lon Acceleration in Laser Wakefield

Transcription

1 J. Plasma Fusin Res. SERES, Vl.4 (2001) ln Aeleratin in Laser Wakefield TO Hiraki*, BAKHTAR Mhammad, MA Masashi, YUGAM Nbru and NSHDA Yasushi Energy and Envirnmental Siene, Graduate Shl f Engineering, Utsunmiya U niversity, U tsunmiya ' Japan (Reeived: 5 Deember 2000 / Aepted: 16 August 2001) Abstrat A prtn and/r heavy in aeleratr utilizing the transverse eletri field f the laser wakefield is prpsed. We have perfrmed the simulatin in the prtn aeleratin emplying the transverse laser wakefield. The results shw that the energy gain per ne stage is nt large enugh but the aeleratin gradient is several hundred times larger than the nventinal prtn aeleratin sheme. The prtn aeleratin by the transverse wakefield is mre effetive in lwer prtn energy. t will be pssible t make the mpat prtn aeleratr with this methd. Keywrds: mpat prtn/in aeleratr, plasma based aeleratr, high pwer laser, laser driven wakefield, plasma wave 1. ntrdutin There has been urrently great interest in the appliatin f the highly energeti eletrns generated frm the interatin f an intense ultra-shrt laser pulse with a plasma. Aeleratin f eletrns by an eletrn plasma wave has been f nsiderable attentin beause it has ptentiality t exeed the aeleratin gradient muh larger than that f a nventinal radi frequeny (rfl linear aeleratr. Several methds have been prpsed fr high energy partile aeleratrs with ultrahigh aeleratin gradients with the help f the plasma wave generated by an intense mirwave r laser, suh as the plasma beat wave aeleratr, laser wakefield aeleratr (LWA) [1] in 1979, Ve x B aeleratr [2] and self-mdulated laser wakefield aeleratr [3]. Present day high pwer laser systems with the hirped pulse amplifiatin tehnique an prdue an ultra shrt pulse with an intensity well abve 1018 Wm2 and enable us t perfrm prf-f-priniple experiments f laser driven plasma aeleratrs. Reently it has been reprted that eletrns aelerated up t the energy f 300 MeV by the laser wakefield and the plasma wave have been bserved t4-61, but plasma based eletrn aeleratrs are t premature t be used as a real linear llider. On the ther hand, the study f aeleratin f prtns and/r ins has a lnger histry than that f eletrn aeleratin. Mre reently the "eletrn ring aeleratr" had been studied until early 1970's in USSR, USA, Germany and Japan [7]. The studies have terminated withut remarkable suesses. The investigatin n the prtn/in aeleratrs has nt been s ative fr several deades in spite f a high demand fr in aeleratrs. Suh develpments f laser systems, hwever, have prmted an interest in mpat in aeleratrs with varius appliatins fr high energy physis and medial field. The abve mentined plasma based aeleratin shemes whih have suessfully aelerated eletrns, annt be emplyed fr the aeleratin fprtns and ins with energy less than 1 GeV, sine the phase velity f the plasma wave is muh faster than the partile's velity beause f their heavier mass than eletrns. Several ideas fr by The Japan Siety f Plasma Siene and Nulear Fusin Researh 335

2 l H. et al., n Aeleratin in Laser Wakefield aelerating prtn/in based n the plasma wave have gt an attentin inluding the bakward Ramman sattering [8] and Alfv6n wave [9] whih slw waves are t trap the aelerated partiles. An aeleratin methd fr aelerating prtn beam using lasers and plasmas is an aeleratin methd using a transverse mpnents f the laser wakefield exited by the interatin f the high intense ultra shrt laser pulse with the plasma. This aeleratin methd has been already prpsed and reprted in the simulatins that prtns are aelerated by transverse laser wakefield [10]. The simulatins in Ref. [10] have been perfrmed fr the ne-dimensinal mtin f prtns, i.e. the transverse diretin. n this paper, we perfrm the simulatins extended t tw-dimensins and disuss in detail the behavir f prtns in the laser driven wakefield and the phase mathing between the prtn beam and the transverse wakefield. 