uspas course on recirculated and energy recovered linacs g. a. krafft and a. bogacz jefferson lab...

USPAS Course onRecirculated and Energy Recovered Linacs

G A Krafft and A Bogacz

Jefferson Lab

Timofey Zolkin

Lecture 12 ERL x-ray light source

USPAS Accelerator Physics June 2013

High Field Spectral Distribution

02222

2

20

2 sin

2

nxnnperp n

c

e

dd

dE

02

2

2

1

22

20

2

cos

sin

sin

cos

sin

cos

2

n

z

n

n

npar

n

S

S

nc

e

dd

dE

(216)

In the beam frame

where

00

00100 sin

sin

nn

nnNnfnfnNn


In the lab frame

nfnS

S

c

e

dd

dE

nNn

n

z

z

nperp

sin

cossin

cos1

cos1

1

2

22

2

2

1

22

22

22

2

nf

n

S

S

c

e

dd

dEnN

zn

zn

z

npar

cossin

cos1sin

cos

cos1

1

22

2

2

1

22

2

0

0

cos1sin

cos1sin

n

nnNnf

zz

zznN


nfnSSc

e

dd

dEnNnn

nperp cossin

sin

22

22

22

21

2

nf

n

S

S

c

e

dd

dEnN

n

z

zn

npar

cossin

sincos1

cos

22

2

2

12

fnN is highly peaked with peak value nN around angular frequency

0 as 21

22

cos1

02

2

020

n

Kn

nn z

z

z


Energy Distribution in Lab Frame

nfnSSc

e

dd

dEnNnn

nperp cossin

sin

22

22

22

21

2

nf

n

S

S

c

e

dd

dEnN

n

z

zn

npar

cossin

sincos1

cos

22

2

2

12

The arguments of the Bessel Functions are now

22

2

0

0

8

cos1

coscos

cos1

cossincossin

Kncdn

Kncdn

z

zzzz

zxx

(217)


In the Forward DirectionIn the forward direction even harmonics vanish (n+2krsquo term vanishes when ldquoxrdquo Bessel function non-zero at zero argument and all other terms in sum vanish with a power higher than 2 as the argument goes to zero) and for odd harmonics only n+2krsquo=1-1 contribute to the sum

0 sin2

222

22

nf

n

KF

c

e

dd

dEnN

nnperp

0 cos2

222

22

nf

n

KF

c

e

dd

dEnN

nnpar

2

2

2

2

12

2

2

12

2

2

2

2 21421414

1

K

nKJ

K

nKJ

KnKF nn

z

n


Number Spectral Angular Density

0 sin

22

22

nf

n

KF

dd

dNnN

nnperp

0 cos

22

22

nf

n

KF

dd

dNnN

nnpar

Converting the energy density into an number density by dividing by the photon energy (donrsquot forget both signs of frequency)

KFNdd

dNn

ntot 22

Peak value in the forward direction


Radiation Pattern Qualitatively

Central cone high angular density region around forward direction

y

x

Central Cone

Doppler DownshiftedHarmonic Radiation

Non-zero AngularDensity Emission ata Given Frequency

r

1n

1l

2l


Dimension Estimates

Harmonic bands at

211 2K

n

lnl

Central cone size estimated by requiring Gaussian distribution with correct peak value integrate over solid angle to the same number of total photons as integrating f

0 2

21

2

1 2

ncLnN

Kn

nr

Much narrower than typical opening angle for bend


Number Spectral Density (Flux)

The flux in the central cone is obtained by estimating solid angle integral by the peak angular density multiplied by the Gaussian integral

Kge

IN n

nF

nKFKKg nn 21 2

2

0

n 2F rntot

d

dN


Power Angular Density

22

22

21

cossin

sin nSSNn

d

dEnn

nperp

2

2

1

cossin

sincos1

cos

n

S

S

Nnd

dE

n

z

zn

npar

Donrsquot forget both signs of frequency


2

2

22

222

coscos1

cos

cos14

sincos14

z

z

z

nparn

z

nperpn

KNF

d

dN

KNF

d

dN

2

2

2

2

12

2

2

122

22

21421421

K

nKJ

K

nKJ

K

KnKF nnn

For K less than or of order one

Compare with (210)



ERL light source ideaThird generation light sources are storage ring based facilities

optimized for production of high brilliance x-rays through spontaneous synchrotron radiation The technology is mature and while some improvement in the future is likely one ought to ask whether an alternative approach exists

Two orthogonal ideas (both linac based) are XFEL and ERL XFEL will not be spontaneous synchrotron radiation source but will deliver GW peak powers of transversely coherent radiation at very low duty factor The source parameters are very interesting and at the same time very different from any existing light source

ERL aspires to do better what storage rings are very good at to provide radiation in quasi-continuous fashion with superior brilliance monochromaticity and shorter pulses


Coherent or incoherent

Radiation field from a single kth electron in a bunch

Radiation field from the whole bunch bunching factor (bf)

Radiation Intensity

1) ldquolong bunchrdquo =gt incoherent (conventional) SR

2) ldquoshort bunchrdquo or -bunching =gt coherent (FELs) SR

ERL hard x-ray source is envisioned to use conventional SR

)exp(0 kk tiEE

eN

kk

e

tiN

fb1

)exp(1

22

0 eNfbII

single electron

eNfb 1~2

eNII 0

1 fb 20~ eNII


Demand for X-rays

~85 structures by ~85 structures by x-ray crystallographyx-ray crystallography

2003 Nobel Prize 2003 Nobel Prize in Chemistryin Chemistry

Roderick MacKinnonRoderick MacKinnon (Rockefeller Univ)(Rockefeller Univ)

11stst K K++ channel structure channel structure by x-ray crystallography by x-ray crystallography

based on CHESS data (1998)based on CHESS data (1998)

Ion channel proteinIon channel protein

CHESSCHESS


X-ray characteristics neededbull for properly tuned undulator X-ray phase space is a replica from electron bunch + convolution with the diffraction limit

bull ideally one wants the phase space to be diffraction limited (ie full transverse coherence) eg rms = 4 or 01 Aring for 8 keV X-rays (Cu K) or01 m normalized at 5 GeV

Flux phs01bw

Brightness phsmrad201bw

Brilliance phsmm2mrad201bw


Introduction

6D Phase Space Area6D Phase Space Areandash Horizontal Emittance x xrsquondash Vertical Emittance y yrsquondash Energy Spread amp Bunch length

ΔE t

Number of Electrons BunchNumber of Electrons BunchBunch Rep RateBunch Rep Rate IIpeakpeak I Iaverageaverage

Letrsquos review why ERL is a good idea for a light sourceLetrsquos review why ERL is a good idea for a light source

Critical electron beam parameters for X-ray productionCritical electron beam parameters for X-ray production


Introduction (contd) adiabatic damping px

p1z

p1

θ1x

electron bunch ε1

linac

px p2

p2z

θ2x

ε2 = ε1 p2z p1z

ε = εn

βγ εn is invariant since

x px = mc2βγθx form canonically conjugate variables

geometricx θx

mc2

normalized x px


Introduction (contd) storage rings (I)

Quantum Excitation

ρ = p

eB ρ =

p eB p

eB

Equilibrium

Eph

22

~ phphE EN

dt

d

Radiative Dampingvs

Emittance (hor) Energy Spread Bunch Length


Introduction (contd) storage rings (II)

Touschek Effect

Beam Lifetime vs Space Charge Density

bull

bull e 1

e 2

x

z

p 1 in

p 2 in

p 1 out p 2 out


Introduction (contd) why ERL

ESRF 6 GeV 200 mAεx = 4 nm mradεy = 002 nm mradB ~ 1020 phsmm2mrad201BWLID = 5 m

ERL 5 GeV 10-100 mAεx = εy 001 nm mradB ~ 1023 phsmm2mrad201BWLID = 25 m

ESRFERL (no compression)

ERL (w compression)

t


Comparing present and future sources

A(nm-rad)2 max Nund

electron beam brilliance electron beam monochromaticity2222 )4()4( yxI )(51 EE

A(nm-rad)2 compares brilliance from two short identical (K Nund) undulators

A(nm-rad)2 max Nund compares maximum achievable brilliance


1 Angstrom brilliance comparison

ERL better by

ERL emittance is taken to be (PRSTAB 8 (2005) 034202)n[mm-mrad] (073+015z[mm]23) q[nC]

plus a factor of 2 emittance growth for horizontal


Cornell vision of ERL light sourceTo continue the long-standing tradition of pioneering research in

synchrotron radiation Cornell University is carefully looking into constructing a first ERL hard x-ray light source

But firsthellip

SASE


Need for the ERL prototypeIssues include

CW injector produce iavg 100 mA qbunch ~ 80 pC 1300 MHz n lt 1 mm mr low halo with very good photo-cathode longevity

Maintain high Q and Eacc in high current beam conditions

Extract HOMrsquos with very high efficiency (PHOM ~ 10x

previous )

Control BBU by improved HOM damping parameterize ithr

How to operate with hi QL (control microphonics amp Lorentz detuning)

Produce + meas t ~ 100 fs with qbunch ~ 03ndash04 nC (iavg 100 mA) understand control CSR understand limits on simultaneous brilliance and short pulses

Check improve beam codes Investigate multipass schemes

Our conclusion An ERL Prototype is needed to resolve outstandingOur conclusion An ERL Prototype is needed to resolve outstandingtechnology and accelerator physics issues before a large ERL is builttechnology and accelerator physics issues before a large ERL is built


Cornell ERL Prototype

Energy 100 MeVMax Avg Current 100 mACharge bunch 1 ndash 400 pCEmittance (norm) 2 mm mr77 pC

Injection Energy 5 ndash 15 MeVEacc Q0 20 MeVm 1010

Bunch Length 2 ndash 01 ps


Cornell ERL Phase I Injector

Beam Energy Range 5 ndash 15a MeVMax Average Beam Current 100 mAMax Bunch Rep Rate 77 pC 13 GHzTransverse Emittance rms (norm) lt 1b mBunch Length rms 21 psEnergy Spread rms 02

a at reduced average currentb corresponds to 77 pCbunch

Injector Parameters


To learn more about Cornell ERL

Two web-sites are available

1) Information about Cornell ERL X-ray science applications other related projects worldwide

httperlchesscornelledu

2) ERL technical memorandum series

httpwwwleppcornelledupublicERL


Bend Undulator Wiggler

endash

endashendash

white source partially coherent source powerful white source

Flu

x [p

hs

01

bw]

Bri

ghtn

ess

[ph

sm

m2

mr2

01

bw]

Flu

x [p

hs

01

bw]


Undulator Radiation from Single Electron

p

N N

N

S

SS

Kz

x

y

zkBB py sin0

]m[]T[493 0 pBK

Halbach permanent magnet undulator

)]81475(exp[333]T[0 B

pgap for SmCo5 here

Approaches1 Solve equation of motion (trivial) grab Jackson and calculate retarded potentials (not so trivial ndash usually done in the far field approximation) Fourier Transform the field seen by the observer to get the spectrum

More intuitively in the electron rest frame2 Doppler shift to the lab frame (nearly) simple harmonic oscillator radiation

3 Doppler shift Thomson back-scattered undulator field ldquophotonsrdquoOr simply

4 Write interference condition of wavefront emitted by the electron


Intuitive understanding of undulator radiation

z

x

endash

in endash frame

pp

d

Pd2sin

N

1

z

x

back to lab frame

1

~

d

dP

1

on a

xis

off-axis

d

dP

1

N

1~

after pin-hole aperture

)1(2

22221

2

Kn

pn

pn nN

1~

(for fixed θ only)


Higher Harmonics Wiggler

z

x

1K

1K

motion in endash frame

z

x1

~even

odd

K le 1 undulatorK gt 1 wiggler

critical harmonic number for wiggler(in analogy to c of bending magnet)

21

4

3 2KKnc

K nc

1 1

2 4

4 27

8 198

16 1548

wiggler and bend spectra after pin-hole aperture

d

dP

log

log

m

eBc 2

3 2 bend

wiggler

2Nspikes

continuum


Total Radiation Power

e

INKKPtot )1(

32

212

1 A][m][

cm][

GeV][726[W]

2

22

ILKE

Pp

tot or

eg about 1 photon from each electron in a 100-pole undulator or1 kW cw power from 1 m insertion device for beam current of

100 mA 5 GeV K = 15 p = 2 cm

Note the radiated power is independent from electron beam energy if one cankeep B0 p const while p ~ 2 to provide the same radiation wavelength (eg low energy synchrotron and Thomson scattering light sources)

However most of this power is discarded (bw ~ 1) Only a small fraction is used

Radiation Neededwavelength 01 ndash 2 Aring (if a hard x-ray source)bw 10-2 ndash 10-4

small source size amp divergence

temporal coherencespatial coherence


Undulator Central Cone

Flux in the central cone from nth harmonic in bw

LnN

K ncen 2

1

2

1 221

Select with a pin-hole aperture the cone

to get bwnNn

1~

n

)(Kge

INN n

nnph

n

Kg

e

I n )(

0

01

02

03

04

05

06

07

08

09

1

0 1 2 3 4 5

Kg

n(K

)

n = 1

3

57

9

)1(

][)(

221

2

K

JJnKKgn

Function

Note the number of photons in bw ~ 1N is about 2 max of the number of endash for any-length undulator

Undulator ldquoefficiencyrdquop

2212

1

)1(

)(3

NKK

Kg

P

P n

tot

cen


A Word on Coherence of Undulator

r

R

d

L

apparent source disk

c

Radiation contained in the central cone is transversely coherent (no beam emittance)

Youngrsquos double-slit interference condition

~R

rd

Lr c~Rrc ~

Lc ~

in Fraunhofer limit

Spatial coherence (rms) 4 cr

Temporal coherence )2(2 cl clt cc

Photon degeneracy ccphc tN

x-ray source

Rings 1

ERLs 1

XFEL 1

c

Next we will study the effect of finite beam 6D emittance on undulator radiation

same as central cone


Brightness Definition Geometric OpticsBrightness is a measure of spatial (transverse) coherence of radiation Spectral brightness (per 01 BW) is usually quoted as a figure of merit which also reflects temporal coherence of the beam The word ldquospectralrdquo is often omitted Peak spectral brightness is proportional to photon degeneracy

For the most parts we will follow K-J Kimrsquos arguments regarding brightness definitions

A ray coordinate in 4D phase space is defined as

Brightness is invariant in lossless linear optics as well as flux

while flux densities are not

)( )(

yxx

22

4

)(dxd

FdzxB

22)( dxdzxBF

invdzxBxd

FdxdzxB

d

Fd )( )( 2

2

22

2

2


Brightness Definition Wave Optics

here electric field in frequency domain is given in either coordinate or angular representation Far-field (angular) pattern is equivalent to the Fourier transform of the near-field (coordinate) pattern

A word of caution brightness as defined in wave optics may have negative values when diffraction becomes important One way to deal with that is to evaluate brightness when diffraction is not important (eg z = 0) and use optics transform thereafter

xikezEzEdT

cdzxB

)2()2(

2)(

20

yikxx ezyxEzyxEyd

T

cd

)2()2(2

2

20

2

2

2 )( )(1

dezxEExdezxEE xikx

xikx


Diffraction LimitGaussian laser beam equation

With corresponding brightness

)(2)(

1cotexp

)()(

220

0 zR

ik

zwx

z

zkzi

zw

wEzxE

R

)1()( 2220

2Rzzwzw

20wzR

)1()( 22 zzzzR R

2

2

2

2

0

)(

2

1exp)(

rr

zxBzxB

00 1 2 kww rr

Rrr

rr

z

42

0

)2(B

Fcoh 20 )2( rr

FB


Effect of Electron DistributionPrevious result from undulator treatment

The field in terms of reference electron trajectory for ith-electron is given by

For brightness we need to evaluate the following ensemble average for all electrons

2nd term is the ldquoFELrdquo term Typically so only the 1st term is important

)21 ( here ))((e24

)0( 2)(

0

ntnntdc

eE tti

)(i0

i

i

e)0()0( cxtie

eEE

eN

EEEE1i

2i

1i

21 )0()0()0()0(

ji

2j

1i

)0()0(

EE

eN

22

e)1( zkee NN

1e22

zkeN

phase of ith-electron


Effect of Electron Distribution (contd)

)0()0(e)0()0( i2

0

i1

0

)(21

21i

eexik

e EENEE e

)0()0( ii0eee xxBNxB

eeeeeee dxdxfxxBN 220 )0()0(

electron distribution

Brightness due to single electron has been already introduced Total brightness becomes a convolution of single electron brightness with electron distribution function

Brightness on axis due to single electron

2

00

)2()000(

F

B

flux in the central cone


Finite Beam Emittance EffectOftentimes brightness from a single electron is approximated by Gaussian

Including the electron beam effects amplitude and sigmarsquos of brightness become

2

2

2

2

2

00

2

1exp

)2()0(

rr

xFxB

LL rr 2 42

TyTyxTTx

FB

2)2(

)000(

2236122

1212222 LLa xxrTx

2236122

121222 LLyyrTy

222xrxT

222yryT


Matching Electron BeamMatched -function is given by (beam waist at the center of undulator)

Brightness on axis becomes

Matched -function has a broad minimum (for )

x

2 Lrropt

yx

41

41

1

)2()000(

2yx

FB transversely coherent fraction

of the central cone flux

)8(formin2

2formin

2formin2

2

L

L

L

TTacceptable still is 6

4~ if also

Lopt

1)4(or 1)4(

Energy Spread of the Beam

Energy spread of the beam can degrade brightness of undulators with many periods

If the number of undulator periods is much greater than brightness will not grow with the number of periods

Maximal spectral brightness on axis becomes

20N

22

1

1

41

41

1

)2()000(

NN

FB

yx


Photon DegeneracyNumber of photons in a single quantum mode

Peak brightness is a measure of photon degeneracy

Eg maximum photon degeneracy that is available from undulator (non-FEL)

2

2

2

tEyx kk

cBpeakc

1

2

3

n

KgNKgNN n

ezyx

ncne

z

nc

)(10 however typicallymore )(

33max

diffraction-limited emittance dominated


More reading on synchrotron radiation

1 KJ Kim Characteristics of Synchrotron Radiation AIP Conference Proceedings 189 (1989) pp565-632

2 RP Walker Insertion Devices Undulators and Wigglers CERN Accelerator School 98-04 (1998) pp129-190 and references therein Available on the Internet at httppreprintscernchcernrep199898-0498-04html

3 B Lengeler Coherence in X-ray physics Naturwissenschaften 88 (2001) pp 249-260 and references therein

4 D Attwood Soft X-rays and Extreme UV Radiation Principles and Applications Cambridge University Press 1999 Chapters 5 (Synchrotron Radiation) and 8 (Coherence at Short Wavelength) and references therein


PowerPoint Presentation


Slide 3

Slide 4


In the Forward Direction



Dimension Estimates



Slide 12

Slide 13

ERL light source idea


Demand for X-rays

X-ray characteristics needed

Introduction

Introduction (contd) adiabatic damping






Cornell vision of ERL light source

Need for the ERL prototype











Brightness Definition Geometric Optics


Diffraction Limit

Effect of Electron Distribution


Finite Beam Emittance Effect

Matching Electron Beam


Photon Degeneracy



02222

2

20

2 sin

2

nxnnperp n

c

e

dd

dE

02

2

2

1

22

20

2

cos

sin

sin

cos

sin

cos

2

n

z

n

n

npar

n

S

S

nc

e

dd

dE

(216)

In the beam frame

where

00

00100 sin

sin

nn

nnNnfnfnNn


In the lab frame

nfnS

S

c

e

dd

dE

nNn

n

z

z

nperp

sin

cossin

cos1

cos1

1

2

22

2

2

1

22

22

22

2

nf

n

S

S

c

e

dd

dEnN

zn

zn

z

npar

cossin

cos1sin

cos

cos1

1

22

2

2

1

22

2

0

0

cos1sin

cos1sin

n

nnNnf

zz

zznN


nfnSSc

e

dd

dEnNnn

nperp cossin

sin

22

22

22

21

2

nf

n

S

S

c

e

dd

dEnN

n

z

zn

npar

cossin

sincos1

cos

22

2

2

12


0 as 21

22

cos1

02

2

020

n

Kn

nn z

z

z



nfnSSc

e

dd

dEnNnn

nperp cossin

sin

22

22

22

21

2

nf

n

S

S

c

e

dd

dEnN

n

z

zn

npar

cossin

sincos1

cos

22

2

2

12


22

2

0

0

8

cos1

coscos

cos1

cossincossin

Kncdn

Kncdn

z

zzzz

zxx

(217)



