Optical Design Concept for LCLSII SXRSS System Yiping

Optical Design Concept for LCLS-II SXRSS System Yiping Feng March 09, 2016

Soft X-ray Self-Seeding (SXRSS) • LCLS-II project seeding deliverables • LCLS-I system & physics requirements • LCLS-II baseline/refined system & physics requirements • LCLS-II high-resolution design concept • • Grating and optics Mode of operation (tuning) Resolution Imaging of source onto re-entrant point Coupling of X-ray and e- beams Efficiency and throughput Tolerances LCLS-II SXRSS Optical Design *LCLS-II SXRSS CDR Scheduled in Sept. 2015 2

Current LCLS-II Efforts in Relation to SXRSS • Tor Raubenheimer, LCLS-II physics • Gabriel Marcus, FEL physics • Yiping Feng, XTES X-ray physics • Michael Rowen, photon system • Dennis Martinez-Galarce, undulator systems CAM including SXRSS system • In consultation with: • Bob Schoenlein, Daniele Cocco, Phil Heimann, Lin Zhang, Zhirong Huang, Daniel Ratner LCLS-II SXRSS Optical Design 3

LCLS-II Baseline Deliverables Cu Linac 4. 0 Ge. V SC Linac High Rep Rate 0 5 10 15 20 25 Photon Energy (ke. V) Legend Cu SASE Self Seeded (Diamond) High Rep Rate SASE Self Seeded (Grating) LCLS-II SXRSS Optical Design Ø Self seeding between 1. 2 - 4 ke. V requires X-ray optics development Ø Self seeding at high rep rate above 4 ke. V will require ~ 4. 5 Ge. V electron beam, not a baseline deliverable today 4

LCLS-II Project Baseline Physics Requirements* LCLS-II SXRSS Optical Design *Marcus et al, LCLS-II SXRSS PRD *Optics expected to be cooled due to high rep rate operation 5

Modify/Upgrade Existing LCLS-I System (w/ cooling modifications for High Rep-Rate as an option) Length of Undulator Segment 3. 870 m 1. 453 m 0. 26 m B 2 18 mm B 1 B 3 E = 1000 e. V Grating (toroidal VLS) (End of Girder) 0. 26 m M 1 (rotating planar mirror) B 4 Dt = 663 fs Slit (fixed) 3. 85 mm M 3 ( plane mirror) FEL M 2 (tangential cylindrical mirror) 0. 0 xx m 1. 347 m 0. 18 m 0. 128 m 1. 190 m 1. 346 m e- beam 0. 8315 m 0. 8243 m 0. 235 m 3. 400 m LCLS-II SXRSS Optical Design Magnetic Length of Undulator 0. 235 m 0. 665 m (End of U 9) (Begin of U 9) (End of U 8) 0. 470 m 6

Optics/Grating Design for LCLS-I Nearly Constant Resolving Power @ 5, 000 • Toroidal VLS grating • Variable-line spacing providing main focusing in dispersion plane • In “fixed incidence angle” mode, focus not fixed • due to variable source location • chromatic aberrations from grating both in VLS and spherical focusing in dispersive conf. • chromatic aberrations from Gaussian beam optics due to Rayleigh range dependences on l and w 0 • Providing additional focusing in dispersion plane • Providing main focusing in sagittal plane LCLS-II SXRSS Optical Design 7

Optics/Grating Design for LCLS-I • Mirrors • Rotating planar M 1, providing energy tuning • Tangential cylindrical M 2 at fixed incidence angle, providing re-focusing in dispersion plane • Planar M 3 at fixed incidence angle, completing optical chicane and providing certain alignment capabilities • Exit slit • Variable size, providing resolution tuning* • In practice, running slit-less and relying on e- beam being the effective slit (more discussion later) LCLS-II SXRSS Optical Design *although effect is different from conventional mono system 8

Refined Physics Requirements under C for Higher Resolving Power* > 30000 LCLS-II SXRSS Optical Design *guidance from LCLS scientific staff based on workshop and SAC recommendations and CD 2/3 review, etc. 9

