ةمجلة إبن الھیثم للعلوم الصرفة و التطبیقی 2012 السنة 25 المجلد 1 العدد Ibn A l-Haitham Journal f or Pure and Applied Science No. 1 Vol. 25 Year 2012 Charge Transport in Magnetized Plasma H. J. M. Al-Agealy, D. H. Yonas , E. A. Jawad and M. A. Hassoony Departme nt of Physics , College of Education I bn Al – Haitham , Unive rsity of Baghdad Received in: 27March2011, Accepted in: 7December 2011 Abstract The p lasma source can restrict the motion of char ges that are localizing in the non equilibr ium distribution of char ge ener gy and reducing the electrons t ransp ort across magn etic field . The electrons & ions motion are controlled by ambipolar electric field and char ge–atom collision . The source density for a given electron t emp erature and a given ion are considered to evaluate the diffusion coefficient . The ambipolar diffusion coeff icient and the cross field diffusion coefficient for charge transfer are calcu lated through magnetized p lasma in a uniform magn etic field , and an app roximation amb ipolar diffusion coefficient is evaluated. The result, showes how t he diffusion p rocess is gradually imbedded as the p rop erties of the p lasma. Key words :- Change transp ort , monetized p lasma , diffusion coefficient Introduction The transfer of wave function energy towards t he long region and the formation of longe scale st ructures is a result of the well–known inverse casc ade in two dimensional and quas i two – dimensional fluids [1] . A comp lete understanding of char ge transp ort is imp ortant for characterizing materials used in the comp onents which are directly exp osed to the charge (p roton) isotop e plasma [2] . The source of electron transp ort in magn etized p lasmas which can be a major obst acle in the way toward p articles nuclear fusion p ower . The observed electron ener gy transp ort is much larger than are would exp ect from diffusion p rocess due to coulomb collisions [3] .The diffusion h as imp ortant technological imp lications in micro electronics [4] . Coalitional cross field transp ort due to electric or magnetic field asy mmetries is imp ortant in many neutral and non n eutral plasma conf inement devices [5] . It is the purp ose of this p ap er to give transp ort description of diffusion across magnetic field in p lasma source . Theory Transp ort in the dischar ge is controlled by equilibrium magn etic field , ambip olar electric field , and ion – atom collisions [4 - 5] . For a p lasma with a single sp ecies of singly charged ions , the am bip olar diffusion coefficient in a weak ly ionized syst em of sufficient size is given by [6] . D = …… 1 ةمجلة إبن الھیثم للعلوم الصرفة و التطبیقی 2012 السنة 25 المجلد 1 العدد Ibn A l-Haitham Journal f or Pure and Applied Science No. 1 Vol. 25 Year 2012 Where is the neutral gas density , and are the tot al scatt ering cross section with neutrals for electrons and ions resp ectively , me is the electron mass , is the ion mass , Te is the electron temp erature , is the ion temp erature and is the ion sound sp eed [7] .is given by [6 – 7] . …... (2) The cross section for electrons or ions are given [8] = 1/nλ ..