CIT and QIT with a Periodic Impulsional Potential

Transcription

1 Adv. Studies Theor. Phys., Vol. 6, 2012, no. 6, nd with Periodic Impulsionl Potentil S. Seddighi Chhrborj Islmic Azd University, Science nd Reserch Brnch Deprtment of Mthemtics, Bushehr, Irn Yousof Gheisri Islmic Azd University Bushehr Brnch, Bushehr, Irn Abstrct The purpose of this rticle is the comprison of cylindricl ion trp supplied by periodic impulsionl potentil with udrupole ion trp. To compute the five stbility regions for the cylindricl ion trp () nd udrupole ion trp () in the plne we use the Runge- Kutt method with the fifth order derivtive pproximtions. The first up to five stbility regions obtined in this rticle for compred with the first up to twelve stbility regions of rticle reported by S. Seddighi Chhrborj nd S. M. Sdt Kii in Keywords: Confinement, Ions, Cylindricl ion trp, Qudrupole ion trp, Impulsionl potentil, Fifth order Runge-Kutt method, Stbility regions, Ion trjectory 1 Introduction Ion trp mss spectrometry hs developed though severl stges to their current stge reltively high performnce nd incresing populrity. Qudrupole ion trp () invented by Pul nd Steinwedel hs been widely pplied to mss spectrometry [2, 3, 6, 4], ion cooling nd spectroscopy, freuency stndrds, untum computing, nd so on. To pply to vrious objectives, vrious geometries of ion trp for the mss spectrometer hs been suggested. An ion trp mss spectrometer my incorporte Penning trp, Pul trp or the Kingdon trp. The Orbitrp, introduced in 2005, is bsed on the Kingdon

2 286 S. Seddighi Chhrborj nd Y. Gheisri trp. The two most common types of ion trps re the Penning trp nd the Pul trp (udrupole ion trp). Other types of mss spectrometers my lso use liner udrupole ion trp s selective mss filter. Computtion of stbility regions is of prticulr importnce in order to design nd ssemble n ion trp. Anlyticl nd mtrix methods, on one hnd, hve been widely used to clculte the stbility regions. A udrupole ion trp mss nlyzer with simplified geometry, the cylindricl ion trp (), ws shown to be well-suited to use in miniture mss spectrometers nd even mss spectrometer rrys. Experiments with single miniture showed cceptble resolution nd sensitivity, limited by the ion trpping cpcity of the miniture device. The hs received much ttention of number of reserch groups becuse of severl merits. The is esier to fbricte thn the Pul ion trp which hs hyperbolic surfces. And the reltive simplicity nd smll size of the mke it n idel cndidte for minituriztion. With these interests, mny groups in, such s Purdue University nd Ok Ridge Ntionl Lbortory hve reserched on the pplictions of the to miniturized mss spectrometer. 2 Study the motions of ion voltge inside Figure (1) show the electronics configurtion of rectngulr, tht is to sy combintions of d.c. voltge, U dc, nd n lterntive voltge V c f(t) with f(t) =V 0 cosωt/(1 kcos2ωt) with 0 k<1is the modultion index prmeter for the ring nd end-cps electrodes, Ψ 0 = ±(U dc V c cos Ωt/(1 kcos2ωt)) with 0 k<1 (1) then the potentil distribution inside the with r 1 = z 1 t ny point of circle of rdius r cn be written s: Ψ(r, z) = i 2Ψ 0 J 0 (m i r) m i r 1 J 1 (m i r 1 ) ch(m i z) ch(m i z 1 ). (2) Here J 0 nd J 1 re the Bessel functions of first kind, of order 0 nd order 1, respectively, ch is the hyperbolic cosine function, m i r is roots of eution J 0 (m i r)=0,u dc nd V c re the mplitudes nd the rdio freuency (rf) drive freuency. Assuming tht r1 2 =2z2 1, then the electric field in cylindricl coordintes (r, z, θ) inside the with r1 2 =2z2 1 cn be written: (E r,e θ,e z )=E = Ψ(r, z). (3) Here is grdient. The bsic eution of the ion motions of mss m nd electric chrge e into the trp tking into ccount the effect of dmping force

