Modelg nd Anlysis of SLED LI L,, FANG WenCheng,WANG Cho-Peng,GU Qing * Shnghi Institte of Applied Physis, Chese Ademy of Sienes, Shnghi 8, Ch University of Chese Ademy of Siene, Beijg 49, Ch Abstrt SLED is ril omponent for C-bnd mirowve elertion nit of SXFEL. To stdy the behvior of SLED (SLAC Energy Dobler), mthemti model is ommonly bilt nd nlyzed. In this pper, new method is proposed to bild the model of SLED t SINAP. With this method, the prmeters of the two vities n be nlyzed seprtely. Also it is sitble to stdy prmeter optimiztion of SLED nd nlyze the effet from the prmeters vritions. Simltion reslts of or method re lso presented. Key works SLED, Mthemti model, Energy mltiplition ftor, oplg oeffiient * Correspondg thor(emil: gqing@sp..n)
Introdtion A ompt soft X-ry Free Eletron Lser (SXFEL) fility is presently plnned t Shnghi Institte of Applied Physis, CAS [], nd some nlytil modelg nd simltion reserh is ongog. The high power RF system for SXFEL omprises RF power sore, onstnt grdient elertg strtre nd wvegide omponents For gettg high onstnt grdient field the elertg strtre, the existg klystron power sore of 5 MW nnot meet the power reqirement of the field trget, nd plse ompressor is reqired to mltiply the power from the klystron []. There re different types of plse ompressor whih stisfies the reqirements. In or se, SLED type plse ompressor is proposed for the C-bnd RF system SXFEL. To stdy the performne of the plse ompressor nd nlyze the prmeters, n effetive wy is bildg mthemti model, then the model bsed simltions n be implemented to verify the design. In this pper, mthemti model of the SLED presented, whih is powerfl tool for ontrol system development. With this model, the prmeters of SLED re optimized nd the effets of the prmeters vritions re nlyzed orrespondgly. Modelg of the SLED. Strtre of the SLED SLED is RF plse ompressor whih ws firstly vented by Frkers Z t 974[4].The SLED is omposed of two identil high Q-ftor vities tthed to db opler. The strtre of SLED is shown Fig.. The performne of SLED is determed by the strtre of the storge vities. The energy mltiplition ftor M n be expressed s: M e T T v g g v () Where T is the fillg time of the elertg strtre, T is the fillg time of the vity., v T T ln g, g is the grdient of the grop veloity long the elertg strtre. e T vity oplg oeffiient. pt pt Fig. The strtre of the SLED vity vity. Modelg SLED sg S, is the Bsed on referenes [][4][5], model of SLED n be onstrted by the energy onservtion. However the models bsed on these methods ont only the mplitde formtion of the pt nd pt signl, no phse formtion n be refleted, nd not sitble for the se of two symmetry vities. In the pper the tehnology of two ports terml network is sed to model the behvior of the vity nd pt opler. The vity itself is eqivlent to RLC irit, nd the pt opler n be presented by n idel trnsformer s show Fig..
Z From trnsimister :n Fig. The eqivlent irit of SLED Z From trnsimister Z v L C R forml of refletion oeffiient n be presented s [6]: S Z Z v () Zv Z s Where Z v Z, s s Q, Q RC is the vity nloded qlity ftor Q R nd is the oplg oeffiient. Q n Z ext X= X=L Fig. Cvity model t the trnsmission le side. Usg the defition of refletion oeffiient for two ports mirowve network Fig., the The pt voltge Sbstittg the impedne Z v to eqtion (), then eqtion () n be represented by the differentil eqtion between the pt nd pt voltge d d d d () nd pt voltge re modlted se wve with the freqeny of, the phse nd mplitde formtion is the most sefl prt tht we shold onsider, so, they n be written to phsor s jt e, Where the e it nd re the omplex mplitde s vetors whih ont the mplitde nd phse formtion, whih n be expressed by their rel d The eqtion () n lso be expressed by the trnsfer fntion s s s s nd imge prts. Pt the phsor defition to the eqtion bove nd ssme defe the detng s, nd. If the detng is smll thn workg freqeny, we will get the pproximtion of. Normlly, the voltge hnges slowly, so the item for the seond derivtion is lwys smller thn others. So the eqtion () n be simplified s d j j (4) j j sled vity s s (5) s s De to the db power divider between the pt nd pt ports, the reltionship between the pt nd pt of the SLED for eh vity n be present respetively s j sled _ (6) j e j s
Sbmitted to Chese Physis C sled vity s e s s j sled _ (7) j j From the strtre of the SLED s shown Fig., eqtions (6) nd (7), the SLED model n be the pt signl of the SLED is formed by the onstrted s Fig.4 refleted signls of the two vities. Bsed on the s SLED_I SLED_Q pi/ _for_r _ref_r _for_i _ref_i _S -K- -K- -Kpi/ _for_r _for_i _S _ref_r _ref_i -K- SLED_I SLED_Q Fig.4 The SLED mode slts of simltion by SLED model Bsed on previos theoretil nlysis, we hve rried some simltions by the SLED model to optimize prmeters.. Stdy of the workg pot of the SLED The oplg oeffiient nd qlity ftor Q of the vity domte the performne of the RF plse ompressor, sh s the energy mltiply ftor nd power effiieny. The prmeters relevnt to the lltion of the energy mltiply ftor nd RF power effiieny is list tble. Usg the prmeters tble nd by tng the oplg oeffiient nd qlity ftor Q, the tendeny of the energy mltiply ftor nd RF power effiieny n be mpped, s shown Fig. 5. The power effiieny nd the energy mltiply rese with the qlity ftor nd the pt oplg oeffiient. Tble lltion RF freqeny Key prmeters for Energy g ftor Aelertg strtre Fillg time RF plse length verse time 57MHz 7 ns.5 s. s The optiml prmeters re deided by the prtil reqirements. The pot on the stright le the Fig.5 shows the optiml opertg pot where both nd Q re smll when the energy mltiply ftor reh the mximm vle. Aordg to the simltion reslts, the opertg pot is seleted when qlity ftor Q 6 nd the oplg oeffiient 7.. And the orrespondg energy mltiply ftor is.99. workg pot ( 8 Compred with the origl Q, 8. 5 ), the fbrition is esier nd the energy mltiplition ftor ws reded by one.%.
