Collisional Ionization in Lithium Vapor Excited by Nanosecond Laser Pulses

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1 Vol. 122 (2012) ACTA PHYSICA POLONICA A No. 1 Collisioal Ioizatio i Lithium Vapor Excited by Naosecod Laser Pulses M.A. Mahmoud, A. El Tabal ad M. Nady Physics Departmet, Faculty of Sciece, Sohag Uiversity, Sohag, Egypt (Received August 24, 2011; i al form April 4, 2012) We report a theoretical study of the collisioal ioizatio processes which occur uder 2s 2p excitatio of lithium vapor excited with a aosecod pulsed laser. The time evolutio of the electro eergy distributio fuctio ad the atomic io desity (Li + ) as well as the molecular io desity (Li + 2 ) at dieret lithium vapor desities was ivestigated. The results show a oliear behavior of the eergy spectra of the electros created durig the iteractio of the laser with the lithium vapor. The oliear behavior results from superelastic collisios betwee the free electros produced by collisioal ioizatio ad photoioizatio with Li(2p). The results also show that a competitio exists betwee the collisioal ioizatio ad photoioizatio processes i producig the atomic io ad the molecular ios. PACS: p, t, Hv 1. Itroductio Collisioal ioizatio ad collisioal excitatio i thermal collisios betwee excited atoms ad molecules i gases has bee the subject of umerous studies durig the last decade. The type of studies of elemetary processes udertake i low-temperature plasma physics is largely dictated by the eeds of applied physics. This i tur presupposes rapid theoretical iterpretatio ad purposeful utilizatio of the experimetal results. I low- -temperature plasma, collisioal ioizatio is traditioally regarded as providig a eective chael for the productio of atomic ad molecular ios. Studies of such iteractios are of great iterest i a variety of elds, both fudametal ad applied. I the plasma eld, the most well kow examples, iclude laser fusio, X-ray laser developmet, laser heatig of magetically coed plasmas [1]. Sice the pioeerig experimet o resoat laser plasma productio i dese sodium vapor by Lucatorto ad McIlrath [2], umerous io ivestigatios i Li [37], Na [8, 9], Rb [10, 11], ad Cs [12, 13] vapors excited by cw or pulsed laser light have bee reported previously. These studies provide isight ito (i) the ioizatio mechaism, (ii) eergy trasfer mechaisms which are implied i or serve the ioizatio. Plasma formatio i these experimets has bee explaied i terms of a propagatig loop of superelastic collisios betwee eutral atoms ad seed electros [14, 15]. The electros gai kietic eergy correspodig author; hameideg@yahoo.com i collisios with excited atoms ad start ruaway collisioal ioizatio process. Recetly, laser iduced ioizatio has bee show to occur i vapors irradiated by aosecod laser pulses [16, 17] whe the ioizatio is oly partial ad does ot exceed a few percet. Due to the iterest i laser excitatio ad ioizatio of lithium vapor, several experimets have bee performed which study the microscopic processes that occur i laser- -irradiated lithium vapor [36]. These microscopic processes dictate the collective behavior of the plasma or discharge ad are therefore importat for a complete uderstadig of the pheomea. Amog the iteractios that cotribute to this complex eviromet are those ivolvig direct photos, such as hν + Li ad hν + Li 2 ad idirectly, for example Li(2p)+Li(2p) eergy poolig collisios. O the other had, resoace ioizatio spectroscopy of lithium vapor by laser radiatio tued to the rst resoace lithium lies has bee widely