3 nd with periodic impulsionl potentil 287 my be treted independently: d 2 u dξ (α 2χ cos 2ξ/(1 kcos4ξ)). 2 i d 2 v dξ +(α 2χcos 2ξ/(1 kcos4ξ)). 2 i with the following substitutions: J 1 (λ i u) J 1 (λ i ). ch(λ iv) z ch(λ 1 i r 1 ) J 0 (λ i u) J 1 (λ i ). sh(λ iv) z ch(λ 1 i r 1 ) = 0, = 0, ξ = Ωt 2, m ir 1 = λ i, r = u, z = v, α = 8 e r 1 r 1 m U dc r1ω,χ=4e 2 2 m V c r1ω, 2 2 where α nd χ re the trpping prmeters, λ i = m i r 1 is roots of eution J 0 (m i r 1 )=0. End plte electrode Ring electrode z 1 r 1 U dc + V ccosωt Figure 1: Schemtic view of cylindricl ion trp (). 3 Results 3.1 Stbility regions Fig. (2) up to Fig. (7) present the stbility regions of cylindricl ion trp () nd udrupol ion trp the - pln for different k, s. We observe tht the pex of the stbility prmeter styed constnt, but the higher limit of decrese substntilly when k increse form 0 to 1. 4 Discussion nd conclusion In this rticle we used the higher order of Runge-Kutt method to compute the five stbility regions for cylindricl ion trp nd udrupole ion trp

4 288 S. Seddighi Chhrborj nd Y. Gheisri () X XI X XI VII XII VII XII V III VIII V V III VI IX III VI IX I II IV I II IV Figure 2: (): The stbility regions I until XII for the cylindricl ion trp with k =0,: The stbility regions I until XII for the udrupole ion trp with k =0. () Figure 3: The first stbility region for the nd with k =0,(): The first stbility region for, : The first stbility region for the nd.

5 nd with periodic impulsionl potentil 289 () Figure 4: The second stbility region for the nd with k =0,(): The second stbility region for, : The second stbility region for the nd. () Figure 5: The third stbility region for the nd with k =0,(): The third stbility region for, : The third stbility region for the nd.

6 290 S. Seddighi Chhrborj nd Y. Gheisri () Figure 6: The forth stbility region for the nd with k =0,(): The forth stbility region for, : The forth stbility region for the nd. () Figure 7: The fifth stbility region for the nd with k =0,(): The fifth stbility region for, : The fifth stbility region for the nd.

7 nd with periodic impulsionl potentil 291 with ccurcy enough. In this computtion, the size of the integrtion step ws considered s The first stbility regions obtined in this rticle compred with the first stbility regions of rticle reported by S. Seddighi Chhrborj nd S. M. Sdt Kii in 2010 [6]. The results of this pper showed tht, the pex of the stbility prmeters z styed the sme nd the pex of the stbility prmeters z decrese when k increse from 0 to 1. References [1] F. Kshnin, S. Nouri, S. Seddighi Chhrborj, A. B. Mohd Rizm, Int. J. Mss Spectrom. 303 (2011) 199. [2] S. M. Sdt Kii, J. Andre, Y. Zereg, G. Brincourt nd R. Ctell, Study of udrupole ion trp supplied with periodic impulsionl potentil, Int. J. Mss Spectrom. nd ion processes. 107 (1991), pp [3] S. M. Sdt Kii, Y. Zereg, G. Brincourt, R. Ctell nd J. Andre, Int. J. Mss Spectrom. nd ion processes. 108 (1991), pp. 65. [4] S. M. Sdt Kii, Confinement of ions in rdio freuency udrupole ion trp supplied with periodic impulsionl potentil, Int. J. Mss Spectrom. 188 (1999), pp [5] S. M. Sdt Kii, S. Seddighi Chhrborj, M. R. Abu Bkr nd I. Fudzih, J. Anl. At. Spectrom., 26 (2011) pp [6] S. Seddighi Chhrborj nd S.M. Sdt Kii, J. Mss Spectrom., 45 (2010) pp [7] S. Seddighi Chhrborj, S. M. Sdt Kii, M. R. Abu Bkr, I. Ziein nd I. Fudzih, Int. J. Mss Spectrom.,(2011), DOI: /j.ijms Received: September, 2011