SLAC Summer School on Electron and Photon Beams · 2) The laser incident angle (scales as G~ T2 / 4 for backscatter) 3) The field strength variation of the laser (G~ a 0 2 / 2) 4)

SLAC Summer School onElectron and Photon Beams

Tor RaubenheimerLecture #2: Inverse Compton and FEL’s

2

Outline

• Synchrotron radiation• Bending magnets• Wigglers and undulators• Inverse Compton scattering• Free Electron Lasers• FEL Oscillators• High gain X-ray FEL’s• Coherence and Seeding

SSSEPB, July 22-26, 2013

Lecture #1

Lecture #2

Lecture #3

Inverse Compton Scattering (ICS) Source

Scatter a laser off a relativistic electron beamTwo views:

Compton (Thomson) scatteringUndulator source with micron period

» Characteristics very similar to undulator radiation with K < 1» Correlated emission angle and wavelength» Single (potentially narrow) emission line

Challenge due to small cross-section for scattering

3SSSEPB, July 22-26, 2013 3

4

Compton Scattering

SSSEPB, July 22-26, 2013 G. StupakovApplied Physics 325, Spring 2013

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Inverse Compton Scattering (ICS) Source

Consider a 50 MeV electron beam ( ~ 100) with a 1um laser (1 eV) directed at it – counter propagating In the electron rest frame, the Doppler shifted photons have an energy of 0/2 eV

The electron recoil will be small with 200 eV photons Thomson

If the photons are scattered in the lab frame, the scattered radiation is boosted by a factor of 2 again 0/4 keV!

The laser wave looks like an undulator of period 0/2 (2x speed of light)


Inverse Compton Scattering Sources

Two primary approaches to beam generation:» Ring-based with high rep rate but larger emittance» Linac-based with brighter beams » Very different technical challenges

X-rays can be generated from 100 MeV beams rather than GeV beams

Brightness of ICS source depends onelectron source brightness

For high energy ’s a linac is likely to provide a compactcost-effective path

Many applications are dose limitedand don’t require huge fluxes

ThomX ICS design

MIT ICS design

6SSSEPB, July 22-26, 2013 6

7

ICS Sources around the WorldMany facilities exist; more are planned

SSSEPB, July 22-26,

AIST, Japan

Lyncean, CA

MAX-IV

HiGS, Duke

Y.K. Wu, Duke

Applied Physics 325, Spring 2013

Some Existing or Planned ICS Sources

Facility TypeX-ray E(keV)

Rep. Rate(Hz)

Bunches/pulse

Source size( m rms)

Spectral flux (approx.)

PLEIADES (LLNL)

Linac 10-100 10 1 10 108 10% BW

AIST LCS (Japan)

Linac 10-40 10 1-100 40 107-109 4-10% BW

TTX, Tsinghua U.(China)

Linac 24-48 20 1 25 107-108 ~10% BW

LUCX (Quantum Beam)

SC linac ~5-50 12.5 Hz 100

(future 8x103) 8 Commissioning

Lyncean Tech(California)

Ring 7-35 65 x 106 1 30-50 109 3-4% BW (future 5 x 1011)

HIGS(Duke, NC)

Ring 1,000 – 10,000 1 x 106 1 700 108-1010 ~10% BW

*NERL (UTNL, Tokyo)

Linac 10-80 10 104 75 x 60 109-2x1010 few % BW

*MIT SC linac 3-30 108 1 2.41014 25% BW

(>1015 future ERL, FEL?) *MXI Systems (Tennessee)

Linac 8-100 10 1 10 1010 10% BW

*PLASMONX (SPARC, Italy)

Linac 20-380 10 1 5-10 109 ~10% BW

*ThomX (France)

Ring 50-90 21 x 106 1 40-70 1013 25% BW

*ELI-NP(Romania)

Linac 1,000 – 13,000 120 100 20 1013 1% BW

Pla

nned

Exi

stin

g

8SSSEPB, July 22-26, 2013

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Undulator Radiation

SSSEPB, July 22-26, 2013 Z. Huang

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Undulator ICS

The scattered photon energy in the lab frame is (Compton scattering):