ivestigated i recet years [1820] ad this method is cosidered to be a useful techique for isotope separatio because of its high selectivity [18]. Our iterest i this work is primarily to study coditios (amely atom desities, irradiatio time) for the collisioal ioizatio ad photoioizatio processes to help better uderstad ioizatio mechaisms i lithium vapor excited by a aosecod pulsed laser. Oe of the pricipal assumptios made i the previous models [1417] was that of a Maxwellia electro eergy distributio fuctio (EEDF). I the preset work the rate coeciet of ioizatio ad excitatio is calculated with a o-equilibrium EEDF. (71)

2 72 M.A. Mahmoud, A. El Tabal, M. Nady 2. Theoretical model Oe assumptio of the model is that the eergy, E c1, ecessary to ioize the workig atom is greater tha twice the eergy E 21 betwee the groud state ad the rst excited state, ad less tha the three times that eergy, i.e. 2E 21 < E c1 3E 21. The alkali metals exhibit this property, ad we will restrict our discussio to lithium. If the laser radiatio is assumed to be suddely applied at t = 0, with a photo eergy hν = E 21, the the subsequet chai of evets ca be viewed i the followig sectio. Figure 1 shows the eergy level diagram of states lithium atom ivolved i the preset model. Li(l) + e(ε 0 ) Li(2s) + e(ε) where ε > ε 0. h) Electro impact excitatio. This process is the iverse of superelastic collisio process Li(l) + e(ε) Li( l ) + e(ε 0 ) where ε > ε 0. i) Electro impact ioizatio. Whe a electro gais eough eergy (through superelastic collisios), which is equal to the ioizatio potetial of the eutral atom, it ca udergo a ioizig collisio by electro impact process, resultig i a low eergy electro of (ε = ε 1 + ε 2 + E io ) ad atomic io Li(l) + e(ε) Li + + e(ε 1 ) + e(ε 2 ) where ε = ε 1 +ε 2 +E io ad E io is the ioizatio eergy. j) Radiative recombiatio Li + + e(ε) Li(l) + hν. k) Three-body recombiatio Li + + e(ε 1 ) + e(ε 2 ) Li(l) + e(ε), where 3s l 7d. For simplicity we have assumed that ε 1 = ε 2 i the electro impact ioizatio ad its iverse three-body recombiatio processes Methods of calculatios Fig. 1. Levels of lithium atom ivolved i the collisioal processes which take place i the lithium vapor excited by laser radiatio Process cosidered a) The absorptio of resoat photo Li(2s) + hν Li(2p). b) Two-photo ioizatio of the 2p level Li(2p) + 2hν Li + + e. c) The associative ioizatio iduced by laser of 2p2p collisio Li(2p) + Li(2p) + hν Li + 2 (2 Σ 2 (v, J)) + e(ε). d) The Peig ioizatio Li(2p) + Li(l) Li + + Li(2s) + e(e 2p E l ), where E l is the bidig eergy of the l electro. e) Laser-iduced Peig ioizatio Li(2p) + Li(2p) + hν Li(2s) + Li + + e. f) The eergy poolig to the 3d or 3p level followed by photoioizatio. Li(2p) + Li(2p) Li(3d, 3p) + Li(2s), Li(3d, 3p) + hν Li + + e. g) Superelastic collisio (SEC). The superelastic collisio is described by the collisio of a low eergy electro with a excited atom. This process ca be writte as The rate of chage of populatio desity of states 2s, 2p ad the highly excited states l is give by dn(2s) = N(2p)(R 21 + A 21 ) N(2s)R 12 dt + N(2p) e (ε)k 21 (ε)dε N(2s) e (ε)k 12 (ε)dε + N(2p)N()k P I N 2 (2p)k EP N(2s) e (ε)k 1c (ε)dε, (1) dn(2p) = N(2s)R 12 N(2p)(R 21 + A 21 ) dt N(2p) e (ε)k 21 (ε)dε + N(2s) e (ε)k 12 (ε)dε 1 2 N 2 (2p)k AI N(2p)N()k P I 1 2 N 2 (2p)k EP N(2p)σ 2c (2)F 2 N(2s) e (ε)k 2c (ε)dε, (2) dn() dt = e (ε)n()k m e (ε)n()k m (ε) >m m> A m N() >m >2 e (ε)n()k c (ε) N(2p)N()k P I N 2 (2p)k EP N()σ (1) c F

