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

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)


ERL Plans: Cornell, KEK/JAERI , APS II

APS II concept

Cornell ERL


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)


Current and Future X-Ray Sources


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


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)


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


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


Diamond C(220) Reflection:E0=4.92 keV


Sapphire Reflectivity @ 14.3 keV


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


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)


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%


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)


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


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


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


Start-up Simulation (Reiche)

Pessimistic case

Ip=4 A, mirror loss=10%

Effective net gain~6%


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!!


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?


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)


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


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


Gun technologies

SCSS: CeB6, thermionic, pulsed gun

LBL 50 MHz, laser driven

Cornell laser-driven 750 kV, DC


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


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


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.


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)

Documents

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