Optical Concept for LCLS-II SXRSS Schematic Layout (U 9) Length of Undulator Segment 4. 400 m 1. 453 m 0. 26 m B 2 18 mm B 1 Grating (rotating plane VLS) M 1 (rotating plane mirror) 0. 26 m B 3 @ E = 1000 e. V B 4 Dt ~ 700 fs Slit (movable) 3. 85 mm e- beam M 3 FEL (rotating & movable plane mirror) M 2 (rotating & movable toroidal mirror) 0. 052 m 1343. 736 -1350. 200 m 0. 1346 - 0. 0645 m 0. 0805 - 0. 1631 m 1. 8757 m 0. 5194 - 0. 5259 m 0. 8243 m 0. 500 m 3. 400 m LCLS-II SXRSS Optical Design Magnetic Length of Undulator 0. 500 m 0. 500 (End of U 9) (Begin of U 9) 1. 000 m 10

Optics/Grating Design for LCLS-II (w/ flexibilities) Nearly Constant Resolving Power @ 30, 000 • Rotating plane VLS grating • Variable-line spacing providing main focusing in dispersion plane • In “fixed-focus” mode* by rotating grating and M 1 for energy tuning, but focus still not fixed due to • Variable source location • Chromatic aberrations from grating in VLS • Chromatic aberrations from Gaussian beam optics due to Rayleigh range dependences on l and w 0, degree of transverse coherence b LCLS-II SXRSS Optical Design *fixed incidence produced large aberrations, was not chosen, and for the more exotic design of variable RP, would not work either 11

Optics/Grating Design for LCLS-II (w/ flexibilities) • Mirrors • Rotating planar M 1, providing tuning in conjunction w/ grating • Rotating and movable toroidal M 2, providing optimal refocusing in both dispersion and sagittal plane • Rotating planar and movable M 3, completing optical chicane and certain alignment capabilities • Exit slit • Variable size and movable, providing resolution tuning* LCLS-II SXRSS Optical Design *cannot run slit-less if high resolving power is required 12

Enhanced Capabilities and Increased Complexities • Higher resolving power • ~ 30, 000, matching state-of-the-art system at synchrotrons • Slit must be used at high RP • Tunability w/ high RP at the expense of increased mechanical complexity • Coarse energy tuning using G, M 1, M 2, M 3, and slit • Fine energy tuning using G and M 1 only • Necessitated by the higher RP, and thus higher demagnification at slit, a short focal length of M 2 for refocusing; aberration must be compensated to achieving better beam size match at reentrant point, and thus higher coupling efficiency LCLS-II SXRSS Optical Design 13

Resolving Power Achieved only w/ Slit • Based on: angular dispersion > beam angular size • Dispersion must overcome diffraction Re-focused beam size at reentrant point Angular dispersion at 5000 resolving power Angular dispersion at 30000 resolving power LCLS-II SXRSS Optical Design 14

Why LCLS-I system can work w/o slit? • Based on: angular dispersion ~ beam angular size LCLS-II SXRSS Optical Design 15

Why Focusing is Required for Resolution? Focusing requirements • Imaging angular size < grating angular dispersion • r ’ ~ 1. 35 m • Image angular size < 1. 05 mrad @ 1. 3 ke. V - w 0’ < 1. 35 mm (to be focused from ~ 50 mm at src. + propagation) l+Dl w 0’ w 0 l r • Possible solutions - r’ Focusing element (VLS) exit slit Focusing pre-mirror Spherical grating (fixed line spacing) Plane variable line spacing (VLS) grating Spherical +VLS grating LCLS-II SXRSS Optical Design 16

High Demagnification at Slit • Based on required resolving power and beam angular size at slit location* • Must be provided by 1 st stage focusing (VLS, or else) Achieved by optics design Required based on resolving power LCLS-II SXRSS Optical Design *1350 mm from grating 17

Source Properties (Based Gabe Marcus’ S 2 E Simulations) • Source location, waist size and 1 D degree of transverse coherence (complete description of photon beam) • Coherent treatment is necessary because of near-field condition upstream end of undulator 8 downstream end of undulator 8 LCLS-II SXRSS Optical Design 18

Gaussian-Schell Model Propagation (Based Gabe Marcus’ S 2 E Simulations) • Source location, waist size and 1 D degree of transverse coherence (complete description of photon beam) Gaussian-Schell Model Fully Coherent LCLS-II SXRSS Optical Design 19

Maximum Resolving Power (limited by illuminated # of grooves) • Maximum RP > 30, 000 @ 1. 3 ke. V • Ideally, resolving should go lower as X-ray energy decreases Current design m al e Id LCLS-II SXRSS Optical Design te ys s 20

Design RP vs. Transform-limited Pulses (Not ideal!) • Partial coverage of phase space • Stretching pulse, especially for shorter pulse at lower energies, thus reducing coupling efficiency LCLS-II SXRSS Optical Design 21