3 Collisioal Ioizatio i Lithium Vapor N Li + e (ε) [ e (ε)k c (ε) + k RD (ε) ]. (3) The rate of growth of the molecular io ad the atomic io is give by dn ( Li + ) 2 = 1 dt 2 N 2 (2p)k AI, (4) dn(li + ) dt = N(2p)N()k P I + N(2p)σ 2c (2)F 2 + N()σ c (1) F + e (ε)n()k c (ε). (5) >2 The electro eergy distributio fuctio equatio is give by d e (ε) dt = m> e (ε)n()k m (ε) e (ε)n()k m (ε) + m< + + >2 N(2p)N()k P I + N(2p)σ 2c (2)F 2 N()σ (1) c F N 2 (2p)k AI N Li + e (ε) The ormalizatio coditios are N 0 = 0 e (ε)n()k c (ε) [ e (ε)k c (ε) + k RD (ε) ]. (6) N() + N(Li + ), (7) e (ε)ε 1/2 dε = 1, (8) where N 0 is the desity of Li atomic vapor. N(2s), N(2p) ad N() are the populatio desity of levels 2s, 2p ad l, respectively, e (ε) represets the free electro desity as a fuctio of electro eergy ε, R 12 is the stimulated absorptio rate coeciet from 2s to 2p level (s 1 ), R 21 is the stimulated emissio rate coeciet from 2p to 2s level (s 1 ), A m is the Eistei coeciet for spotaeous emissio for the trasitio m (s 1 ), k EP represets the eergy poolig collisios rate coeciet (cm 3 s 1 ), k AI represets the associatio ioizatio rate coeciet (cm 3 s 1 ) k P I represets peig ioizatio rate coeciet for level (cm 3 s 1 ), k 21 represets the electro collisio rate coeciet for trasitio from (2p 2s) as a fuctio of electro eergy (ε) (cm 3 s 1 ), k 12 represets the electro collisio rate coeciet for trasitio from (2 2p) as a fuctio of electro eergy (ε) (cm 3 s 1 ), k 2c represets electro collisio ioizatio rate coeciet for level 2p (cm 3 s 1 ), k 1c represets electro collisio ioizatio rate coeciet for level 2s (cm 1 s 1 ), k c (ε) represets electro collisio ioizatio rate coeciet for level (cm 3 s 1 ), k m represets the electro collisio rate coeciet for trasitio from ( m) as a fuctio of electro eergy (ε) (cm 3 s 1 ), k m (ε) represets the electro collisio rate coeciet for trasitio from (m ) as a fuctio of electro eergy ε (cm 3 s 1 ), σ c (1) represets the sigle photo ioizatio cross-sectio, σ (2) 2c represets the two-photo ioizatio cross-sectio, F is the photo ux (photo s 1 cm 2 ), k c represets the three body recombiatio rate coeciet for level (cm 6 s 1 ), k RD represets the radiative recombiatio rate coeciet (cm 3 s 1 ), N Li + represets the desity of atomic ios, N Li + represets the desity 2 of molecular ios. Let us ote that the factor 1/2 with k EP ad k AI corrects for possible double coutig of each collidig pair of idetical particles [21]. The rate coeciets of collisioal ioizatio processes ad the cross-sectios of the photoioizatio processes i our model is idicated i Table. The cross sectio values of the physical processes. TABLE Process Cross sectio Referece Li(2p) + 2hν Li cm 2 [22] Li(2p) + Li(2p) + hν Li e cm 2 [23] Li(2p) + Li(2p) Li(3p, 3d) + Li(2s) cm 2 (12] Li(2p) + Li(2p) + hν Li(2s) + Li + + e cm 4 s [24] Cross sectios of photoioizatio for lithium (Mb) 3s 1.48 [22] 4s 1.40 [22] 5s 1.33 [22] 2p [22] 3p [22] 4p 41.7 [22] 5p 56.2 [22] 3d 18.2 [22] 4d 36.2 [22]

4 74 M.A. Mahmoud, A. El Tabal, M. Nady 2.3. Lithium data The computatioal model cosists of a large umber of rate equatios describig the desities of the various excited states of the lithium atom, the atomic ad molecular ios ad the eergy distributio of the free electros which are created durig the iteractio of lithium vapor with aosecod pulsed laser. The rate equatio for the electro eergy distributio (8) is divided ito 54 equatios, where the ioizatio eergy of Li = 5.39 ev ad the eergy step equal 0.1 ev. To calculate the electro eergy distributio fuctio, umerous data have to be compiled from the literature to be used i the Boltzma equatio computatioal code [25, 26]. By the use of suitable approximatios for the eergy depedece of the cross-sectios, the rate coef- ciets ca be expressed by simple aalytical formula. The rate coeciets k c, k c is give by Vries ad Smeets [27]. The rate coeciet k m ad k m have bee take from Ref. [15]. For the radiative recombiatio rate coeciet we have used the empirical formula give by Drawi [28]. 