An X-Ray FEL Oscillator with ERL-Like E-Beams Kwang-Je Kim ANL & Univ. of Chicago May 23, 2008...

An X-Ray FEL Oscillator with ERL-Like E-Beams

Kwang-Je Kim

ANL & Univ. of ChicagoMay 23, 2008

Seminar at Wilson Lab

Cornell University

2KJK, Cornell, May 23, 2008

Next Generation X-Ray Sources

High-gain FELs (SASE) will provide an enormous jump in peak brightness from the 3rd generation sources– Intense, low emittance bunches; Q= 1 nC, IP~ several kA, x

n~ 1 mm-mr

– LCLS, European X-FEL, SCSS, Fermi,..

Multi-GeV Energy Recovery Linacs (ERLs) will provide high average brightness with low intensity, ultra-low emittance bunches at high rep rate x

n~ 0.1 mm-mr, Q=20 pC, ~2ps, frep~1.3 GHz, IAV up to 100 mA

– Cornell, MARS, KEK-JAERI, APS,..

ERLs have so far been regarded only as a spontaneous emission source

We show that an X-ray FEL Oscillator (X-FELO) for ~1-Å based on high energy ERL beams is feasible with peak spectral brightness comparable to and average spectral brightness much higher than SASEs (to be published in PRL)

3KJK, Cornell, May 23, 2008

ERL Plans: Cornell, KEK/JAERI , APS II

APS II concept

Cornell ERL

4KJK, Cornell, May 23, 2008

X-Ray Cvities for Oscillators: History X-ray FEL Oscillator (XFEL-O) using Bragg reflector was first

proposed by R. Colella and A. Luccio at a BNL workshop in 1984.

This was also the workshop where a high-gain FEL(SASE) was proposed by R. Bonifacio, C. Pellegrini, and L. M. Narducci

X-Ray optical cavities to improve the performance of high-gain FELs have been studied recently:– Electron out-coupling scheme by B. Adams and G. Materlik

(1996)– Regenerative amplifier using LCLS beam ( Z. Huang and R.

Ruth, 2006)

5KJK, Cornell, May 23, 2008

Current and Future X-Ray Sources

6KJK, Cornell, May 23, 2008

Electron Beam Qualities Enabling X-FELO Laser-driven DC gun being developed at Cornell for frep=1.3 GHz

Thermionic cathod and bunch manipulation for frep=1-100 MHz

E=1.4 MeV, el=2ps

Q (nC) Ip (A) nx(10-7 m)

Pessimistic 19 4 1.64

Cornell High-Coherence Mode 19 4 0.82

Optimistic 40 8 0.82

7KJK, Cornell, May 23, 2008

Principles of an FEL Oscillator

Small signal gain G= Pintra/Pintra

– Start-up: (1+G0) R1 R2 >1 (R1& R2 : mirror reflectivity)

– Saturation: (1+Gsat) R1 R2 =1

Synchronism– Spacing between electron bunches=2L/n ( L: length of the cavity)

8KJK, Cornell, May 23, 2008

Bragg Mirrors Requiring total loss per pass to be < 20%, the

reflectivity of each Bragg mirror should be well over 90%

Possible crystal candidates are– Diamond

• Highest reflectivity & hard ( small Debye-Waller reduction)• Multiple beam diffraction in exact backscattering needs to be

avoided ( can use as a coupling mechanism?)

– Sapphire• High reflectivity without multiple beam diffraction• Small thermal expansion coefficient and large heat conductivity at

T=40K

9KJK, Cornell, May 23, 2008

Backscattering Reflectivity's for Sapphire and Diamond ( Perfect Crystals)

10KJK, Cornell, May 23, 2008

Diamond C(220) Reflection:E0=4.92 keV

11KJK, Cornell, May 23, 2008

Sapphire Reflectivity @ 14.3 keV

12KJK, Cornell, May 23, 2008

Sapphire Crystal Quality

Back-reflection topographs of HEMEX sapphire wafers cut from different boules show different dislocation densities:

(a) 103 cm-2, (b) much lower dislocation density.