Image (Waist) Location near Slit • Image location not “fixed” completely moveable slit • Aberrations from VLS, variable src. location, etc. Gaussian. Schell optics, some of them not known a priori Coherent-optics Ray-optics slit LCLS-II SXRSS Optical Design 22

Tuning of energy (Incident & Exit Angles vs. Energy) • In “fixed-focus” mode defined for incoherent optics in the small angle limit, incidence, exit, and included angle all variable • It is possible to vary incidence angle to completely fix focus exit on grating incidence on M 1 incidence on grating LCLS-II SXRSS Optical Design 23

Focusing in Dispersion/Sagittal Planes • Tangential/dispersion plane Focusing (VLS) src. point Exit slit M 2 tangential focusing re-ent. point w 0’ l+Dl w 0 l • Sagittal/non-dispersive plane Exit slit src. point l+Dl w 0 M 2 sagittal focusing re-ent. point w 0’ l LCLS-II SXRSS Optical Design 24

Re-focusing in Dispersion Plane (optimized to couple w/ e- beam) • Achieved by optimizing M 2 location, incidence angle, and slit translation/size for required RP Source waist size Waist size in reentrant undulator LCLS-II SXRSS Optical Design 25

Re-focusing in Dispersion Plane (optimized to couple w/ e- beam) • Location of waist not fixed, but moves within undulator • Rayleigh range ~ 1. 1 to 3. 8 m so it helps somewhat ator th Leng dul of un Beam size LCLS-II SXRSS Optical Design 26

Re-focusing in Sagittal Plane (optimized to couple w/ e- beam) • Achieved by concurrently optimizing M 2 location, incidence angle, and slit translation/size for required RP Source waist size Waist size in reentrant undulator LCLS-II SXRSS Optical Design 27

Re-focusing in Sagittal Plane (optimized to couple w/ e- beam) • Location of waist not fixed, but moves within undulator • Rayleigh range ~ 1. 0 to 4. 8 m so it helps somewhat 200 e. V 1. 3 ke. V Location in undulator after chicane (mm) LCLS-II SXRSS Optical Design 28

Quality Factor of Overlapping (optimized to couple w/ e- beam) • Complex optimization process, involving slit-M 2 distance, M 2 incidence angle, M 2 radii of curvature in tangential/sagittal directions LCLS-II SXRSS Optical Design 29

Grating/Optics Efficiency (not including bandwidth reduction factor) • For lamella grating w/o shadowing, but blazed design can help compensate, especially at higher energies • Whether or not sufficient? S 2 E simulation Max. grating efficiency Est. reflectivity Overall grating efficiency LCLS-II SXRSS Optical Design 30

Optical Time Delay (not constant due to varying included angle) • Not constant due to included angle changing, especially at low energies, but the Dt/ev is very small, and can be reduced by limiting number of motions Max. grating efficiency Est. reflectivity Overall grating efficiency LCLS-II SXRSS Optical Design 31

How Would Slit Work? (required for achieving high resolving power) • Translation of slit to “track” waist of focused beam necessary • Very small Rayleigh range of the focused beam near slit Beam size at slit if not moved Rayleigh range Waist size near slit LCLS-II SXRSS Optical Design 32

How Would Slit Work? (required for achieving high resolving power) • To optimize beam size matching, tangential and sagittal focal length were made variable • M 2 motion must be follow prescribed trajectory Prescribed M 2 to Image(slit if movable) distance Focal length LCLS-II SXRSS Optical Design 33

How Would Slit Work? (required for achieving high resolving power) • To optimize beam size matching, tangential and sagittal focal length were made variable • M 2 Incidence angle must follow prescribed trajectory LCLS-II SXRSS Optical Design 34

Ideal System Concept (Resolving power on demand) • Full coverage of phase space • Variable resolving power vs. energy at constant pulse length • Multiple configurations cover different pulse length conf. I How to adjust RP for constant bunch length? conf. III I. Vary incidence angle II. Adjust slit opening LCLS-II SXRSS Optical Design 35

Re-mixing of Separated Colors (Transform-limited resolving power for a given pulse length ) • Varying exit slit opening • By opening up exit slit, allowing more colors to go thru. , of each color pulse length stretched to many times of transform-limited due to narrower than necessary bandwidth • Phases of colors remain locked at slit location, will remain locked at re-entrant point after collimation • Many colors of longer pulses re-combine to form shorter pulse with greater bandwidth (requires verification) Focusing (VLS) src. point Exit slit l+Dl w 0 M 2 tangential focusing re-ent. point w 0’ l LCLS-II SXRSS Optical Design 36