3. Results ad discussio The set of equatios specied i Sect. 2.2 are solved umerically uder the experimetal coditios of Skederovic et al. [5]. I this istace the lithium umber desity was varied i the rage from to cm 3 ad the vapor temperature was 650 K. The pulse half- -width of the laser beam is about 20 s ad the repetitio rate ca be varied from 1 to 10 Hz. The typical eergy of sigle pulse (E) is 2 mj ad the laser beam diameter was about 2.5 mm. The laser itesity (I) is give by E I = τ πr 2, where τ is the laser pulse duratio ad r is the laser beam radius. Uder these coditios, the laser light was tued to the rst resoace 2s 2p, at λ = m. We calculate (i) the time evolutio of the electro eergy distributio fuctio for dieret values of lithium atom, (ii) the time evolutio of the atomic io for dieret values of lithium atomic vapor ad (iii) the time evolutio of the molecular io for dieret values of lithium atomic vapor The time evolutio of electro eergy distributio fuctio The time evolutio of the electro eergy distributio fuctio at lithium vapour desity equal to cm 3 is show i Fig. 2. From this gure we otice that the spectral structure is observed with certai peaks (A, B, C, D, E, ad F ) lyig at eergies 0.2, 1, 1.5, 2.25, 2.75, ad 3.75 ev, respectively. The eergy distributio of the electros produced i peak A is cetered at a mea eergy E m 0.2 ev by sigle photoioizatio of 3p ad 3d, laser iduced peig ioizatio of 2p ad two-photo ioizatio of 2p which are described by the followig equatios: Li(2p) + 2hν Li + + e two-photo ioizatio), Li(2p) + Li(2p) + hν Li + + Li(2s) + e laser-iduced Peig ioizatio). The peak B correspods to electros produced by the laser iduced associative ioizatio process Li(2p) + Li(2p) + hν Li e. The peak C correspods to sigle-photo ioizatio Li(3p, 3d) + hν Li + + e. The peak D correspods to the electros produced by the Peig ioizatio of Li(3d) which is described by the followig collisio: Li(2p) + Li(2p) Li + + Li(2s) + e (2E 2p E io ). The two peaks E, F are attributed to the superelastic collisios Li(l) + e(ε 0 ) Li(2s) + e(ε), where ε > ε 0. Fig. 2. Time developmet of the electro eergy distributio fuctio i lithium vapor with excitatio by pulsed laser at vapor desity equal to cm 3. The depedece of the electro eergy distributio fuctio o the lithium vapor desity is idicated i Fig. 3. This gure eables us to study the evolutio of the electros seedig ad growig processes. Also this gure cormed the observed peaks (A, B, C, D, E ad F ), which chage i height as the lithium vapor desity icreases. However the iterestig poit from our perspective is that the collisioal ioizatio ad photoioizatio are the domiat processes durig the plasma formatio i laser excited lithium vapor [36]. Also, Gorbuov et al. [6] have demostrated that excitatio processes from Li(2p) ca play a sigicat role i determiig the EEDF ad the major iuece is the excitatio of 3s state havig the threshold of 2p 3s = 1.5 ev The time evolutio of atomic io Li + The growth rate of the Li + as a fuctio of time for differet values of lithium vapor desity is give by Fig. 4.

