synchrotron radiation and free electron lasers · synchrotron radiation and free electron lasers...

Operated by the Southeastern Universities Research Association for the U.S. Department of Energy

Thomas Jefferson National Accelerator Facility

Synchrotron Radiation and

Free Electron Lasers

Gwyn P. Williams

Jefferson Lab12000 Jefferson Avenue - MS 7A

Newport News, VA [email protected]

UVa April 14, 2004



Synchrotron Radiation and Free Electron Lasers

This lecture is aimed at teaching the physics of the productionof very bright light, from a user perspective, NOT an accelerator perspective.

It is not a rigorous presentation of the theory, although it will contain all the critical theoretical arguments and equations.

But most importantly it bridges the gap between Krafft et al’s lectures and practical calculations of light output.

See G.P. Williams, Rep. Prog. Phys. 69 310-326, 2006



X-Ray Brightness Growth vs Time Compared with Computers

1960 1970 1980 1990 2000107

108

109

1010

1011

1012

1013

1014

1015

1016

1017

1018

1019

1020

1021

1022

x1023

200 mA Diff. Limit

3rd. Gen.original design

2nd. Gen.

1st. Gen. Synch. Rad.

CDC 6600

Cray 1

Cray T90

GROWTH IN LEADING EDGECOMPUTING SPEED(Millions of operations/sec)

GROWTH IN SYNCHROTRON X-RAY SOURCE BRIGHTNESS

(Photons/sec/0.1%bw/sq.mm/mrad2)

Calendar Year

10-1

100

101

102

103

104

105

106

107

108

109

1010

1011

1012

1013

1014

1015



How do we make light?

Light (electromagnetic waves) is made by waving an electron around.

e- light



Radiation from Accelerated Electron - Power

electronBut dimensions of power are:

acceleration2 2 3

c

MLT L ML TT

Force Distan eTimePower

− −× =

×

=

=field

Electric field goes linearly in the electric charge and the acceleration- so intensity (power) goes like e2a2

2 22

e MLTL

−=

Now for an electric charge, force ise2/L2, so we can derive dimensions for e thus:

So e2a2 has dimensions of :ML3 T-2×L2T-4 = ML5T-6

And if we divide by c3, or L3T-3, we get ML2T-3.



Radiation from Accelerated Electron - Power

Larmor’s Formula2 2

323e ac

Power=

Also we note that radiation is emitted in only 2 out of 3 directions, so we have a 2/3 factor, yielding:

Noting that the dimensions of power are ML2T-3, and noting That M goes like gamma, L goes like 1/gamma and T goes likegamma in the moving frame, in the rest frame the relativistic version is :

42 23

23e ac

Power γ=

N.B. Radiated energy and elapsed time transform in the same manner under Lorentz transforms 25102 −×≈

νddE J/cm-1/electron



Theory

D.H. Tomboulian & P.L. Hartman, Phys. Rev. 102 1423 (1956)J. Schwinger, Phys. Rev. 75 1912 (1949)J.D. Jackson, Classical Electrodynamics, Wiley, NY 1975H. Winick, Synchrotron Radiation Research, Chap. 2, Plenum Press 1980.K.J. Kim AIP Proceedings 184 565 (1989).S.L. Hulbert and G.P., Williams, "Synchrotron radiation sources." In Handbook of Optics: Classical, Vision, and X-Ray Optics, 2nd ed., vol. III, chap. 32. Michael Bass, Jay M. Enoch, Eric W. Van Stryland, and William L. Wolfe (eds.). New York: McGraw-Hill, , pp. 32.1--32.20 (2001).C. A. Brau, Modern Problems in Classical Electrodynamics, Oxford University Press (2004).


Thomas Jefferson National Accelerator Facilitytime freq. (1/time)

Inte

nsity

e2

electron(s)2 9 8

1 2t 10 Attosecondsc 10 3 10ρ∆ γγ

= = ≈× ×

cc

c c t 30 Angstromsλ ∆ω= ≈ ≈

Radiation from Accelerated Electron – SpectrumEl

e ctri

c fie

ld



Radiation from Accelerated Electron – Emission Angle

sintan( ) (cos )r tt

θθ γ θ β=−

r is lab (receiving frame) t is transmitting frameSo θt = 900 transforms to ~1/γin the lab frame