0 sin2

222

22

nf

n

KF

c

e

dd

dEnN

nnperp

0 cos2

222

22

nf

n

KF

c

e

dd

dEnN

nnpar

2

2

2

2

12

2

2

12

2

2

2

2 21421414

1

K

nKJ

K

nKJ

KnKF nn

z

n



0 sin

22

22

nf

n

KF

dd

dNnN

nnperp

0 cos

22

22

nf

n

KF

dd

dNnN

nnpar


KFNdd

dNn

ntot 22





y

x

Central Cone



r

1n

1l

2l


Dimension Estimates

Harmonic bands at

211 2K

n

lnl


0 2

21

2

1 2

ncLnN

Kn

nr





Kge

IN n

nF

nKFKKg nn 21 2

2

0

n 2F rntot

d

dN



22

22

21

cossin

sin nSSNn

d

dEnn

nperp

2

2

1

cossin

sincos1

cos

n

S

S

Nnd

dE

n

z

zn

npar



2

2

22

222

coscos1

cos

cos14

sincos14

z

z

z

nparn

z

nperpn

KNF

d

dN

KNF

d

dN

2

2

2

2

12

2

2

122

22

21421421

K

nKJ

K

nKJ

K

KnKF nnn


Compare with (210)











Radiation Intensity




)exp(0 kk tiEE

eN

kk

e

tiN

fb1

)exp(1

22

0 eNfbII

single electron

eNfb 1~2

eNII 0

1 fb 20~ eNII


Demand for X-rays







CHESSCHESS




Flux phs01bw




Introduction


ΔE t






p1z

p1

θ1x

electron bunch ε1

linac

px p2

p2z

θ2x

ε2 = ε1 p2z p1z

ε = εn



geometricx θx

mc2

normalized x px



Quantum Excitation

ρ = p

eB ρ =

p eB p

eB

Equilibrium

Eph

22

~ phphE EN

dt

d

Radiative Dampingvs




Touschek Effect


bull

bull e 1

e 2

x

z

p 1 in

p 2 in

p 1 out p 2 out






ERL (w compression)

t



A(nm-rad)2 max Nund






ERL better by






But firsthellip

SASE






previous )















Injector Parameters










endash

endashendash


Flu

x [p

hs

01

bw]

Bri

ghtn

ess

[ph

sm

m2

mr2

01

bw]

Flu

x [p

hs

01

bw]



p

N N

N

S

SS

Kz

x

y

zkBB py sin0

]m[]T[493 0 pBK


)]81475(exp[333]T[0 B

pgap for SmCo5 here







z

x

endash

in endash frame

pp

d

Pd2sin

N

1

z

x

back to lab frame

1

~

d

dP

1

on a

xis

off-axis

d

dP

1

N

1~


)1(2

22221

2

Kn

pn

pn nN

1~

(for fixed θ only)



z

x

1K

1K


z

x1

~even

odd



21

4

3 2KKnc

K nc

1 1

2 4

4 27

8 198

16 1548


d

dP

log

log

m

eBc 2

3 2 bend

wiggler

2Nspikes

continuum



e

INKKPtot )1(

32

212

1 A][m][

cm][

GeV][726[W]

2

22

ILKE

Pp

tot or


100 mA 5 GeV K = 15 p = 2 cm









LnN

K ncen 2

1

2

1 221


to get bwnNn

1~

n

)(Kge

INN n

nnph

n

Kg

e

I n )(

0

01

02

03

04

05

06

07

08

09

1

0 1 2 3 4 5

Kg

n(K

)

n = 1

3

57

9

)1(

][)(

221

2

K

JJnKKgn

Function



2212

1

)1(

)(3

NKK

Kg

P

P n

tot

cen



r

R

d

L


c



~R

rd

Lr c~Rrc ~

Lc ~

in Fraunhofer limit




x-ray source

Rings 1

ERLs 1

XFEL 1

c









)( )(

yxx

22

4

)(dxd

FdzxB

22)( dxdzxBF

invdzxBxd

FdxdzxB

d

Fd )( )( 2

2

22

2

2





xikezEzEdT

cdzxB

)2()2(

2)(

20

yikxx ezyxEzyxEyd

T

cd

)2()2(2

2

20

2

2

2 )( )(1

dezxEExdezxEE xikx

xikx




)(2)(

1cotexp

)()(

220

0 zR

ik

zwx

z

zkzi

zw

wEzxE

R

)1()( 2220

2Rzzwzw

20wzR

)1()( 22 zzzzR R

2

2

2

2

0

)(

2

1exp)(

rr

zxBzxB

00 1 2 kww rr

Rrr

rr

z

42

0

)2(B

Fcoh 20 )2( rr

FB






)21 ( here ))((e24

)0( 2)(

0

ntnntdc

eE tti

)(i0

i

i

e)0()0( cxtie

eEE

eN

EEEE1i

2i

1i

21 )0()0()0()0(

ji

2j

1i

)0()0(

EE

eN

22

e)1( zkee NN

1e22

zkeN




)0()0(e)0()0( i2

0

i1

0

)(21

21i

eexik

e EENEE e






2

00

)2()000(

F

B





2

2

2

2

2

00

2

1exp

)2()0(

rr

xFxB

LL rr 2 42

TyTyxTTx

FB

2)2(

)000(

2236122

1212222 LLa xxrTx

2236122

121222 LLyyrTy

222xrxT

222yryT





x

2 Lrropt

yx

41

41

1

)2()000(

2yx



)8(formin2

2formin

2formin2

2

L

L

L


4~ if also

Lopt

1)4(or 1)4(





20N

22

1

1

41

41

1

)2()000(

NN

FB

yx





2

2

2

tEyx kk

cBpeakc

1

2

3

n

KgNKgNN n

ezyx

ncne

z

nc


33max











Slide 3

Slide 4





Dimension Estimates



Slide 12

Slide 13



Demand for X-rays


Introduction





















Diffraction Limit






Photon Degeneracy


In the lab frame

nfnS

S

c

e

dd

dE

nNn

n

z

z

nperp

sin

cossin

cos1

cos1

1

2

22

2

2

1

22

22

22

2

nf

n

S

S

c

e

dd

dEnN

zn

zn

z

npar

cossin

cos1sin

cos

cos1

1

22

2

2

1

22

2

0

0

cos1sin

cos1sin

n

nnNnf

zz

zznN


nfnSSc

e

dd

dEnNnn

nperp cossin

sin

22

22

22

21

2

nf

n

S

S

c

e

dd

dEnN

n

z

zn

npar

cossin

sincos1

cos

22

2

2

12


0 as 21

22

cos1

02

2

020

n

Kn

nn z

z

z



nfnSSc

e

dd

dEnNnn

nperp cossin

sin

22

22

22

21

2

nf

n

S

S

c

e

dd

dEnN

n

z

zn

npar

cossin

sincos1

cos

22

2

2

12


22

2

0

0

8

cos1

coscos

cos1

cossincossin

Kncdn

Kncdn

z

zzzz

zxx

(217)



0 sin2

222

22

nf

n

KF

c

e

dd

dEnN

nnperp

0 cos2

222

22

nf

n

KF

c

e

dd

dEnN

nnpar

2

2

2

2

12

2

2

12

2

2

2

2 21421414

1

K

nKJ

K

nKJ

KnKF nn

z

n



0 sin

22

22

nf

n

KF

dd

dNnN

nnperp

0 cos

22

22

nf

n

KF

dd

dNnN

nnpar


KFNdd

dNn

ntot 22





y

x

Central Cone



r

1n

1l

2l


Dimension Estimates

Harmonic bands at

211 2K

n

lnl


0 2

21

2

1 2

ncLnN

Kn

nr





Kge

IN n

nF

nKFKKg nn 21 2

2

0

n 2F rntot

d

dN



22

22

21

cossin

sin nSSNn

d

dEnn

nperp

2

2

1

cossin

sincos1

cos

n

S

S

Nnd

dE

n

z

zn

npar



2

2

22

222

coscos1

cos

cos14

sincos14

z

z

z

nparn

z

nperpn

KNF

d

dN

KNF

d

dN

2

2

2

2

12

2

2

122

22

21421421

K

nKJ

K

nKJ

K

KnKF nnn


Compare with (210)











Radiation Intensity




)exp(0 kk tiEE

eN

kk

e

tiN

fb1

)exp(1

22

0 eNfbII

single electron

eNfb 1~2

eNII 0

1 fb 20~ eNII


Demand for X-rays







CHESSCHESS




Flux phs01bw




Introduction


ΔE t






p1z

p1

θ1x

electron bunch ε1

linac

px p2

p2z

θ2x

ε2 = ε1 p2z p1z

ε = εn



geometricx θx

mc2

normalized x px



Quantum Excitation

ρ = p

eB ρ =

p eB p

eB

Equilibrium

Eph

22

~ phphE EN

dt

d

Radiative Dampingvs




Touschek Effect


bull

bull e 1

e 2

x

z

p 1 in

p 2 in

p 1 out p 2 out






ERL (w compression)

t



A(nm-rad)2 max Nund






ERL better by






But firsthellip

SASE






previous )















Injector Parameters










endash

endashendash


Flu

x [p

hs

01

bw]

Bri

ghtn

ess

[ph

sm

m2

mr2

01

bw]

Flu

x [p

hs

01

bw]



p

N N

N

S

SS

Kz

x

y

zkBB py sin0

]m[]T[493 0 pBK


)]81475(exp[333]T[0 B

pgap for SmCo5 here







z

x

endash

in endash frame

pp

d

Pd2sin

N

1

z

x

back to lab frame

1

~

d

dP

1

on a

xis

off-axis

d

dP

1

N

1~


)1(2

22221

2

Kn

pn

pn nN

1~

(for fixed θ only)



z

x

1K

1K


z

x1

~even

odd



21

4

3 2KKnc

K nc

1 1

2 4

4 27

8 198

16 1548


d

dP

log

log

m

eBc 2

3 2 bend

wiggler

2Nspikes

continuum



e

INKKPtot )1(

32

212

1 A][m][

cm][

GeV][726[W]

2

22

ILKE

Pp

tot or


100 mA 5 GeV K = 15 p = 2 cm









LnN

K ncen 2

1

2

1 221


to get bwnNn

1~

n

)(Kge

INN n

nnph

n

Kg

e

I n )(

0

01

02

03

04

05

06

07

08

09

1

0 1 2 3 4 5

Kg

n(K

)

n = 1

3

57

9

)1(

][)(

221

2

K

JJnKKgn

Function



2212

1

)1(

)(3

NKK

Kg

P

P n

tot

cen



r

R

d

L


c



~R

rd

Lr c~Rrc ~

Lc ~

in Fraunhofer limit




x-ray source

Rings 1

ERLs 1

XFEL 1

c









)( )(

yxx

22

4

)(dxd

FdzxB

22)( dxdzxBF

invdzxBxd

FdxdzxB

d

Fd )( )( 2

2

22

2

2





xikezEzEdT

cdzxB

)2()2(

2)(

20

yikxx ezyxEzyxEyd

T

cd

)2()2(2

2

20

2

2

2 )( )(1

dezxEExdezxEE xikx

xikx




)(2)(

1cotexp

)()(

220

0 zR

ik

zwx

z

zkzi

zw

wEzxE

R

)1()( 2220

2Rzzwzw

20wzR

)1()( 22 zzzzR R

2

2

2

2

0

)(

2

1exp)(

rr

zxBzxB

00 1 2 kww rr

Rrr

rr

z

42

0

)2(B

Fcoh 20 )2( rr

FB






)21 ( here ))((e24

)0( 2)(

0

ntnntdc

eE tti

)(i0

i

i

e)0()0( cxtie

eEE

eN

EEEE1i

2i

1i

21 )0()0()0()0(

ji

2j

1i

)0()0(

EE

eN

22

e)1( zkee NN

1e22

zkeN




)0()0(e)0()0( i2

0

i1

0

)(21

21i

eexik

e EENEE e






2

00

)2()000(

F

B





2

2

2

2

2

00

2

1exp

)2()0(

rr

xFxB

LL rr 2 42

TyTyxTTx

FB

2)2(

)000(

2236122

1212222 LLa xxrTx

2236122

121222 LLyyrTy

222xrxT

222yryT





x

2 Lrropt

yx

41

41

1

)2()000(

2yx



)8(formin2

2formin

2formin2

2

L

L

L


4~ if also

Lopt

1)4(or 1)4(





20N

22

1

1

41

41

1

)2()000(

NN

FB

yx





2

2

2

tEyx kk

cBpeakc

1

2

3

n

KgNKgNN n

ezyx

ncne

z

nc


33max











Slide 3

Slide 4





Dimension Estimates



Slide 12

Slide 13



Demand for X-rays


Introduction





















Diffraction Limit






Photon Degeneracy


nfnSSc

e

dd

dEnNnn

nperp cossin

sin

22

22

22

21

2

nf

n

S

S

c

e

dd

dEnN

n

z

zn

npar

cossin

sincos1

cos

22

2

2

12


0 as 21

22

cos1

02

2

020

n

Kn

nn z

z

z



nfnSSc

e

dd

dEnNnn

nperp cossin

sin

22

22

22

21

2

nf

n

S

S

c

e

dd

dEnN

n

z

zn

npar

cossin

sincos1

cos

22

2

2

12


22

2

0

0

8

cos1

coscos

cos1

cossincossin

Kncdn

Kncdn

z

zzzz

zxx

(217)



0 sin2

222

22

nf

n

KF

c

e

dd

dEnN

nnperp

0 cos2

222

22

nf

n

KF

c

e

dd

dEnN

nnpar

2

2

2

2

12

2

2

12

2

2

2

2 21421414

1

K

nKJ

K

nKJ

KnKF nn

z

n



0 sin

22

22

nf

n

KF

dd

dNnN

nnperp

0 cos

22

22

nf

n

KF

dd

dNnN

nnpar


KFNdd

dNn

ntot 22





y

x

Central Cone



r

1n

1l

2l


Dimension Estimates

Harmonic bands at

211 2K

n

lnl


0 2

21

2

1 2

ncLnN

Kn

nr





Kge

IN n

nF

nKFKKg nn 21 2

2

0

n 2F rntot

d

dN



22

22

21

cossin

sin nSSNn

d

dEnn

nperp

2

2

1

cossin

sincos1

cos

n

S

S

Nnd

dE

n

z

zn

npar



2

2

22

222

coscos1

cos

cos14

sincos14

z

z

z

nparn

z

nperpn

KNF

d

dN

KNF

d

dN

2

2

2

2

12

2

2

122

22

21421421

K

nKJ

K

nKJ

K

KnKF nnn


Compare with (210)











Radiation Intensity




)exp(0 kk tiEE

eN

kk

e

tiN

fb1

)exp(1

22

0 eNfbII

single electron

eNfb 1~2

eNII 0

1 fb 20~ eNII


Demand for X-rays







CHESSCHESS




Flux phs01bw




Introduction


ΔE t






p1z

p1

θ1x

electron bunch ε1

linac

px p2

p2z

θ2x

ε2 = ε1 p2z p1z

ε = εn



geometricx θx

mc2

normalized x px



Quantum Excitation

ρ = p

eB ρ =

p eB p

eB

Equilibrium

Eph

22

~ phphE EN

dt

d

Radiative Dampingvs




Touschek Effect


bull

bull e 1

e 2

x

z

p 1 in

p 2 in

p 1 out p 2 out






ERL (w compression)

t



A(nm-rad)2 max Nund






ERL better by






But firsthellip

SASE






previous )















Injector Parameters










endash

endashendash


Flu

x [p

hs

01

bw]

Bri

ghtn

ess

[ph

sm

m2

mr2

01

bw]

Flu

x [p

hs

01

bw]



p

N N

N

S

SS

Kz

x

y

zkBB py sin0

]m[]T[493 0 pBK


)]81475(exp[333]T[0 B

pgap for SmCo5 here







z

x

endash

in endash frame

pp

d

Pd2sin

N

1

z

x

back to lab frame

1

~

d

dP

1

on a

xis

off-axis

d

dP

1

N

1~


)1(2

22221

2

Kn

pn

pn nN

1~

(for fixed θ only)



z

x

1K

1K


z

x1

~even

odd



21

4

3 2KKnc

K nc

1 1

2 4

4 27

8 198

16 1548


d

dP

log

log

m

eBc 2

3 2 bend

wiggler

2Nspikes

continuum



e

INKKPtot )1(

32

212

1 A][m][

cm][

GeV][726[W]

2

22

ILKE

Pp

tot or


100 mA 5 GeV K = 15 p = 2 cm









LnN

K ncen 2

1

2

1 221


to get bwnNn

1~

n

)(Kge

INN n

nnph

n

Kg

e

I n )(

0

01

02

03

04

05

06

07

08

09

1

0 1 2 3 4 5

Kg

n(K

)

n = 1

3

57

9

)1(

][)(

221

2

K

JJnKKgn

Function



2212

1

)1(

)(3

NKK

Kg

P

P n

tot

cen



r

R

d

L


c



~R

rd

Lr c~Rrc ~

Lc ~

in Fraunhofer limit




x-ray source

Rings 1

ERLs 1

XFEL 1

c









)( )(

yxx

22

4

)(dxd

FdzxB

22)( dxdzxBF

invdzxBxd

FdxdzxB

d

Fd )( )( 2

2

22

2

2





xikezEzEdT

cdzxB

)2()2(

2)(

20

yikxx ezyxEzyxEyd

T

cd

)2()2(2

2

20

2

2

2 )( )(1

dezxEExdezxEE xikx

xikx




)(2)(

1cotexp

)()(

220

0 zR

ik

zwx

z

zkzi

zw

wEzxE

R

)1()( 2220

2Rzzwzw

20wzR

)1()( 22 zzzzR R

2

2

2

2

0

)(

2

1exp)(

rr

zxBzxB

00 1 2 kww rr

Rrr

rr

z

42

0

)2(B

Fcoh 20 )2( rr

FB






)21 ( here ))((e24

)0( 2)(

0

ntnntdc

eE tti

)(i0

i

i

e)0()0( cxtie

eEE

eN

EEEE1i

2i

1i

21 )0()0()0()0(

ji

2j

1i

)0()0(

EE

eN

22

e)1( zkee NN

1e22

zkeN




)0()0(e)0()0( i2

0

i1

0

)(21

21i

eexik

e EENEE e






2

00

)2()000(

F

B





2

2

2

2

2

00

2

1exp

)2()0(

rr

xFxB

LL rr 2 42

TyTyxTTx

FB

2)2(

)000(

2236122

1212222 LLa xxrTx

2236122

121222 LLyyrTy

222xrxT

222yryT





x

2 Lrropt

yx

41

41

1

)2()000(

2yx



)8(formin2

2formin

2formin2

2

L

L

L


4~ if also

Lopt

1)4(or 1)4(





20N

22

1

1

41

41

1

)2()000(

NN

FB

yx





2

2

2

tEyx kk

cBpeakc

1

2

3

n

KgNKgNN n

ezyx

ncne

z

nc


33max











Slide 3

Slide 4





Dimension Estimates



Slide 12

Slide 13



Demand for X-rays


Introduction





















Diffraction Limit






Photon Degeneracy



nfnSSc

e

dd

dEnNnn

nperp cossin

sin

22

22

22

21

2

nf

n

S

S

c

e

dd

dEnN

n

z

zn

npar

cossin

sincos1

cos

22

2

2

12


22

2

0

0

8

cos1

coscos

cos1

cossincossin

Kncdn

Kncdn

z

zzzz

zxx

(217)



0 sin2

222

22

nf

n

KF

c

e

dd

dEnN

nnperp

0 cos2

222

22

nf

n

KF

c

e

dd

dEnN

nnpar

2

2

2

2

12

2

2

12

2

2

2

2 21421414

1

K

nKJ

K

nKJ

KnKF nn

z

n



0 sin

22

22

nf

n

KF

dd

dNnN

nnperp

0 cos

22

22

nf

n

KF

dd

dNnN

nnpar


KFNdd

dNn

ntot 22





y

x

Central Cone



r

1n

1l

2l


Dimension Estimates

Harmonic bands at

211 2K

n

lnl


0 2

21

2

1 2

ncLnN

Kn

nr





Kge

IN n

nF

nKFKKg nn 21 2

2

0

n 2F rntot

d

dN



22

22

21

cossin

sin nSSNn

d

dEnn

nperp

2

2

1

cossin

sincos1

cos

n

S

S

Nnd

dE

n

z

zn

npar



2

2

22

222

coscos1

cos

cos14

sincos14

z

z

z

nparn

z

nperpn

KNF

d

dN

KNF

d

dN

2

2

2

2

12

2

2

122

22

21421421

K

nKJ

K

nKJ

K

KnKF nnn


Compare with (210)