…. (3) Where λ is the collisonal mean free p ath . The ion – atom collision fr equency is given by [6] . υ = v ( ….. (4) When no is the gasses density and v is the ion velocity is given by However when the electron – ion mass ratio << and small v alue that can be ignor ed in Equ(1) and results . D = …… (5) The magnetic field can inhibit electron motion p erp endicular to the magnetic field lines described by cross field diffusion co efficient and given [7] . = ..…. (6) ةمجلة إبن الھیثم للعلوم الصرفة و التطبیقی 2012 السنة 25 المجلد 1 العدد Ibn A l-Haitham Journal f or Pure and Applied Science No. 1 Vol. 25 Year 2012 Here is the electron t hermal sp eed and ρe is the electron gy ro radius is given by [6] ρe = = .….. (7) Whene the p lasma frequency is given by [9] . ….. (8) Herne B is t he static magnetic field strength Results In order to determine the diffusion coefficient of charge transp ort in magnetized p lasma theoretically using the equation (1) , one must initially evaluate the values of the ions sound sp eed cs form equation (2) for a variety ions Hy drogen , Argon , and Nitrogen where the ener gies of e lectrons kTe taken between (1 to 2.4) ev [10] . The values of mass of ions are mH = 1.67826*10 -27 , mar = 2.67*10 -26 kg , and mn = 2.5*10 -26 k g were extracted from the literature [11-12] . Amore gener al exp ression equation (2) was ap p lied to evaluate the sound sp eed of Argon , Hy drogen , and Nitrogen cons ions with masses of these ions , the results have been summarized in table (1) . We use the results of sound sp eed ions cs in table (1) to calculate the diffusion coefficient char ge st imulated by p lasma by using equation (1) with values of Ti = 0.1 ev [7] , na= 7.2*10 19 m -3 [13] , and σi , mi , and me from table (2) , the results are tabulated in table (3) . Anot her imp ortant p arameter for diffusion is the overall ion – atom collision frequency vi – atom that can be calculated from equation (4) , where the gas density n = 7.2*10 -19 m 2 and the values of v , σe , and σi are taken fro m table (2) , the values of vi – atom are sum marized in table (4) . So the other variable in diffusion of charge transp ort is the collisonal mean free p ath can be evalu ated by using equation (3) and σi from table (2) , these calculated values are shown in table (5) . The diffusion coefficient of am bipolar that caused by the direct ion motion mod ify the am bipolar flow can be calculated by equation (5) with used value of cs from table (1) and σe , σi , Ti , and Te from table (2) . results are summarized in table (6) also , the cross–field diffusion coefficient Dρ that describe the electron motion p erp endicular to the magnetic field can calcu lated by used equation (6) after estimated the value of electron gy ro radius we estimate the transp ort p rop erties of the magne�zed electrons by used equa�on (7) and (8) the plasma frequency w ca n be es�mated by using equa�on (8) , the results are show in table (7) . The gyro ra dius of e le ctron ρ can be evaluated whe n inser�ng va lues of w in