γ = mass / rest mass



2.nr( t )ˆi t c2 2 2

2d I e n n e dtd d 4 c

ωω βω Ω π

⎛ ⎞⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠

⎛ ⎞⎜ ⎟⎜ ⎟⎝ ⎠

−∞

−∞= × ×∫

Synchrotron Radiation Generation - theory

Jackson, Classical Electrodynamics, Wiley, NY 1975



where e is the charge of an electron, β is the ratio of the velocity of the particle to the speed of light, n is a unit vector and (t) is the particle position.Kim has shown that one can re-write this to give the total flux emitted in practical units, per horizontal milliradian per ampere into a 0.1% bandwidth (Dλ/ λ or DE/E), integrated over qV as:

F tot= 2.547 x 10 13 E (GeV) I (A) G1(y)where G1(y) is the Bessel function:

1 5/3( ) ( )y

G y K dη η∞

= ∫cy λλ=

03

5.59 ( )( )(cmetersA

E GeVρλ =with and



Bessel Functions!!!

The function G1(y)



Bessel Functions!!!

1 5/3( ) ( )y

G y K dη η∞

= ∫

can be shown to be equivalent to:

1 r=1

(0.5 )( ) 0.5 + (0.5 )2 (0.5 )y y cosh kreG y e cosh r cosh r

⎛ ⎞⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠

∞− −= ∑

V. Kostroun, Nucl. Instr. & Methods 172 371 (1980).



Brightness

Brightness is sometimes called brilliance, or spectral radiance.It has units of power per unit area per unit solid angle.

ρ

ϑΗ

ϑv

svsH

ρ

ϑΗ

ϑv

svsH



Emitted Flux as Function of Vertical Angle

222 2 216 2 2 2 2cv v V V V2/ 3F ( ) 1.325 10 E 1 K ( 1 )λθ γ θ ζ γ θ γ θ ζλ

⎛ ⎞⎛ ⎞ ⎛ ⎞⎛ ⎞ ⎛ ⎞⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠⎜ ⎟⎝ ⎠⎝ ⎠ ⎝ ⎠

= × + + + 21/3K (parallel perpendicular

to orbit plane

ρ

ϑΗ

ϑv

svsH

ρ

ϑΗ

ϑv

svsH

Units: photons/sec/mrad.(horiz)/mrad.(vert)/amp/0.1%bw

γ = 1957E(GeV)

32 2 2(1 )2

c vλζ γ θλ= +



Emitted Flux as Function of Vertical Angle

-20 0 20

Pow

er p

er u

nit v

ertic

al a

ngle

Vertical angle (mradians)

Parallelto orbit plane

Perpendicularto orbit plane

10 µ 10 µ 100 µ 100 µ 1 µ 1 µ



Synchrotron Radiation Source at JLab



Synchrotron Radiation SourceBrightnesscomparedwith table-top

Sp e

ctr a

l Bri g

htne

ssP

h oto

ns/s

e c/m

m2/

mra

d2/ 0

. 1%

ba n

dwi d

t h



Looking at some brightness numbers

Standard x-ray tube is a 10 keV beam of 10 mA.Power in the electron beam is 100 Watts.X-ray power is then at most ~ 1 watt.

Solid angle of emission = 4π steradiansArea of source = 1 mm2

Brightness is 1 / (4 × π × 1) = 0.08 watts/str/mm2

Synchrotron is, say 3 GeV, at 300 mA.Power in the beam is then 1000 MegawattsX-ray power is then about 10 Megawatts.Questions: What is gamma for this ring, how fast are the electrons going, and how many electrons are circulating in the ring assuming a circumference of 200 m?Solid angle of emission = 2π × 10-3 steradiansArea of source = 0.1 mm2

Brightness is 107 / (2π × 10-3 × 0.1) = 1.6 × 1010 watts/str/mm2

Ratio of synchrotron / x-ray tube = 2 × 1011




Up to this point we have assumed that each electron emitted independently within the bunch.

Now we are going to advance considerably into a new regime in which electrons are going to radiate coherently, meaning that their electric fields will be in phase with each other.



How do we make light more powerful?

2e-light

42 23

2( )3

2e ac

Power γ=

e is charge on electrona is accelerationc is speed of lightγ is relativistic mass increase

4 times the power!!!