Sample area illuminated by x-rays is 2.1 x 1.7 mm2

Chen, McNally et al., Phys. Stat. Solidi. (a) 186 (2001) 365

13KJK, Cornell, May 23, 2008

X-Ray Focusing

Focusing is required to adjust the mode profile Bending the Bragg mirrors for a desired curvature

(~50m) may destroy high-reflectivity Possible options:

– Grazing-incidence, curved-mirrors for non backscattering configuration

– Compound refractive lenses of high transmissivity can be constructed ( B.Lengeler, C. Schroer, et. Al., JSR 6 (1999) 1153)

14KJK, Cornell, May 23, 2008

Options for XFEL-O Cavities (Y. Shvyd’ko)

Al2O3xAl2O3 @14.3 keV

RT=0.87, Gsat=15%, T=3%

CxCxmirror @12.4 keV

RT=0.91, Gsat=10%, T=4%

Al2O3xAl2O3xSiO2@ 14.4125 keV

RT=0.82, Gsat=22 %, T=4%

15KJK, Cornell, May 23, 2008

Gain Calculation

Analytic formula for low signal including diffraction and electron beam profile – Sufficiently simple for Mathematica evaluation if electron beam

is not focused, distributions are Gaussian, and ZRayleigh =*

Steady state GENISIS simulation for general intra-cavity power to determine saturation power (Sven Reiche)

16KJK, Cornell, May 23, 2008

Saturation: As circulating power increases, the gain drops and reaches steady state when gain=loss

E=7 GeV, λ=1ÅQ=19 pC (Ip=3.8A), Nu=3000 Mirror reflectivity=90%Saturation power=19 MW

E=7 GeV, λ=1ÅQ=40 pC (Ip=8 A), Nu=3000Mirror reflectivity=80% Saturation power=21 MW

0.00

10.00

20.00

30.00

40.00

50.00

60.00

70.00

0.00E+00 5.00E+06 1.00E+07 1.50E+07 2.00E+07 2.50E+07 3.00E+07 3.50E+07 4.00E+07 4.50E+07

Intra Cavity Power (W)

Gai

n (

%)

Saturation Point

0.00

5.00

10.00

15.00

20.00

25.00

30.00

0.00E+00 5.00E+06 1.00E+07 1.50E+07 2.00E+07 2.50E+07 3.00E+07 3.50E+07 4.00E+07 4.50E+07

Intra Cavity Power (W)

Gai

n (

%)

Saturation Point

17KJK, Cornell, May 23, 2008

Examples XFEL-O

Å) E

(GeV)Q

(pC)nx

(10-7m)

K U

(cm)

NU G0 (%) RT

(%)Psat

(MW)

2.48 7 19 1.64 2.5 2.26 2600 35 83 10

1 7 19 0.82 1.414 1.88 3000 28 90 19

1 7 40 0.82 1.414 1.88 3000 66 83 21

0.84 7.55 19 0.82 1.414 1.88 3000 28 90 20

0.84 10 19 0.82 2 2.2 2800 45 83 18

=2 ps, =1.4 MeV, ZR=*=10~12 m

Electrons are not focused but matched to the optical mode determined by cavity configuration

18KJK, Cornell, May 23, 2008

Simulation of Oscillator Start-up

Time-dependent oscillator simulation using GENO (GENESIS for Oscillator) written by Sven– Taking into account FEL interaction (GENESIS), optical cavity

layout, and mirror bandwidth (Reiche)

To reduce CPU– Follow a short time-window (25 fs) – Track a single frequency component for all radiation

wavefronts since other components are outside the crystal bandpass

– Even with these simplifications, one pass takes about 2 hr

19KJK, Cornell, May 23, 2008

Start-up Simulation (Reiche)

Pessimistic case

Ip=4 A, mirror loss=10%

Effective net gain~6%

20KJK, Cornell, May 23, 2008

Super-mode Analysis (adapted from G. Dattoli, P. Elleaume)

Describes gain and spectrum narrowing in the exponential gain regime taking into account the profiles of I(z-ct) and Gmono()

Eigenmode: Gauss-Hermite function opt=(2el*M)1/2/g1/4 : M=1/(2

M) : M=mirror bandwidth

Amplitude growth rate of the fundamental mode0=0.5(g-a)-(0.5u/M)2-0.5g1/2(M/el): u=pulse displacement

hM=2.8 meV, el=2 ps

Bandwidth of the fundamental mode– h

opt=2.3 meV =2 10-7!!