In an undulator, the parameter K describes the field strength:

x = K/ * cos( w*s)

In ICS, the laser electric field is parameterized by:a0 = eE0/mc = x* a0 = K with w = 0/2

a0 = 0.85x10-9 I1/2 [W/cm2] [ m] where I = PL / 2 L2


E ~ 4 2EL / (1 + 2 2) for back scatter ( 1= , 2=0)

Compton term

(Does not include laser field strength term)

11

Flux of ICS


12

Photon Emittance (Gaussian Beams)


function

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Flux of ICS (II)

Collision usually limited by laser emittance (Rayleigh length), i.e. if the electron and laser sizes are matched at the waist, the laser beam increases in size much more rapidly away from the waist.

Two limits: 1) laser pulse shorter than Rayleigh length, 2) L >> zR

Case (1):N = T * NeNL / 2 ( e

2 + L2) for round beams

N 4 x 103 Ne UL [J] / zR [ m] assuming matched spots

For example, 150 pC e-, 0.1 Joule 1 um laser in a 35 um spot 1e8 ’s(with I ~ 1 x 1015 W/cm2)

Case (2) – solve for homework

SSSEPB, July 22-26, 2013 G. Krafft, Reviews of Accelerator Science and Technology, Vol. 3 (2010) 147–163

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Spectrum of ICS (I)

The total number of photons is conserved but the emission angles are shifted by the boost.

90-degree emission in beam frameis boosted to an angle of 1/and, from p. 15, this has ½ themaximum energy

½ the number of photons are emitted in the central cone of 1/ and the width of the cone for smaller energy deviations is ~ sqrt( )/

For example, a 50 MeV e- beam scattering with a 1um laser 40 keVphotons and the central cone of 300 urad has a spectrum of 0.1% … Except


http://members.home.nl/fg.marcelis/specrelpart2.htm

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Spectrum of ICS (II)

Measured spectrum from Lyncean Technologies ICS source


Full x-ray spectrum, 4 mrad fwhmPeak x-ray energy =13.8 keVElectron beam energy = 27.85 MeV

X-ray Energy in KeV

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Spectrum of ICS (III)

There are four other terms that increase the spectrum (see p. 10):1) The beam energy spectrum (change change boost)2) The laser incident angle (scales as ~ 2 / 4 for backscatter)3) The field strength variation of the laser ( ~ a0

2 / 2)4) The electron beam emittance ( ~ ( / x)2)

Limits to achieving narrow energy spectrum, e.g. 0.1%:Term (1) can be typically limited to 0.1%, term (2) is weak for typical convergence angles, term (3) is important when a0 ~ 0.05 (I ~ 1015 W/cm2) at 1 um, and term (4) is important when focusing to small spots x < 35 um


17

Brightness of ICS

The spot size depends on the overlap of the laser and electron beams:2 = ( e

2 * L2) / ( e

2 + L2)

The angular divergence is dominated by the electron beam emittance’ 2 ~ [( / x)2 + / 2]

The pulse length (backscattering) is determined by the electron bunch length and the total flux is (for short pulses):

N 4 x 103 Ne UL [J] / zR [ m] Using example from before

B ~ 108 per (mm2 mrad2 0.1% pulse)Low average brightness but high peak brightness and the brightness increases as 2 better performance than 3rd generation E >> 100 keV


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ICS Brightness scales as 2

Complements 3rd generation light sources at high photon energy

1.E+08

1.E+09

1.E+10

1.E+11

1.E+12

1.E+13

1.E+14

1.E+15

1.E+16

1.E+17

1.E+18

1.E+03 1.E+04 1.E+05 1.E+06

Aver

age

brig

htne

ss (p

h/s*

mra

d^2*

mm

^2*0

.1%

BW

)

energy (eV)

SSRL BL4/7 2.0T

SSRL Bend 1.25T

ICE-X


Example of ICS source averagebrightness

Additional ReferencesInverse Compton Scattering x-ray SourcesZ. Huang and R.D. Ruth, “Laser-Electron Storage Ring”, Phys. Rev. Lett., 80:976-979 (1998).Roderick J. Loewen, “A Compact Light Source: Design and Technical Feasibility Study of a Laser-Electron Storage ring X-ray Source,” SLAC-Report-632 (2003).