Thomas Jefferson National Accelerator Facilitytime freq. (1/time)

Inte

nsity

e2

electron(s)2 9 8

1 2t 10 Attosecondsc 10 3 10ρ∆ γγ

= = ≈× ×

cc

c c t 30 Angstromsλ ∆ω= ≈ ≈

Radiation from Accelerated Electron – SpectrumEl

e ctri

c fie

ld



Ele c

tric

field

electron(s)

super-radiantenhancement

N

E/N

Inte

nsity

E2

Radiation from Accelerated Electrons – Spectrum

time freq. (1/time)



Radiation from Accelerated Electrons - physics

Statistics of an electron bunch in a storage ring



2.nr( t )ˆi t c2 2 2

2d I e n n e dtd d 4 c

ωω βω Ω π

⎛ ⎞⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠

⎛ ⎞⎜ ⎟⎜ ⎟⎝ ⎠

−∞

−∞= × ×∫

Coherent Synchrotron Radiation Generation - theory




where e is the charge of an electron, β is the ratio of the velocity of the particle to the speed of light, n is a unit vector and (t) is the particle position.Kim has shown that one can re-write this to give the total flux emitted in practical units, per horizontal milliradian per ampere into a 0.1% bandwidth (Dl/l or DE/E), integrated over qV as:

F tot= 2.547 x 10 13 E (GeV) I (A) G1(y)

where G1(y) is the Bessel function:

1 5/3( ) ( )y

G y K dη η∞

= ∫cy λλ=

03

5.59 ( )( )(cmetersA

E GeVρλ =with and



2/ˆi n z cf e S z dzωω⎛ ⎞ ⎛ ⎞

⎜ ⎟ ⎜ ⎟⎜ ⎟⎜ ⎟ ⎝ ⎠⎝ ⎠

∞ ⋅−∞

= ∫

2.nr( t )ˆi t c2 2 22

2d I eN[1 f ( )] N f ( ) n n e dtd d 4 c

ωωω ω βω Ω π

⎛ ⎞⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠

⎛ ⎞⎡ ⎤⎜ ⎟⎢ ⎥ ⎜ ⎟⎢ ⎥⎣ ⎦ ⎝ ⎠

−∞

−∞= − + × × ×∫

S.L. Hulbert and G.P. Williams, Handbook of Optics: Classical, Vision, and X-Ray Optics, 2nd ed., vol. III. Bass, Michael, Enoch, Jay M., Van Stryland, Eric W. and Wolfe William L. (eds.). New York: McGraw-Hill, 32.1-32.20 (2001).S. Nodvick and D.S. Saxon, Suppression of coherent radiation by electrons in a synchrotron. Physical Review 96, 180-184 (1954).Carol J. Hirschmugl, Michael Sagurton and Gwyn P. Williams, Multiparticle Coherence Calculations for Synchrotron Radiation Emission, Physical Review A44, 1316, (1991).


f(ω) is the form factor – the Fourier transform of the normalized longitudinal particle distribution within the bunch, S(z)


REFERENCES




We have manipulated the electrons, now let’s manipulate their radiation paths.

Instead of a single pass, let’s have an alternating series of magnets.

electron(s)



New Undulator at Jefferson Lab

Wavelength 20 cmNumber of periods 12 ea.Gap 26 mm



Undulator and Free Electron Laser

|NE(ω)|2

Ne-

e-




C. J. Hirschmugl, M. Sagurton and G. P. Williams, Physical Review A44, 1316, (1991).



Synchrotron Radiation SourceBrightnesscomparedwith table-topincludingundulatorsand FELs



Synchrotron Radiation



Synchrotron Radiation - so what’s new here?

Showstopper…….3 GeV at 100 mA is 300 Megawatts!!!!!

radio-freq.cavity

Solution……..Energy Recovery



First of a new generation of light source – The Energy Recovered Linac



Jefferson Lab Free-electron Laser



The JLab 10kW IR FEL and 1 kW UV FEL

Injector

Beam dump

IR wiggler

Superconducting rf linac

UV wiggler

Injector

Beam dump

IR wiggler

Superconducting rf linac

UV wiggler

Presently under commissioning

First light achieved on June 17, 2003

1000 TIMES BRIGHTER THAN ANY SUB-ps TABLE_TOP LASER



Jefferson Lab FEL Superconducting Linac



Superconducting Radio-Freq. Linac




C. J. Hirschmugl, M. Sagurton and G. P. Williams, Physical Review A44, 1316, (1991).



R.A. Bosch, Nuclear Instr. & Methods A431 320 (1999).M. Buess, G.L. Carr, O. Chubar, J.B. Murphy, I. Schmid & G. P. Williams “Exploring New Limits in Understanding The Emission of Light from Relativistic Electrons” in preparation for Nature.O. Chubar, P. Elleaume, "Accurate And Efficient Computation Of Synchrotron Radiation In The Near Field Region", proc. of the EPAC98 Conference, 22-26 June 1998, p.1177-1179.