Radiation Intensity




)exp(0 kk tiEE

eN

kk

e

tiN

fb1

)exp(1

22

0 eNfbII

single electron

eNfb 1~2

eNII 0

1 fb 20~ eNII


Demand for X-rays







CHESSCHESS




Flux phs01bw




Introduction


ΔE t






p1z

p1

θ1x

electron bunch ε1

linac

px p2

p2z

θ2x

ε2 = ε1 p2z p1z

ε = εn



geometricx θx

mc2

normalized x px



Quantum Excitation

ρ = p

eB ρ =

p eB p

eB

Equilibrium

Eph

22

~ phphE EN

dt

d

Radiative Dampingvs




Touschek Effect


bull

bull e 1

e 2

x

z

p 1 in

p 2 in

p 1 out p 2 out






ERL (w compression)

t



A(nm-rad)2 max Nund






ERL better by






But firsthellip

SASE






previous )















Injector Parameters










endash

endashendash


Flu

x [p

hs

01

bw]

Bri

ghtn

ess

[ph

sm

m2

mr2

01

bw]

Flu

x [p

hs

01

bw]



p

N N

N

S

SS

Kz

x

y

zkBB py sin0

]m[]T[493 0 pBK


)]81475(exp[333]T[0 B

pgap for SmCo5 here







z

x

endash

in endash frame

pp

d

Pd2sin

N

1

z

x

back to lab frame

1

~

d

dP

1

on a

xis

off-axis

d

dP

1

N

1~


)1(2

22221

2

Kn

pn

pn nN

1~

(for fixed θ only)



z

x

1K

1K


z

x1

~even

odd



21

4

3 2KKnc

K nc

1 1

2 4

4 27

8 198

16 1548


d

dP

log

log

m

eBc 2

3 2 bend

wiggler

2Nspikes

continuum



e

INKKPtot )1(

32

212

1 A][m][

cm][

GeV][726[W]

2

22

ILKE

Pp

tot or


100 mA 5 GeV K = 15 p = 2 cm









LnN

K ncen 2

1

2

1 221


to get bwnNn

1~

n

)(Kge

INN n

nnph

n

Kg

e

I n )(

0

01

02

03

04

05

06

07

08

09

1

0 1 2 3 4 5

Kg

n(K

)

n = 1

3

57

9

)1(

][)(

221

2

K

JJnKKgn

Function



2212

1

)1(

)(3

NKK

Kg

P

P n

tot

cen



r

R

d

L


c



~R

rd

Lr c~Rrc ~

Lc ~

in Fraunhofer limit




x-ray source

Rings 1

ERLs 1

XFEL 1

c









)( )(

yxx

22

4

)(dxd

FdzxB

22)( dxdzxBF

invdzxBxd

FdxdzxB

d

Fd )( )( 2

2

22

2

2





xikezEzEdT

cdzxB

)2()2(

2)(

20

yikxx ezyxEzyxEyd

T

cd

)2()2(2

2

20

2

2

2 )( )(1

dezxEExdezxEE xikx

xikx




)(2)(

1cotexp

)()(

220

0 zR

ik

zwx

z

zkzi

zw

wEzxE

R

)1()( 2220

2Rzzwzw

20wzR

)1()( 22 zzzzR R

2

2

2

2

0

)(

2

1exp)(

rr

zxBzxB

00 1 2 kww rr

Rrr

rr

z

42

0

)2(B

Fcoh 20 )2( rr

FB






)21 ( here ))((e24

)0( 2)(

0

ntnntdc

eE tti

)(i0

i

i

e)0()0( cxtie

eEE

eN

EEEE1i

2i

1i

21 )0()0()0()0(

ji

2j

1i

)0()0(

EE

eN

22

e)1( zkee NN

1e22

zkeN




)0()0(e)0()0( i2

0

i1

0

)(21

21i

eexik

e EENEE e






2

00

)2()000(

F

B





2

2

2

2

2

00

2

1exp

)2()0(

rr

xFxB

LL rr 2 42

TyTyxTTx

FB

2)2(

)000(

2236122

1212222 LLa xxrTx

2236122

121222 LLyyrTy

222xrxT

222yryT





x

2 Lrropt

yx

41

41

1

)2()000(

2yx



)8(formin2

2formin

2formin2

2

L

L

L


4~ if also

Lopt

1)4(or 1)4(





20N

22

1

1

41

41

1

)2()000(

NN

FB

yx





2

2

2

tEyx kk

cBpeakc

1

2

3

n

KgNKgNN n

ezyx

ncne

z

nc


33max











Slide 3

Slide 4





Dimension Estimates



Slide 12

Slide 13



Demand for X-rays


Introduction





















Diffraction Limit






Photon Degeneracy



0 sin2

222

22

nf

n

KF

c

e

dd

dEnN

nnperp

0 cos2

222

22

nf

n

KF

c

e

dd

dEnN

nnpar

2

2

2

2

12

2

2

12

2

2

2

2 21421414

1

K

nKJ

K

nKJ

KnKF nn

z

n



0 sin

22

22

nf

n

KF

dd

dNnN

nnperp

0 cos

22

22

nf

n

KF

dd

dNnN

nnpar


KFNdd

dNn

ntot 22





y

x

Central Cone



r

1n

1l

2l


Dimension Estimates

Harmonic bands at

211 2K

n

lnl


0 2

21

2

1 2

ncLnN

Kn

nr





Kge

IN n

nF

nKFKKg nn 21 2

2

0

n 2F rntot

d

dN



22

22

21

cossin

sin nSSNn

d

dEnn

nperp

2

2

1

cossin

sincos1

cos

n

S

S

Nnd

dE

n

z

zn

npar



2

2

22

222

coscos1

cos

cos14

sincos14

z

z

z

nparn

z

nperpn

KNF

d

dN

KNF

d

dN

2

2

2

2

12

2

2

122

22

21421421

K

nKJ

K

nKJ

K

KnKF nnn


Compare with (210)











Radiation Intensity




)exp(0 kk tiEE

eN

kk

e

tiN

fb1

)exp(1

22

0 eNfbII

single electron

eNfb 1~2

eNII 0

1 fb 20~ eNII


Demand for X-rays







CHESSCHESS




Flux phs01bw




Introduction


ΔE t






p1z

p1

θ1x

electron bunch ε1

linac

px p2

p2z

θ2x

ε2 = ε1 p2z p1z

ε = εn



geometricx θx

mc2

normalized x px



Quantum Excitation

ρ = p

eB ρ =

p eB p

eB

Equilibrium

Eph

22

~ phphE EN

dt

d

Radiative Dampingvs




Touschek Effect


bull

bull e 1

e 2

x

z

p 1 in

p 2 in

p 1 out p 2 out






ERL (w compression)

t



A(nm-rad)2 max Nund






ERL better by






But firsthellip

SASE






previous )















Injector Parameters










endash

endashendash


Flu

x [p

hs

01

bw]

Bri

ghtn

ess

[ph

sm

m2

mr2

01

bw]

Flu

x [p

hs

01

bw]



p

N N

N

S

SS

Kz

x

y

zkBB py sin0

]m[]T[493 0 pBK


)]81475(exp[333]T[0 B

pgap for SmCo5 here







z

x

endash

in endash frame

pp

d

Pd2sin

N

1

z

x

back to lab frame

1

~

d

dP

1

on a

xis

off-axis

d

dP

1

N

1~


)1(2

22221

2

Kn

pn

pn nN

1~

(for fixed θ only)



z

x

1K

1K


z

x1

~even

odd



21

4

3 2KKnc

K nc

1 1

2 4

4 27

8 198

16 1548


d

dP

log

log

m

eBc 2

3 2 bend

wiggler

2Nspikes

continuum



e

INKKPtot )1(

32

212

1 A][m][

cm][

GeV][726[W]

2

22

ILKE

Pp

tot or


100 mA 5 GeV K = 15 p = 2 cm









LnN

K ncen 2

1

2

1 221


to get bwnNn

1~

n

)(Kge

INN n

nnph

n

Kg

e

I n )(

0

01

02

03

04

05

06

07

08

09

1

0 1 2 3 4 5

Kg

n(K

)

n = 1

3

57

9

)1(

][)(

221

2

K

JJnKKgn

Function



2212

1

)1(

)(3

NKK

Kg

P

P n

tot

cen



r

R

d

L


c



~R

rd

Lr c~Rrc ~

Lc ~

in Fraunhofer limit




x-ray source

Rings 1

ERLs 1

XFEL 1

c









)( )(

yxx

22

4

)(dxd

FdzxB

22)( dxdzxBF

invdzxBxd

FdxdzxB

d

Fd )( )( 2

2

22

2

2





xikezEzEdT

cdzxB

)2()2(

2)(

20

yikxx ezyxEzyxEyd

T

cd

)2()2(2

2

20

2

2

2 )( )(1

dezxEExdezxEE xikx

xikx




)(2)(

1cotexp

)()(

220

0 zR

ik

zwx

z

zkzi

zw

wEzxE

R

)1()( 2220

2Rzzwzw

20wzR

)1()( 22 zzzzR R

2

2

2

2

0

)(

2

1exp)(

rr

zxBzxB

00 1 2 kww rr

Rrr

rr

z

42

0

)2(B

Fcoh 20 )2( rr

FB






)21 ( here ))((e24

)0( 2)(

0

ntnntdc

eE tti

)(i0

i

i

e)0()0( cxtie

eEE

eN

EEEE1i

2i

1i

21 )0()0()0()0(

ji

2j

1i

)0()0(

EE

eN

22

e)1( zkee NN

1e22

zkeN




)0()0(e)0()0( i2

0

i1

0

)(21

21i

eexik

e EENEE e






2

00

)2()000(

F

B





2

2

2

2

2

00

2

1exp

)2()0(

rr

xFxB

LL rr 2 42

TyTyxTTx

FB

2)2(

)000(

2236122

1212222 LLa xxrTx

2236122

121222 LLyyrTy

222xrxT

222yryT





x

2 Lrropt

yx

41

41

1

)2()000(

2yx



)8(formin2

2formin

2formin2

2

L

L

L


4~ if also

Lopt

1)4(or 1)4(





20N

22

1

1

41

41

1

)2()000(

NN

FB

yx





2

2

2

tEyx kk

cBpeakc

1

2

3

n

KgNKgNN n

ezyx

ncne

z

nc


33max











Slide 3

Slide 4





Dimension Estimates



Slide 12

Slide 13



Demand for X-rays


Introduction





















Diffraction Limit






Photon Degeneracy



0 sin

22

22

nf

n

KF

dd

dNnN

nnperp

0 cos

22

22

nf

n

KF

dd

dNnN

nnpar


KFNdd

dNn

ntot 22





y

x

Central Cone



r

1n

1l

2l


Dimension Estimates

Harmonic bands at

211 2K

n

lnl


0 2

21

2

1 2

ncLnN

Kn

nr





Kge

IN n

nF

nKFKKg nn 21 2

2

0

n 2F rntot

d

dN



22

22

21

cossin

sin nSSNn

d

dEnn

nperp

2

2

1

cossin

sincos1

cos

n

S

S

Nnd

dE

n

z

zn

npar



2

2

22

222

coscos1

cos

cos14

sincos14

z

z

z

nparn

z

nperpn

KNF

d

dN

KNF

d

dN

2

2

2

2

12

2

2

122

22

21421421

K

nKJ

K

nKJ

K

KnKF nnn


Compare with (210)











Radiation Intensity




)exp(0 kk tiEE

eN

kk

e

tiN

fb1

)exp(1

22

0 eNfbII

single electron

eNfb 1~2

eNII 0

1 fb 20~ eNII


Demand for X-rays







CHESSCHESS




Flux phs01bw




Introduction


ΔE t






p1z

p1

θ1x

electron bunch ε1

linac

px p2

p2z

θ2x

ε2 = ε1 p2z p1z

ε = εn



geometricx θx

mc2

normalized x px



Quantum Excitation

ρ = p

eB ρ =

p eB p

eB

Equilibrium

Eph

22

~ phphE EN

dt

d

Radiative Dampingvs




Touschek Effect


bull

bull e 1

e 2

x

z

p 1 in

p 2 in

p 1 out p 2 out






ERL (w compression)

t



A(nm-rad)2 max Nund






ERL better by






But firsthellip

SASE






previous )















Injector Parameters










endash

endashendash


Flu

x [p

hs

01

bw]

Bri

ghtn

ess

[ph

sm

m2

mr2

01

bw]

Flu

x [p

hs

01

bw]



p

N N

N

S

SS

Kz

x

y

zkBB py sin0

]m[]T[493 0 pBK


)]81475(exp[333]T[0 B

pgap for SmCo5 here







z

x

endash

in endash frame

pp

d

Pd2sin

N

1

z

x

back to lab frame

1

~

d

dP

1

on a

xis

off-axis

d

dP

1

N

1~


)1(2

22221

2

Kn

pn

pn nN

1~

(for fixed θ only)



z

x

1K

1K


z

x1

~even

odd



21

4

3 2KKnc

K nc

1 1

2 4

4 27

8 198

16 1548


d

dP

log

log

m

eBc 2

3 2 bend

wiggler

2Nspikes

continuum



e

INKKPtot )1(

32

212

1 A][m][

cm][

GeV][726[W]

2

22

ILKE

Pp

tot or


100 mA 5 GeV K = 15 p = 2 cm









LnN

K ncen 2

1

2

1 221


to get bwnNn

1~

n

)(Kge

INN n

nnph

n

Kg

e

I n )(

0

01

02

03

04

05

06

07

08

09

1

0 1 2 3 4 5

Kg

n(K

)

n = 1

3

57

9

)1(

][)(

221

2

K

JJnKKgn

Function



2212

1

)1(

)(3

NKK

Kg

P

P n

tot

cen



r

R

d

L


c



~R

rd

Lr c~Rrc ~

Lc ~

in Fraunhofer limit




x-ray source

Rings 1

ERLs 1

XFEL 1

c









)( )(

yxx

22

4

)(dxd

FdzxB

22)( dxdzxBF

invdzxBxd

FdxdzxB

d

Fd )( )( 2

2

22

2

2





xikezEzEdT

cdzxB

)2()2(

2)(

20

yikxx ezyxEzyxEyd

T

cd

)2()2(2

2

20

2

2

2 )( )(1

dezxEExdezxEE xikx

xikx




)(2)(

1cotexp

)()(

220

0 zR

ik

zwx

z

zkzi

zw

wEzxE

R

)1()( 2220

2Rzzwzw

20wzR

)1()( 22 zzzzR R

2

2

2

2

0

)(

2

1exp)(

rr

zxBzxB

00 1 2 kww rr

Rrr

rr

z

42

0

)2(B

Fcoh 20 )2( rr

FB






)21 ( here ))((e24

)0( 2)(

0

ntnntdc

eE tti

)(i0

i

i

e)0()0( cxtie

eEE

eN

EEEE1i

2i

1i

21 )0()0()0()0(

ji

2j

1i

)0()0(

EE

eN

22

e)1( zkee NN

1e22

zkeN




)0()0(e)0()0( i2

0

i1

0

)(21

21i

eexik

e EENEE e






2

00

)2()000(

F

B





2

2

2

2

2

00

2

1exp

)2()0(

rr

xFxB

LL rr 2 42

TyTyxTTx

FB

2)2(

)000(

2236122

1212222 LLa xxrTx

2236122

121222 LLyyrTy

222xrxT

222yryT





x

2 Lrropt

yx

41

41

1

)2()000(

2yx



)8(formin2

2formin

2formin2

2

L

L

L


4~ if also

Lopt

1)4(or 1)4(





20N

22

1

1

41

41

1

)2()000(

NN

FB

yx





2

2

2

tEyx kk

cBpeakc

1

2

3

n

KgNKgNN n

ezyx

ncne

z

nc


33max











Slide 3

Slide 4





Dimension Estimates



Slide 12

Slide 13



Demand for X-rays


Introduction





















Diffraction Limit






Photon Degeneracy




y

x

Central Cone



r

1n

1l

2l


Dimension Estimates

Harmonic bands at

211 2K

n

lnl


0 2

21

2

1 2

ncLnN

Kn

nr





Kge

IN n

nF

nKFKKg nn 21 2

2

0

n 2F rntot

d

dN



22

22

21

cossin

sin nSSNn

d

dEnn

nperp

2

2

1

cossin

sincos1

cos

n

S

S

Nnd

dE

n

z

zn

npar



2

2

22

222

coscos1

cos

cos14

sincos14

z

z

z

nparn

z

nperpn

KNF

d

dN

KNF

d

dN

2

2

2

2

12

2

2

122

22

21421421

K

nKJ

K

nKJ

K

KnKF nnn


Compare with (210)











Radiation Intensity




)exp(0 kk tiEE

eN

kk

e

tiN

fb1

)exp(1

22

0 eNfbII

single electron

eNfb 1~2

eNII 0

1 fb 20~ eNII


Demand for X-rays







CHESSCHESS




Flux phs01bw




Introduction


ΔE t






p1z

p1

θ1x

electron bunch ε1

linac

px p2

p2z

θ2x

ε2 = ε1 p2z p1z

ε = εn



geometricx θx

mc2

normalized x px



Quantum Excitation

ρ = p

eB ρ =

p eB p

eB

Equilibrium

Eph

22

~ phphE EN

dt

d

Radiative Dampingvs




Touschek Effect


bull

bull e 1

e 2

x

z

p 1 in

p 2 in

p 1 out p 2 out






ERL (w compression)

t



A(nm-rad)2 max Nund






ERL better by






But firsthellip

SASE






previous )















Injector Parameters










endash

endashendash


Flu

x [p

hs

01

bw]

Bri

ghtn

ess

[ph

sm

m2

mr2

01

bw]

Flu

x [p

hs

01

bw]



p

N N

N

S

SS

Kz

x

y

zkBB py sin0

]m[]T[493 0 pBK


)]81475(exp[333]T[0 B

pgap for SmCo5 here







z

x

endash

in endash frame

pp

d

Pd2sin

N

1

z

x

back to lab frame

1

~

d

dP

1

on a

xis

off-axis

d

dP

1

N

1~


)1(2

22221

2

Kn

pn

pn nN

1~

(for fixed θ only)



z

x

1K

1K


z

x1

~even

odd



21

4

3 2KKnc

K nc

1 1

2 4

4 27

8 198

16 1548


d

dP

log

log

m

eBc 2

3 2 bend

wiggler

2Nspikes

continuum



e

INKKPtot )1(

32

212

1 A][m][

cm][

GeV][726[W]

2

22

ILKE

Pp

tot or


100 mA 5 GeV K = 15 p = 2 cm









LnN

K ncen 2

1

2

1 221


to get bwnNn

1~

n

)(Kge

INN n

nnph

n

Kg

e

I n )(

0

01

02

03

04

05

06

07

08

09

1

0 1 2 3 4 5

Kg

n(K

)

n = 1

3

57

9

)1(

][)(

221

2

K

JJnKKgn

Function



2212

1

)1(

)(3

NKK

Kg

P

P n

tot

cen



r

R

d

L


c



~R

rd

Lr c~Rrc ~

Lc ~

in Fraunhofer limit




x-ray source

Rings 1

ERLs 1

XFEL 1

c









)( )(

yxx

22

4

)(dxd

FdzxB

22)( dxdzxBF

invdzxBxd

FdxdzxB

d

Fd )( )( 2

2

22

2

2





xikezEzEdT

cdzxB

)2()2(

2)(

20

yikxx ezyxEzyxEyd

T

cd

)2()2(2

2

20

2

2

2 )( )(1

dezxEExdezxEE xikx

xikx




)(2)(

1cotexp

)()(

220

0 zR

ik

zwx

z

zkzi

zw

wEzxE

R

)1()( 2220

2Rzzwzw

20wzR

)1()( 22 zzzzR R

2

2

2

2

0

)(

2

1exp)(

rr

zxBzxB

00 1 2 kww rr

Rrr

rr

z

42

0

)2(B

Fcoh 20 )2( rr

FB






)21 ( here ))((e24

)0( 2)(

0

ntnntdc

eE tti

)(i0

i

i

e)0()0( cxtie

eEE

eN

EEEE1i

2i

1i

21 )0()0()0()0(

ji

2j

1i

)0()0(

EE

eN

22

e)1( zkee NN

1e22

zkeN




)0()0(e)0()0( i2

0

i1

0

)(21

21i

eexik

e EENEE e






2

00

)2()000(

F

B





2

2

2

2

2

00

2

1exp

)2()0(

rr

xFxB

LL rr 2 42

TyTyxTTx

FB

2)2(

)000(

2236122

1212222 LLa xxrTx

2236122

121222 LLyyrTy

222xrxT

222yryT





x

2 Lrropt

yx

41

41

1

)2()000(

2yx



)8(formin2

2formin

2formin2

2

L

L

L


4~ if also

Lopt

1)4(or 1)4(





20N

22

1

1

41

41

1

)2()000(

NN

FB

yx





2

2

2

tEyx kk

cBpeakc

1

2

3

n

KgNKgNN n

ezyx

ncne

z

nc


33max











Slide 3

Slide 4





Dimension Estimates



Slide 12

Slide 13



Demand for X-rays


Introduction





















Diffraction Limit






Photon Degeneracy


Dimension Estimates

Harmonic bands at

211 2K

n

lnl


0 2

21

2

1 2

ncLnN

Kn

nr





Kge

IN n

nF

nKFKKg nn 21 2

2

0

n 2F rntot

d

dN



22

22

21

cossin

sin nSSNn

d

dEnn

nperp

2

2

1

cossin

sincos1

cos

n

S

S

Nnd

dE

n

z

zn

npar



2

2

22

222

coscos1

cos

cos14

sincos14

z

z

z

nparn

z

nperpn

KNF

d

dN

KNF

d

dN

2

2

2

2

12

2

2

122

22

21421421

K

nKJ

K

nKJ

K

KnKF nnn


Compare with (210)