9 8 7 M X= 6 Y= 7 Level=.99.9.85.8 ftor error of the vity is shown Fig. 6(). The design vle is not optiml vles for gettg the mximm energy mltiplition ftor whih grees well with nlysis the bove setion. 6.75 8 M / M 5.7 6 -.% 4.65 4..4.6.8 Q x 5 f(khz) -4.% 9 8 7 X= 6 Y= 7 Level=.69795 7% 68% 66% 64% 6% - -4-6 -8-8 -6-4 - 4 6 8 f(khz) -6.% -8.% 6 6% 58% b M/ M -.% 5 56%.5 -.4% 4..4.6.8 Q x 5 54% 5% 5%.5 -.6% -.8% -.% Fig.5 The energy mltiply ftor nd RF power effiieny mpped with the nloded qlity ftor Q nd oplg oeffiient. Corse tng before opertion In prtie, more ttentions re pid on the energy mltiply ftor. There re some freqeny devition from the opertg freqeny de to the tempertre drift, some oplg oeffiient devition from the desired vle nd the nloded qlity ftor error of the vity de to mhg tolerne. Usg the SLED model, we n get the Energy mltiplition ftor hnge sed by the vity freqeny devition, the pt oplg oeffiient devition nd the nloded qlity ftor flttion, s shown Fig.6. Fig. 6() nd (b) shows tht the energy mltiplition ftor deles with the resg of freqeny devition nd the oplg oeffiient fr from the desired vle. The ffet sed by the nloded qlity Q -.5 - -.5 - - -.5 - -.5.5.5 4 x 4 - - - M/ M -4-4 - - - 4 Q x 4 Fig. 6 The Energy mltiplition ftor hnge with the vity freqeny devition (), the pt oplg oeffiient devition (b) nd nloded qlity ftor Q ). flttion ( 7., 6 -.% -.4% -.6% -.8%.5%.% -.5% -.% -.5% -.% -.5% -.% Before the tl opertion, the RF plse ompressor shold be tned to mted the
energy mltiply ftor flttion less thn %. Aordg to the Fig.6, the freqeny shold be ontrolled the rnge of khz, the ry of the the rnge of, whih is identil with the reslt Fig. 5() nd the Q the rnge of±x 4. Se the oplg oeffiient nd Q nnot be tned drg the opertion, so drg the old test they shold be tng n optiml rnge order to get high preision, sh s ±.5 for the oplg onstnt nd±x for Q order to tt the fltness of the energy g ftor.%.. Fe tng drg opertion After old test, the oplg oeffiient nd nloded qlity ftor re tned t the proper vles nd drg the opertion of the RF plse ompressor, they re fixed nd nnot be tned. There is only one prmeter, freqeny devition, n be hnged nd tned by ontrollg the tempertre oolg wter. Drg the opertion, s the reqirement of the fltness of the energy g ftor is less thn.%, the freqeny of the vity shold be ontrolled with ±. khz. As the tempertre expnsion oeffiient of the SLED vity is b 6 khz/ C, the wter tempertre shold be ontrolled with ±. C. f(khz) 5 4 - - - -4 M / M -5-5 5 f(khz) x -4 - -.5 - -.5 - -.5 Fig. 7 The Energy mltiplition ftor hnge with the vity freqeny devition Aordg to the nlysis bove, the prmeters reqirements for gettg energy mltiplition ftor fltness.% re list tble. Tble prmeter ontrol rnge Prmeters Corse tng Fe tng freqeny devition tempertre oplg effiient devition nloded qlity ftor differene 4 Conlsion ±khz ±.5 ±x 4 ±. C (±khz) RF ompressor s key tehnology for prtile elertors hs been widely stdied mny elertor lbortories, sh s KEK, CERN, IHEP nd SLAC. Bt there re only few reserhers sg eqivlent irit model to stdy the behvior of SLED nd nlyze the prmeters. A detil proess for bildg mthemti model is shown this pper. The simltion reslts nd the nlysis of the prmeters devition of the vities re lso presented. Drg or modelg nlysis, the fltness of the energy g ftor.% n be hieved with or model when the tempertre of the oolg wter T,. C then the mximm freqeny detng will be ontrolled khz. The SLED model n be sed to mke frther stdy of the RF plse ompressor, more speifi mesrements will be rried the ftre. ferenes Feng C, Zho Z T. Hrd X-ry free-eletron lser bsed on eho-enbled stged hrmoni genertion sheme. Chses Si Bll,, 55: -7. FANG WenCheng, GU Qing, et l. Design optimiztion of C-bn trvelg-wve elertg strtre for ompt
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