equa� on (7) wi th va lues of Vi from table (4) the results are s ummarized in table (8) . finall y by using the results of ρ from ta ble (7) with eq (6) , we can calculate the cross field diffusion c oefficient the results are liste d in table (9) . ةمجلة إبن الھیثم للعلوم الصرفة و التطبیقی 2012 السنة 25 المجلد 1 العدد Ibn A l-Haitham Journal f or Pure and Applied Science No. 1 Vol. 25 Year 2012 All results the ion sound speed Cs , diffusion coefficie nt D , ion-atom collisions frequency , υ , collision and mean frequency path λ , ambi pola r diffusion coeffic ient , ions angular gyro frequency W , and ions gyro radius ρi are calculated using amatlab program . Discussion For all t he result s reported here we co nsider the dimensions of t he plasmas are small t o justify a t ransport that relies on t hermal equilibrat ion of the electrons. For the discharge considered here t he ion t emp erat ure is exp ect ed to be reasonably clo se to the t emp erat ure of t he neut rals roughly 0.1ev . The resulting values of the ion sound speed cs was unusually high for nit rogen and argon comparin g with low for hy dro gen t his indicat e of cs proportional with 1/mi . Table (3) shows t he overall diffusion co efficient are large for Nit rogen co mparing wit h Argon and Hydrogen for all t he same spect rum temperat ure value for (1to2.4) ev . This in dicates t hat the diffusion coefficient is depending on t he v alue of cs sound speed of ion and the scatt ering cro ss sect ion for ions that is very view in t ables (1) and (2) respectively . It t urned out t hat t he diffusion pat h way st ron gly depends on the cross sect ion σi . Whereas the diffusion is favored in Nitrogen compare with other elem ent s , t hat s mean when σi small then mean pat h λ is Large an d diffusion coefficient is Large and vice versa . For elect ron temp erat ure around ( 1 to 2.4 ) ev the rat io of Ti / T e in equat ion (1) can be ignored [7 ] and the directed ion mot ion modify t he am bipolar flow caused t he am bipolar diffusion coefficient equat ion (5) t he result of am bipo lar diffusion coefficient indicat es the diffusion in Nit rogen is mo re act ive comparing with Argon and Hydrogen t hese depending on value o f cs , i an d T e . T able (9) shows t hat t he cro ss – field diffusion coefficient Dρ that described the magnet ic field can inh ibit electron mot ion perpendicular to the magnetic field lines . The t ransport of elect rons acro ss magnet ic field lines is affect ed by the magnet ic field st rength when cross – field diffusion of elect ron gyro – orbits becomes smaller t han t he am bipolar diffusion . Conclusions In t his wor k , t he change t ransport in magnet ized plasma source operation are st udies in which t he ions mot ion is cont rolled by the am bipolar electric field and ion – atom collisions . The sound speed of ion are calculat ed and found large values for nit rogen an d mid large fo r argon an d small fo r Hydro gen . the mo st large sound speed leads t o height value of diffusion coefficient . in summ ary , t he diffusion coefficient s are calculat ed using equat ion s (1) , (5) and (6) Sho wing large v alue for nitrogen compared wit h argon and hydrogen depending or co an d speed of ion and scat terin g cro ss sect ion for ions Re ferences 1.Smoly akov , A . I .; Diamond , P. H. ; Gruzionr , I .; das , A . M alkov , M . and Shevchenk o , V . I . (2005) , shear flow in st abilities in magn etized plasma, Phys , Rev , 66 . 