Radiation Intensity




)exp(0 kk tiEE

eN

kk

e

tiN

fb1

)exp(1

22

0 eNfbII

single electron

eNfb 1~2

eNII 0

1 fb 20~ eNII


Demand for X-rays







CHESSCHESS




Flux phs01bw




Introduction


ΔE t






p1z

p1

θ1x

electron bunch ε1

linac

px p2

p2z

θ2x

ε2 = ε1 p2z p1z

ε = εn



geometricx θx

mc2

normalized x px



Quantum Excitation

ρ = p

eB ρ =

p eB p

eB

Equilibrium

Eph

22

~ phphE EN

dt

d

Radiative Dampingvs




Touschek Effect


bull

bull e 1

e 2

x

z

p 1 in

p 2 in

p 1 out p 2 out






ERL (w compression)

t



A(nm-rad)2 max Nund






ERL better by






But firsthellip

SASE






previous )















Injector Parameters










endash

endashendash


Flu

x [p

hs

01

bw]

Bri

ghtn

ess

[ph

sm

m2

mr2

01

bw]

Flu

x [p

hs

01

bw]



p

N N

N

S

SS

Kz

x

y

zkBB py sin0

]m[]T[493 0 pBK


)]81475(exp[333]T[0 B

pgap for SmCo5 here







z

x

endash

in endash frame

pp

d

Pd2sin

N

1

z

x

back to lab frame

1

~

d

dP

1

on a

xis

off-axis

d

dP

1

N

1~


)1(2

22221

2

Kn

pn

pn nN

1~

(for fixed θ only)



z

x

1K

1K


z

x1

~even

odd



21

4

3 2KKnc

K nc

1 1

2 4

4 27

8 198

16 1548


d

dP

log

log

m

eBc 2

3 2 bend

wiggler

2Nspikes

continuum



e

INKKPtot )1(

32

212

1 A][m][

cm][

GeV][726[W]

2

22

ILKE

Pp

tot or


100 mA 5 GeV K = 15 p = 2 cm









LnN

K ncen 2

1

2

1 221


to get bwnNn

1~

n

)(Kge

INN n

nnph

n

Kg

e

I n )(

0

01

02

03

04

05

06

07

08

09

1

0 1 2 3 4 5

Kg

n(K

)

n = 1

3

57

9

)1(

][)(

221

2

K

JJnKKgn

Function



2212

1

)1(

)(3

NKK

Kg

P

P n

tot

cen



r

R

d

L


c



~R

rd

Lr c~Rrc ~

Lc ~

in Fraunhofer limit




x-ray source

Rings 1

ERLs 1

XFEL 1

c









)( )(

yxx

22

4

)(dxd

FdzxB

22)( dxdzxBF

invdzxBxd

FdxdzxB

d

Fd )( )( 2

2

22

2

2





xikezEzEdT

cdzxB

)2()2(

2)(

20

yikxx ezyxEzyxEyd

T

cd

)2()2(2

2

20

2

2

2 )( )(1

dezxEExdezxEE xikx

xikx




)(2)(

1cotexp

)()(

220

0 zR

ik

zwx

z

zkzi

zw

wEzxE

R

)1()( 2220

2Rzzwzw

20wzR

)1()( 22 zzzzR R

2

2

2

2

0

)(

2

1exp)(

rr

zxBzxB

00 1 2 kww rr

Rrr

rr

z

42

0

)2(B

Fcoh 20 )2( rr

FB






)21 ( here ))((e24

)0( 2)(

0

ntnntdc

eE tti

)(i0

i

i

e)0()0( cxtie

eEE

eN

EEEE1i

2i

1i

21 )0()0()0()0(

ji

2j

1i

)0()0(

EE

eN

22

e)1( zkee NN

1e22

zkeN




)0()0(e)0()0( i2

0

i1

0

)(21

21i

eexik

e EENEE e






2

00

)2()000(

F

B





2

2

2

2

2

00

2

1exp

)2()0(

rr

xFxB

LL rr 2 42

TyTyxTTx

FB

2)2(

)000(

2236122

1212222 LLa xxrTx

2236122

121222 LLyyrTy

222xrxT

222yryT





x

2 Lrropt

yx

41

41

1

)2()000(

2yx



)8(formin2

2formin

2formin2

2

L

L

L


4~ if also

Lopt

1)4(or 1)4(





20N

22

1

1

41

41

1

)2()000(

NN

FB

yx





2

2

2

tEyx kk

cBpeakc

1

2

3

n

KgNKgNN n

ezyx

ncne

z

nc


33max











Slide 3

Slide 4





Dimension Estimates



Slide 12

Slide 13



Demand for X-rays


Introduction





















Diffraction Limit






Photon Degeneracy




Kge

IN n

nF

nKFKKg nn 21 2

2

0

n 2F rntot

d

dN



22

22

21

cossin

sin nSSNn

d

dEnn

nperp

2

2

1

cossin

sincos1

cos

n

S

S

Nnd

dE

n

z

zn

npar



2

2

22

222

coscos1

cos

cos14

sincos14

z

z

z

nparn

z

nperpn

KNF

d

dN

KNF

d

dN

2

2

2

2

12

2

2

122

22

21421421

K

nKJ

K

nKJ

K

KnKF nnn


Compare with (210)











Radiation Intensity




)exp(0 kk tiEE

eN

kk

e

tiN

fb1

)exp(1

22

0 eNfbII

single electron

eNfb 1~2

eNII 0

1 fb 20~ eNII


Demand for X-rays







CHESSCHESS




Flux phs01bw




Introduction


ΔE t






p1z

p1

θ1x

electron bunch ε1

linac

px p2

p2z

θ2x

ε2 = ε1 p2z p1z

ε = εn



geometricx θx

mc2

normalized x px



Quantum Excitation

ρ = p

eB ρ =

p eB p

eB

Equilibrium

Eph

22

~ phphE EN

dt

d

Radiative Dampingvs




Touschek Effect


bull

bull e 1

e 2

x

z

p 1 in

p 2 in

p 1 out p 2 out






ERL (w compression)

t



A(nm-rad)2 max Nund






ERL better by






But firsthellip

SASE






previous )















Injector Parameters










endash

endashendash


Flu

x [p

hs

01

bw]

Bri

ghtn

ess

[ph

sm

m2

mr2

01

bw]

Flu

x [p

hs

01

bw]



p

N N

N

S

SS

Kz

x

y

zkBB py sin0

]m[]T[493 0 pBK


)]81475(exp[333]T[0 B

pgap for SmCo5 here







z

x

endash

in endash frame

pp

d

Pd2sin

N

1

z

x

back to lab frame

1

~

d

dP

1

on a

xis

off-axis

d

dP

1

N

1~


)1(2

22221

2

Kn

pn

pn nN

1~

(for fixed θ only)



z

x

1K

1K


z

x1

~even

odd



21

4

3 2KKnc

K nc

1 1

2 4

4 27

8 198

16 1548


d

dP

log

log

m

eBc 2

3 2 bend

wiggler

2Nspikes

continuum



e

INKKPtot )1(

32

212

1 A][m][

cm][

GeV][726[W]

2

22

ILKE

Pp

tot or


100 mA 5 GeV K = 15 p = 2 cm









LnN

K ncen 2

1

2

1 221


to get bwnNn

1~

n

)(Kge

INN n

nnph

n

Kg

e

I n )(

0

01

02

03

04

05

06

07

08

09

1

0 1 2 3 4 5

Kg

n(K

)

n = 1

3

57

9

)1(

][)(

221

2

K

JJnKKgn

Function



2212

1

)1(

)(3

NKK

Kg

P

P n

tot

cen



r

R

d

L


c



~R

rd

Lr c~Rrc ~

Lc ~

in Fraunhofer limit




x-ray source

Rings 1

ERLs 1

XFEL 1

c









)( )(

yxx

22

4

)(dxd

FdzxB

22)( dxdzxBF

invdzxBxd

FdxdzxB

d

Fd )( )( 2

2

22

2

2





xikezEzEdT

cdzxB

)2()2(

2)(

20

yikxx ezyxEzyxEyd

T

cd

)2()2(2

2

20

2

2

2 )( )(1

dezxEExdezxEE xikx

xikx




)(2)(

1cotexp

)()(

220

0 zR

ik

zwx

z

zkzi

zw

wEzxE

R

)1()( 2220

2Rzzwzw

20wzR

)1()( 22 zzzzR R

2

2

2

2

0

)(

2

1exp)(

rr

zxBzxB

00 1 2 kww rr

Rrr

rr

z

42

0

)2(B

Fcoh 20 )2( rr

FB






)21 ( here ))((e24

)0( 2)(

0

ntnntdc

eE tti

)(i0

i

i

e)0()0( cxtie

eEE

eN

EEEE1i

2i

1i

21 )0()0()0()0(

ji

2j

1i

)0()0(

EE

eN

22

e)1( zkee NN

1e22

zkeN




)0()0(e)0()0( i2

0

i1

0

)(21

21i

eexik

e EENEE e






2

00

)2()000(

F

B





2

2

2

2

2

00

2

1exp

)2()0(

rr

xFxB

LL rr 2 42

TyTyxTTx

FB

2)2(

)000(

2236122

1212222 LLa xxrTx

2236122

121222 LLyyrTy

222xrxT

222yryT





x

2 Lrropt

yx

41

41

1

)2()000(

2yx



)8(formin2

2formin

2formin2

2

L

L

L


4~ if also

Lopt

1)4(or 1)4(





20N

22

1

1

41

41

1

)2()000(

NN

FB

yx





2

2

2

tEyx kk

cBpeakc

1

2

3

n

KgNKgNN n

ezyx

ncne

z

nc


33max











Slide 3

Slide 4





Dimension Estimates



Slide 12

Slide 13



Demand for X-rays


Introduction





















Diffraction Limit






Photon Degeneracy



22

22

21

cossin

sin nSSNn

d

dEnn

nperp

2

2

1

cossin

sincos1

cos

n

S

S

Nnd

dE

n

z

zn

npar



2

2

22

222

coscos1

cos

cos14

sincos14

z

z

z

nparn

z

nperpn

KNF

d

dN

KNF

d

dN

2

2

2

2

12

2

2

122

22

21421421

K

nKJ

K

nKJ

K

KnKF nnn


Compare with (210)











Radiation Intensity




)exp(0 kk tiEE

eN

kk

e

tiN

fb1

)exp(1

22

0 eNfbII

single electron

eNfb 1~2

eNII 0

1 fb 20~ eNII


Demand for X-rays







CHESSCHESS




Flux phs01bw




Introduction


ΔE t






p1z

p1

θ1x

electron bunch ε1

linac

px p2

p2z

θ2x

ε2 = ε1 p2z p1z

ε = εn



geometricx θx

mc2

normalized x px



Quantum Excitation

ρ = p

eB ρ =

p eB p

eB

Equilibrium

Eph

22

~ phphE EN

dt

d

Radiative Dampingvs




Touschek Effect


bull

bull e 1

e 2

x

z

p 1 in

p 2 in

p 1 out p 2 out






ERL (w compression)

t



A(nm-rad)2 max Nund






ERL better by






But firsthellip

SASE






previous )















Injector Parameters










endash

endashendash


Flu

x [p

hs

01

bw]

Bri

ghtn

ess

[ph

sm

m2

mr2

01

bw]

Flu

x [p

hs

01

bw]



p

N N

N

S

SS

Kz

x

y

zkBB py sin0

]m[]T[493 0 pBK


)]81475(exp[333]T[0 B

pgap for SmCo5 here







z

x

endash

in endash frame

pp

d

Pd2sin

N

1

z

x

back to lab frame

1

~

d

dP

1

on a

xis

off-axis

d

dP

1

N

1~


)1(2

22221

2

Kn

pn

pn nN

1~

(for fixed θ only)



z

x

1K

1K


z

x1

~even

odd



21

4

3 2KKnc

K nc

1 1

2 4

4 27

8 198

16 1548


d

dP

log

log

m

eBc 2

3 2 bend

wiggler

2Nspikes

continuum



e

INKKPtot )1(

32

212

1 A][m][

cm][

GeV][726[W]

2

22

ILKE

Pp

tot or


100 mA 5 GeV K = 15 p = 2 cm









LnN

K ncen 2

1

2

1 221


to get bwnNn

1~

n

)(Kge

INN n

nnph

n

Kg

e

I n )(

0

01

02

03

04

05

06

07

08

09

1

0 1 2 3 4 5

Kg

n(K

)

n = 1

3

57

9

)1(

][)(

221

2

K

JJnKKgn

Function



2212

1

)1(

)(3

NKK

Kg

P

P n

tot

cen



r

R

d

L


c



~R

rd

Lr c~Rrc ~

Lc ~

in Fraunhofer limit




x-ray source

Rings 1

ERLs 1

XFEL 1

c









)( )(

yxx

22

4

)(dxd

FdzxB

22)( dxdzxBF

invdzxBxd

FdxdzxB

d

Fd )( )( 2

2

22

2

2





xikezEzEdT

cdzxB

)2()2(

2)(

20

yikxx ezyxEzyxEyd

T

cd

)2()2(2

2

20

2

2

2 )( )(1

dezxEExdezxEE xikx

xikx




)(2)(

1cotexp

)()(

220

0 zR

ik

zwx

z

zkzi

zw

wEzxE

R

)1()( 2220

2Rzzwzw

20wzR

)1()( 22 zzzzR R

2

2

2

2

0

)(

2

1exp)(

rr

zxBzxB

00 1 2 kww rr

Rrr

rr

z

42

0

)2(B

Fcoh 20 )2( rr

FB






)21 ( here ))((e24

)0( 2)(

0

ntnntdc

eE tti

)(i0

i

i

e)0()0( cxtie

eEE

eN

EEEE1i

2i

1i

21 )0()0()0()0(

ji

2j

1i

)0()0(

EE

eN

22

e)1( zkee NN

1e22

zkeN




)0()0(e)0()0( i2

0

i1

0

)(21

21i

eexik

e EENEE e






2

00

)2()000(

F

B





2

2

2

2

2

00

2

1exp

)2()0(

rr

xFxB

LL rr 2 42

TyTyxTTx

FB

2)2(

)000(

2236122

1212222 LLa xxrTx

2236122

121222 LLyyrTy

222xrxT

222yryT





x

2 Lrropt

yx

41

41

1

)2()000(

2yx



)8(formin2

2formin

2formin2

2

L

L

L


4~ if also

Lopt

1)4(or 1)4(





20N

22

1

1

41

41

1

)2()000(

NN

FB

yx





2

2

2

tEyx kk

cBpeakc

1

2

3

n

KgNKgNN n

ezyx

ncne

z

nc


33max











Slide 3

Slide 4





Dimension Estimates



Slide 12

Slide 13



Demand for X-rays


Introduction





















Diffraction Limit






Photon Degeneracy


2

2

22

222

coscos1

cos

cos14

sincos14

z

z

z

nparn

z

nperpn

KNF

d

dN

KNF

d

dN

2

2

2

2

12

2

2

122

22

21421421

K

nKJ

K

nKJ

K

KnKF nnn


Compare with (210)











Radiation Intensity




)exp(0 kk tiEE

eN

kk

e

tiN

fb1

)exp(1

22

0 eNfbII

single electron

eNfb 1~2

eNII 0

1 fb 20~ eNII


Demand for X-rays







CHESSCHESS




Flux phs01bw




Introduction


ΔE t






p1z

p1

θ1x

electron bunch ε1

linac

px p2

p2z

θ2x

ε2 = ε1 p2z p1z

ε = εn



geometricx θx

mc2

normalized x px



Quantum Excitation

ρ = p

eB ρ =

p eB p

eB

Equilibrium

Eph

22

~ phphE EN

dt

d

Radiative Dampingvs




Touschek Effect


bull

bull e 1

e 2

x

z

p 1 in

p 2 in

p 1 out p 2 out






ERL (w compression)

t



A(nm-rad)2 max Nund






ERL better by






But firsthellip

SASE






previous )















Injector Parameters










endash

endashendash


Flu

x [p

hs

01

bw]

Bri

ghtn

ess

[ph

sm

m2

mr2

01

bw]

Flu

x [p

hs

01

bw]



p

N N

N

S

SS

Kz

x

y

zkBB py sin0

]m[]T[493 0 pBK


)]81475(exp[333]T[0 B

pgap for SmCo5 here







z

x

endash

in endash frame

pp

d

Pd2sin

N

1

z

x

back to lab frame

1

~

d

dP

1

on a

xis

off-axis

d

dP

1

N

1~


)1(2

22221

2

Kn

pn

pn nN

1~

(for fixed θ only)



z

x

1K

1K


z

x1

~even

odd



21

4

3 2KKnc

K nc

1 1

2 4

4 27

8 198

16 1548


d

dP

log

log

m

eBc 2

3 2 bend

wiggler

2Nspikes

continuum



e

INKKPtot )1(

32

212

1 A][m][

cm][

GeV][726[W]

2

22

ILKE

Pp

tot or


100 mA 5 GeV K = 15 p = 2 cm









LnN

K ncen 2

1

2

1 221


to get bwnNn

1~

n

)(Kge

INN n

nnph

n

Kg

e

I n )(

0

01

02

03

04

05

06

07

08

09

1

0 1 2 3 4 5

Kg

n(K

)

n = 1

3

57

9

)1(

][)(

221

2

K

JJnKKgn

Function



2212

1

)1(

)(3

NKK

Kg

P

P n

tot

cen



r

R

d

L


c



~R

rd

Lr c~Rrc ~

Lc ~

in Fraunhofer limit




x-ray source

Rings 1

ERLs 1

XFEL 1

c









)( )(

yxx

22

4

)(dxd

FdzxB

22)( dxdzxBF

invdzxBxd

FdxdzxB

d

Fd )( )( 2

2

22

2

2





xikezEzEdT

cdzxB

)2()2(

2)(

20

yikxx ezyxEzyxEyd

T

cd

)2()2(2

2

20

2

2

2 )( )(1

dezxEExdezxEE xikx

xikx




)(2)(

1cotexp

)()(

220

0 zR

ik

zwx

z

zkzi

zw

wEzxE

R

)1()( 2220

2Rzzwzw

20wzR

)1()( 22 zzzzR R

2

2

2

2

0

)(

2

1exp)(

rr

zxBzxB

00 1 2 kww rr

Rrr

rr

z

42

0

)2(B

Fcoh 20 )2( rr

FB






)21 ( here ))((e24

)0( 2)(

0

ntnntdc

eE tti

)(i0

i

i

e)0()0( cxtie

eEE

eN

EEEE1i

2i

1i

21 )0()0()0()0(

ji

2j

1i

)0()0(

EE

eN

22

e)1( zkee NN

1e22

zkeN




)0()0(e)0()0( i2

0

i1

0

)(21

21i

eexik

e EENEE e






2

00

)2()000(

F

B





2

2

2

2

2

00

2

1exp

)2()0(

rr

xFxB

LL rr 2 42

TyTyxTTx

FB

2)2(

)000(

2236122

1212222 LLa xxrTx

2236122

121222 LLyyrTy

222xrxT

222yryT





x

2 Lrropt

yx

41

41

1

)2()000(

2yx



)8(formin2

2formin

2formin2

2

L

L

L


4~ if also

Lopt

1)4(or 1)4(





20N

22

1

1

41

41

1

)2()000(

NN

FB

yx





2

2

2

tEyx kk

cBpeakc

1

2

3

n

KgNKgNN n

ezyx

ncne

z

nc


33max











Slide 3

Slide 4





Dimension Estimates



Slide 12

Slide 13



Demand for X-rays


Introduction





















Diffraction Limit






Photon Degeneracy











Radiation Intensity




)exp(0 kk tiEE

eN

kk

e

tiN

fb1

)exp(1

22

0 eNfbII

single electron

eNfb 1~2

eNII 0

1 fb 20~ eNII


Demand for X-rays







CHESSCHESS




Flux phs01bw




Introduction


ΔE t






p1z

p1

θ1x

electron bunch ε1

linac

px p2

p2z

θ2x

ε2 = ε1 p2z p1z

ε = εn



geometricx θx

mc2

normalized x px



Quantum Excitation

ρ = p

eB ρ =

p eB p

eB

Equilibrium

Eph

22

~ phphE EN

dt

d

Radiative Dampingvs




Touschek Effect


bull

bull e 1

e 2

x

z

p 1 in

p 2 in

p 1 out p 2 out






ERL (w compression)

t



A(nm-rad)2 max Nund






ERL better by






But firsthellip

SASE






previous )















