Simulation of the Trickle Heating Effect

Transcription

1 Simulation of the Tickle Heating Effect LCLS Tickle Heating, Measuement and Theoy (SLAC PUB 3854 Z. Huang et. al.) Poisson Solve fo Peiodic Mico Stuctues LCLS Tickle Heating, Simulation EuXFEL Tickle Heating, Simulation

2 LCLS Tickle Heating, Measuement and Theoy (SLAC PUB 3854 Z. Huang et. al.) it is induced enegy modulation afte the dogleg ms ap LH (SLAC PUB 3854 Z. Huang et. al.)

3 3D Impedance E z 4 3D dv z z y y z z 3 Fouie tansfomation on ais: E E z z k dz E ze ep ikz ik ik k z k ddydz, y, ze K z z with phase space: dd dydydzd f,, y, y, z, z (SLAC PUB 3854 Z. Huang et. al.)

4 z z z z integation fo (nominal) Gaussian tansvese phase space (ound beam): E z k J k ep k ii Z 5 56 ep k 56 L k fo k with,, initial Twiss paametes induced enegy modulation (ound beam, on ais): LSC e Ez k dz (SLAC PUB 3854 Z. Huang et. al.)

5 L L amplitude of elative enegy modulation in LH, assumption: offset independent LSC J 5 k dz ep k 56 L i k I I A optical function assumptions: ound beam, petubation,, L inf LSC amplitude of induced enegy modulation on ais total ms enegy spead ms,befoe ms, L ms, LSC f L f L LSC LSC ms spead befoe LH ms spead induced by LH, with shape facto ms spead induced by tickle heating, with shape facto f L flsc ms ms,befoe ms,l ms,lsc if these effects ae uncoelated! (SLAC PUB 3854 Z. Huang et. al.)

6 (SLAC PUB 3854 Z. Huang et. al.)

7 beam optics EuXFEL Lase Heate beam is not ound LH 3 M, aleady with chip ms / LH.4%

8 I y ( o, y o ) non aial ovelap (photon electon) ep, I E E paticle beam: lase beam: ep, y o o y y y y y P bette spectum insensitive to hoizontal offset moe feedom fo optics EuXFEL: paticle beam is vetically shifted but moe lase powe needed heating is non unifom vs. coss section needs 3D analysis of paasitic effects

9 Poisson Solve the full (non peiodic) poblem (LCLS case) 6 6mm z 5, y mesh lines N z N, y 7 LH 76 nm LH 6 paticles N p Q e tot 9 is possible; has been done scans ae time consuming! tick : educe bunch length tick : solve peiodic poblem N z N p Iˆ ec LH 6 inceasing maco effects distinguish fom mico effects! fast even on single CPU bette esolution possible

10 Poisson Solve fo Peiodic Mico Stuctues Loentz tansfomation electostatic poblem V d 4 3 E peiodic souce distibution n p n p p V d n n dv n n p p p n p p E Geen s function G() peiodic Geen s function G p (, p )

11 E, 4 p G p p dv implementation: paticle mesh method p fast convolution (with scala Geen s function) diffeentiation (on mesh) intepolation E E V eample (tacking longitudinal phase space): full model peiodic model see session Tu : C. Lechne, K. Hacke

12 LCLS Tickle Heating, Simulation beam and setup paametes fom q= 5 pc numeical paametes peiod paticles/peiod longitudinal mesh, dz tansvese mesh cpu time 8 nm (in z diection) E6 8 nm / 5 = 6 nm dz = 4 µm (about 38 lines) 5 min

13 ms enegy spead =. k befoe LH = 5. k afte LH undulato m z /m m z /m

14 ms enegy spead =. k befoe LH = 5. k afte LH undulato 6.5 k at 5.5m m z /m 5.5 m z /m

15 ms enegy spead =. k befoe LH = 5. k afte LH undulato 6.5 k at 5.5 m 9.5 k at 7.5 m m z /m 7.5 m z /m

16 gowth of ms enegy spead and modification of enegy spectum ms Z /m

17 5 56 LSC ep k dz I I k i k J A L

18 ms Z /m

19 scan: ms out vesus ms in ms out / ms in /

20 compaison with measuement SLAC PUB 3854 simulation ms enegy spead / 3D, meshlines / lambda peiodic 5 meshlines / lambda ms in lase powe / MW

21 LCLS, 5 pc nomalized spectum ms,in / 5 / /

22 EuXFEL Tickle Heating, Simulation LH ACC dogleg 56 = 4mm BC paticles: ACC 3 M qbunch k nc ˆ q I 5 A nc bunch m qbunch nc 5 ka lase: I 3 μm LH 64 nm aial displacement: y o o.5 I

23 XFEL, nc C tot ms enegy spead ms ms,out ms,out C tot 3 M Z /m ms,in

24 XFEL, nc nomalized spectum ms,in 5 / / 3

25 XFEL, 5 pc C tot ms enegy spead ms ms,out ms,out C tot 3 M Z /m ms,in

26 XFEL, 5 pc nomalized spectum ms,in 5 / 5 / 5

27 XFEL, 5 pc C tot 4 ms enegy spead ms ms,out Z /m ms,in

28 XFEL, 5 pc nomalized spectum ms,in 65 / 5 / 75

29 XFEL, pc C tot ms enegy spead ms ms,out Z /m ms,in ms ms,befoe ms,l ms,lsc these effects ae coelated!

30 ms Z /m, y LSC J 5 k dz ep k 56 L i k I I A

31 XFEL, pc nomalized spectum ms,in 5 / / 3

32 Conclusions, Summay analytic estimation coves many essential effects qualitative teatment of shape factos EuXFEL is eally 3D (not z) fast and efficient quantitative teatment with peiodic SC solve LCLS case: qualitative ageement (of num. calc.) with measuement tickle heating changes ms enegy spead and enegy spectum (good { gaussian} spectum is cucial fo effective suppession of µb amplification) EuXFEL case: weak tickle heating, specta ae not spoiled

33 Thank You

34 z y y z y y 5 6 const 5 6 z z z z z z z /m m