Variable Resolving Power Design (Transform-limited resolving power for a given pulse length ) • Varying incidence angle on grating to match transform-limited resolving power requirement const. RP design variable RP design LCLS-II SXRSS Optical Design 37

Variable Resolving Power Design (Transform-limited resolving power for a given pulse length ) • Coupling of variable RP design suffers a bit at lower energies due to large aberration, but reasonable, range of motion adjustments are similar const. RP design variable RP design LCLS-II SXRSS Optical Design 38

Optics Specs for Const. RP Design 39 Grating specifications Parameter symbol value unit Line spacing s 0. 4452 mm Linear coeff Ds/Dx -6. 621 x 10 -7 Groove height h 15. 6 Grating profile nm Blazed @ 2. 0° Incident angle q 11. 11 - 4. 37 mrad Exit angle q’ 167. 45 - 65. 61 mrad Included angle 2 q 169. 77 - 175. 99 degree Object distance Lobj 2. 648 - 4. 277 m Image distance Limg 1. 344 -1. 350 m Exit slit opening s 1. 47 - 0. 56 mm

Optics Specs for Const. RP Design 40 Mirror specifications Parameter symbol value unit M 2 Sagittal Radius Rs 0. 10452 m focal length f 1 2. 1868 - 4. 4289 m Incident angle qi 23. 9 - 11. 8 mrad M 2 Tangential Radius Rd 11. 00845 m focal length f 3 0. 1315 - 0. 0650 m Incident angle qi 23. 9 - 11. 8 mrad

Optics Specs for Const. RP Design 41 Performance Parameter symbol value unit Energy range E 0. 200 – 1. 300 ke. V Bunch charge Q 100 p. C Pulse length (FWHM) t 100 fs Pulse energy e 6 - 1. 4 m. J Peak Power Pinput 60 - 14 MW g-beam size (2 s) w. G 46. 78 - 40. 00 mm g-beam DTC-1 D b 94. 3 - 90. 6 % Resolving power R ~ 30000 - Grating efficiency h. Grating 3. 77 - 0. 58 % Coupling efficiency hg-e- 59. 7 - 84. 5 % Bandwidth ratio Dwo/Dwi - Output peak Power Poutput k. W Time delay (variable) DT 1457 - 601 fs

Quality Factor of Overlapping (tolerance studies) • Varying DTC-1 D • From highly coherent to 0. 9, 0. 8, . . . , 0. 1 1. 0 0. 5 0. 1 LCLS-II SXRSS Optical Design 42

M 2 Parameters (Incidence Angle, location) (tolerance studies) • Varying M 2 parameters • Incidence angle, location, aberration, and all of the three effects Including all three effects not including aberration const. offset const. incidence angle LCLS-II SXRSS Optical Design 43

Source Parameters (Source location) (tolerance studies) • Varying source parameters • Constant source location, varying source location +/- 0. 5 m variable source location + 0. 5 m variable source location - 0. 5 m const. source location LCLS-II SXRSS Optical Design 44

Grating Parameters (Incidence Angle) (tolerance studies) • Varying grating parameters • Constant incidence angle won’t work well const. incidence angle on grating LCLS-II SXRSS Optical Design 45

M 2 Radius of Curvature (Tangential) (tolerance studies) • Varying M 2 radius of curvature • Optimal, +/- 10% 0% -10% +10% LCLS-II SXRSS Optical Design 46

M 2 Radius of Curvature (Sagittal) (tolerance studies) • Varying M 2 radius of curvature • Optimal, +/- 10% 0% -10% +10% LCLS-II SXRSS Optical Design 47

VLS 1 st Order Coeff. (tolerance studies) • Varying VLS 1 st order coefficient • Optimal, +/- 0. 1% 0% -0. 1% +0. 1% LCLS-II SXRSS Optical Design 48

VLS Grating Period (tolerance studies) • Varying VLS grating period, similar to 1 st order coeff. • Optimal, +/- 0. 1% 0% +0. 1% -0. 1% LCLS-II SXRSS Optical Design 49

Higher Order Effects (due to large incidence angle on M 1) • Large incidence angle on M 1 will lead to • Under-rotation of M 1, Shift in slit location (up in y), landing point on M 1 close to grating h/2 qi+q 0 pivot h/2 c c exit slit M 1 S S Dy • z. M 1 z. S Exit ray not parallel to S-S line, shift at slit location (down in y), landing point on M 1 away from grating h/2 pivot h/2 S qi+q 0 z z>x z’M 1 LCLS-II SXRSS Optical Design Dy’ M 1 exit slit S z. S 50