Injector Parameters










endash

endashendash


Flu

x [p

hs

01

bw]

Bri

ghtn

ess

[ph

sm

m2

mr2

01

bw]

Flu

x [p

hs

01

bw]



p

N N

N

S

SS

Kz

x

y

zkBB py sin0

]m[]T[493 0 pBK


)]81475(exp[333]T[0 B

pgap for SmCo5 here







z

x

endash

in endash frame

pp

d

Pd2sin

N

1

z

x

back to lab frame

1

~

d

dP

1

on a

xis

off-axis

d

dP

1

N

1~


)1(2

22221

2

Kn

pn

pn nN

1~

(for fixed θ only)



z

x

1K

1K


z

x1

~even

odd



21

4

3 2KKnc

K nc

1 1

2 4

4 27

8 198

16 1548


d

dP

log

log

m

eBc 2

3 2 bend

wiggler

2Nspikes

continuum



e

INKKPtot )1(

32

212

1 A][m][

cm][

GeV][726[W]

2

22

ILKE

Pp

tot or


100 mA 5 GeV K = 15 p = 2 cm









LnN

K ncen 2

1

2

1 221


to get bwnNn

1~

n

)(Kge

INN n

nnph

n

Kg

e

I n )(

0

01

02

03

04

05

06

07

08

09

1

0 1 2 3 4 5

Kg

n(K

)

n = 1

3

57

9

)1(

][)(

221

2

K

JJnKKgn

Function



2212

1

)1(

)(3

NKK

Kg

P

P n

tot

cen



r

R

d

L


c



~R

rd

Lr c~Rrc ~

Lc ~

in Fraunhofer limit




x-ray source

Rings 1

ERLs 1

XFEL 1

c









)( )(

yxx

22

4

)(dxd

FdzxB

22)( dxdzxBF

invdzxBxd

FdxdzxB

d

Fd )( )( 2

2

22

2

2





xikezEzEdT

cdzxB

)2()2(

2)(

20

yikxx ezyxEzyxEyd

T

cd

)2()2(2

2

20

2

2

2 )( )(1

dezxEExdezxEE xikx

xikx




)(2)(

1cotexp

)()(

220

0 zR

ik

zwx

z

zkzi

zw

wEzxE

R

)1()( 2220

2Rzzwzw

20wzR

)1()( 22 zzzzR R

2

2

2

2

0

)(

2

1exp)(

rr

zxBzxB

00 1 2 kww rr

Rrr

rr

z

42

0

)2(B

Fcoh 20 )2( rr

FB






)21 ( here ))((e24

)0( 2)(

0

ntnntdc

eE tti

)(i0

i

i

e)0()0( cxtie

eEE

eN

EEEE1i

2i

1i

21 )0()0()0()0(

ji

2j

1i

)0()0(

EE

eN

22

e)1( zkee NN

1e22

zkeN




)0()0(e)0()0( i2

0

i1

0

)(21

21i

eexik

e EENEE e






2

00

)2()000(

F

B





2

2

2

2

2

00

2

1exp

)2()0(

rr

xFxB

LL rr 2 42

TyTyxTTx

FB

2)2(

)000(

2236122

1212222 LLa xxrTx

2236122

121222 LLyyrTy

222xrxT

222yryT





x

2 Lrropt

yx

41

41

1

)2()000(

2yx



)8(formin2

2formin

2formin2

2

L

L

L


4~ if also

Lopt

1)4(or 1)4(





20N

22

1

1

41

41

1

)2()000(

NN

FB

yx





2

2

2

tEyx kk

cBpeakc

1

2

3

n

KgNKgNN n

ezyx

ncne

z

nc


33max











Slide 3

Slide 4





Dimension Estimates



Slide 12

Slide 13



Demand for X-rays


Introduction





















Diffraction Limit






Photon Degeneracy


Demand for X-rays







CHESSCHESS




Flux phs01bw




Introduction


ΔE t






p1z

p1

θ1x

electron bunch ε1

linac

px p2

p2z

θ2x

ε2 = ε1 p2z p1z

ε = εn



geometricx θx

mc2

normalized x px



Quantum Excitation

ρ = p

eB ρ =

p eB p

eB

Equilibrium

Eph

22

~ phphE EN

dt

d

Radiative Dampingvs




Touschek Effect


bull

bull e 1

e 2

x

z

p 1 in

p 2 in

p 1 out p 2 out






ERL (w compression)

t



A(nm-rad)2 max Nund






ERL better by






But firsthellip

SASE






previous )















Injector Parameters










endash

endashendash


Flu

x [p

hs

01

bw]

Bri

ghtn

ess

[ph

sm

m2

mr2

01

bw]

Flu

x [p

hs

01

bw]



p

N N

N

S

SS

Kz

x

y

zkBB py sin0

]m[]T[493 0 pBK


)]81475(exp[333]T[0 B

pgap for SmCo5 here







z

x

endash

in endash frame

pp

d

Pd2sin

N

1

z

x

back to lab frame

1

~

d

dP

1

on a

xis

off-axis

d

dP

1

N

1~


)1(2

22221

2

Kn

pn

pn nN

1~

(for fixed θ only)



z

x

1K

1K


z

x1

~even

odd



21

4

3 2KKnc

K nc

1 1

2 4

4 27

8 198

16 1548


d

dP

log

log

m

eBc 2

3 2 bend

wiggler

2Nspikes

continuum



e

INKKPtot )1(

32

212

1 A][m][

cm][

GeV][726[W]

2

22

ILKE

Pp

tot or


100 mA 5 GeV K = 15 p = 2 cm









LnN

K ncen 2

1

2

1 221


to get bwnNn

1~

n

)(Kge

INN n

nnph

n

Kg

e

I n )(

0

01

02

03

04

05

06

07

08

09

1

0 1 2 3 4 5

Kg

n(K

)

n = 1

3

57

9

)1(

][)(

221

2

K

JJnKKgn

Function



2212

1

)1(

)(3

NKK

Kg

P

P n

tot

cen



r

R

d

L


c



~R

rd

Lr c~Rrc ~

Lc ~

in Fraunhofer limit




x-ray source

Rings 1

ERLs 1

XFEL 1

c









)( )(

yxx

22

4

)(dxd

FdzxB

22)( dxdzxBF

invdzxBxd

FdxdzxB

d

Fd )( )( 2

2

22

2

2





xikezEzEdT

cdzxB

)2()2(

2)(

20

yikxx ezyxEzyxEyd

T

cd

)2()2(2

2

20

2

2

2 )( )(1

dezxEExdezxEE xikx

xikx




)(2)(

1cotexp

)()(

220

0 zR

ik

zwx

z

zkzi

zw

wEzxE

R

)1()( 2220

2Rzzwzw

20wzR

)1()( 22 zzzzR R

2

2

2

2

0

)(

2

1exp)(

rr

zxBzxB

00 1 2 kww rr

Rrr

rr

z

42

0

)2(B

Fcoh 20 )2( rr

FB






)21 ( here ))((e24

)0( 2)(

0

ntnntdc

eE tti

)(i0

i

i

e)0()0( cxtie

eEE

eN

EEEE1i

2i

1i

21 )0()0()0()0(

ji

2j

1i

)0()0(

EE

eN

22

e)1( zkee NN

1e22

zkeN




)0()0(e)0()0( i2

0

i1

0

)(21

21i

eexik

e EENEE e






2

00

)2()000(

F

B





2

2

2

2

2

00

2

1exp

)2()0(

rr

xFxB

LL rr 2 42

TyTyxTTx

FB

2)2(

)000(

2236122

1212222 LLa xxrTx

2236122

121222 LLyyrTy

222xrxT

222yryT





x

2 Lrropt

yx

41

41

1

)2()000(

2yx



)8(formin2

2formin

2formin2

2

L

L

L


4~ if also

Lopt

1)4(or 1)4(





20N

22

1

1

41

41

1

)2()000(

NN

FB

yx





2

2

2

tEyx kk

cBpeakc

1

2

3

n

KgNKgNN n

ezyx

ncne

z

nc


33max











Slide 3

Slide 4





Dimension Estimates



Slide 12

Slide 13



Demand for X-rays


Introduction





















Diffraction Limit






Photon Degeneracy




Flux phs01bw




Introduction


ΔE t






p1z

p1

θ1x

electron bunch ε1

linac

px p2

p2z

θ2x

ε2 = ε1 p2z p1z

ε = εn



geometricx θx

mc2

normalized x px



Quantum Excitation

ρ = p

eB ρ =

p eB p

eB

Equilibrium

Eph

22

~ phphE EN

dt

d

Radiative Dampingvs




Touschek Effect


bull

bull e 1

e 2

x

z

p 1 in

p 2 in

p 1 out p 2 out






ERL (w compression)

t



A(nm-rad)2 max Nund






ERL better by






But firsthellip

SASE






previous )















Injector Parameters










endash

endashendash


Flu

x [p

hs

01

bw]

Bri

ghtn

ess

[ph

sm

m2

mr2

01

bw]

Flu

x [p

hs

01

bw]



p

N N

N

S

SS

Kz

x

y

zkBB py sin0

]m[]T[493 0 pBK


)]81475(exp[333]T[0 B

pgap for SmCo5 here







z

x

endash

in endash frame

pp

d

Pd2sin

N

1

z

x

back to lab frame

1

~

d

dP

1

on a

xis

off-axis

d

dP

1

N

1~


)1(2

22221

2

Kn

pn

pn nN

1~

(for fixed θ only)



z

x

1K

1K


z

x1

~even

odd



21

4

3 2KKnc

K nc

1 1

2 4

4 27

8 198

16 1548


d

dP

log

log

m

eBc 2

3 2 bend

wiggler

2Nspikes

continuum



e

INKKPtot )1(

32

212

1 A][m][

cm][

GeV][726[W]

2

22

ILKE

Pp

tot or


100 mA 5 GeV K = 15 p = 2 cm









LnN

K ncen 2

1

2

1 221


to get bwnNn

1~

n

)(Kge

INN n

nnph

n

Kg

e

I n )(

0

01

02

03

04

05

06

07

08

09

1

0 1 2 3 4 5

Kg

n(K

)

n = 1

3

57

9

)1(

][)(

221

2

K

JJnKKgn

Function



2212

1

)1(

)(3

NKK

Kg

P

P n

tot

cen



r

R

d

L


c



~R

rd

Lr c~Rrc ~

Lc ~

in Fraunhofer limit




x-ray source

Rings 1

ERLs 1

XFEL 1

c









)( )(

yxx

22

4

)(dxd

FdzxB

22)( dxdzxBF

invdzxBxd

FdxdzxB

d

Fd )( )( 2

2

22

2

2





xikezEzEdT

cdzxB

)2()2(

2)(

20

yikxx ezyxEzyxEyd

T

cd

)2()2(2

2

20

2

2

2 )( )(1

dezxEExdezxEE xikx

xikx




)(2)(

1cotexp

)()(

220

0 zR

ik

zwx

z

zkzi

zw

wEzxE

R

)1()( 2220

2Rzzwzw

20wzR

)1()( 22 zzzzR R

2

2

2

2

0

)(

2

1exp)(

rr

zxBzxB

00 1 2 kww rr

Rrr

rr

z

42

0

)2(B

Fcoh 20 )2( rr

FB






)21 ( here ))((e24

)0( 2)(

0

ntnntdc

eE tti

)(i0

i

i

e)0()0( cxtie

eEE

eN

EEEE1i

2i

1i

21 )0()0()0()0(

ji

2j

1i

)0()0(

EE

eN

22

e)1( zkee NN

1e22

zkeN




)0()0(e)0()0( i2

0

i1

0

)(21

21i

eexik

e EENEE e






2

00

)2()000(

F

B





2

2

2

2

2

00

2

1exp

)2()0(

rr

xFxB

LL rr 2 42

TyTyxTTx

FB

2)2(

)000(

2236122

1212222 LLa xxrTx

2236122

121222 LLyyrTy

222xrxT

222yryT





x

2 Lrropt

yx

41

41

1

)2()000(

2yx



)8(formin2

2formin

2formin2

2

L

L

L


4~ if also

Lopt

1)4(or 1)4(





20N

22

1

1

41

41

1

)2()000(

NN

FB

yx





2

2

2

tEyx kk

cBpeakc

1

2

3

n

KgNKgNN n

ezyx

ncne

z

nc


33max











Slide 3

Slide 4





Dimension Estimates



Slide 12

Slide 13



Demand for X-rays


Introduction





















Diffraction Limit






Photon Degeneracy


Introduction


ΔE t






p1z

p1

θ1x

electron bunch ε1

linac

px p2

p2z

θ2x

ε2 = ε1 p2z p1z

ε = εn



geometricx θx

mc2

normalized x px



Quantum Excitation

ρ = p

eB ρ =

p eB p

eB

Equilibrium

Eph

22

~ phphE EN

dt

d

Radiative Dampingvs




Touschek Effect


bull

bull e 1

e 2

x

z

p 1 in

p 2 in

p 1 out p 2 out






ERL (w compression)

t



A(nm-rad)2 max Nund






ERL better by






But firsthellip

SASE






previous )















Injector Parameters










endash

endashendash


Flu

x [p

hs

01

bw]

Bri

ghtn

ess

[ph

sm

m2

mr2

01

bw]

Flu

x [p

hs

01

bw]



p

N N

N

S

SS

Kz

x

y

zkBB py sin0

]m[]T[493 0 pBK


)]81475(exp[333]T[0 B

pgap for SmCo5 here







z

x

endash

in endash frame

pp

d

Pd2sin

N

1

z

x

back to lab frame

1

~

d

dP

1

on a

xis

off-axis

d

dP

1

N

1~


)1(2

22221

2

Kn

pn

pn nN

1~

(for fixed θ only)



z

x

1K

1K


z

x1

~even

odd



21

4

3 2KKnc

K nc

1 1

2 4

4 27

8 198

16 1548


d

dP

log

log

m

eBc 2

3 2 bend

wiggler

2Nspikes

continuum



e

INKKPtot )1(

32

212

1 A][m][

cm][

GeV][726[W]

2

22

ILKE

Pp

tot or


100 mA 5 GeV K = 15 p = 2 cm









LnN

K ncen 2

1

2

1 221


to get bwnNn

1~

n

)(Kge

INN n

nnph

n

Kg

e

I n )(

0

01

02

03

04

05

06

07

08

09

1

0 1 2 3 4 5

Kg

n(K

)

n = 1

3

57

9

)1(

][)(

221

2

K

JJnKKgn

Function



2212

1

)1(

)(3

NKK

Kg

P

P n

tot

cen



r

R

d

L


c



~R

rd

Lr c~Rrc ~

Lc ~

in Fraunhofer limit




x-ray source

Rings 1

ERLs 1

XFEL 1

c









)( )(

yxx

22

4

)(dxd

FdzxB

22)( dxdzxBF

invdzxBxd

FdxdzxB

d

Fd )( )( 2

2

22

2

2





xikezEzEdT

cdzxB

)2()2(

2)(

20

yikxx ezyxEzyxEyd

T

cd

)2()2(2

2

20

2

2

2 )( )(1

dezxEExdezxEE xikx

xikx




)(2)(

1cotexp

)()(

220

0 zR

ik

zwx

z

zkzi

zw

wEzxE

R

)1()( 2220

2Rzzwzw

20wzR

)1()( 22 zzzzR R

2

2

2

2

0

)(

2

1exp)(

rr

zxBzxB

00 1 2 kww rr

Rrr

rr

z

42

0

)2(B

Fcoh 20 )2( rr

FB






)21 ( here ))((e24

)0( 2)(

0

ntnntdc

eE tti

)(i0

i

i

e)0()0( cxtie

eEE

eN

EEEE1i

2i

1i

21 )0()0()0()0(

ji

2j

1i

)0()0(

EE

eN

22

e)1( zkee NN

1e22

zkeN




)0()0(e)0()0( i2

0

i1

0

)(21

21i

eexik

e EENEE e






2

00

)2()000(

F

B





2

2

2

2

2

00

2

1exp

)2()0(

rr

xFxB

LL rr 2 42

TyTyxTTx

FB

2)2(

)000(

2236122

1212222 LLa xxrTx

2236122

121222 LLyyrTy

222xrxT

222yryT





x

2 Lrropt

yx

41

41

1

)2()000(

2yx



)8(formin2

2formin

2formin2

2

L

L

L


4~ if also

Lopt

1)4(or 1)4(





20N

22

1

1

41

41

1

)2()000(

NN

FB

yx





2

2

2

tEyx kk

cBpeakc

1

2

3

n

KgNKgNN n

ezyx

ncne

z

nc


33max











Slide 3

Slide 4





Dimension Estimates



Slide 12

Slide 13



Demand for X-rays


Introduction





















Diffraction Limit






Photon Degeneracy



p1z

p1

θ1x

electron bunch ε1

linac

px p2

p2z

θ2x

ε2 = ε1 p2z p1z

ε = εn



geometricx θx

mc2

normalized x px



Quantum Excitation

ρ = p

eB ρ =

p eB p

eB

Equilibrium

Eph

22

~ phphE EN

dt

d

Radiative Dampingvs




Touschek Effect


bull

bull e 1

e 2

x

z

p 1 in

p 2 in

p 1 out p 2 out






ERL (w compression)

t



A(nm-rad)2 max Nund






ERL better by






But firsthellip

SASE






previous )















Injector Parameters










endash

endashendash


Flu

x [p

hs

01

bw]

Bri

ghtn

ess

[ph

sm

m2

mr2

01

bw]

Flu

x [p

hs

01

bw]



p

N N

N

S

SS

Kz

x

y

zkBB py sin0

]m[]T[493 0 pBK


)]81475(exp[333]T[0 B

pgap for SmCo5 here







z

x

endash

in endash frame

pp

d

Pd2sin

N

1

z

x

back to lab frame

1

~

d

dP

1

on a

xis

off-axis

d

dP

1

N

1~


)1(2

22221

2

Kn

pn

pn nN

1~

(for fixed θ only)



z

x

1K

1K


z

x1

~even

odd



21

4

3 2KKnc

K nc

1 1

2 4

4 27

8 198

16 1548


d

dP

log

log

m

eBc 2

3 2 bend

wiggler

2Nspikes

continuum



e

INKKPtot )1(

32

212

1 A][m][

cm][

GeV][726[W]

2

22

ILKE

Pp

tot or


100 mA 5 GeV K = 15 p = 2 cm









LnN

K ncen 2

1

2

1 221


to get bwnNn

1~

n

)(Kge

INN n

nnph

n

Kg

e

I n )(

0

01

02

03

04

05

06

07

08

09

1

0 1 2 3 4 5

Kg

n(K

)

n = 1

3

57

9

)1(

][)(

221

2

K

JJnKKgn

Function



2212

1

)1(

)(3

NKK

Kg

P

P n

tot

cen



r

R

d

L


c



~R

rd

Lr c~Rrc ~

Lc ~

in Fraunhofer limit




x-ray source

Rings 1

ERLs 1

XFEL 1

c









)( )(

yxx

22

4

)(dxd

FdzxB

22)( dxdzxBF

invdzxBxd

FdxdzxB

d

Fd )( )( 2

2

22

2

2





xikezEzEdT

cdzxB

)2()2(

2)(

20

yikxx ezyxEzyxEyd

T

cd

)2()2(2

2

20

2

2

2 )( )(1

dezxEExdezxEE xikx

xikx




)(2)(

1cotexp

)()(

220

0 zR

ik

zwx

z

zkzi

zw

wEzxE

R

)1()( 2220

2Rzzwzw

20wzR

)1()( 22 zzzzR R

2

2

2

2

0

)(

2

1exp)(

rr

zxBzxB

00 1 2 kww rr

Rrr

rr

z

42

0

)2(B

Fcoh 20 )2( rr

FB






)21 ( here ))((e24

)0( 2)(

0

ntnntdc

eE tti

)(i0

i

i

e)0()0( cxtie

eEE

eN

EEEE1i

2i

1i

21 )0()0()0()0(

ji

2j

1i

)0()0(

EE

eN

22

e)1( zkee NN

1e22

zkeN




)0()0(e)0()0( i2

0

i1

0

)(21

21i

eexik

e EENEE e






2

00

)2()000(

F

B





2

2

2

2

2

00

2

1exp

)2()0(

rr

xFxB

LL rr 2 42

TyTyxTTx

FB

2)2(

)000(

2236122

1212222 LLa xxrTx

2236122

121222 LLyyrTy

222xrxT

222yryT





x

2 Lrropt

yx

41

41

1

)2()000(

2yx



)8(formin2

2formin

2formin2

2

L

L

L


4~ if also

Lopt

1)4(or 1)4(





20N

22

1

1

41

41

1

)2()000(

NN

FB

yx





2

2

2

tEyx kk

cBpeakc

1

2

3

n

KgNKgNN n

ezyx

ncne

z

nc


33max











Slide 3

Slide 4





Dimension Estimates



Slide 12

Slide 13



Demand for X-rays


Introduction





















Diffraction Limit






Photon Degeneracy



Quantum Excitation

ρ = p

eB ρ =

p eB p

eB

Equilibrium

Eph

22

~ phphE EN

dt

d

Radiative Dampingvs




Touschek Effect


bull

bull e 1

e 2

x

z

p 1 in

p 2 in

p 1 out p 2 out






ERL (w compression)

t



A(nm-rad)2 max Nund






ERL better by






But firsthellip

SASE






previous )















