electros accelerated y the dc voltage ear the cathode ecame a electro eam piercig the plasma. The eam excites high frequecy eige mode of the system as show i the top two paels i Figure 6. I the areas of itese highly-localized high-frequecy electric field, the poderomotive force pushes electros sideward ad 3 Joit Coferece of 30th ISTS, 34th IEPC ad 6th NSAT, Koe-Hyogo, Japa

4 Figure 4. Electro velocity distriutio at the ceter: red-total, mageta-ulk (ewly created), lue - SEE from the right wall, ad gree SEE from the left wall. Time t=394 s; 1.0 cm<x<1.5 cm. Figure 5. Same as i Fig.4 ut for 0<x<0.5 cm. creates amipolar electric field which moves ios ad forms desity cavities (see Figure 6 ear 6, 8, ad 0 mm). The cavities tur ito desity pulses propagatig with the velocity close to the io acoustic speed (see Figure 7). Geeratio of io-acoustic waves was also oserved i simulatios of aother ouded plasma cofiguratio with a cold electro eam, amely a Peig discharge used to study spoke pheomea i E B devices. Lastly, we ote that a fiite plasma size y itself ca strogly affect the istaility process, as was recetly show i Ref. 7, where it was demostrated that susoic io flows i a ouded plasma result i io-acoustic istaility. III. Theory of Io Acoustic Istaility Excited y Electro eam due to Negative Pressure The mai cause of io acoustic istaility is egative pressure cotriutio of the utrapped electro eams propagatig from oe wall to aother. Ideed if the eam with velocity ad velocity v is affected y a small potetial perturatio, the desity perturatio is give y v v / m mv. (3) That is a positive perturatio of potetial will accelerate electros ad reduce their desity. Effective pressure that drive acoustic waves is the modifies from stadard case of the trapped Boltzma distriutio as followig. The desity perturatio of ios as a fuctio of the potetial perturatio is p i e p T e mv. (4) The effective pressure is give y e p i p eff i p. (5) Te mv Therefore if the eam desity is aove critical value give y 4 Joit Coferece of 30th ISTS, 34th IEPC ad 6th NSAT, Koe-Hyogo, Japa

5 This criterio is verified i simulatios. mv p T e. (6) IV. Coclusio I coclusio, Hall thruster plasmas may exhiit io-acoustic waves drive y electro eams produced due to electro emissio from the chael walls. The likely cause is oset of io-acoustic istaility whe the emissio curret is sufficietly strog. Aother possile process is a two-stream io-io istaility, due to the distict groups of ios, movig with supersoic ad with susoic velocities, preset whe the sheath evolves from the spacecharge limited to the iverse regime. Yet aother mechaism that ca excite io-acoustic waves is the electro two- Figure 6. Sequeces of profiles of potetial (top), electric field (middle), ad io desity (ottom) i simulatio with 800 V dc voltage. The cathode is at x=40 mm (ot show). Figure 7. Io desity vs time i poits placed with a step of 1 mm alog the system i the simulatio of a 800 V dc plasma. The curves are shifted upward i proportio to the coordiate of the oservatio poit. stream istaility etwee the ulk ad secodary electros. Noliear processes such as modulatio istaility may the trasfer eergy from the electro plasma waves to the io-acoustic mode. Further ivestigatios are eeded to idetify the processes i questio. Sice the istaility depeds strogly o ratio of trapped ad passig/eam electros ad these desities deped o the way plasma is produced icludig collisios ad ioizatio processes. This work was supported y the AFOSR. Ackowledgmets Refereces 1 Raitses, Y., ad Fisch, N. J., Parametric Ivestigatios of a Nocovetioal Hall Thruster, Phys. Plasmas, Vol. 8, No. 5, 001, pp Raitses, Y., Effect of Magetic Field o Electro Kietics i a Weakly-Collisioal Plasma, DOE Ceter for Predictive Cotrol of Plasma Kietics: Multi-Phase ad Bouded Systems, 3rd Aual Meetig, May 17-18, Wag, H., Campaell, M. D., Kagaovich, I. D., ad Cai G. B., Effect of asymmetric secodary emissio i ouded lowcollisioal E x B plasma o sheath ad plasma properties, J. Phys. D-Appl. Phys., Vol. 47, 014, p Campaell M. D., Khrarov, A. V., ad Kagaovich, I. D., Asece of Deye Sheaths due to Secodary Electro Emissio, Phys. Rev. Lett., Vol. 108, 01, p Joit Coferece of 30th ISTS, 34th IEPC ad 6th NSAT, Koe-Hyogo, Japa

6 5 Taccoga, F., No-classical plasma sheaths: space-charge-limited ad iverse regimes uder strog emissio from surfaces, Eur. Phys. J. D, Vol. 68, 014, p Sydoreko, D., Smolyakov, A., Kagaovich, I., ad Raitses, Y., Effects of o-maxwellia electro velocity distriutio fuctio o two-stream istaility i low-pressure discharges, Phys. Plasmas, Vol. 14, 007, p Koshkarov, O., Smolyakov, A. I., Kagaovich, I. D., ad Ilgisois, V. I., Io soud istaility drive y the io flows, Phys. Plasmas, Vol., 015, p Joit Coferece of 30th ISTS, 34th IEPC ad 6th NSAT, Koe-Hyogo, Japa