5 Collisioal Ioizatio i Lithium Vapor cosiderig that the mai processes for producig these molecular ios are associative ioizatio [4]. Fig. 3. The depedece of the electro eergy distributio fuctio o the lithium vapor desity after 20 s from the laser pulse. From this gure it ca be see that the Li + shows a fast icrease durig the early stages of the iteractio which icreases up to 20 s. The curves show almost the same behavior with descedig values of the lithium vapor desity for dieret irradiatio times. This behavior is due to the Li + maily produced by the photoioizatio ad laser iduced Peig ioizatio processes [35]. Fig. 5. Time evolutio of molecular ios (Li + 2 ) at differet values of lithium vapor desities The time evolutio of the total cocetratio of electros The growth rate of electros N e as a fuctio of time is idicated i Fig. 6 for dieret values of lithium vapor desity. From this gure we ca see that the electro desity icreases up to 30 s. Immediately after this time the electro desity shows a slow icrease durig the late stages of the iteractio. The explaatio of this growth ca be described as follows. Durig the early stages of the iteractio, a rapid growth of free electros appears due to two-photo ioizatio of the resoace level ad laser iduced Peig ioizatio. These electros ow give rise to a expoetial growth due to both direct collisioal ioizatio of the resoace level ad sigle photo ioizatio of the populated itermediate levels. Beyod this time, the growth rate of the electros becomes slower due to the competitio betwee the geeratio of the electros through Peig ioizatio or photoioizatio, as well as collisioal ioizatio of the groud state ad excited losses of the ios by radiative recombiatio ad three-body recombiatio [5]. Fig. 4. Time evolutios of atomic ios (Li + ) at dieret values of lithium vapor desities The time evolutio of molecular io Li + 2 The growth rate of the molecular ios Li + 2 as a fuctio of time is illustrated i Fig. 5 for dieret values of lithium vapor desity. From this gure we ca see that the Li + 2 desity icreases rapidly durig the period 0.1 s up to 2 s followed by a slow icrease up to 20 s for the dieret values of the lithium vapor desity. The explaatio of the liear growth ca be described as follows. Durig the early stages, the molecular ios are created at a high rate through associative ioizatio process. Immediately, after this time the Li + 2 desity shows a slow icrease durig the late stages of the irradiatio time. A uderstadig of this behavior ca be attaied by Fig. 6. Time evolutio of electro desity (N e) at differet values of lithium vapor desities.

6 76 M.A. Mahmoud, A. El Tabal, M. Nady 3.5. The N e, Li + ad Li + 2 as a fuctio of the lithium vapor desity The growth rate of the N e, Li + ad Li + 2 as a fuctio of the lithium vapor desity is show i Fig. 7. The curves show almost the same behavior ad the atomic io Li + is greater tha the molecular io Li + 2. This behavior is due to the rate coeciet of photoioizatio ad Peig ioizatio processes beig greater tha the rate coeciet of the associative ioizatio process. Skederovic et al. [5] reported that, after the absorptio of a resoat photo, Li(2s) + hν Li(2p), ios ca be created by followig paths. The rst is a two photo ioizatio of the 2p level Li(2p) + 2hν Li + + e. The secod path is eergy poolig to the 3d or 3p level followed by photoioizatio: Li(2p) + Li(2p) Li(3d, 3p) + Li(2s), Li(3d, 3p) + hν Li + + e. The third oe is radiatio-assisted Peig ioizatio Li(2p) + Li(2p) + hν Li(2s) + Li + + e. O the other had, photoioizatio ca play a remarkable role at a low ioizatio degree of the medium, whe the basic mechaism of the Li(2p, 3d) populatio are eergy-poolig [6, 7] collisios: Li(2p) + Li(2p) Li(3d, 3p) + Li(2s). Through this process electro excitatio prevails whe k EP N(2p) > k m e. As far as we kow, there is o deite value for k EP for lithium. The