2. Thery An eletrn plasma wave (EPW) is exited by the pndermtive fre f the EM wave exiting a density sillatin with the plasma frequeny in an underdense plasma. The EPW with large amplitude driven by the laser pulse has bth transverse and lngitudinal mpnents. The transverse mpnent is indued bth by the tempral and radial prfiles f the laser pulse and the lngitudinal mpnent rrespnds t the lngitudinal mtin indued by the tempral prfile f the pulse. The plasma eletrns are desribed by ld fluid equatins with the pndermtive ptential term indued by the spatial and tempral prfiles f the laser pulse. Assuming the linear apprximatin, in whih the eletrn density perturbatin is small mpared with the equilibrium eletrn density and that ins are fixed, the equatins an be slved. The lngitudinal mpnent f the density perturbatin 6n, rrespnds t lngitudinal eletrn sillatins. The eletri field E, dedued by the Pissn equatin is als lngitudinal. The transverse ntributin 6n. rrespnds t ylindrial eletrn sillatins assiated with the radial eletri field E. Eah mpnent f a linear EPW exited by the intense laser with Gaussian radial prfile and a Gaussian tempral distributin, an be expressed [11,12] as /lr.t E,= Akps(arr-kef expl-:' rl. w' u,= ffisin (arr - rz)exp ( #) (l) (2) n Laser fr plasma prdutin gtrttruttl N rntttdtrntn L Ylllltt tan?=w/ :4 / (q :n velity) r, = ^ Fig. 1 Shemati diagram fr the prtn aeleratin by the laser driven wakefield. wltn Laser fr wakefield vt--s +: - (9ln /.. A=rtr a^r ex[ -%' -!t-' " ' 412 m"a2 where 1.u* is the maximum laser intensity, u is the pulse duratin at FWHM, w6 is the spt radius f the EM wave at fus, a4 is the plasma frequeny, m" is the rest mass f the eletrn, and e is the dieletri nstant in vauum. The rati f the tw mpnents f the density perturbatin n the laser axis is given by 6n,/5n"= (Ll nws)2, wher p = 2nlap is the wavelength f the exited plasma wave. Thus, the eletrn density perturbatin an be treated as lngitudinal when $pi ftws )) ),0 and radial when 7tw0 11 X. [13,14J. n the nventinal LWA, the transverse field is strnger than the lngitudinal eletri field, sine EPW exitatin takes plae mainly in the radial regin. We prpsed the in aeleratin by emplying the transverse wakefield, i.e. the in beam is injeted int the wakefield frm the radial diretin. Depending n its relative phase q = 6r - ftz with respet t the wakefield, an injeted in is aelerated r deelerated by E. and fussed r defused by E,. Thus, as shwn in Fig. whih represents the in mtin in the frame f the wakefield, the mst effetive aeleratin urs when the in always stays in the aeleratin phase during the wakefield. The laser driven wakefield useful fr the harged partile aeleratin is limited within the spt size, sine it dereases expnentially in the radial 336

3 th. et al., n Aeleratin in Laser Wakefield diretin as seen in Eqs. (1) and (2). The nditin fr the mst effetive aeleratin, whih require phase mathing between the transverse wakefield and the in beam, is given by vit, = 2w, where v1 is the in velity arss the area where the wakefield is exited and Z = 2n/rt, is the perid f wakefield. This nditin an be satisfied by adjusting the plasma density, sine ar depends n the plasma density, ar= (n"lel2lqm)tt2.the plasma density required fr the apprpriate in aeleratin is rewritten as n.1"rn-t =6x l0r7 t' MeV uw'^ltml' (3) where q is the initial in energy and M is the rati f the in mass t the prtn mass. n the ideal ase in whih the abve nditin is satisfied and the effet f lngitudinal wakefield is negligibly small, the maximum energy gain is btained as r=2, [n* E,dr =2A(l -er)(ev). (4) The effiient A is a funtin f the prdut a4r and is maximum when a)? = i7. F. the prtn