Higher Order Effects (due to large incidence angle on M 1) • Varying slit location in y • Much larger than waist size at slit, so it is important LCLS-II SXRSS Optical Design 51

LCLS-I System (comparison of coupling efficiency) • LCLS-I system design very rigid for stability, no adjustments • Source parameters require verification/testing LCLS-II system LCLS-I system as specified LCLS-II SXRSS Optical Design 52

Summary • High resolution system feasible • Resolving power ~ 30, 000 over entire energy range • Use of slit necessary for high resolving power • Efficiency reasonable ~ 1% • Imaging properties in both transverse directions can be optimized, but requires many degrees of freedom • Incidence angle, location of re-focusing optics • Tuning can be achieved w/ certain mechanical complexities • However tuning over small energy range can work w/ motion of one mirror only LCLS-II SXRSS Optical Design 53

Additional Information

Current LCLS-I Soft X-ray Self Seeding System Installed in place of U 9 LCLS-II SXRSS Optical Design 55

Current LCLS-I System Physics Specifications* resolving power LCLS-II SXRSS Optical Design 5000 *D. Ratner, et al, PDR for SXRSS 56

Current Performance of LCLS-I System at 930 e. V, 50 fs, ~ x 3 transform-limited LCLS-II SXRSS Optical Design *D. Ratner, et al, Phys. Rev. Lett. 114, 054801 (2015) 57

BESAC Recommendations for Future Light Sources* Transform-limited pulses • For a (temporal) Gaussian beam *Approved by BESAC, July 25, 2013 LCLS-II SXRSS Optical Design 58

Comments from LCLS-II CD 3 B Review The project should solicit broad input from LCLS/LCLS-II user community concerning target energy resolution in SXR seeding. Achieving very high resolving power (e. g. , > 105) on an FEL will be very challenging and is probably not wellsuited to LCLS-II science. LCLS-II SXRSS Optical Design 59

LCLS-II Scientific Opportunities Workshop Will help refine science case and will provide guidance on operating modes Close coordination with LCLS and Photon Science Directorates LCLS-II SXRSS Optical Design 60

Requirements Performance requirements • Resolving power to make pulse fully transform-limited, assuming Gaussian profile - 200 e. V - 1300 e. V • R ~ 20000 - 30000 • Seeding power after all optics - 200 e. V: > 10 k. W - 1300 e. V: > 20 k. W • Seeding beam collinear w/ original beam - Transverse profile maintained if possible • Time delay - < 1 ps - Variable delay in tuning range is acceptable if within 10% LCLS-II SXRSS Optical Design 61

Things to consider • Tuning capability • High resolving power • Variable resolving power to retain short pulse characteristics • Two-stage implementation • Two-color seeding SS LCLS-II SXRSS Optical Design SS 62

Requirements 63 Transform-limited pulses For a (temporal) Gaussian beam For a (temporal) flat-top beam Photon Division X-ray Science Department

FEL performance requirements • Large tuning range • 0. 20 - 5. 0 ke. V in baseline Parameter Value Unit SXR • Small bandwidth • Self-seeding for both SXR and HXR in baseline • High rep-rate • • 0. 20 – 1. 3 ke. V Self-seeding 0. 20 – 1. 3 ke. V Pulse duration < 100 fs Rep. rate > 100 k. Hz Up to 1 MHz Average x-ray power • • Photon energy 20 W without distortions Up to 200 W hard cap HXR Photon energy 1. 0 – 5. 0 ke. V Self-seeding* 1. 0 – 4. 0 ke. V Pulse duration < 100 fs Rep. rate > 100 k. Hz * Not part of baseline LCLS-II SXRSS Optical Design 64

Nominal e-beam and undulator parameters Symbol Value Unit Parameter Value SXR (HXR) Unit Energy E 4. 0 Ge. V Type Hybrid PM, planar - Charge Q 100 p. C Full gap height Variable - Peak current I 1. 0 k. A Period 39 (26) mm Emittance ϵn 4. 5 x 10 -7 m-rad Segment length 3. 4 m Energy spread σE 500 ke. V Break length 1. 0 m <β> 12 (13) m # segments 21 (32) - Total length 96 (140) m Parameter Beta function • Undulator • • • AL, rectangular pipe 5 mm chamber height Relaxation time, τ = 8 fs LCLS-II SXRSS Optical Design 65