REFERENCES

2

1 21 [( ) ] exp[ / )]

(1 )( ) (e e

e

ecR nn nE ec i R c dn Rω

β β ω τβ

γ β τ+∞

−

−

−

∞

−× − += −× +−∫

2nd. extra term

Need to consider the term in the velocity, or the Coulomb or near-field term, particularly when R is small and gamma is small.






Brightness of IR Sources

1 10 100 1000 100001E-121E-111E-101E-91E-81E-71E-61E-51E-41E-30.010.1

110

1001000

10000

Energy (meV)

Flux

(Wat

ts/c

m-1)

Wavenumbers (cm-1)

1 10 100 1000

JLab THz

Synchrotrons

Globar

JLab FEL

Table-top sub-ps lasers

FEL proof of principle:Neil et al. Phys. Rev.Letts 84, 662 (2000)

THz proof of principle:Carr, Martin, McKinney, Neil, Jordan & WilliamsNature 420, 153 (2002)



The THz Gap



1 10 100 1000 10000

1E-10

1E-8

1E-6

1E-4

0.01

THz

Wat

ts/c

m-1/m

m2 /s

r

Frequency (cm-1)

2000K Black Body

0.1 1 10 100

Electronics - radios Photonics – light bulbsThe Real THz Gap

Tom Crowe, UVa



October 2002



THz Expt and Calculation

1 10 100 10000.0

0.2

0.4

0.6

Frequency (THz)

Measured Calculated (500fs bunch length)

Wat

ts/c

m-1

Frequency (cm-1)

0.1 1 10

Diffraction losses ~ 20 Watts integrated

Carr, Martin, McKinney, Neil, Jordan & WilliamsNature 420, 153 (2002)



THz Imaging

A tooth cavity shows up clearly in red. Teraview Ltd.



THz Imaging

Basal cell carcinoma shows malignancy in red. Teraview Ltd.



Terahertz computerized tomography

3cm

Turkey Bone Test Object

Ferguson et. al. Phys. Med. Biol. 47 3735 (2002)



Terahertz Imaging

Clery, Science 297 763 (2002)



Introduction

High power* THz light is critical for communications, imaging and remote sensing.

Jefferson Lab operates a 100 Watt average, Megawatt peak power broadband THz source.

Implementation of the above has become possible only recently with advances in the laboratory, particularly

combining modern ultra-fast lasers with superconductivity and relativity.

We have established a user facility which is equipped for spectroscopy and imaging proof of principle experiments

in this new arena.





JLab Terahertz Beam Extraction and Transport

M1

M2M3

diamondwindow

Shutter/viewer &camera

M1V1



Terahertz Beamline Schematic with Optical Ray-tracing

M1

-4x10-2 m

-2

0

2

4

Ver

tical

Pos

ition

-40mm -20 0 20 40

Horizontal Position

200x200mm

-3x10-2 m

-2

-1

0

1

2

3

Ver

tical

Pos

ition

-30mm -20 -10 0 10 20 30

Horizontal Position60x60mm

F2

-1.0x10-1 m

-0.5

0.0

0.5

1.0

Ver

tical

Pos

ition

-100mm -50 0 50 100

Horizontal Position

200x200mm

M2

-1.0x10-1 m

-0.5

0.0

0.5

1.0

Ver

tical

Pos

ition

-100mm -50 0 50 100


M4 F3

-3x10-2 m

-2

-1

0

1

2

3

Ver

tical

Pos

ition

-30mm -20 -10 0 10 20 30


THz Generation

THz To UserFacility

Optical calculations by Oleg Chubar, Paul Dumas

FundingUS Army NVL

Fundingstart 7/2003



JLab power permits large area imaging ~ m2



Optical transport output in User Lab Real time image from IR Demo



Coherent Synchrotron Radiation Effect of Pulse Length

1 10 100 10001E-10

1E-9

1E-8

1E-7

1E-6

1E-5

1E-4

1E-3

0.01

0.1

1

10

100

1000

10000

100000

Frequency (THz)

Wat

ts/c

m-1

Frequency (cm-1)

100 MHz 100 pC 150 x 150 mr

0.1 ps 0.3 ps 1.0 ps

0.1 1 10

840 W540 W54 W



FWHM



Coherent Synchrotron Radiation Effect of Pulse Charge

1 10 100 10001E-10

1E-9

1E-8

1E-7

1E-6

1E-5

1E-4

1E-3

0.01

0.1

1

10

100

1000

10000

100000

Frequency (THz)

Wat

ts/c

m-1

Frequency (cm-1)

100 MHz 100 fs FWHM 150 x 150 mr

10 pC 100 pC 1000 pC

0.1 1 10

Total power = 800 W

Total power = 80 kW

Total power = 8 W





Applications – proof of principle expts.

