للعلوم الصرفة و التطبیقیةمجلة إبن الھیثم 2012 السنة 25 المجلد 1 العدد Ibn Al-Haitham Journal for 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 Department of Physics , College of Education Ibn Al – Haitham , University of Baghdad Received in: 27March2011, Accepted in: 7December 2011 Abstract The plasma source can restrict the motion of charges that are localizing in the non equilibrium distribution of charge energy and reducing the electrons transport across magnetic field . The electrons & ions motion are controlled by ambipolar electric field and charge–atom collision . The source density for a given electron temperature and a given ion are considered to evaluate the diffusion coefficient . The ambipolar diffusion coefficient and the cross field diffusion coefficient for charge transfer are calculated through magnetized plasma in a uniform magnetic field , and an approximation ambipolar diffusion coefficient is evaluated. The result, showes how the diffusion process is gradually imbedded as the properties of the plasma. Key words :- Change transport , monetized plasma , diffusion coefficient Introduction The transfer of wave function energy towards the long region and the formation of longe scale structures is a result of the well–known inverse cascade in two dimensional and quasi two – dimensional fluids [1] . A complete understanding of charge transport is important for characterizing materials used in the components which are directly exposed to the charge (proton) isotope plasma [2] . The source of electron transport in magnetized plasmas which can be a major obstacle in the way toward particles nuclear fusion power . The observed electron energy transport is much larger than are would expect from diffusion process due to coulomb collisions [3] .The diffusion has important technological implications in micro electronics [4] . Coalitional cross field transport due to electric or magnetic field asymmetries is important in many neutral and non neutral plasma confinement devices [5] . It is the purpose of this paper to give transport description of diffusion across magnetic field in plasma source . Theory Transport in the discharge is controlled by equilibrium magnetic field , ambipolar electric field , and ion – atom collisions [4 - 5] . For a plasma with a single species of singly charged ions , the am bipolar diffusion coefficient in a weakly ionized system of sufficient size is given by [6] . D = …… 1 للعلوم الصرفة و التطبیقیةمجلة إبن الھیثم 2012 السنة 25 المجلد 1 العدد Ibn Al-Haitham Journal for Pure and Applied Science No. 1 Vol. 25 Year 2012 Where is the neutral gas density , and are the total scattering cross section with neutrals for electrons and ions respectively , me is the electron mass , is the ion mass , Te is the electron temperature , is the ion temperature and is the ion sound speed [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 path . The ion – atom collision frequency 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 value that can be ignored in Equ(1) and results . D = …… (5) The magnetic field can inhibit electron motion perpendicular to the magnetic field lines described by cross field diffusion coefficient and given [7] . = ..…. (6) للعلوم الصرفة و التطبیقیةمجلة إبن الھیثم 2012 السنة 25 المجلد 1 العدد Ibn Al-Haitham Journal for Pure and Applied Science No. 1 Vol. 25 Year 2012 Here is the electron thermal speed and ρe is the electron gyro radius is given by [6] ρe = = .….. (7) Whene the plasma frequency is given by [9] . ….. (8) Herne B is the static magnetic field strength Results In order to determine the diffusion coefficient of charge transport in magnetized plasma theoretically using the equation (1) , one must initially evaluate the values of the ions sound speed cs form equation (2) for a variety ions Hydrogen , Argon , and Nitrogen where the energies of electrons 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 kg were extracted from the literature [11-12] . Amore general expression equation (2) was applied to evaluate the sound speed of Argon , Hydrogen , and Nitrogen cons ions with masses of these ions , the results have been summarized in table (1) . We use the results of sound speed ions cs in table (1) to calculate the diffusion coefficient charge stimulated by plasma by using equation (1) with values of Ti = 0.1 ev [7] , na= 7.2*1019 m-3 [13] , and σi , mi , and me from table (2) , the results are tabulated in table (3) . Another important parameter 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 m2 and the values of v , σe , and σi are taken from table (2) , the values of vi – atom are summarized in table (4) . So the other variable in diffusion of charge transport is the collisonal mean free path can be evaluated 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 modify 