energy q - MeV, fr examples, the maximum energy gain is expeted when the plasma density is n" = 16t m-3 and the laser pulse duratin is z = 250 fse. 3. Simulatin Results The aeleratin mehanism f heavy in is the same as that f prtn in priniple in spite f the differene between the prtn and heavy in, i.e. mass 'and harge state. Fr the simplest disussin, let us nsider the energy gain fr the prtn aeleratin utilizing the laser-driven transverse wakefield. We have perfrmed tw-dimensinal time dependent simulatins based n the mmentum equatin in rder t study the behavir f prtns in the laser wakefield in detail. Eah small displaement f prtn fr the time step is alulated by the Time enter Leap Frg methd [15]. The final prtn energy is btained by repeating the predure until the prtn passes thrugh the wakefield. The simulatin has been perfrmed in the ase where the laser fr the exitatin f EPW has the parameters f wavelength 1, = 800 nm, and maximum pwer P = TW fused int the spt size 2w - l0 pm, rrespnding t a Ti-Sapphire laser system. Assuming that the prtn is injeted in the +r diretin, we need t take int aunt the dependene f the eletri field E, n the relative phase E fr btaining mre effiient aeleratin f the prtn by the laser wakefield. Thus, in the simulatins the prtn is injeted int the wakefield when its phase is e = x. Figve 2 represents the typial simulatin result fr the prtn with an initial energy e, = 1 MeV, where the plasma density is n. = 1016 m-3 satisfing vit, = 3w. n this simulatin, the laser pulse duratin is assumed t be r = 250 fse, sine the wakefield amplitude is maximum at ar = "Ji as abve-mentined. The slid and dashed lines represent respetively the prtn energy and the eletri field f the wakefield ating n the prtn while the prtn travels thrugh the wakefield. t is evident frm Fig. 2 that the prtn ntinuusly feels the ' > g llj SO (a) Er,,l tl Radius (in w units) a fi.s 15p,q 10ir e.9d 58]u tr (b) E, /^ 1, /l, /l t l tl -:./ tl Radius (in w units) 2.5 E -(, r) 1.5 il E,) ']l) 0.5 E ) 0lU Fig. 2 Variatin f the prtn energy and the eletri field f wakefield aelerating prtn as the prtn travels. (a) and (b) represent the radial and axial mpnent f the prtn's mtin. Slid and dashed lines are the prtn energy gain and the eletri field f the wakefield, respetively

4 th. et al., n Aeleratin in Laser Wakefield aeleratin fre in the wakefield and is aelerated with the energy gain f abut 175 kev. Cnsidering that the aeleratin length is 3w =lj pm, the aeleratin gradient is estimated t be 12 GeV/m, whih is muh larger than the nventinal rf aeleratr. On the ther hand, it is bvius frm Fig. 2 that the lngitudinal eletri field is ten times smaller than the transverse ne and that the prtn is aelerated little in the axial diretin. Negleting the nnlinear effet, we an expet that the prtn is aelerated t high energy in prprtin t the laser pwer, beause E. is diretly prprtinal t the amplitude f the laser wakefield and s the inident laser pwer. f the laser with pwer l0 TW is used fr the exitatin f the wakefield, the prtn with the same injetin energy an be aelerated with the energy gain f abut 1.7 MeV. The amplitude f the wakefield depends n the initial prtn energy, sine the mean plasma density need t be adjusted t satisfy the phase mathing nditin between the laser wakefield and the prtn. t is imprtant t perfrm the simulatin f the dependene f the energy gain n the initial injetin energy. The simulatin result is shwn in Fig. 3, where the laser pulse duratin is 100 fse and ther parameters are the same as the abve simulatin. t is seen that this aeleratin methd emplying the transverse wakefield is nt suitable fr the high energy prtn aeleratin. t is readily shwn frm Eq. (2) that the wakefield amplitude dereases expnentially beynd the maximum.r:-. pint Cpt =!2. Thus. the wakefield aeleratin