2.Shu , W . U. and kuniak i , W. (1995) , , a gener al for mula for simultaneous p lasma J , Phy s , Chem , 15 , 65 – 74 . 3.Wong , k . l. ; kay e , S. ; M ikkelsen , D . R. ; krommes,J. ; A hill , K. ; bell , R. and leblane , b . (2007) , p hy s , rev , letter , micro tearing instabilities and electron transp ort in the wst x sp herical to Kama ,31, 135003 . 4.Zhu , Y . G. ; Kan g , E . T. ; Neoh , K . G. ; Osipowicz , T . and cham , (2005) , p lasma graft copolymerization of 4-viny lpy ridine on dense and p orous sik , chem. , Soc, G , e lect 152 (9 ): 107 – 114 . ةمجلة إبن الھیثم للعلوم الصرفة و التطبیقی 2012 السنة 25 المجلد 1 العدد Ibn A l-Haitham Journal f or Pure and Applied Science No. 1 Vol. 25 Year 2012 5.Cluggish , B. P.and Driscoil , C. F. (1995) , let , transp ort and damp ing from rotational p ump ing in ma gnetized electron p lasma , phy s rev , 74 ( 21): 4213. 6.Boris ,N . B. and Al ekey , V . A .( 2001) , ion kin etics in magnetized plasma source , inst , fus , st , Texas urine . 7.Carter , M . D. ; Ry an , P . M .; Hoffman , D .; lee , W . S . and Guchbager , D . (2006) , combined rf and transp ort effect in magnetized capacitive dischar ges app le , J , p hys ,, 100 , 73305 . 8.Kittel , (1986), book , solid stabe p hy sics, willey eub . 9.Burning , N .; M erlino , K.l. ; lund in, D. ; Raad , U.A . and Helmersson , U . (2009), , fast er than 80hm cross .b e lectron t ransp ort in strongly p ulsed p lasma, am p hys.soc 103 , 225003- 1 . 10.Ferreira , J.I. ; Da silv a , S.F. and R ego , D.S .( 2004) , amulti magn etic mirror machine for p lasma production with electron cyclotron resonance , rev . p hys . ap p l . & inst , 17 (2 ): 54 11.John , w . (1987) , Tokamakx , o xford p ress , clarenbon press . 12.John , w .( 1987) , Tokamakx , o xford p ress , clarenbon press . 13.Cave ago , M . (2006), use of co u sol metap hy sics in the modelin g of ion source extraction , in comsol conf erence, M ilano , C.W.K.O.M , 4 , no & ,9766 . 14.Butenko, V.I. ; Ivanovo, 8. I. ; p rish chep ov ,V.P.(2005), exp erimental st udies of some features of beam plasma disch arge in itial st age , atom . sci . & techno 10(1) : 149-151 15.Cluggish , B.P. ; and Driscoll , C.F. (1995) , transp ort and damp ing from rotational p ump ing in ma gnetized electron p lasma , phy s . rev . lett , 74 ( 21) , 4213 – 4216 . ةمجلة إبن الھیثم للعلوم الصرفة و التطبیقی 2012 السنة 25 المجلد 1 العدد Ibn A l-Haitham Journal f or Pure and Applied Science No. 1 Vol. 25 Year 2012 Table ( 1 ):The ion sound speed value s for Hydrogen , Argon , and Nitrogen cs(m/s) N2 Ar H2 Te(ev) 80 00 24 47.96 30 9.34 1 83 90.47 25 67.44 32 44.44 1.1 83 63.56 26 81.60 33 8.80 1.2 91 21.40 27 91.10 35 2.70 1.3 94 