W.J. Brown and F. V. Hartemann, “Three-dimensional time and frequency-domain theory of femtosecond x-ray pulse generation through Thomson scattering”, PRST-STAB, Vol. 7, 060703 (2004).W. Graves, et al., “MIT inverse Compton source concept”, NIM, A608, (2009).

ThomX Conceptual Design Report, LAL/Soleil/ESRF/THALES Collaboration, LAL RT 09/28 (2010).W. Graves, et al., “High Repetition Rate Inverse Compton Scattering Source”, presented at ICFA Future Light Sources 2010 Workshop (FLS2010), Stanford, CA, March 2, 2010.

G. Krafft, Reviews of Accelerator Science and Technology, Vol. 3, 147–163, 2010

kW Lasers and laser cavitiesD. Rand, et al,, “Cryogenic Yb3+ - doped materials for pulsed solid state laser applications” Optical Materials Express 1(3) 434-450 (2011).

J. Limpert, et al., “The Rising Power of Fiber Lasers and Amplifiers,” J. Sel. Top. Quantum Electron. 13(3), 537–545 (2007).J. Limpert, et al., “High Repetition Rate Gigawatt Peak Power Fiber Laser-Systems: Challenges, Design, and Experiment” IEEE JSTQE 15, 1, 159 (2009).

F. Krausz, et al., “Power Scaling of a high repetition rate enhancement cavity” Opt. Lett., 35(12) (2010).W. Putnam, et al., “High intensity Bessel-Gauss beam enhancement cavities” CLEO/QELS CMD1 (2010).

19SSSEPB, July 22-26, 2013

The Free Electron Laser (FEL)

SSSEPB, July 22-26, 2013 20

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FEL Interaction (I)

Undulator radiation is calculated ignoring other electrons and the resulting radiation field. Is there a way to couple the beam to the radiation field?

dW = F ds = -e E v dtNeed a component of the electron velocity aligned with the electric field

Back to motion in an undulator (#1, p. 20):


)2cos(42

2/11

)](sin1[1111

2

2

2

2

222

22

2

uz

uxz

skKK

skK

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FEL Interaction (II)

SSSEPB, July 22-26, 2013dW > 0 dW = 0 dW < 0

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FEL Interaction (III)


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Pendulum Equation

Pendulum equation described the transfer of energy to and from the electrons as a function of the pondermotive phase


Small amplitude oscillationswhere

with aL = eE0/mc L (sometimesrefered to as as)

ssin0

22 LLu kakK

Large amplitude oscillationsoscillation frequency decreases as afunction of amplitude

Bucket height which dependson the undulator strength and the laser field

)2/1(2

2max KaK L

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Pendulum Equation (II)

In general the electrons will simply oscillate in the bucket. However, if the initial energy of the electrons is higher than the resonant energy of the undulator energy loss on average


No net energy transfer Energy loss by electrons

Open circlesare initial positions andstars are finalpositions

From R. Ischebeck

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Small Signal Gain – Madey’s theorem

The small signal gain curve is the derivative of the sontaneous emission spectrum and gain is positive at positive detuning (higher beam energy)

where


xx

dxd

IINJJKgA

uuss

2

23

3222 sin][2

)( uNx 2

Maximum gain at x ~ 1.3 or ~ 1/5Nu

Power grows as Nu cubed

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FEL Oscillator

Resonant optical cavity allows radiation to build up as new electron bunches are passed through the undulator until saturation is reached


Documents

SLAC Summer School on Electron and Photon Beams · 2) The laser incident angle (scales as G~ T2 / 4 for backscatter) 3) The field strength variation of the laser (G~ a 0 2 / 2) 4)