rf kick of 3 rd harmonic cavities about kick factors, symmetries & compensation FLASH setup XFEL assumptions calculation of rf kick factors

Transcription

1 rf kick of 3 rd harmonic cavities about kick factors, smmetries & compensation FLASH setup XFEL assumptions calculation of rf kick factors summar

2 about kick factors, smmetries & compensation discrete coupler kick: (,, s) ( ϕ ks) cav cos cav { cav } i ϕ ks n { e, } i( ϕcav ks) ( n (,, s) Re e ) (, ) ( cav ) ( (,, s) Re ) ( ) cav Talor epansion: ( n) (, ) d 0 + d d (, ) f + f f + ( n) 0 + compensation of s- (or time-) dependent fields: iϕcav iϕ { d } = Re{ d e } cos ks + Im{ d e } sin ks i( ϕcav ks) (,0, s) Re e 0 cav Im cav iϕcav { d e } 0 cav 0 = 0 cav 0 cav 0 arg { d0} = ϕ cav depends on cavit phase depends on compression scenario

3 from summar comple coupler kick: cav cav+mirror- cav+rot -ais a,b arbitrar: (, ) d 0 + d d (, ) f + f f ( n) + ( n) 0 + SW: a=b, (equal for sub-structures) SW: a=b, (equal for sub-structures) ( Σ, n) (, ) 2i Im{ d0 + d d } (, ) 2i Im{ f + f f } ( Σ, n) + ( ) 2Re{ d } + 2i Im{ d } + 2Re{ d }, 0 d = d ( a, ), 0 0 b ( Σ, n) 0 + ( Σ, n) ( ) 2i Im{ f } + 2Re{ f } + 2i Im{ f }, 0 cav+mirror- cav+rot -ais a,b arbitrar (but equal for sub-str.) a,b arbitrar (but equal for sub-str.) (, ) d ( Σ, n) 2 ( ) 2 f + f ( Σ, n), 0 2 (, ) 2d + d (, ) 2 f + f ( Σ, n) 2 ( Σ, n) 2

4 FLASH setup side view: TESLA module & 3.9GH sstem

5 horiontal rotation = rot

6 XFEL assumptions initial particle distribution: tracked with ASTRA as described in Feb. 2008, beam dnamics seminar reference solution without coupler kicks in TESLA modules parameters for 20 5 compression (= present design) ϕ st 2deg; ϕ 3rd 46.6deg (spatial phases); 3rd 92 M 576Me 500Me β /m E/0Me β /m 3 rd harmonic section EXCEL table: 2 modules = 24 cavities discrete kicks of 48 couplers (effect depends on field not on number of cavities)

7 XFEL assumptions = rot = rot

8 from FEL Beam Dnamics Group Talks st Estimation of RF Coupler Kicks of 3rd Harmonic Cavit calculation of rf kick factors a) Timergali s HFSS calculation

9 calculation of rf kick factors a) Timergali s HFSS calculation - in detail onl forward wave (a=0): j44 upstream = 0 6+ j45 6 downstream 78 = 26 + j263 0 j99 6 onl backward wave (b=0): the numbers deviate less than 0-7 from the values for forward wave therefore: the coupler kick depends essentiall on the SW part of the field it does not depend on the reflection coefficient at the input coupler

10 calculation of rf kick factors b) MWS calculation for 2 cells, scaled onl forward wave (a=0): j202 upstream = j222 6 downstream 267 j672 = j340 6 results are quite uncertain: HFSS ver nois MWS two cells are not enough both calculations: discretied beam pipe is too short (cancellation effects in integrated kick) sstematic difference in accelerating field and in Qet

11 calculation of rf kick factors comparison of HFSS & MWS fields MWS, 2 cells, Cartesian mesh HFSS, 9 cells, tetraeder grid

12 calculation of rf kick factors b) MWS calculation for 2 cells, scaled but MWS results are smooth enough to estimate spatial derivatives of kicks: m j j upstream downstream m j j m j j m j j for one 3 rd harm. cavit is about 0 50 times larger for one 3 rd harm. cavit is about 5 0 times larger than for one TESLA cavit total kick (= ) of all 3 rd harm cavities before BC is about 00 to 200% of that of all TESLA cavities

13 calculation with HFSS kicks, offset independent upstream j44 = 0 6+ j45 6 downstream 78 = 26 + j263 0 j = 0 m = 0 m = 0 m = 0 m 3 ε n / µm ε n / µm no coupler kicks identical orientation rot of each second rot of each second

14 calculation with HFSS kicks, offset independent identical orientation ε n / ε n0 =.96 /m with kicks no coupler kicks ε n / ε n0 =.03 /m

15 calculation with HFSS kicks, offset independent rot of each 2 nd ε n / ε n0 =.38 /m with kicks no coupler kicks ε n / ε n0 =.04 /m

16 calculation with HFSS kicks, offset independent rot of each 2 nd ε n / ε n0 =.02 /m with kicks no coupler kicks ε n / ε n0 =.02 /m

17 calculation with MWS kicks upstream j202 = j222 6 downstream 267 j672 = j j34 = 28 j67 0 m j53 = 33 + j75 0 m 3 28 = 44 + j66 0 j34 m j75 0 = j53 m 3 ε n / µm ε n / µm no coupler kicks identical orientation rot of each second rot of each second

18 calculation with MWS kicks identical orientation ε n / ε n0 = 3.57 /m with kicks no coupler kicks ε n / ε n0 =.42 /m

19 calculation with MWS kicks rot of each 2 nd ε n / ε n0 = 2.0 /m with kicks no coupler kicks ε n / ε n0 =.46 /m

20 calculation with MWS kicks rot of each 2 nd ε n / ε n0 =.03 /m with kicks no coupler kicks ε n / ε n0 =.02 /m

21 calculation with MWS / HFFS rot of each 2 nd with kicks, MWS with kicks, HFFS offset independent no coupler kicks /m

22 calculation with MWS / HFFS rot of each 2 nd with kicks, MWS with kicks, HFFS offset independent no coupler kicks

23 calculation with MWS / HFFS rot of each 2 nd with kicks, MWS with kicks, HFFS offset independent no coupler kicks /m

24 calculation with MWS / HFFS rot of each 2 nd with kicks, MWS with kicks, HFFS offset independent no coupler kicks

25 summar off crest operation of cavities: onl rot setup compensates offset independent kick completel; reduction of Re or Im does not help in general! imprecise & uncertain calculation of rf kick factors offset independent kicks ~ 5..0 larger than in TESLA cavities significant emittance growth for identical orientation and rot setup below 3% emittance growth for rot setup even for the worst kick numbers weak influence of offset dependenc rot setup foreseen in FLASH; effects not investigated here rot setup recommended for XFEL