21KJK, Cornell, May 23, 2008

Tolerances

Reduction in gain<1%– Pulse to pulse overlap u<20 fs– Cavity detuning (tolerance on cavity length)<3m

Change in optical axis<0.1*mode angle– angular tolerance of crystals <8 nrad

LIGO technology?

22KJK, Cornell, May 23, 2008

X-FELO Repetition Rate frep= 1.5 MHz when one x-ray pulse stored in 100 m

optical cavity– I=60 A (Q=40 pC), P=0.4 MW May not need ERL

frep=100 MHz with ERL?– Thermal loading on crystals is tolerable (probably)– Electron rms energy spread increases from 0.02 % to 0.05%– With increased energy spread, the loss in the ERL return pass

becomes 2 10-5

– These problems may be solved by increasing the minimum recovery energy to 30 MeV (higher than usual 10 MeV)

23KJK, Cornell, May 23, 2008

Tunability with two crystals

Tuning range is very limited (<2 10-6) due to the need to keep 2< 4 mr for high reflectivity of grazing incidence miror

L

2

Grazing Incidence Mirror

Crystal

H

Crystal

24KJK, Cornell, May 23, 2008

Tunable Cavity Scheme (KJK)

For tuning; increase H and decrease S keeping the round trip path length the same

– L=100m, H0=1m, S0=0.1m=5 10-4 (Hmax=3.3 m)

– L=100m, H0=1m, S0=2m =1% (Hmax=14.3 m)

With this scheme, diamond may be used for most cases:

– With 2max~60 degree: (444) for 12<<15 keV

– (220) for 5<<6 keV

S

A B

C D

H

2

L

25KJK, Cornell, May 23, 2008

Gun technologies

SCSS: CeB6, thermionic, pulsed gun

LBL 50 MHz, laser driven

Cornell laser-driven 750 kV, DC

26KJK, Cornell, May 23, 2008

Ultra-Low Emittance <50 MHz Injector(P. Ostroumov, Ph. Piot, KJK)

Use a small diameter thermionic cathode to extract low emittance beam Provide 500 kV extracting voltage using low frequency ~50 MHz room

temperature RF cavity Using chicane and slits form a short ~ 1 nsec bunch Remove energy modulation by a 6th harmonic cavity Use a pre-buncher an booster buncher to form low longitudinal emittance of

the bunched beam Accelerate to ~50 MeV using higher harmonic SC cavities Use an RF cosine-wave chopper to form any required bunch repetition rate

between 1 MHz and 50 MHz. (ANL Invention Application, IN-06-093)

1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10

27KJK, Cornell, May 23, 2008

Performance of X-FELO Spectral range: 5 keV<<20 keV

Full transverse and temporal coherence in ~1 ps (rms) /FWHM=2.5 10-7 ; h=2 meV (rms)

Tunable 109 photons (~ 1 J) /pulse

– Peak spectral brightness~LCLS

Rep rate 1-100 MHz average spectral brightness (1026 -1029) #/(mm-mr)2(0.1%BW)

The average spectral brightness is higher by a factor of– 105-107 than other future light sources considered so far, ERL-

based or high-gain FEL-based – Current APS about 100-1000 less than ERL

28KJK, Cornell, May 23, 2008

Science Drivers for XFEL-O Inelastic x-ray scattering (IXS) and nuclear resonant

scattering (NRS) are flux limited experiments! Need more spectral flux in a meV bandwidth!

Undulators at storage rings generate radiation with ≈ 100−200 eV bandwidth. Only ≈ 10−5 is used, the rest is filtered out by meV monochromators.

Presently @ APS: ≈ 5 × 109 photons/s/meV (14.4 keV)

XFEL-O is a perfect x-ray source for:– high-energy-resolution spectroscopy (meV IXS, neV NRS, etc.), and

– imaging requiring large coherent volumes.

– Expected with XFEL-O ≈ 1015 photons/s/meV (14.4 keV) with 107 Hz repetition rate.

29KJK, Cornell, May 23, 2008

Concluding Remarks

A X-FELO around 1-Å is feasible with high-quality e-beams contemplated from future ERLs

However, the rep rate of an X-FELO can be 100 MHz or lower to 1 MHzInjector may be less challenging

An X-FELO is new type of future light sources ( in addition to high-gain FELs and ERLs)