fr prtns is nt adequate fr the high energy partiles. t is nt als easy t exite the wakefield with large amplitude in high density regin. Figure 4 shws the energy gain as a funtin f the plasma density. The mst effetive aeleratin urs at the plasma density whih satisfies the mathing nditin Eq. (3). The prtn traverses the deeleratin phase f wakefield, sine the sillatin perid f plasma wave bemes large with inrease f the plasma density. t turns ut frm Fig. 4 that the mathing nditin an be satisfied by adjusting the plasma density. Finally, we prpse the mpat prtn aeleratr r. (E 6-10 LU,/,/ _F nitial Energy (MeV) Fig. 3 Prtn energy gain as a funtin f the initial energy. The laser parameters are ).= 800 nm, P= 1 TW. and u = 100 fse CD g LU L nitial Energy: 1 MeV fre: 1.0 x 1016 /ml 1.5 x l016 /m: 0.8 x 1016 /ml 2.0x1016 /mz Radius (in w units) Fig. 4 Dependene f prtn energy n plasma density. 338

5 th. et al.. n Aeleratin in Laser Wakefield emplying the abve-mentined aeleratin methd. n rder t realize this aeleratr, the multistage aeleratin has t be used, sine the energy gain per ne stage is small. We expet that this methd an be realized by preisely arranging the psitin and the interval f mirrrs. 4. Summary We have prpsed a prtn aeleratin methd and the design f the aeleratr emplyed this methd mentined in this paper. Pssibility f the prtn aeleratin due t the laser driven wakefield has been nfirmed frm the simulatins. Thus, it has been demnstrated that this aeleratin methd an be used fr the heavy in. The energy gain per ne stage is nt large, the aeleratin gradient, hwever, is several hundred times larger than a nventinal rf aeleratin sheme. We expet that the mpat prtn aeleratr emplying this sheme an be realized by using the present apparatuses. The inrease f laser pwer an lead t inreased gain in prtn energy per stage at the st f the aeleratr's mpatness. Suh a prtn aeleratr using a huge laser system annt be regarded as a mpat aeleratr. Similar t the eletrn aeleratr whih the lngitudinal mpnent f wakefield traveling with the inident laser is used, there are sme limitatins in the aeleratr with this aeleratin sheme. 1) The radius f aelerated beam annt be larger than the laser spt size.2) The length f the beam will be smaller than the pulse f laser. Hwever, we nsider that these prblems may be slved by using sme parallel lasers. There seems t be sme rm fr making imprvements inluding new aeleratin shemes. Mre detailed disussins are required fr further imprvement f the aeleratin effiieny. Aknwledgement This wrk is supprted in part by the Grant-in-Aid fr Sientifi Researh frm the Ministry f Eduatin, Siene, Sprts and Culture, Japan. Referenes tll T. Tajima and J.M. Dawsn, Phys. Rev. Lett.43, 267 (1979). l2l Y. Nishida, M. Yshizumi and R. Sugihara, Phys. Lett. 105A, 300 (1984), Y. Nishida, M. Yshizumi and R. Sugihara, Phys. Fluids. 2E,1574 (1985). t3l N.E. Andreev, L.M. Grbunv et al., JETP Lett. ss,571 (1992). t4l H. Dewa et a/., Nul. nst. and Meth. A410, 357 (l998). t5l D. Bernard er a/., Nul. nst. and Meth. L432,227 (1999). [6] J.R. Marqu6s et al., Phys. Rev. Lett. 76, 3566 (1996), C.W. Siders et al., Phys. Rev. Lett. 76, 3570 (1996). t7l M. Reiser, Seminar n New Trends in Partile Aeleratin Tehniques, Capri (1982). t8l A. Ogata and T. Katsuleas, Pr Wrkshp n Advaned Aeleratr Cnepts, AP Cnf. 472, 551 (1999). t9l B. Rau and T. Tajima, Phys. Plasmas 5, 3575 fl998). ll0l M. Bakhtiari, H. lt et al., Jpn. J. Appl. Phys. 39, L1097 (2000). l] E. Esarey, P. Sprangle et al.,eee Trans. Plasma Si. 24, 252 (1996). ll2l F. Amiranff et a/., Phys. Rev. Lett. 81, 995 (1998). t13l J.R. Marquds et al.,phys. Plasmas 5,1162 (1998). [14] F. Drhies, F. Amiranff et a/., Phys. Plasmas 6, 2903 (1999. t15l C.K. Birdsall and A.B. Langdn, Plasma Physis via Cmputer Simulatin (MGraw-Hill, NY 1985). 339