Injector Parameters










endash

endashendash


Flu

x [p

hs

01

bw]

Bri

ghtn

ess

[ph

sm

m2

mr2

01

bw]

Flu

x [p

hs

01

bw]



p

N N

N

S

SS

Kz

x

y

zkBB py sin0

]m[]T[493 0 pBK


)]81475(exp[333]T[0 B

pgap for SmCo5 here







z

x

endash

in endash frame

pp

d

Pd2sin

N

1

z

x

back to lab frame

1

~

d

dP

1

on a

xis

off-axis

d

dP

1

N

1~


)1(2

22221

2

Kn

pn

pn nN

1~

(for fixed θ only)



z

x

1K

1K


z

x1

~even

odd



21

4

3 2KKnc

K nc

1 1

2 4

4 27

8 198

16 1548


d

dP

log

log

m

eBc 2

3 2 bend

wiggler

2Nspikes

continuum



e

INKKPtot )1(

32

212

1 A][m][

cm][

GeV][726[W]

2

22

ILKE

Pp

tot or


100 mA 5 GeV K = 15 p = 2 cm









LnN

K ncen 2

1

2

1 221


to get bwnNn

1~

n

)(Kge

INN n

nnph

n

Kg

e

I n )(

0

01

02

03

04

05

06

07

08

09

1

0 1 2 3 4 5

Kg

n(K

)

n = 1

3

57

9

)1(

][)(

221

2

K

JJnKKgn

Function



2212

1

)1(

)(3

NKK

Kg

P

P n

tot

cen



r

R

d

L


c



~R

rd

Lr c~Rrc ~

Lc ~

in Fraunhofer limit




x-ray source

Rings 1

ERLs 1

XFEL 1

c









)( )(

yxx

22

4

)(dxd

FdzxB

22)( dxdzxBF

invdzxBxd

FdxdzxB

d

Fd )( )( 2

2

22

2

2





xikezEzEdT

cdzxB

)2()2(

2)(

20

yikxx ezyxEzyxEyd

T

cd

)2()2(2

2

20

2

2

2 )( )(1

dezxEExdezxEE xikx

xikx




)(2)(

1cotexp

)()(

220

0 zR

ik

zwx

z

zkzi

zw

wEzxE

R

)1()( 2220

2Rzzwzw

20wzR

)1()( 22 zzzzR R

2

2

2

2

0

)(

2

1exp)(

rr

zxBzxB

00 1 2 kww rr

Rrr

rr

z

42

0

)2(B

Fcoh 20 )2( rr

FB






)21 ( here ))((e24

)0( 2)(

0

ntnntdc

eE tti

)(i0

i

i

e)0()0( cxtie

eEE

eN

EEEE1i

2i

1i

21 )0()0()0()0(

ji

2j

1i

)0()0(

EE

eN

22

e)1( zkee NN

1e22

zkeN




)0()0(e)0()0( i2

0

i1

0

)(21

21i

eexik

e EENEE e






2

00

)2()000(

F

B





2

2

2

2

2

00

2

1exp

)2()0(

rr

xFxB

LL rr 2 42

TyTyxTTx

FB

2)2(

)000(

2236122

1212222 LLa xxrTx

2236122

121222 LLyyrTy

222xrxT

222yryT





x

2 Lrropt

yx

41

41

1

)2()000(

2yx



)8(formin2

2formin

2formin2

2

L

L

L


4~ if also

Lopt

1)4(or 1)4(





20N

22

1

1

41

41

1

)2()000(

NN

FB

yx





2

2

2

tEyx kk

cBpeakc

1

2

3

n

KgNKgNN n

ezyx

ncne

z

nc


33max











Slide 3

Slide 4





Dimension Estimates



Slide 12

Slide 13



Demand for X-rays


Introduction





















Diffraction Limit






Photon Degeneracy



Touschek Effect


bull

bull e 1

e 2

x

z

p 1 in

p 2 in

p 1 out p 2 out






ERL (w compression)

t



A(nm-rad)2 max Nund






ERL better by






But firsthellip

SASE






previous )















Injector Parameters










endash

endashendash


Flu

x [p

hs

01

bw]

Bri

ghtn

ess

[ph

sm

m2

mr2

01

bw]

Flu

x [p

hs

01

bw]



p

N N

N

S

SS

Kz

x

y

zkBB py sin0

]m[]T[493 0 pBK


)]81475(exp[333]T[0 B

pgap for SmCo5 here







z

x

endash

in endash frame

pp

d

Pd2sin

N

1

z

x

back to lab frame

1

~

d

dP

1

on a

xis

off-axis

d

dP

1

N

1~


)1(2

22221

2

Kn

pn

pn nN

1~

(for fixed θ only)



z

x

1K

1K


z

x1

~even

odd



21

4

3 2KKnc

K nc

1 1

2 4

4 27

8 198

16 1548


d

dP

log

log

m

eBc 2

3 2 bend

wiggler

2Nspikes

continuum



e

INKKPtot )1(

32

212

1 A][m][

cm][

GeV][726[W]

2

22

ILKE

Pp

tot or


100 mA 5 GeV K = 15 p = 2 cm









LnN

K ncen 2

1

2

1 221


to get bwnNn

1~

n

)(Kge

INN n

nnph

n

Kg

e

I n )(

0

01

02

03

04

05

06

07

08

09

1

0 1 2 3 4 5

Kg

n(K

)

n = 1

3

57

9

)1(

][)(

221

2

K

JJnKKgn

Function



2212

1

)1(

)(3

NKK

Kg

P

P n

tot

cen



r

R

d

L


c



~R

rd

Lr c~Rrc ~

Lc ~

in Fraunhofer limit




x-ray source

Rings 1

ERLs 1

XFEL 1

c









)( )(

yxx

22

4

)(dxd

FdzxB

22)( dxdzxBF

invdzxBxd

FdxdzxB

d

Fd )( )( 2

2

22

2

2





xikezEzEdT

cdzxB

)2()2(

2)(

20

yikxx ezyxEzyxEyd

T

cd

)2()2(2

2

20

2

2

2 )( )(1

dezxEExdezxEE xikx

xikx




)(2)(

1cotexp

)()(

220

0 zR

ik

zwx

z

zkzi

zw

wEzxE

R

)1()( 2220

2Rzzwzw

20wzR

)1()( 22 zzzzR R

2

2

2

2

0

)(

2

1exp)(

rr

zxBzxB

00 1 2 kww rr

Rrr

rr

z

42

0

)2(B

Fcoh 20 )2( rr

FB






)21 ( here ))((e24

)0( 2)(

0

ntnntdc

eE tti

)(i0

i

i

e)0()0( cxtie

eEE

eN

EEEE1i

2i

1i

21 )0()0()0()0(

ji

2j

1i

)0()0(

EE

eN

22

e)1( zkee NN

1e22

zkeN




)0()0(e)0()0( i2

0

i1

0

)(21

21i

eexik

e EENEE e






2

00

)2()000(

F

B





2

2

2

2

2

00

2

1exp

)2()0(

rr

xFxB

LL rr 2 42

TyTyxTTx

FB

2)2(

)000(

2236122

1212222 LLa xxrTx

2236122

121222 LLyyrTy

222xrxT

222yryT





x

2 Lrropt

yx

41

41

1

)2()000(

2yx



)8(formin2

2formin

2formin2

2

L

L

L


4~ if also

Lopt

1)4(or 1)4(





20N

22

1

1

41

41

1

)2()000(

NN

FB

yx





2

2

2

tEyx kk

cBpeakc

1

2

3

n

KgNKgNN n

ezyx

ncne

z

nc


33max











Slide 3

Slide 4





Dimension Estimates



Slide 12

Slide 13



Demand for X-rays


Introduction





















Diffraction Limit






Photon Degeneracy






ERL (w compression)

t



A(nm-rad)2 max Nund






ERL better by






But firsthellip

SASE






previous )















Injector Parameters










endash

endashendash


Flu

x [p

hs

01

bw]

Bri

ghtn

ess

[ph

sm

m2

mr2

01

bw]

Flu

x [p

hs

01

bw]



p

N N

N

S

SS

Kz

x

y

zkBB py sin0

]m[]T[493 0 pBK


)]81475(exp[333]T[0 B

pgap for SmCo5 here







z

x

endash

in endash frame

pp

d

Pd2sin

N

1

z

x

back to lab frame

1

~

d

dP

1

on a

xis

off-axis

d

dP

1

N

1~


)1(2

22221

2

Kn

pn

pn nN

1~

(for fixed θ only)



z

x

1K

1K


z

x1

~even

odd



21

4

3 2KKnc

K nc

1 1

2 4

4 27

8 198

16 1548


d

dP

log

log

m

eBc 2

3 2 bend

wiggler

2Nspikes

continuum



e

INKKPtot )1(

32

212

1 A][m][

cm][

GeV][726[W]

2

22

ILKE

Pp

tot or


100 mA 5 GeV K = 15 p = 2 cm









LnN

K ncen 2

1

2

1 221


to get bwnNn

1~

n

)(Kge

INN n

nnph

n

Kg

e

I n )(

0

01

02

03

04

05

06

07

08

09

1

0 1 2 3 4 5

Kg

n(K

)

n = 1

3

57

9

)1(

][)(

221

2

K

JJnKKgn

Function



2212

1

)1(

)(3

NKK

Kg

P

P n

tot

cen



r

R

d

L


c



~R

rd

Lr c~Rrc ~

Lc ~

in Fraunhofer limit




x-ray source

Rings 1

ERLs 1

XFEL 1

c









)( )(

yxx

22

4

)(dxd

FdzxB

22)( dxdzxBF

invdzxBxd

FdxdzxB

d

Fd )( )( 2

2

22

2

2





xikezEzEdT

cdzxB

)2()2(

2)(

20

yikxx ezyxEzyxEyd

T

cd

)2()2(2

2

20

2

2

2 )( )(1

dezxEExdezxEE xikx

xikx




)(2)(

1cotexp

)()(

220

0 zR

ik

zwx

z

zkzi

zw

wEzxE

R

)1()( 2220

2Rzzwzw

20wzR

)1()( 22 zzzzR R

2

2

2

2

0

)(

2

1exp)(

rr

zxBzxB

00 1 2 kww rr

Rrr

rr

z

42

0

)2(B

Fcoh 20 )2( rr

FB






)21 ( here ))((e24

)0( 2)(

0

ntnntdc

eE tti

)(i0

i

i

e)0()0( cxtie

eEE

eN

EEEE1i

2i

1i

21 )0()0()0()0(

ji

2j

1i

)0()0(

EE

eN

22

e)1( zkee NN

1e22

zkeN




)0()0(e)0()0( i2

0

i1

0

)(21

21i

eexik

e EENEE e






2

00

)2()000(

F

B





2

2

2

2

2

00

2

1exp

)2()0(

rr

xFxB

LL rr 2 42

TyTyxTTx

FB

2)2(

)000(

2236122

1212222 LLa xxrTx

2236122

121222 LLyyrTy

222xrxT

222yryT





x

2 Lrropt

yx

41

41

1

)2()000(

2yx



)8(formin2

2formin

2formin2

2

L

L

L


4~ if also

Lopt

1)4(or 1)4(





20N

22

1

1

41

41

1

)2()000(

NN

FB

yx





2

2

2

tEyx kk

cBpeakc

1

2

3

n

KgNKgNN n

ezyx

ncne

z

nc


33max











Slide 3

Slide 4





Dimension Estimates



Slide 12

Slide 13



Demand for X-rays


Introduction





















Diffraction Limit






Photon Degeneracy



A(nm-rad)2 max Nund






ERL better by






But firsthellip

SASE






previous )















Injector Parameters










endash

endashendash


Flu

x [p

hs

01

bw]

Bri

ghtn

ess

[ph

sm

m2

mr2

01

bw]

Flu

x [p

hs

01

bw]



p

N N

N

S

SS

Kz

x

y

zkBB py sin0

]m[]T[493 0 pBK


)]81475(exp[333]T[0 B

pgap for SmCo5 here







z

x

endash

in endash frame

pp

d

Pd2sin

N

1

z

x

back to lab frame

1

~

d

dP

1

on a

xis

off-axis

d

dP

1

N

1~


)1(2

22221

2

Kn

pn

pn nN

1~

(for fixed θ only)



z

x

1K

1K


z

x1

~even

odd



21

4

3 2KKnc

K nc

1 1

2 4

4 27

8 198

16 1548


d

dP

log

log

m

eBc 2

3 2 bend

wiggler

2Nspikes

continuum



e

INKKPtot )1(

32

212

1 A][m][

cm][

GeV][726[W]

2

22

ILKE

Pp

tot or


100 mA 5 GeV K = 15 p = 2 cm









LnN

K ncen 2

1

2

1 221


to get bwnNn

1~

n

)(Kge

INN n

nnph

n

Kg

e

I n )(

0

01

02

03

04

05

06

07

08

09

1

0 1 2 3 4 5

Kg

n(K

)

n = 1

3

57

9

)1(

][)(

221

2

K

JJnKKgn

Function



2212

1

)1(

)(3

NKK

Kg

P

P n

tot

cen



r

R

d

L


c



~R

rd

Lr c~Rrc ~

Lc ~

in Fraunhofer limit




x-ray source

Rings 1

ERLs 1

XFEL 1

c









)( )(

yxx

22

4

)(dxd

FdzxB

22)( dxdzxBF

invdzxBxd

FdxdzxB

d

Fd )( )( 2

2

22

2

2





xikezEzEdT

cdzxB

)2()2(

2)(

20

yikxx ezyxEzyxEyd

T

cd

)2()2(2

2

20

2

2

2 )( )(1

dezxEExdezxEE xikx

xikx




)(2)(

1cotexp

)()(

220

0 zR

ik

zwx

z

zkzi

zw

wEzxE

R

)1()( 2220

2Rzzwzw

20wzR

)1()( 22 zzzzR R

2

2

2

2

0

)(

2

1exp)(

rr

zxBzxB

00 1 2 kww rr

Rrr

rr

z

42

0

)2(B

Fcoh 20 )2( rr

FB






)21 ( here ))((e24

)0( 2)(

0

ntnntdc

eE tti

)(i0

i

i

e)0()0( cxtie

eEE

eN

EEEE1i

2i

1i

21 )0()0()0()0(

ji

2j

1i

)0()0(

EE

eN

22

e)1( zkee NN

1e22

zkeN




)0()0(e)0()0( i2

0

i1

0

)(21

21i

eexik

e EENEE e






2

00

)2()000(

F

B





2

2

2

2

2

00

2

1exp

)2()0(

rr

xFxB

LL rr 2 42

TyTyxTTx

FB

2)2(

)000(

2236122

1212222 LLa xxrTx

2236122

121222 LLyyrTy

222xrxT

222yryT





x

2 Lrropt

yx

41

41

1

)2()000(

2yx



)8(formin2

2formin

2formin2

2

L

L

L


4~ if also

Lopt

1)4(or 1)4(





20N

22

1

1

41

41

1

)2()000(

NN

FB

yx





2

2

2

tEyx kk

cBpeakc

1

2

3

n

KgNKgNN n

ezyx

ncne

z

nc


33max











Slide 3

Slide 4





Dimension Estimates



Slide 12

Slide 13



Demand for X-rays


Introduction





















Diffraction Limit






Photon Degeneracy



ERL better by






But firsthellip

SASE






previous )















Injector Parameters










endash

endashendash


Flu

x [p

hs

01

bw]

Bri

ghtn

ess

[ph

sm

m2

mr2

01

bw]

Flu

x [p

hs

01

bw]



p

N N

N

S

SS

Kz

x

y

zkBB py sin0

]m[]T[493 0 pBK


)]81475(exp[333]T[0 B

pgap for SmCo5 here







z

x

endash

in endash frame

pp

d

Pd2sin

N

1

z

x

back to lab frame

1

~

d

dP

1

on a

xis

off-axis

d

dP

1

N

1~


)1(2

22221

2

Kn

pn

pn nN

1~

(for fixed θ only)



z

x

1K

1K


z

x1

~even

odd



21

4

3 2KKnc

K nc

1 1

2 4

4 27

8 198

16 1548


d

dP

log

log

m

eBc 2

3 2 bend

wiggler

2Nspikes

continuum



e

INKKPtot )1(

32

212

1 A][m][

cm][

GeV][726[W]

2

22

ILKE

Pp

tot or


100 mA 5 GeV K = 15 p = 2 cm









LnN

K ncen 2

1

2

1 221


to get bwnNn

1~

n

)(Kge

INN n

nnph

n

Kg

e

I n )(

0

01

02

03

04

05

06

07

08

09

1

0 1 2 3 4 5

Kg

n(K

)

n = 1

3

57

9

)1(

][)(

221

2

K

JJnKKgn

Function



2212

1

)1(

)(3

NKK

Kg

P

P n

tot

cen



r

R

d

L


c



~R

rd

Lr c~Rrc ~

Lc ~

in Fraunhofer limit




x-ray source

Rings 1

ERLs 1

XFEL 1

c









)( )(

yxx

22

4

)(dxd

FdzxB

22)( dxdzxBF

invdzxBxd

FdxdzxB

d

Fd )( )( 2

2

22

2

2





xikezEzEdT

cdzxB

)2()2(

2)(

20

yikxx ezyxEzyxEyd

T

cd

)2()2(2

2

20

2

2

2 )( )(1

dezxEExdezxEE xikx

xikx




)(2)(

1cotexp

)()(

220

0 zR

ik

zwx

z

zkzi

zw

wEzxE

R

)1()( 2220

2Rzzwzw

20wzR

)1()( 22 zzzzR R

2

2

2

2

0

)(

2

1exp)(

rr

zxBzxB

00 1 2 kww rr

Rrr

rr

z

42

0

)2(B

Fcoh 20 )2( rr

FB






)21 ( here ))((e24

)0( 2)(

0

ntnntdc

eE tti

)(i0

i

i

e)0()0( cxtie

eEE

eN

EEEE1i

2i

1i

21 )0()0()0()0(

ji

2j

1i

)0()0(

EE

eN

22

e)1( zkee NN

1e22

zkeN




)0()0(e)0()0( i2

0

i1

0

)(21

21i

eexik

e EENEE e






2

00

)2()000(

F

B





2

2

2

2

2

00

2

1exp

)2()0(

rr

xFxB

LL rr 2 42

TyTyxTTx

FB

2)2(

)000(

2236122

1212222 LLa xxrTx

2236122

121222 LLyyrTy

222xrxT

222yryT





x

2 Lrropt

yx

41

41

1

)2()000(

2yx



)8(formin2

2formin

2formin2

2

L

L

L


4~ if also

Lopt

1)4(or 1)4(





20N

22

1

1

41

41

1

)2()000(

NN

FB

yx





2

2

2

tEyx kk

cBpeakc

1

2

3

n

KgNKgNN n

ezyx

ncne

z

nc


33max











Slide 3

Slide 4





Dimension Estimates



Slide 12

Slide 13



Demand for X-rays


Introduction





















Diffraction Limit






Photon Degeneracy




But firsthellip

SASE






previous )















Injector Parameters










endash

endashendash


Flu

x [p

hs

01

bw]

Bri

ghtn

ess

[ph

sm

m2

mr2

01

bw]

Flu

x [p

hs

01

bw]



p

N N

N

S

SS

Kz

x

y

zkBB py sin0

]m[]T[493 0 pBK


)]81475(exp[333]T[0 B

pgap for SmCo5 here







z

x

endash

in endash frame

pp

d

Pd2sin

N

1

z

x

back to lab frame

1

~

d

dP

1

on a

xis

off-axis

d

dP

1

N

1~


)1(2

22221

2

Kn

pn

pn nN

1~

(for fixed θ only)



z

x

1K

1K


z

x1

~even

odd



21

4

3 2KKnc

K nc

1 1

2 4

4 27

8 198

16 1548


d

dP

log

log

m

eBc 2

3 2 bend

wiggler

2Nspikes

continuum



e

INKKPtot )1(

32

212

1 A][m][

cm][

GeV][726[W]

