Sub-picosecond Megavolt Electron Diffraction International Symposium on Molecular Spectroscopy June...

$: Sub-picosecond Megavolt Electron Diffraction International Symposium on Molecular Spectroscopy June 21, 2006 Fedor Rudakov Department of Chemistry, Brown.$
Sub-picosecond Megavolt

Electron Diffraction

International Symposium on Molecular Spectroscopy

June 21, 2006

Fedor RudakovDepartment of Chemistry,

Brown University, Providence, R.I, USA.

Stanford Linear Accelerator: • J. Hastings• D. Dowell• J. Schmerge

Brown University:• Peter Weber• Job Cardoza

Funding: Department of Energy

Army Research Office

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Electron diffraction experiment.

r = 3.027 Å

r = 2.667 Å I2 ground state

I2 excited state



Time resolution limitations:

•Space charge effect

•Laser pulse and electron pulse velocity mismatch

•Initial electron velocity spread.

Megavolt electron diffraction.

Advantages of relativistic electron beams for ultrafast electron diffraction:

Shorter electron bunches

• AC field allows electron pulse compression

• Velocity spread for highly relativistic particles becomes becomes

negligible even though the energy spread can be large.

Higher charge per pulse possibility to obtain diffraction patterns

with a single electron pulse.



Problem: scattering angles of relativistic electrons are very small

Electron Bunch Parameters

Parameter Value Units

Charge 16 pC

Number of electrons 108 -

Energy 5.5 MeV

rms Energy Spread 36 keV

rms Pulse Length 0.44 ps

rms Beam Size 1.7 mm

rms Beam Divergence 45 rad

Solenoid Field 1.7 kG

Gun Gradient 110 MV/m



GTF (gun test facility) beam line at SLAC



Simulated Single-Shot Diffraction

Theoretical scattering image, and radially averaged scattering signal of aluminum foil

2 pC (1.2x107) No aperture



Space-Charge Effects: Spatial Patterns

Calculated diffraction pattern of a 1500 nm aluminum foil:

5 pC electron pulse 2 pC electron pulse

Both images obtained with optimal focusing conditions.

Effect of Charge and Laser Pulse on Electron Pulse

Duration

First MeV results

1600 Ångstrom Foil in Foil out

Tot

al b

unch

cha

rge:

3 p

C =

2·1

07 ele

ctro

nsA

lum

inum

foi

l thi

ckne

ss: 1

60 n

mD

rift

tube

leng

th: 3

.95

mB

eam

Ene

rgy:

5.5

MeV

kin

etic

Puls

e du

rati

on: 5

00 f

s

Important parameters:

Single Shots!

Dark current image subtracted



Comparison to a theoretical pattern

(111)(200)

(220)(311)Theory: calculation

with GPT; inclusion of quadrupole and all elements

Experiment

Comparison of electron probe techniques

UED(10’s of kV) MeV-UED

Application Small MoleculesSmall MoleculesPhase transitions

Time scales ≈ 1 ps ≈ 100 fs

Limitations Space chargeScattering angle

resolution?

Summary on MeV-UED

• MeV-UED is a feasible tool for measuring structural dynamics!

• We obtained diffraction patterns with single shots …

• … of femtosecond electron pulses!

This opens the door for: Electron diffraction with 100 fs time resolution



Acknowledgments

• Peter Weber

•David Dowell

•John Schmerge

•Jerome

Haistings



Differential Scattering Cross Sections

• The differential cross section increases with increasing energy

• This just balances the loss of signal from the small scattering angles!

Overall: there is no signal penalty in going to relativistic electrons!

Relativistic Scattering Cross Section

Rutherford differential scattering cross section of a single point charge:



m m0

1 2

dd

s 2me2

2 s2

2

Total Scattering Cross Section

Total Scattering Cross Section

F. Salvat, Phys. Rev. A, 43, 578

(1991)

•The total scattering cross section is largely unchanged

• The diffraction signal is highly centered at small scattering angles

Does the signal decrease dramatically?

The case for MeV

Advantages of relativistic electron beams for ultrafast electron diffraction:

Shorter electron bunches

• AC field allows electron pulse compression

• Velocity spread for highly relativistic particles becomes becomes

negligible even though the energy spread can be large.

Higher charge per pulse possibility to obtain diffraction patterns

with a single electron pulse.

Larger Penetration Depth

Smaller Scattering Angles



Electron Wavelength

Experimentsat SLAC:5 MeV

= 230 fm = v/c =0.995



Electron BunchesCharacterization: D. Dowell, J. Schmerge

0 50 100 150 200 250 3000

0.5

1

1.5

2

RMS Bunch Length (ps)

Bunch Charge (pC)-1 -0.5 0 0.5 1

-20

-10

0

10

20

Time (ps)

En

ergy

(k

eV)

Electron Bunch Length vs. Charge



Simulation of the MeV RF Gun



mm0

1

1 2

vc

RF amplitude:

Scattering Angles

Bragg’s law:

2d sinBB = Bragg angle d = lattice constant

Example: 5 MeV kinetic energy for the electronsλ=0.00223Å 2.34Å d-spacing for Al (111) Bragg angle: 476 micro-radians

Conclude:• Detector can be far separated from sample: 5 - 10 m• MeV-ED is useful to make structural measurements on samples that are far from the detector!



MeV-UED simulations• Program: GTP (General Particle Tracer)• Realistic geometries• Includes AC & DC fields• Charge per pulse 2pC• No Collimator• Total number of particles in the

simulation – 300.000

Question: are the beam parameters sufficient to resolve diffraction patterns?

Conclude:

• Divergence is sufficiently small

• 2 pC = 1.2x107 electrons within the pulse is okay

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