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 perpendicular to the magnetic field can calculated by used equation (6) after estimated the value of electron gyro radius we estimate the transport properties of the magne�zed electrons by used equa�on (7) and (8) the plasma frequency w can be es�mated by using equa�on (8) , the results are show in table (7) . The gyro radius of electron ρ can be evaluated when inser�ng values of w in equa�on (7) with values of Vi from table (4) the results are summarized in table (8) . finally by using the results of ρ from table (7) with eq (6) , we can calculate the cross field diffusion coefficient the results are listed in table (9) . للعلوم الصرفة و التطبیقیةمجلة إبن الھیثم 2012 السنة 25 المجلد 1 العدد Ibn Al-Haitham Journal for Pure and Applied Science No. 1 Vol. 25 Year 2012 All results the ion sound speed Cs , diffusion coefficient D , ion-atom collisions frequency , υ , collision and mean frequency path λ , ambipolar diffusion coefficient , ions angular gyro frequency W , and ions gyro radius ρi are calculated using amatlab program . Discussion For all t he results reported here we consider the dimensions of the plasmas are small to justify a transport that relies on thermal equilibrat ion of the electrons. For the discharge considered here the ion temperature is expected to be reasonably close to the temperature of the neutrals roughly 0.1ev . The resulting values of the ion sound speed cs was unusually high for nitrogen and argon comparing with low for hydrogen this indicate of cs proportional with 1/mi . Table (3) shows the overall diffusion coefficient are large for Nitrogen comparing with Argon and Hydrogen for all the same spectrum temperature value for (1to2.4) ev . This indicates that the diffusion coefficient is depending on the value of cs sound speed of ion and the scattering cross section for ions that is very view in tables (1) and (2) respectively . It turned out that the diffusion path way strongly depends on the cross section σi . Whereas the diffusion is favored in Nitrogen compare with other elements , thats mean when σi small then mean path λ is Large and diffusion coefficient is Large and vice versa . For electron temperature around ( 1 to 2.4 ) ev the ratio of Ti / T e in equation (1) can be ignored [7] and the directed ion motion modify the am bipolar flow caused the am bipolar diffusion coefficient equation (5) the result of am bipolar diffusion coefficient indicates the diffusion in Nitrogen is more act ive comparing with Argon and Hydrogen these depending on value of cs , i and T e . Table (9) shows that the cross – field diffusion coefficient Dρ that described the magnetic field can inhibit electron motion perpendicular to the magnetic field lines . The t ransport of electrons across magnetic field lines is affected by the magnetic field strength when cross – field diffusion of elect ron gyro – orbits becomes smaller than the am bipolar diffusion . Conclusions In this work , the change transport in magnetized plasma source operation are studies in which the ions motion is controlled by the am bipolar electric field and ion – atom collisions . The sound speed of ion are calculated and found large values for nitrogen and mid large for argon and small for Hydrogen . the most large sound speed leads to height value of diffusion coefficient . in summary , the diffusion coefficients are calculated using equations (1) , (5) and (6) Showing large value for nitrogen compared with argon and hydrogen depending or co and speed of ion and scattering cross section for ions References 1.Smolyakov , A . I .; Diamond , P. H. ; Gruzionr , I .; das , A . M alkov , M . and Shevchenko , V . I . (2005) , shear flow in stabilities in magnetized plasma, Phys , Rev , 66 . 2.Shu , W . U. and kuniaki , W. (1995) , , a general formula for simultaneous p lasma J , Phys , Chem , 15 , 65 – 74 . 3.Wong , k . l. ; kaye , S. ; Mikkelsen , D . R. ; krommes,J. ; A hill , K. ; bell , R. and leblane , b . (2007) , phys , rev , letter , micro tearing instabilities and electron transport in the wstx spherical to Kama ,31, 135003 . 4.Zhu , Y . G. ; Kang , E . T. ; Neoh , K . G. ; Osipowicz , T. and cham , (2005) , plasma graft copolymerization of 4-vinylpyridine on dense and porous sik , chem. , Soc, G , elect 152 (9 ): 107 – 114 . للعلوم الصرفة و التطبیقیةمجلة إبن الھیثم 2012 السنة 25 المجلد 1 العدد Ibn Al-Haitham Journal for Pure and Applied Science No. 1 Vol. 25 Year 2012 5.Cluggish , B. P.and Driscoil , C. F. (1995) , let , transport and damping from rotational pumping in magnetized electron plasma , phys rev , 74 ( 21): 4213. 6.Boris ,N . B. and Alekey, V . A .( 2001) , ion kinetics in magnetized plasma source , inst , fus , st , Texas urine . 