2. Military/Commercial(b) Remote Sensing, high

spatial resolution, with active imaging



10 meters

2m

10.2meters

30cm

0.3cm of a 10cm radius spherewill be normal to the beam,which is 0.1%.

Calculations using antenna coupled bolometer sensitivitiesIndicate that about 100 W is required for this application

Clery, Science 297 763 (2002)

Passive Image



FEL Team at JLab

This work supported by the Office of Naval Research, the Joint Technology Office, the Commonwealth of Virginia, the Air Force Research Laboratory, Army Night Vision Lab, and by DOE Contract DE-AC05-84ER40150.



Addendum, an Application - Protein Structure

Carboxypeptidase

α-helix

β-sheetβ-turn

extended coil

synchrotron

scattering

film



Application to Protein Crystallography

Synchrotron Radiation Brightness is 107 / (2π × 10-3 × 0.1) = 1.6 × 1010 watts/str/mm2

How many photons can we shine on a 100 micron × 100 micron protein crystal?

Throughput (étendue) is area × angle, and let’s say we are limited by 5 milliradiansof angle.

Area × angle = 0.01 × 5 × 10-3 × 5 × 10-3 = 2.5 × 10-7 mm2 str

Flux on sample is therefore 1.6 × 1010 × 2.5 × 10-7 = 4000 watts

However to get a good diffraction pattern, we need to monochromatize the beam, to get a bandwidth of, say, 0.1%, making the power 4 watts.

Question: How many photons is this at hν = 10 keV and what is their wavelength?



Answers to Questions

Questions: What is gamma for this ring, how fast are the electrons going, and how many electrons are circulating in the ring assuming a circumference of 200 m?

Rest mass of electron is 0.5 MeV, so gamma is 3 × 109 / 0.5 × 106 = 6000

From relativity: putting in numbers: v = 0.999999986 c

Last is a trick question, but 1 ampere is 1 coulomb per second, and each electron carries a charge of 1.6 × 10-19 coulombs, and that would make 0.3 / 1.6 × 10-19 = 1.9 × 1018 electrons. However, for a 200 meter circumference ring, the circulation time is 0.66 microseconds, so each electron is used 1.5 million times. So the actual number of electrons is 1 .9 × 1018 / 1.5 × 106 = 1.2 × 1012

221

ommvc

=−



Answers to Questions

Question: How many photons is 4 watts at 10 keV?

1 eV is the energy required to accelerate an electron through 1 eV potential.

1 watt is 1 amp / second at 1 volt, so 1 eV is 1.6 × 10-19 joules.

If each photon carries 10 keV of energy, it carries 1.6 × 10-15 joules.

Therefore the number of photons is 4 / 1.6 × 10-15 = 2.5 × 1015 / second.

and what is their wavelength?

Energy = hν, and c = lambda ν, so hcEhcE

λλ

=

=34 8 10

156.6 10 3 10 1.24 10

1.6 10hc metersEλ

− −−

× × ×= = = ××



Conventional THz Sources - Auston Switch for producing THz light

Auston, D.H., Cheung, K.P., Valdmanis, J.A. and Kleinman, D.A., Phys. Rev.Letters 53 1555-1558 (1984).

2 2

3

2Larmor's Formula: Power (cgs units)3e ac

=



THz pulseSub-picosecondlaser pulse

Si orGaAs



Comparing Coherent THz Synchrotron and Conventional THz Sources

a=accelerationc=vel. of lightγ=mass/rest mass

units) (cgs Power :Formula sLarmor' 43

22

23 γ

cae

=

~100 V

fseclaserpulseGaAs

THz

64

6 6 8 2

2 6

172

100V VE 10 m10 mF 10 V e / m 10 ( 3 10 )am .5MeV / c 0.5 10

m10 sec

−= =

⋅ ×= = =

×

≅

fseclaserpulse

e- -> 40 MeV

ρ THzGaAs

2 8 217

2c ( 3 10 ) ma 10 secρ 1

if ρ 1 m

×= = ≅

=4 780 80 10 !!!!andγ = =

synchrotron radiation and free electron lasers · synchrotron radiation and free electron lasers...

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