65.72 28 96.46 36 6.02 1.4 97 97.95 29 98.12 37 8.86 1.5 10 119 .28 30 96.45 39 1.29 1.6 10 430 .72 31 91.74 40 3.33 1.7 10 733 .12 32 84.28 41 5.020 1.8 11 027 .23 33 74.28 42 6.40 1.9 11 313 .70 34 61.93 43 7.47 2 11 593 .10 35 47.43 44 8.28 2.1 11 86.91 36 30.91 45 8.83 2.2 12 123 .60 37 12.51 46 9.14 2.3 12 393 .54 37 92.36 47 9.23 2.4 Tabl e ( 2 ): Vel ocity of Nitrogen , Argon , an d Hydrogen ion s and electron Vi*10 3 m/sec Ti(eV)[7] σi(m 2 )[14] mi(Kg) ion 3.577708 m/s 0.1 ev 2.5*10 -17 m2 2.5*10 -26 kg N2 1.094761103 m/s 0.1 ev 3.4*10 -17 m2 2.6*10 -26 kg Ar 4.374786393 m/s 0.1 ev 3.9*10 -17 m2 1.672*10 -27 kg H2 1 – 2.4 ev 5*10 -19 m 2 [7] 9.1*10 -31 kg Electron ةمجلة إبن الھیثم للعلوم الصرفة و التطبیقی 2012 السنة 25 المجلد 1 العدد Ibn A l-Haitham Journal f or Pure and Applied Science No. 1 Vol. 25 Year 2012 Table ( 3 ):The ambipolar diffusion coefficient for Nitrogen , Argon , and Hydrogen ions Di ffusi on coefficient D(m 2 eV/Kg) 1/2 Te(ev) H2 Ar N2 1 0.215491275 1.95580081 8.688021893 1.1 0.229542527 2.083315415 9.254354662 1.2 0.24327549 2.208376575 9.809789195 1.3 0.256843827 2.33110882 10.35484973 1.4 0.270142231 2.451753318 10.890642 1.5 0.283219488 2.570477453 11.41790119 1.6 0.296109499 2.687429174 11.9372269 1.7 0.309242861 2.802691618 12.44915585 1.8 0.321338248 2.916426174 12.95422078 1.9 0.333714949 3.028698493 13.45278679 2 0.345936101 3.13965136 13.94553699 2.1 0.358012275 3.249205352 14.4320167 2.2 0.369960597 3.357631219 14.91349599 2.3 0.381775697 3.4648666566 15.38971383 2.4 0.393478486 3.571073853 15.86132399 Table ( 4 ): Ion - atom collision freque ncy for Nitrogen , Argon , and Hydrogen ions ion σion (m 2 ) Mion(kg) VAr(m/sec) υ i on(1/sec) N2 2.5*10 -17 2.5*10 -26 3577.708764 656873.291 Ar 3.4*10 -17 2.67*10 -26 1094.761103 2719386.58 H2 3.9*10 -17 1.6726*10 -27 4374.786393 12441892.5 ةمجلة إبن الھیثم للعلوم الصرفة و التطبیقی 2012 السنة 25 المجلد 1 العدد Ibn A l-Haitham Journal f or Pure and Applied Science No. 1 Vol. 25 Year 2012 Table ( 5 ):The collisional mean free path λ and cross section σion for Nitrogen ,Argon , and Hydrogen i ons ion σio n (m 2 ) λio n(m) N2 2.5*10 -17 5.555555*10 -4 Ar 3.4*10 -17 4.08496732*10 -4 H2 3.9*10 -17 3.561253561*10 -4 Ta ble ( 6 ):The ambipolar diffusi on coefficient approximati on for Nitrogen , Argon , and Hy drogen ions D:ambipolar diffusion coefficient (m 2 /sec) Te(ev) H2 Ar N2 1 0.348377135 0.399609066 0.54346833 1.1 0.383208883 0.439563131 0.597805858 1.2 0.417969552 0.479435662 0.652032501 1.3 0.452876917 0.519476464 0.706487991 1.4 0.487723575 0.559447631 0.755197372 1.5 0.522551113 0.599396865 0.815179737 1.6 0.557393162 0.639362745 0.869533333 1.7 0.59222809 0.679320456 0.92387582 1.8 0.62706468 0.719280075 0.978220902 1.9 0.661908994 0.759246235 1.03257488 2 0.696753844 0.799189444 1.086935997 2.1 0.73158014 0.839165455 1.141265019 2.2 0.766420863 0.879130185 1.195617052 2.3 0.801252279 0.919083497 1.249953556 2.4 0.836105966 0.959062751 1.304325342 ةمجلة إبن الھیثم للعلوم الصرفة و التطبیقی 2012 السنة 25 المجلد 1 العدد Ibn A l-Haitham Journal f or Pure and Applied