2

22

ILKE

Pp

tot or


100 mA 5 GeV K = 15 p = 2 cm









LnN

K ncen 2

1

2

1 221


to get bwnNn

1~

n

)(Kge

INN n

nnph

n

Kg

e

I n )(

0

01

02

03

04

05

06

07

08

09

1

0 1 2 3 4 5

Kg

n(K

)

n = 1

3

57

9

)1(

][)(

221

2

K

JJnKKgn

Function



2212

1

)1(

)(3

NKK

Kg

P

P n

tot

cen



r

R

d

L


c



~R

rd

Lr c~Rrc ~

Lc ~

in Fraunhofer limit




x-ray source

Rings 1

ERLs 1

XFEL 1

c









)( )(

yxx

22

4

)(dxd

FdzxB

22)( dxdzxBF

invdzxBxd

FdxdzxB

d

Fd )( )( 2

2

22

2

2





xikezEzEdT

cdzxB

)2()2(

2)(

20

yikxx ezyxEzyxEyd

T

cd

)2()2(2

2

20

2

2

2 )( )(1

dezxEExdezxEE xikx

xikx




)(2)(

1cotexp

)()(

220

0 zR

ik

zwx

z

zkzi

zw

wEzxE

R

)1()( 2220

2Rzzwzw

20wzR

)1()( 22 zzzzR R

2

2

2

2

0

)(

2

1exp)(

rr

zxBzxB

00 1 2 kww rr

Rrr

rr

z

42

0

)2(B

Fcoh 20 )2( rr

FB






)21 ( here ))((e24

)0( 2)(

0

ntnntdc

eE tti

)(i0

i

i

e)0()0( cxtie

eEE

eN

EEEE1i

2i

1i

21 )0()0()0()0(

ji

2j

1i

)0()0(

EE

eN

22

e)1( zkee NN

1e22

zkeN




)0()0(e)0()0( i2

0

i1

0

)(21

21i

eexik

e EENEE e






2

00

)2()000(

F

B





2

2

2

2

2

00

2

1exp

)2()0(

rr

xFxB

LL rr 2 42

TyTyxTTx

FB

2)2(

)000(

2236122

1212222 LLa xxrTx

2236122

121222 LLyyrTy

222xrxT

222yryT





x

2 Lrropt

yx

41

41

1

)2()000(

2yx



)8(formin2

2formin

2formin2

2

L

L

L


4~ if also

Lopt

1)4(or 1)4(





20N

22

1

1

41

41

1

)2()000(

NN

FB

yx





2

2

2

tEyx kk

cBpeakc

1

2

3

n

KgNKgNN n

ezyx

ncne

z

nc


33max











Slide 3

Slide 4





Dimension Estimates



Slide 12

Slide 13



Demand for X-rays


Introduction





















Diffraction Limit






Photon Degeneracy






previous )















Injector Parameters










endash

endashendash


Flu

x [p

hs

01

bw]

Bri

ghtn

ess

[ph

sm

m2

mr2

01

bw]

Flu

x [p

hs

01

bw]



p

N N

N

S

SS

Kz

x

y

zkBB py sin0

]m[]T[493 0 pBK


)]81475(exp[333]T[0 B

pgap for SmCo5 here







z

x

endash

in endash frame

pp

d

Pd2sin

N

1

z

x

back to lab frame

1

~

d

dP

1

on a

xis

off-axis

d

dP

1

N

1~


)1(2

22221

2

Kn

pn

pn nN

1~

(for fixed θ only)



z

x

1K

1K


z

x1

~even

odd



21

4

3 2KKnc

K nc

1 1

2 4

4 27

8 198

16 1548


d

dP

log

log

m

eBc 2

3 2 bend

wiggler

2Nspikes

continuum



e

INKKPtot )1(

32

212

1 A][m][

cm][

GeV][726[W]

2

22

ILKE

Pp

tot or


100 mA 5 GeV K = 15 p = 2 cm









LnN

K ncen 2

1

2

1 221


to get bwnNn

1~

n

)(Kge

INN n

nnph

n

Kg

e

I n )(

0

01

02

03

04

05

06

07

08

09

1

0 1 2 3 4 5

Kg

n(K

)

n = 1

3

57

9

)1(

][)(

221

2

K

JJnKKgn

Function



2212

1

)1(

)(3

NKK

Kg

P

P n

tot

cen



r

R

d

L


c



~R

rd

Lr c~Rrc ~

Lc ~

in Fraunhofer limit




x-ray source

Rings 1

ERLs 1

XFEL 1

c









)( )(

yxx

22

4

)(dxd

FdzxB

22)( dxdzxBF

invdzxBxd

FdxdzxB

d

Fd )( )( 2

2

22

2

2





xikezEzEdT

cdzxB

)2()2(

2)(

20

yikxx ezyxEzyxEyd

T

cd

)2()2(2

2

20

2

2

2 )( )(1

dezxEExdezxEE xikx

xikx




)(2)(

1cotexp

)()(

220

0 zR

ik

zwx

z

zkzi

zw

wEzxE

R

)1()( 2220

2Rzzwzw

20wzR

)1()( 22 zzzzR R

2

2

2

2

0

)(

2

1exp)(

rr

zxBzxB

00 1 2 kww rr

Rrr

rr

z

42

0

)2(B

Fcoh 20 )2( rr

FB






)21 ( here ))((e24

)0( 2)(

0

ntnntdc

eE tti

)(i0

i

i

e)0()0( cxtie

eEE

eN

EEEE1i

2i

1i

21 )0()0()0()0(

ji

2j

1i

)0()0(

EE

eN

22

e)1( zkee NN

1e22

zkeN




)0()0(e)0()0( i2

0

i1

0

)(21

21i

eexik

e EENEE e






2

00

)2()000(

F

B





2

2

2

2

2

00

2

1exp

)2()0(

rr

xFxB

LL rr 2 42

TyTyxTTx

FB

2)2(

)000(

2236122

1212222 LLa xxrTx

2236122

121222 LLyyrTy

222xrxT

222yryT





x

2 Lrropt

yx

41

41

1

)2()000(

2yx



)8(formin2

2formin

2formin2

2

L

L

L


4~ if also

Lopt

1)4(or 1)4(





20N

22

1

1

41

41

1

)2()000(

NN

FB

yx





2

2

2

tEyx kk

cBpeakc

1

2

3

n

KgNKgNN n

ezyx

ncne

z

nc


33max











Slide 3

Slide 4





Dimension Estimates



Slide 12

Slide 13



Demand for X-rays


Introduction





















Diffraction Limit






Photon Degeneracy










Injector Parameters










endash

endashendash


Flu

x [p

hs

01

bw]

Bri

ghtn

ess

[ph

sm

m2

mr2

01

bw]

Flu

x [p

hs

01

bw]



p

N N

N

S

SS

Kz

x

y

zkBB py sin0

]m[]T[493 0 pBK


)]81475(exp[333]T[0 B

pgap for SmCo5 here







z

x

endash

in endash frame

pp

d

Pd2sin

N

1

z

x

back to lab frame

1

~

d

dP

1

on a

xis

off-axis

d

dP

1

N

1~


)1(2

22221

2

Kn

pn

pn nN

1~

(for fixed θ only)



z

x

1K

1K


z

x1

~even

odd



21

4

3 2KKnc

K nc

1 1

2 4

4 27

8 198

16 1548


d

dP

log

log

m

eBc 2

3 2 bend

wiggler

2Nspikes

continuum



e

INKKPtot )1(

32

212

1 A][m][

cm][

GeV][726[W]

2

22

ILKE

Pp

tot or


100 mA 5 GeV K = 15 p = 2 cm









LnN

K ncen 2

1

2

1 221


to get bwnNn

1~

n

)(Kge

INN n

nnph

n

Kg

e

I n )(

0

01

02

03

04

05

06

07

08

09

1

0 1 2 3 4 5

Kg

n(K

)

n = 1

3

57

9

)1(

][)(

221

2

K

JJnKKgn

Function



2212

1

)1(

)(3

NKK

Kg

P

P n

tot

cen



r

R

d

L


c



~R

rd

Lr c~Rrc ~

Lc ~

in Fraunhofer limit




x-ray source

Rings 1

ERLs 1

XFEL 1

c









)( )(

yxx

22

4

)(dxd

FdzxB

22)( dxdzxBF

invdzxBxd

FdxdzxB

d

Fd )( )( 2

2

22

2

2





xikezEzEdT

cdzxB

)2()2(

2)(

20

yikxx ezyxEzyxEyd

T

cd

)2()2(2

2

20

2

2

2 )( )(1

dezxEExdezxEE xikx

xikx




)(2)(

1cotexp

)()(

220

0 zR

ik

zwx

z

zkzi

zw

wEzxE

R

)1()( 2220

2Rzzwzw

20wzR

)1()( 22 zzzzR R

2

2

2

2

0

)(

2

1exp)(

rr

zxBzxB

00 1 2 kww rr

Rrr

rr

z

42

0

)2(B

Fcoh 20 )2( rr

FB






)21 ( here ))((e24

)0( 2)(

0

ntnntdc

eE tti

)(i0

i

i

e)0()0( cxtie

eEE

eN

EEEE1i

2i

1i

21 )0()0()0()0(

ji

2j

1i

)0()0(

EE

eN

22

e)1( zkee NN

1e22

zkeN




)0()0(e)0()0( i2

0

i1

0

)(21

21i

eexik

e EENEE e






2

00

)2()000(

F

B





2

2

2

2

2

00

2

1exp

)2()0(

rr

xFxB

LL rr 2 42

TyTyxTTx

FB

2)2(

)000(

2236122

1212222 LLa xxrTx

2236122

121222 LLyyrTy

222xrxT

222yryT





x

2 Lrropt

yx

41

41

1

)2()000(

2yx



)8(formin2

2formin

2formin2

2

L

L

L


4~ if also

Lopt

1)4(or 1)4(





20N

22

1

1

41

41

1

)2()000(

NN

FB

yx





2

2

2

tEyx kk

cBpeakc

1

2

3

n

KgNKgNN n

ezyx

ncne

z

nc


33max











Slide 3

Slide 4





Dimension Estimates



Slide 12

Slide 13



Demand for X-rays


Introduction





















Diffraction Limit






Photon Degeneracy










endash

endashendash


Flu

x [p

hs

01

bw]

Bri

ghtn

ess

[ph

sm

m2

mr2

01

bw]

Flu

x [p

hs

01

bw]



p

N N

N

S

SS

Kz

x

y

zkBB py sin0

]m[]T[493 0 pBK


)]81475(exp[333]T[0 B

pgap for SmCo5 here







z

x

endash

in endash frame

pp

d

Pd2sin

N

1

z

x

back to lab frame

1

~

d

dP

1

on a

xis

off-axis

d

dP

1

N

1~


)1(2

22221

2

Kn

pn

pn nN

1~

(for fixed θ only)



z

x

1K

1K


z

x1

~even

odd



21

4

3 2KKnc

K nc

1 1

2 4

4 27

8 198

16 1548


d

dP

log

log

m

eBc 2

3 2 bend

wiggler

2Nspikes

continuum



e

INKKPtot )1(

32

212

1 A][m][

cm][

GeV][726[W]

2

22

ILKE

Pp

tot or


100 mA 5 GeV K = 15 p = 2 cm









LnN

K ncen 2

1

2

1 221


to get bwnNn

1~

n

)(Kge

INN n

nnph

n

Kg

e

I n )(

0

01

02

03

04

05

06

07

08

09

1

0 1 2 3 4 5

Kg

n(K

)

n = 1

3

57

9

)1(

][)(

221

2

K

JJnKKgn

Function



2212

1

)1(

)(3

NKK

Kg

P

P n

tot

cen



r

R

d

L


c



~R

rd

Lr c~Rrc ~

Lc ~

in Fraunhofer limit




x-ray source

Rings 1

ERLs 1

XFEL 1

c









)( )(

yxx

22

4

)(dxd

FdzxB

22)( dxdzxBF

invdzxBxd

FdxdzxB

d

Fd )( )( 2

2

22

2

2





xikezEzEdT

cdzxB

)2()2(

2)(

20

yikxx ezyxEzyxEyd

T

cd

)2()2(2

2

20

2

2

2 )( )(1

dezxEExdezxEE xikx

xikx




)(2)(

1cotexp

)()(

220

0 zR

ik

zwx

z

zkzi

zw

wEzxE

R

)1()( 2220

2Rzzwzw

20wzR

)1()( 22 zzzzR R

2

2

2

2

0

)(

2

1exp)(

rr

zxBzxB

00 1 2 kww rr

Rrr

rr

z

42

0

)2(B

Fcoh 20 )2( rr

FB






)21 ( here ))((e24

)0( 2)(

0

ntnntdc

eE tti

)(i0

i

i

e)0()0( cxtie

eEE

eN

EEEE1i

2i

1i

21 )0()0()0()0(

ji

2j

1i

)0()0(

EE

eN

22

e)1( zkee NN

1e22

zkeN




)0()0(e)0()0( i2

0

i1

0

)(21

21i

eexik

e EENEE e






2

00

)2()000(

F

B





2

2

2

2

2

00

2

1exp

)2()0(

rr

xFxB

LL rr 2 42

TyTyxTTx

FB

2)2(

)000(

2236122

1212222 LLa xxrTx

2236122

121222 LLyyrTy

222xrxT

222yryT





x

2 Lrropt

yx

41

41

1

)2()000(

2yx



)8(formin2

2formin

2formin2

2

L

L

L


4~ if also

Lopt

1)4(or 1)4(





20N

22

1

1

41

41

1

)2()000(

NN

FB

yx





2

2

2

tEyx kk

cBpeakc

1

2

3

n

KgNKgNN n

ezyx

ncne

z

nc


33max











Slide 3

Slide 4





Dimension Estimates



Slide 12

Slide 13



Demand for X-rays


Introduction





















Diffraction Limit






Photon Degeneracy



p

N N

N

S

SS

Kz

x

y

zkBB py sin0

]m[]T[493 0 pBK


)]81475(exp[333]T[0 B

pgap for SmCo5 here







z

x

endash

in endash frame

pp

d

Pd2sin

N

1

z

x

back to lab frame

1

~

d

dP

1

on a

xis

off-axis

d

dP

1

N

1~


)1(2

22221

2

Kn

pn

pn nN

1~

(for fixed θ only)



z

x

1K

1K


z

x1

~even

odd



21

4

3 2KKnc

K nc

1 1

2 4

4 27

8 198

16 1548


d

dP

log

log

m

eBc 2

3 2 bend

wiggler

2Nspikes

continuum



e

INKKPtot )1(

32

212

1 A][m][

cm][

GeV][726[W]

2

22

ILKE

Pp

tot or


100 mA 5 GeV K = 15 p = 2 cm









LnN

K ncen 2

1

2

1 221


to get bwnNn

1~

n

)(Kge

INN n

nnph

n

Kg

e

I n )(

0

01

02

03

04

05

06

07

08

09

1

0 1 2 3 4 5

Kg

n(K

)

n = 1

3

57

9

)1(

][)(

221

2

K

JJnKKgn

Function



2212

1

)1(

)(3

NKK

Kg

P

P n

tot

cen



r

R

d

L


c



~R

rd

Lr c~Rrc ~

Lc ~

in Fraunhofer limit




x-ray source

Rings 1

ERLs 1

XFEL 1

c









)( )(

yxx

22

4

)(dxd

FdzxB

22)( dxdzxBF

invdzxBxd

FdxdzxB

d

Fd )( )( 2

2

22

2

2





xikezEzEdT

cdzxB

)2()2(

2)(

20

yikxx ezyxEzyxEyd

T

cd

)2()2(2

2

20

2

2

2 )( )(1

dezxEExdezxEE xikx

xikx




)(2)(

1cotexp

)()(

220

0 zR

ik

zwx

z

zkzi

zw

wEzxE

R

)1()( 2220

2Rzzwzw

20wzR

)1()( 22 zzzzR R

2

2

2

2

0

)(

2

1exp)(

rr

zxBzxB

00 1 2 kww rr

Rrr

rr

z

42

0

)2(B

Fcoh 20 )2( rr

FB






)21 ( here ))((e24

)0( 2)(

0

ntnntdc

eE tti

)(i0

i

i

e)0()0( cxtie

eEE

eN

EEEE1i

2i

1i

21 )0()0()0()0(

ji

2j

1i

)0()0(

EE

eN

22

e)1( zkee NN

1e22

zkeN




)0()0(e)0()0( i2

0

i1

0

)(21

21i

eexik

e EENEE e






2

00

)2()000(

F

B





2

2

2

2

2

00

2

1exp

)2()0(

rr

xFxB

LL rr 2 42

TyTyxTTx

FB

2)2(

)000(

2236122

1212222 LLa xxrTx

2236122

121222 LLyyrTy

222xrxT

222yryT





x

2 Lrropt

yx

41

41

1

)2()000(

2yx



)8(formin2

2formin

2formin2

2

L

L

L


4~ if also

Lopt

1)4(or 1)4(





20N

22

1

1

41

41

1

)2()000(

NN

FB

yx





2

2

2

tEyx kk

cBpeakc

1

2

3

n

KgNKgNN n

ezyx

ncne

z

nc


33max











Slide 3

Slide 4





Dimension Estimates



Slide 12

Slide 13



Demand for X-rays


Introduction





















Diffraction Limit






Photon Degeneracy



z

x

endash

in endash frame

pp

d

Pd2sin

N

1

z

x

back to lab frame

1

~

d

dP

1

on a

xis

off-axis

d

dP

1

N

1~


)1(2

22221

2

Kn

pn

pn nN

1~

(for fixed θ only)



z

x

1K

1K


z

x1

~even

odd



21

4

3 2KKnc

K nc

1 1

2 4

4 27

8 198

16 1548


d

dP

log

log

m

eBc 2

3 2 bend

wiggler

2Nspikes

continuum



e

INKKPtot )1(

32

212

1 A][m][

cm][

GeV][726[W]

2

22

ILKE

Pp

tot or


100 mA 5 GeV K = 15 p = 2 cm









LnN

K ncen 2

1

2

1 221


to get bwnNn

1~

n

)(Kge

INN n

nnph

n

Kg

e

I n )(

0

01

02

03

04

05

06

07

08

09

1

0 1 2 3 4 5

Kg

n(K

)

n = 1

3

57

9

)1(

][)(

221

2

K

JJnKKgn

Function



2212

1

)1(

)(3

NKK

Kg

P

P n

tot

cen



r

R

d

L


c



~R

rd

Lr c~Rrc ~

Lc ~

in Fraunhofer limit




x-ray source

Rings 1

ERLs 1

XFEL 1

c









)( )(

yxx

22

4

)(dxd

FdzxB

22)( dxdzxBF

invdzxBxd

FdxdzxB

d

Fd )( )( 2

2

22

2

2





xikezEzEdT

cdzxB

)2()2(

2)(

20

yikxx ezyxEzyxEyd

T

cd

)2()2(2

2

20

2

2

2 )( )(1

dezxEExdezxEE xikx

xikx




)(2)(

1cotexp

)()(

220

0 zR

ik

zwx

z

zkzi

zw

wEzxE

R

)1()( 2220

2Rzzwzw

20wzR

)1()( 22 zzzzR R

2

2

2

2

0

)(

2

1exp)(

rr

zxBzxB

00 1 2 kww rr

Rrr

rr

z

42

0

)2(B

Fcoh 20 )2( rr

FB






)21 ( here ))((e24

)0( 2)(

0

ntnntdc

eE tti

)(i0

i

i

e)0()0( cxtie

eEE

eN

EEEE1i

2i

1i

21 )0()0()0()0(

ji

2j

1i

)0()0(

EE

eN

22

e)1( zkee NN

1e22

zkeN




)0()0(e)0()0( i2

0

i1

0

)(21

21i

eexik

e EENEE e






2

00

)2()000(

F

B





2

2

2

2

2

00

2

1exp

)2()0(

rr

xFxB

LL rr 2 42

TyTyxTTx

FB

2)2(

)000(

2236122

1212222 LLa xxrTx

2236122

121222 LLyyrTy

222xrxT

222yryT





x

2 Lrropt

yx

41

41

1

)2()000(

2yx



)8(formin2

2formin

2formin2

2

L

L

L


4~ if also

Lopt

1)4(or 1)4(





20N

22

1

1

41

41

1

)2()000(

NN

FB

yx





2

2

2

tEyx kk

cBpeakc

1

2

3

n

KgNKgNN n

ezyx

ncne

z

nc


33max











Slide 3

Slide 4





Dimension Estimates



Slide 12

Slide 13



Demand for X-rays


Introduction





















Diffraction Limit






Photon Degeneracy



z

x

1K

1K


z

x1

~even

odd



21

4

3 2KKnc

K nc

1 1

2 4

4 27

8 198

16 1548


d

dP

log

log

m

eBc 2

3 2 bend

wiggler

2Nspikes

continuum



e

INKKPtot )1(

32

212

1 A][m][

cm][

GeV][726[W]