7.Carter , M . D. ; Ryan , P . M .; Hoffman , D .; lee , W . S . and Guchbager , D . (2006) , combined rf and transport effect in magnetized capacitive discharges apple , J , phys ,, 100 , 73305 . 8.Kittel , (1986), book , solid stabe physics, willey eub . 9.Burning , N .; Merlino , K.l. ; lundin, D. ; Raad , U.A . and Helmersson , U . (2009), , faster than 80hm cross .b electron transport in strongly pulsed plasma, am phys.soc 103 , 225003- 1 . 10.Ferreira , J.I. ; Da silva , S.F. and Rego , D.S .( 2004) , amulti magnetic mirror machine for plasma production with electron cyclotron resonance , rev . phys . ap pl . & inst , 17 (2 ): 54 11.John , w . (1987) , Tokamakx , oxford press , clarenbon press . 12.John , w .( 1987) , Tokamakx , oxford press , clarenbon press . 13.Cave ago , M. (2006), use of co u sol metaphysics in the modeling of ion source extraction , in comsol conference, Milano , C.W.K.O.M , 4 , no & ,9766 . 14.Butenko, V.I. ; Ivanovo, 8. I. ; prish chepov ,V.P.(2005), experimental studies of some features of beam plasma discharge initial stage , atom . sci . & techno 10(1): 149-151 15.Cluggish , B.P. ; and Driscoll , C.F. (1995) , transport and damping from rotational pumping in magnetized electron plasma , phys . rev . lett , 74 ( 21) , 4213 – 4216 . للعلوم الصرفة و التطبیقیةمجلة إبن الھیثم 2012 السنة 25 المجلد 1 العدد Ibn Al-Haitham Journal for Pure and Applied Science No. 1 Vol. 25 Year 2012 Table ( 1 ):The ion sound speed values for Hydrogen , Argon , and Nitrogen cs(m/s) N2 Ar H2 Te(ev) 8000 2447.96 309.34 1 8390.47 2567.44 3244.44 1.1 8363.56 2681.60 338.80 1.2 9121.40 2791.10 352.70 1.3 9465.72 2896.46 366.02 1.4 9797.95 2998.12 378.86 1.5 10119.28 3096.45 391.29 1.6 10430.72 3191.74 403.33 1.7 10733.12 3284.28 415.020 1.8 11027.23 3374.28 426.40 1.9 11313.70 3461.93 437.47 2 11593.10 3547.43 448.28 2.1 1186.91 3630.91 458.83 2.2 12123.60 3712.51 469.14 2.3 12393.54 3792.36 479.23 2.4 Table ( 2 ): Velocity of Nitrogen , Argon , and Hydrogen ions and electron Vi*103m/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 m2[7] 9.1*10-31 kg Electron للعلوم الصرفة و التطبیقیةمجلة إبن الھیثم 2012 السنة 25 المجلد 1 العدد Ibn Al-Haitham Journal for Pure and Applied Science No. 1 Vol. 25 Year 2012 Table ( 3 ):The ambipolar diffusion coefficient for Nitrogen , Argon , and Hydrogen ions Diffusion coefficient D(m2eV/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 frequency for Nitrogen , Argon , and Hydrogen ions ion σion (m 2 ) Mion(kg) VAr(m/sec) υ ion(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 للعلوم الصرفة و التطبیقیةمجلة إبن الھیثم 2012 السنة 25 المجلد 1 العدد Ibn Al-Haitham Journal for 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 ions ion σion (m 2 ) λion(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 Table ( 6 ):The ambipolar diffusion coefficient approximation for Nitrogen , Argon , and Hydrogen 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 للعلوم الصرفة و التطبیقیةمجلة إبن الھیثم 2012 السنة 25 المجلد 1 العدد Ibn Al-Haitham Journal for Pure and Applied Science No. 1 Vol. 25 Year 2012 Table ( 7 ):The ions angular gyro frequency w(sec)-1 for Nitrogen , Argon , and Hydrogen ions 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. 79 77 53 *1 011 2. 03 74 5* 10 11 2. 27 71 53 *1 011 2. 51 68 53 9* 10 11 2. 75 65 5* 10 11 2. 99 62 5* 10 11 3. 23 59 5* 10 11 H2 2. 87 42 5* 10 9 3. 25 74 65 *1 0 9 3. 64 07 18 *1 0 9 4. 02 39 52 09 *1 0 9 4. 40 71 85 6* 10 9 4. 79 04 19 *1 0 9 5. 17 36 52 69 2* 10 9 N2 1. 92 *1 0 12 2. 17 6* 10 12 2. 43 2* 10 12 2. 68 8* 10 12 2. 94 4* 10 12 3. 2* 10 12 3. 45 6* 10 12 Table ( 8 ):The ions gyro radius ρ for Nitrogen , Argon , and Hydrogen ions 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. 15 12 65 87 8 0. 13 34 69 89 2 0. 11 94 20 43 0. 10 80 47 05 6 0. 09 86 51 65 9 0. 09 07 59 52 8 0. 08 40 36 59 9 H2 43 .2 87 41 76 6 38 .1 94 78 02 8 34 .1 74 27 71 30 .9 19 58 40 4 2. 82 30 92 45 6 25 .9 72 45 05 9 24 .0 48 56 53 6 N2 0. 03 42 11 84 0. 03 01 86 91 7 0. 02 70 09 34 7 0. 02 44 34 70 28 0. 02 23 12 06 9 0. 02 05 27 10 4 0. 01 90 06 57 7 للعلوم الصرفة و التطبیقیةمجلة إبن الھیثم 2012 السنة 25 المجلد 1 العدد Ibn Al-Haitham Journal for 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 38 61 7. 01 66 30 06 5. 15 11 7 24 06 8. 77 76 6 19 70 2. 55 95 9 16 42 5. 00 68 7 13 90 2. 12 63 4 11 91 8. 83 23 1 H2 31 62 42 42 43 24 62 09 49 98 19 71 04 00 41 16 13 48 17 57 13 45 07 64 74 11 38 47 27 27 97 6 05 68 64 .7 N2 19 75 .3 75 38 8 15 37 .9 21 94 9 12 31 .1 89 61 2 10 07 .8 44 53 8 84 0. 19 00 10 2 71 1. 13 51 39 5 60 9. 68 37 11 7 للعلوم الصرفة و التطبیقیةمجلة إبن الھیثم 2012 السنة 25 المجلد 1 العدد Ibn Al-Haitham Journal for 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 رة الالزمة لحساب معامل االنتشار . وتصادمات الشحنة معامل . اعتمد مصدر الكثافة الواجب لاللكترونات واالیونات الحرا 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