Science No. 1 Vol. 25 Year 2012 Tabl e ( 7 ):The ion s an gular gyro fre quen cy w(sec) -1 fo r Ni trogen , Argon , an d Hy drogen ion s Magnetic f ield strength B[15] ions 3*10 4 Gaus 3.4*10 4 Gaus 3.8*10 4 Gaus 4.2*10 4 Gaus 4.6*10 4 Gaus 5*10 4 Gaus 5.4*10 4 Gaus Ar 1 .7 9 7 7 5 3 * 1 0 1 1 2 .0 3 7 4 5 * 1 0 1 1 2 .2 7 7 1 5 3 * 1 0 1 1 2 .5 1 6 8 5 3 9 * 1 0 11 2 .7 5 6 5 5 * 1 0 1 1 2 .9 9 6 2 5 * 1 0 1 1 3 .2 3 5 9 5 * 1 0 1 1 H2 2 .8 7 4 2 5 * 1 0 9 3 .2 5 7 4 6 5 * 1 0 9 3 .6 4 0 7 1 8 * 1 0 9 4 .0 2 3 9 5 2 0 9 * 1 0 9 4 .4 0 7 1 8 5 6 * 1 0 9 4 .7 9 0 4 1 9 * 1 0 9 5 .1 7 3 6 5 2 6 9 2 * 1 0 9 N2 1 .9 2 * 1 0 1 2 2 .1 7 6 * 1 0 12 2 .4 3 2 * 1 0 12 2 .6 8 8 * 1 0 12 2 .9 4 4 * 1 0 12 3 .2 * 1 0 12 3 .4 5 6 * 1 0 12 Tabl e ( 8 ):The ion s gyro radiu s ρ for Nitrogen , Argon , an d Hydrogen i ons ions 3*10 4 Gaus 3.4*10 4 Gaus 3.8*10 4 Gaus 4.2*10 4 Gaus 4.6*10 4 Gaus 5*10 4 Gaus 5.4*10 4 Gaus Ar 0 .1 5 1 2 6 5 8 7 8 0 .1 3 3 4 6 9 8 9 2 0 .1 1 9 4 2 0 4 3 0 .1 0 8 0 4 7 0 5 6 0 .0 9 8 6 5 1 6 5 9 0 .0 9 0 7 5 9 5 2 8 0 .0 8 4 0 3 6 5 9 9 H2 4 3 .2 8 7 4 1 7 6 6 3 8 .1 9 4 7 8 0 2 8 3 4 .1 7 4 2 7 7 1 3 0 .9 1 9 5 8 4 0 4 2 .8 2 3 0 9 2 4 5 6 2 5 .9 7 2 4 5 0 5 9 2 4 .0 4 8 5 6 5 3 6 N2 0 .0 3 4 2 1 1 8 4 0 .0 3 0 1 8 6 9 1 7 0 .0 2 7 0 0 9 3 4 7 0 .0 2 4 4 3 4 7 0 2 8 0 .0 2 2 3 1 2 0 6 9 0 .0 2 0 5 2 7 1 0 4 0 .0 1 9 0 0 6 5 7 7 ةمجلة إبن الھیثم للعلوم الصرفة و التطبیقی 2012 السنة 25 المجلد 1 العدد Ibn A l-Haitham Journal f or Pure and Applied Science No. 1 Vol. 25 Year 2012 Table ( 9 ):The cross field diffusion coefficient for Nitrogen , Argon , and Hydrogen ions (1/sec) (1/sec) (1/sec) (1/sec) (1/sec) (1/sec) (1/sec) Ar 3 8 6 1 7 .0 1 6 6 3 0 0 6 5 .1 5 1 1 7 2 4 0 6 8 .7 7 7 6 6 1 9 7 0 2 .5 5 9 5 9 1 6 4 2 5 .0 0 6 8 7 1 3 9 0 2 .1 2 6 3 4 1 1 9 1 8 .8 3 2 3 1 H2 3 1 6 2 4 2 4 2 4 3 2 4 6 2 0 9 4 9 9 8 1 9 7 1 0 4 0 0 4 1 1 6 1 3 4 8 1 7 5 7 1 3 4 5 0 7 6 4 7 4 1 1 3 8 4 7 2 7 2 7 9 7 6 0 5 6 8 6 4 .7 N2 1 9 7 5 .3 7 5 3 8 8 1 5 3 7 .9 2 1 9 4 9 1 2 3 1 .1 8 9 6 1 2 1 0 0 7 .8 4 4 5 3 8 8 4 0 .1 9 0 0 1 0 2 7 1 1 .1 3 5 1 3 9 5 6 0 9 .6 8 3 7 1 1 7 ةمجلة إبن الھیثم للعلوم الصرفة و التطبیقی 2012 السنة 25 المجلد 1 العدد Ibn A l-Haitham Journal f or Pure and Applied Science No. 1 Vol. 25 Year 2012 انتقال الشحنة في البالزما الممغنطة محسن عنید حسوني، ایناس احمد جواد ، درید هاني یونس ، هادي جبار مجبل العجیلي ابن الهیثم ، جامعة بغداد- قسم الفیزیاء ، كلیة التربیة 2011 كانون االول 7 :قبل البحث في،2011اذار27:ستلم البحث في ا الخالصة ر مصدر البالزما یحدد حركة الشحنات في التوزیع غیر المتوازن لطاقة الشحنة ویحد من انتقال االلكترونات عب الكترون –الثنائي ایون حركة االلكترونات والشحنات مسیطر علیها بالمجال الكهربائي للتمدد . المجال الممغنط معامل . اعتمد مصدر الكثافة الواجب لاللكترونات واالیونات الحرارة الالزمة لحساب معامل االنتشار . وتصادمات الشحنة االنتشار الناشىء من تمدد الكترون ایون، ومعامل االنتشار للشحنة المنتقلة، ومعامل االنتشار التقریبي لتمدد ایونات حصار عملیات االنتشار من خالل ناظهرت النتائج الحقیقیة كیفیة ا. بت من خالل مجال البالزما المنتظم االلكترون حس . خصائص البالزما معامل االنتشار ، البالزما الممغنطة ، انتقال الشحنة -:الكلمات المفتاحیة