cosidered reactio is a edothermic oe. For the eergy poolig reactio with resoat Cs atoms with a similar eergy gap ( E p 0.18 ev) the rate coeciets are of a order k EP cm 3 s 1 [12]. I fact, the two processes, (superelastic trasfer to the free electros ad eergy poolig collisios) work i tadem to create quasicotiuous populatio iversios. The idirect eergy trasfer through electros is ideed faster ad more eciet compared with direct eergy poolig. However, oce a high populatio of states 3p ad 3d is achieved, the radiative loss icreases sice these states have short radiative lifetimes [57]. 4. Coclusios We have carried out a computatioal study o the i- uece of collisioal ioizatio ad collisioal excitatio processes o the electro eergy distributio fuctio, as well as the molecular ios ad atomic ios i laser- -excited lithium vapor. I particular, the time evolutio of the electro desity, the atomic ad the molecular io at dieret values of lithium desity was ivestigated. The results claried that there is a rapid growth of free electros due to two-photo ioizatio of resoace level ad laser iduced ioizatio. The electros created by these iitial processes rapidly gai eergy through superelastic collisios with laser sustaied resoace state populatio, eectively quechig that state, as well as the eergy poolig collisios which play role i populatig the 3p ad 3d states. I geeral, it is show that for a reasoable amout of laser eergy tued to the rst resoace state of lithium a rapid ioizatio is possible through photoioizatio ad collisioal ioizatio processes ad lithium plasmas of high desity could be produced. Refereces Fig. 7. Variatio of electros desity N e, atomic ios Li + ad molecular ios Li + 2 desity with lithium vapor desity N 0 at 20 s from the laser pulse. [1] A.N. Klyucharev, Phys. Usp. 36, 486 (1993). [2] T.B. Lucatorto, T.J. McIlrath, Phys. Rev. Lett. 37, 428 (1976). [3] D. Veza, C.J. Sasoetti, Z. Phys. D, At. Mol. Clust. 22, 463 (1992). [4] I. Labaza, S. Milosevic, Eur. Phys. J. D 8, 41 (2000). [5] H. Skederovic, I. Labaza, S. Milosevic, G. Pichler, Phys. Rev. A 62, (2000). [6] N.A. Gorbuov, A.S. Melikov, I. Smurov, I. Bray, J. Phys. D, Appl. Phys. 34, 1379 (2001). [7] Ch. He, R.A. Berheim, Chem. Phys. Lett. 190, 494 (1992). [8] V. Horvatic, Fizika A 12, 97 (2003). [9] T. Stacewicz, Acta Phys. Pol. A 84, 259 (1993). [10] A. Ekers, M. Glodz, J. Szoert, B. Bieiak, K. Froc, T. Radeltiski, Eur. Phys. J. D 8, 49 (2000). [11] R. Beuc, M. Movre, V. Horvatic, C. Vadla, O. Dulieu, M. Aymar, Phys. Rev. A 75, (2007). [12] F. de Tomas, S. Milosevic, P. Verkerk, A. Fioretti, M. Allegrii, Z.J. Jabbour, J. Hueekes, J. Phys. B, At. Mol. Opt. Phys. 30, 4991 (1997). [13] V. Horvatic, T. Correll, N. Omeetto, C. Vadla, J. Wieforder, Spectrochim. Acta Part B 61, 1260 (2006). [14] R.M. Measures, J. Appl. Phys. 48, 2673 (1977). [15] R.M. Measures, P.G. Cardial, Phys. Rev. A 23, 804 (1981).

7 Collisioal Ioizatio i Lithium Vapor [16] T. Stacewicz, G. Topulos, Phys. Scr. 38, 560 (1988). [17] T. Stacewicz, W. Latek, Phys. Scr. 38, 658 (1990). [18] T. Arisawa, Y. Maruyama, Y. Suzuki, K. Shiba, Appl. Phys. B 28, 73 (1982). [19] I.E. Olivares, A.E. Durate, E.A. Saravia, F.J. Durate, Appl. Opt. 41, 2973 (2002). [20] M. Saleem, S. Hussai, M. Raq, M.A. Baig, J. Appl. Phys. 100, (2006). [21] N.N. Bezuglov, A.N. Klyucharev, V.A. Sheverev, J. Phys. B, At. Mol. Phys. 20, 2497 (1987). [22] M. Aymar, E. Luc-Koeig, F. Combet Faroux, J. Phys B, At. Mol. Phys. 9, 1279 (1976). [23] A.V. Hellfeld, J. Caddick, J. Weier, Phys. Rev. Lett. 40, 1369 (1978). [24] S. Geltma, J. Phys. B 10, 3057 (1977). [25] Y.E.E. Gamal, M.A. Mahmoud, H.A. Abd El Rahma, J. Quat. Spectrosc. Radiat. Trasfer 90, 29 (2005). [26] M.A. Mahmoud, J. Phys. B, At. Mol. Opt. Phys. 38, 1545 (2005). [27] L. Vries, A.H.M. Smeets, Phys. Rev. A 22, 940 (1980). [28] W.H. Drawi, Raport Euratom CEAFC, 1967, p. 38.