2

22

ILKE

Pp

tot or


100 mA 5 GeV K = 15 p = 2 cm









LnN

K ncen 2

1

2

1 221


to get bwnNn

1~

n

)(Kge

INN n

nnph

n

Kg

e

I n )(

0

01

02

03

04

05

06

07

08

09

1

0 1 2 3 4 5

Kg

n(K

)

n = 1

3

57

9

)1(

][)(

221

2

K

JJnKKgn

Function



2212

1

)1(

)(3

NKK

Kg

P

P n

tot

cen



r

R

d

L


c



~R

rd

Lr c~Rrc ~

Lc ~

in Fraunhofer limit




x-ray source

Rings 1

ERLs 1

XFEL 1

c









)( )(

yxx

22

4

)(dxd

FdzxB

22)( dxdzxBF

invdzxBxd

FdxdzxB

d

Fd )( )( 2

2

22

2

2





xikezEzEdT

cdzxB

)2()2(

2)(

20

yikxx ezyxEzyxEyd

T

cd

)2()2(2

2

20

2

2

2 )( )(1

dezxEExdezxEE xikx

xikx




)(2)(

1cotexp

)()(

220

0 zR

ik

zwx

z

zkzi

zw

wEzxE

R

)1()( 2220

2Rzzwzw

20wzR

)1()( 22 zzzzR R

2

2

2

2

0

)(

2

1exp)(

rr

zxBzxB

00 1 2 kww rr

Rrr

rr

z

42

0

)2(B

Fcoh 20 )2( rr

FB






)21 ( here ))((e24

)0( 2)(

0

ntnntdc

eE tti

)(i0

i

i

e)0()0( cxtie

eEE

eN

EEEE1i

2i

1i

21 )0()0()0()0(

ji

2j

1i

)0()0(

EE

eN

22

e)1( zkee NN

1e22

zkeN




)0()0(e)0()0( i2

0

i1

0

)(21

21i

eexik

e EENEE e






2

00

)2()000(

F

B





2

2

2

2

2

00

2

1exp

)2()0(

rr

xFxB

LL rr 2 42

TyTyxTTx

FB

2)2(

)000(

2236122

1212222 LLa xxrTx

2236122

121222 LLyyrTy

222xrxT

222yryT





x

2 Lrropt

yx

41

41

1

)2()000(

2yx



)8(formin2

2formin

2formin2

2

L

L

L


4~ if also

Lopt

1)4(or 1)4(





20N

22

1

1

41

41

1

)2()000(

NN

FB

yx





2

2

2

tEyx kk

cBpeakc

1

2

3

n

KgNKgNN n

ezyx

ncne

z

nc


33max











Slide 3

Slide 4





Dimension Estimates



Slide 12

Slide 13



Demand for X-rays


Introduction





















Diffraction Limit






Photon Degeneracy



e

INKKPtot )1(

32

212

1 A][m][

cm][

GeV][726[W]

2

22

ILKE

Pp

tot or


100 mA 5 GeV K = 15 p = 2 cm









LnN

K ncen 2

1

2

1 221


to get bwnNn

1~

n

)(Kge

INN n

nnph

n

Kg

e

I n )(

0

01

02

03

04

05

06

07

08

09

1

0 1 2 3 4 5

Kg

n(K

)

n = 1

3

57

9

)1(

][)(

221

2

K

JJnKKgn

Function



2212

1

)1(

)(3

NKK

Kg

P

P n

tot

cen



r

R

d

L


c



~R

rd

Lr c~Rrc ~

Lc ~

in Fraunhofer limit




x-ray source

Rings 1

ERLs 1

XFEL 1

c









)( )(

yxx

22

4

)(dxd

FdzxB

22)( dxdzxBF

invdzxBxd

FdxdzxB

d

Fd )( )( 2

2

22

2

2





xikezEzEdT

cdzxB

)2()2(

2)(

20

yikxx ezyxEzyxEyd

T

cd

)2()2(2

2

20

2

2

2 )( )(1

dezxEExdezxEE xikx

xikx




)(2)(

1cotexp

)()(

220

0 zR

ik

zwx

z

zkzi

zw

wEzxE

R

)1()( 2220

2Rzzwzw

20wzR

)1()( 22 zzzzR R

2

2

2

2

0

)(

2

1exp)(

rr

zxBzxB

00 1 2 kww rr

Rrr

rr

z

42

0

)2(B

Fcoh 20 )2( rr

FB






)21 ( here ))((e24

)0( 2)(

0

ntnntdc

eE tti

)(i0

i

i

e)0()0( cxtie

eEE

eN

EEEE1i

2i

1i

21 )0()0()0()0(

ji

2j

1i

)0()0(

EE

eN

22

e)1( zkee NN

1e22

zkeN




)0()0(e)0()0( i2

0

i1

0

)(21

21i

eexik

e EENEE e






2

00

)2()000(

F

B





2

2

2

2

2

00

2

1exp

)2()0(

rr

xFxB

LL rr 2 42

TyTyxTTx

FB

2)2(

)000(

2236122

1212222 LLa xxrTx

2236122

121222 LLyyrTy

222xrxT

222yryT





x

2 Lrropt

yx

41

41

1

)2()000(

2yx



)8(formin2

2formin

2formin2

2

L

L

L


4~ if also

Lopt

1)4(or 1)4(





20N

22

1

1

41

41

1

)2()000(

NN

FB

yx





2

2

2

tEyx kk

cBpeakc

1

2

3

n

KgNKgNN n

ezyx

ncne

z

nc


33max











Slide 3

Slide 4





Dimension Estimates



Slide 12

Slide 13



Demand for X-rays


Introduction





















Diffraction Limit






Photon Degeneracy




LnN

K ncen 2

1

2

1 221


to get bwnNn

1~

n

)(Kge

INN n

nnph

n

Kg

e

I n )(

0

01

02

03

04

05

06

07

08

09

1

0 1 2 3 4 5

Kg

n(K

)

n = 1

3

57

9

)1(

][)(

221

2

K

JJnKKgn

Function



2212

1

)1(

)(3

NKK

Kg

P

P n

tot

cen



r

R

d

L


c



~R

rd

Lr c~Rrc ~

Lc ~

in Fraunhofer limit




x-ray source

Rings 1

ERLs 1

XFEL 1

c









)( )(

yxx

22

4

)(dxd

FdzxB

22)( dxdzxBF

invdzxBxd

FdxdzxB

d

Fd )( )( 2

2

22

2

2





xikezEzEdT

cdzxB

)2()2(

2)(

20

yikxx ezyxEzyxEyd

T

cd

)2()2(2

2

20

2

2

2 )( )(1

dezxEExdezxEE xikx

xikx




)(2)(

1cotexp

)()(

220

0 zR

ik

zwx

z

zkzi

zw

wEzxE

R

)1()( 2220

2Rzzwzw

20wzR

)1()( 22 zzzzR R

2

2

2

2

0

)(

2

1exp)(

rr

zxBzxB

00 1 2 kww rr

Rrr

rr

z

42

0

)2(B

Fcoh 20 )2( rr

FB






)21 ( here ))((e24

)0( 2)(

0

ntnntdc

eE tti

)(i0

i

i

e)0()0( cxtie

eEE

eN

EEEE1i

2i

1i

21 )0()0()0()0(

ji

2j

1i

)0()0(

EE

eN

22

e)1( zkee NN

1e22

zkeN




)0()0(e)0()0( i2

0

i1

0

)(21

21i

eexik

e EENEE e






2

00

)2()000(

F

B





2

2

2

2

2

00

2

1exp

)2()0(

rr

xFxB

LL rr 2 42

TyTyxTTx

FB

2)2(

)000(

2236122

1212222 LLa xxrTx

2236122

121222 LLyyrTy

222xrxT

222yryT





x

2 Lrropt

yx

41

41

1

)2()000(

2yx



)8(formin2

2formin

2formin2

2

L

L

L


4~ if also

Lopt

1)4(or 1)4(





20N

22

1

1

41

41

1

)2()000(

NN

FB

yx





2

2

2

tEyx kk

cBpeakc

1

2

3

n

KgNKgNN n

ezyx

ncne

z

nc


33max











Slide 3

Slide 4





Dimension Estimates



Slide 12

Slide 13



Demand for X-rays


Introduction





















Diffraction Limit






Photon Degeneracy



r

R

d

L


c



~R

rd

Lr c~Rrc ~

Lc ~

in Fraunhofer limit




x-ray source

Rings 1

ERLs 1

XFEL 1

c









)( )(

yxx

22

4

)(dxd

FdzxB

22)( dxdzxBF

invdzxBxd

FdxdzxB

d

Fd )( )( 2

2

22

2

2





xikezEzEdT

cdzxB

)2()2(

2)(

20

yikxx ezyxEzyxEyd

T

cd

)2()2(2

2

20

2

2

2 )( )(1

dezxEExdezxEE xikx

xikx




)(2)(

1cotexp

)()(

220

0 zR

ik

zwx

z

zkzi

zw

wEzxE

R

)1()( 2220

2Rzzwzw

20wzR

)1()( 22 zzzzR R

2

2

2

2

0

)(

2

1exp)(

rr

zxBzxB

00 1 2 kww rr

Rrr

rr

z

42

0

)2(B

Fcoh 20 )2( rr

FB






)21 ( here ))((e24

)0( 2)(

0

ntnntdc

eE tti

)(i0

i

i

e)0()0( cxtie

eEE

eN

EEEE1i

2i

1i

21 )0()0()0()0(

ji

2j

1i

)0()0(

EE

eN

22

e)1( zkee NN

1e22

zkeN




)0()0(e)0()0( i2

0

i1

0

)(21

21i

eexik

e EENEE e






2

00

)2()000(

F

B





2

2

2

2

2

00

2

1exp

)2()0(

rr

xFxB

LL rr 2 42

TyTyxTTx

FB

2)2(

)000(

2236122

1212222 LLa xxrTx

2236122

121222 LLyyrTy

222xrxT

222yryT





x

2 Lrropt

yx

41

41

1

)2()000(

2yx



)8(formin2

2formin

2formin2

2

L

L

L


4~ if also

Lopt

1)4(or 1)4(





20N

22

1

1

41

41

1

)2()000(

NN

FB

yx





2

2

2

tEyx kk

cBpeakc

1

2

3

n

KgNKgNN n

ezyx

ncne

z

nc


33max











Slide 3

Slide 4





Dimension Estimates



Slide 12

Slide 13



Demand for X-rays


Introduction





















Diffraction Limit






Photon Degeneracy







)( )(

yxx

22

4

)(dxd

FdzxB

22)( dxdzxBF

invdzxBxd

FdxdzxB

d

Fd )( )( 2

2

22

2

2





xikezEzEdT

cdzxB

)2()2(

2)(

20

yikxx ezyxEzyxEyd

T

cd

)2()2(2

2

20

2

2

2 )( )(1

dezxEExdezxEE xikx

xikx




)(2)(

1cotexp

)()(

220

0 zR

ik

zwx

z

zkzi

zw

wEzxE

R

)1()( 2220

2Rzzwzw

20wzR

)1()( 22 zzzzR R

2

2

2

2

0

)(

2

1exp)(

rr

zxBzxB

00 1 2 kww rr

Rrr

rr

z

42

0

)2(B

Fcoh 20 )2( rr

FB






)21 ( here ))((e24

)0( 2)(

0

ntnntdc

eE tti

)(i0

i

i

e)0()0( cxtie

eEE

eN

EEEE1i

2i

1i

21 )0()0()0()0(

ji

2j

1i

)0()0(

EE

eN

22

e)1( zkee NN

1e22

zkeN




)0()0(e)0()0( i2

0

i1

0

)(21

21i

eexik

e EENEE e






2

00

)2()000(

F

B





2

2

2

2

2

00

2

1exp

)2()0(

rr

xFxB

LL rr 2 42

TyTyxTTx

FB

2)2(

)000(

2236122

1212222 LLa xxrTx

2236122

121222 LLyyrTy

222xrxT

222yryT





x

2 Lrropt

yx

41

41

1

)2()000(

2yx



)8(formin2

2formin

2formin2

2

L

L

L


4~ if also

Lopt

1)4(or 1)4(





20N

22

1

1

41

41

1

)2()000(

NN

FB

yx





2

2

2

tEyx kk

cBpeakc

1

2

3

n

KgNKgNN n

ezyx

ncne

z

nc


33max











Slide 3

Slide 4





Dimension Estimates



Slide 12

Slide 13



Demand for X-rays


Introduction





















Diffraction Limit






Photon Degeneracy





xikezEzEdT

cdzxB

)2()2(

2)(

20

yikxx ezyxEzyxEyd

T

cd

)2()2(2

2

20

2

2

2 )( )(1

dezxEExdezxEE xikx

xikx




)(2)(

1cotexp

)()(

220

0 zR

ik

zwx

z

zkzi

zw

wEzxE

R

)1()( 2220

2Rzzwzw

20wzR

)1()( 22 zzzzR R

2

2

2

2

0

)(

2

1exp)(

rr

zxBzxB

00 1 2 kww rr

Rrr

rr

z

42

0

)2(B

Fcoh 20 )2( rr

FB






)21 ( here ))((e24

)0( 2)(

0

ntnntdc

eE tti

)(i0

i

i

e)0()0( cxtie

eEE

eN

EEEE1i

2i

1i

21 )0()0()0()0(

ji

2j

1i

)0()0(

EE

eN

22

e)1( zkee NN

1e22

zkeN




)0()0(e)0()0( i2

0

i1

0

)(21

21i

eexik

e EENEE e






2

00

)2()000(

F

B





2

2

2

2

2

00

2

1exp

)2()0(

rr

xFxB

LL rr 2 42

TyTyxTTx

FB

2)2(

)000(

2236122

1212222 LLa xxrTx

2236122

121222 LLyyrTy

222xrxT

222yryT





x

2 Lrropt

yx

41

41

1

)2()000(

2yx



)8(formin2

2formin

2formin2

2

L

L

L


4~ if also

Lopt

1)4(or 1)4(





20N

22

1

1

41

41

1

)2()000(

NN

FB

yx





2

2

2

tEyx kk

cBpeakc

1

2

3

n

KgNKgNN n

ezyx

ncne

z

nc


33max











Slide 3

Slide 4





Dimension Estimates



Slide 12

Slide 13



Demand for X-rays


Introduction





















Diffraction Limit






Photon Degeneracy




)(2)(

1cotexp

)()(

220

0 zR

ik

zwx

z

zkzi

zw

wEzxE

R

)1()( 2220

2Rzzwzw

20wzR

)1()( 22 zzzzR R

2

2

2

2

0

)(

2

1exp)(

rr

zxBzxB

00 1 2 kww rr

Rrr

rr

z

42

0

)2(B

Fcoh 20 )2( rr

FB






)21 ( here ))((e24

)0( 2)(

0

ntnntdc

eE tti

)(i0

i

i

e)0()0( cxtie

eEE

eN

EEEE1i

2i

1i

21 )0()0()0()0(

ji

2j

1i

)0()0(

EE

eN

22

e)1( zkee NN

1e22

zkeN




)0()0(e)0()0( i2

0

i1

0

)(21

21i

eexik

e EENEE e






2

00

)2()000(

F

B





2

2

2

2

2

00

2

1exp

)2()0(

rr

xFxB

LL rr 2 42

TyTyxTTx

FB

2)2(

)000(

2236122

1212222 LLa xxrTx

2236122

121222 LLyyrTy

222xrxT

222yryT





x

2 Lrropt

yx

41

41

1

)2()000(

2yx



)8(formin2

2formin

2formin2

2

L

L

L


4~ if also

Lopt

1)4(or 1)4(





20N

22

1

1

41

41

1

)2()000(

NN

FB

yx





2

2

2

tEyx kk

cBpeakc

1

2

3

n

KgNKgNN n

ezyx

ncne

z

nc


33max











Slide 3

Slide 4





Dimension Estimates



Slide 12

Slide 13



Demand for X-rays


Introduction





















Diffraction Limit






Photon Degeneracy






)21 ( here ))((e24

)0( 2)(

0

ntnntdc

eE tti

)(i0

i

i

e)0()0( cxtie

eEE

eN

EEEE1i

2i

1i

21 )0()0()0()0(

ji

2j

1i

)0()0(

EE

eN

22

e)1( zkee NN

1e22

zkeN




)0()0(e)0()0( i2

0

i1

0

)(21

21i

eexik

e EENEE e






2

00

)2()000(

F

B





2

2

2

2

2

00

2

1exp

)2()0(

rr

xFxB

LL rr 2 42

TyTyxTTx

FB

2)2(

)000(

2236122

1212222 LLa xxrTx

2236122

121222 LLyyrTy

222xrxT

222yryT





x

2 Lrropt

yx

41

41

1

)2()000(

2yx



)8(formin2

2formin

2formin2

2

L

L

L


4~ if also

Lopt

1)4(or 1)4(





20N

22

1

1

41

41

1

)2()000(

NN

FB

yx





2

2

2

tEyx kk

cBpeakc

1

2

3

n

KgNKgNN n

ezyx

ncne

z

nc


33max











Slide 3

Slide 4





Dimension Estimates



Slide 12

Slide 13



Demand for X-rays


Introduction





















Diffraction Limit






Photon Degeneracy



)0()0(e)0()0( i2

0

i1

0

)(21

21i

eexik

e EENEE e






2

00

)2()000(

F

B





2

2

2

2

2

00

2

1exp

)2()0(

rr

xFxB

LL rr 2 42

TyTyxTTx

FB

2)2(

)000(

2236122

1212222 LLa xxrTx

2236122

121222 LLyyrTy

222xrxT

222yryT





x

2 Lrropt

yx

41

41

1

)2()000(

2yx



)8(formin2

2formin

2formin2

2

L

L

L


4~ if also

Lopt

1)4(or 1)4(





20N

22

1

1

41

41

1

)2()000(

NN

FB

yx





2

2

2

tEyx kk

cBpeakc

1

2

3

n

KgNKgNN n

ezyx

ncne

z

nc


33max











Slide 3

Slide 4





Dimension Estimates



Slide 12

Slide 13



Demand for X-rays


Introduction





















Diffraction Limit






Photon Degeneracy




2

2

2

2

2

00

2

1exp

)2()0(

rr

xFxB

LL rr 2 42

TyTyxTTx

FB

2)2(

)000(

2236122

1212222 LLa xxrTx

2236122

121222 LLyyrTy

222xrxT

222yryT





x

2 Lrropt

yx

41

41

1

)2()000(

2yx



)8(formin2

2formin

2formin2

2

L

L

L


4~ if also

Lopt

1)4(or 1)4(





20N

22

1

1

41

41

1

)2()000(

NN

FB

yx





2

2

2

tEyx kk

cBpeakc

1

2

3

n

KgNKgNN n

ezyx

ncne

z

nc


33max











Slide 3

Slide 4





Dimension Estimates



Slide 12

Slide 13



Demand for X-rays


Introduction





















Diffraction Limit






Photon Degeneracy





x

2 Lrropt

yx

41

41

1

)2()000(

2yx



)8(formin2

2formin

2formin2

2

L

L

L


4~ if also

Lopt

1)4(or 1)4(





20N

22

1

1

41

41

1

)2()000(

NN

FB

yx





2

2

2

tEyx kk

cBpeakc

1

2

3

n

KgNKgNN n

ezyx

ncne

z

nc


33max











Slide 3

Slide 4





Dimension Estimates



Slide 12

Slide 13



Demand for X-rays


Introduction





















Diffraction Limit






Photon Degeneracy






20N

22

1

1

41

41

1

)2()000(

NN

FB

yx





2

2

2

tEyx kk

cBpeakc

1

2

3

n

KgNKgNN n

ezyx

ncne

z

nc


33max











Slide 3

Slide 4





Dimension Estimates



Slide 12

Slide 13



Demand for X-rays


Introduction





















Diffraction Limit






Photon Degeneracy





2

2

2

tEyx kk

cBpeakc

1

2

3

n

KgNKgNN n

ezyx

ncne

z

nc


33max











Slide 3

Slide 4





Dimension Estimates



Slide 12

Slide 13



Demand for X-rays


Introduction





















Diffraction Limit






Photon Degeneracy










Slide 3

Slide 4





Dimension Estimates



Slide 12

Slide 13



Demand for X-rays


Introduction





















Diffraction Limit






Photon Degeneracy


uspas course on recirculated and energy recovered linacs g. a. krafft and a. bogacz jefferson lab...

Documents