Introduction to X-ray Free Electron Lasers

A The LCLS Primer

Daniel Ratner

Ultra-Bright

10 Orders of Magnitude!

Ultra-Fast

• World’s fastest shutter camera – Muybridge achieved milliseconds – LCLS aims for 0.000000000000001 second

Laser Components

• Energy Source (flashlamp, e discharge) • Radiation Source (electron transition) • Wavelength Selection (gain medium): • Gain (oscillator cavity) Energy pump Cavity Gain Medium

Free Electron Laser Basics: Energy Source

• SLAC Linac: last km gives 14 GeV beam • Lots of energy in this beam! – LCLS will extract less than 0.1% as radiation

Free Electron Laser Basics: Radiation Source

• Bending high energy electrons  X-rays Synchrotron Radiation • Modern light sources use Undulators: N S N S N S N g

e -

S N S N S N S S N l

1

Free Electron Laser Basics: Resonant Condition

• Electrons travel farther than photons – Match slippage to exactly one radiation wavelength – Only resonant wavelength is amplified g

e -

N S N S N S N S l

1

S N S l

u

N S N S N

Free Electron Laser Basics: Resonant Condition

Free Electron Laser Basics: Gain

• High Gain FEL: single pass for electrons – No mirrors, no cavity g • For LCLS use ~3000 periods “SASE FEL”

e -

33 sections undulators, 100 m

Free Electron Laser Basics: Gain

Linac Coherent Light Source at

SLAC

Injector (35 º º ) ) at 2 km point

e



X ray

12

Resonant Condition

e- path length: sin( 2 

s



ds

/ l

u

)  l

u

  1 

K

4 g 2 2   Avg. e velocity: 

z

Photons travel

l

u in time

l

u /c electrons slip behind by length

 L

=



L

l

1 :

  l

u

 l 2 g

u

2 l

u



z c

  1  

K

2 2 l

u

  1  1  1 / 1 

K

2   / 2 g 4 g 2 2      1  

K

4 g 2 2  

Pendulum equations

 Define new variables energy (g

-

g

0 )/

g

0

phase 

=(k r +k u )z-



r t

radiation wavenumber undulator wavenumber arrival time at undulator distance Electron phase,  , is longitudinal position relative to radiation phase

Pendulum equations

Longitudinal electron motion described by pendulum equations

d

  2 

k u

,

dz d

   1 ( ~

E e i

  ~

E

*

e



i

 

dz

for planar undulator =1 for helical undulator   l

r



 

Cubic Equation (1D)

Radiation scales as e bunching:

d A dz



e

field amplitude 

i



j



b Slice

e bunching Altogether then we have

d

   ,

d z d



d z



A e i

 

A

*

e



i

 ,

d A



d z e



i



j Slice

 3 coupled equations reduce to cubic equation:  And finally exponential radiation growth

d

3 ~

A

 ~

i A d z

3 ~

A

(

z

)  1 3   ~

A

( 0 ) 

i b

( 0 )  3 

iP

( 0 )  3  

e



i

 3

z

,  3   1  2 3

i

Radiation seed Initial bunching Initial momentum

Self-amplified spontaneous emission (SASE)

 No initial seed: process picks resonant frequency from random noise

Slippage and FEL slices

 Due to resonant condition, light overtakes e-beam by one radiation wavelength l 1 per undulator period Interaction length = undulator length optical pulse electron bunch optical pulse electron bunch Slippage length = l 1 × undulator period (LCLS: slippage length = 1.5 fs, e-bunch length = 200 fs) z  Each part of optical pulse is amplified by those electrons within a slippage length (an FEL slice)

SASE temporal spikes

• SASE starts from noise • Many independent spikes • Final LCLS spike: ~1000 l 1 = 0.5 fs!

• No correlation between spikes: Each slice lases independently!

1 % of X-Ray Pulse Length

Transverse coherence

• Initially many transverse modes X’ Electrons: 2  x x Photons: l 1 /2 (diffraction limit) • SASE: higher-order modes have stronger diffraction • FEL gain is localized within the electrons  selection of the fundamental mode ( gain guiding )

LCLS transverse mode simulation

from S. Reiche Z=25 m Z=37.5 m Z=50 m Z=62.5 m Z=75 m Z=87.5 m m  n  1.2  m , g28000, l 1 1.5 Ǻ ,  n / g =  x,y = 3.6 l 1 /(4  )

Alternatives to SASE

Macromolecular Crystallography

• Structural biology in 4 steps: – Isolate and make protein – Crystallize protein – Measure diffraction pattern from crystal – Recover structure from diffraction data    

Macromolecular Crystallography

• Structural biology in 4 steps: – Isolate and make protein – Crystallize protein – Can we avoid bottleneck?

– Measure diffraction pattern from crystal – Recover structure from diffraction data    

Sequential Crystallography

Questions?