Ultrafast x-ray-matter interaction at LCLS...4/2/08 sphr_slac_ais 14 Elastic vs. inelastic scattering • Photon scattering by a free electron • Classical treatment (Thomson formula)

4/2/08 sphr_slac_ais 1

Advanced Instrumentation Seminar (AIS)Stanford Linear Accelerator (SLAC)

Stefan P. Hau-RiegeLawrence Livermore National Laboratory

[email protected]

This work was performed under the auspices of the U.S. Department of Energyby Lawrence Livermore National Laboratory under Contract No. DE-AC52-07NA27344.

Ultrafast x-ray-matter interaction at LCLSOptics design, photon diagnostics, and imaging


Thanks to all collaborators:

LLNL: R. Bionta, R. London, D. Ryutov, A. Barty,M. Bogan, M. Frank, S. Friedrich, M. Pivovaroff,N. Rohringer, R. Soufli, A. Szoke, B. Woods,

and R. Lee

LBNL: S. Marchesini

DESY/FLASH: H. Chapman, S. Bajt, and K. Tiedtke

SLAC: S. Boutet and J. Krzywinski

Uppsala U.: J. Hajdu

CAS Prague: L. Juha and J. Chalupsky

PAS Warsaw: R. Sobieraski


Outline

1. Introduction to XFELs

2. Fundamentals of XFEL x-ray-matter interaction

3. Applications:1. Optics design and damage2. Photon diagnostics (e.g. gas detector)3. Coherent x-ray imaging


10-2 100 102

1018

1020

1022

1024

1026

1028

1030

1032

1034

Photon Energy (keV)

ALS undulator

APS undulator

FLASH

Euro XFEL

LCLS

Peak Brightness(photons/s/mm2/mrad2/0.1% bandwidth)

X-ray free electron lasers will produce extremely bright,ultrashort, coherent x-ray pulses

FLASH operational now48 - 6 nm,

< 25 fs,> 1012 photons

DESY, Hamburg

operational 20091.5 - 0.15 nm,

< 100 fs,>1012 photons

Linac Coherent Light Source(LCLS), SLAC, Stanford

LCLS

operational 20126 - 0.1 nm,< 100 fs,

>1012 photons

DESY, HamburgEuro XFEL


The principle of SASE x-ray free electron lasers

1. An electron bunch is acceleratedand compressed

2. The short electron bunch is injectedinto an undulator

3. The undulator radiation interactswith the electrons:Undulator radiation overtakes electronsby one wavelength per undulator period,leading to the formation of electronbunches (“microbunching”)

4. Microbunched electron beam radiatecoherently

electroninjector linac undulator experiments

x rayselectrons

1 2 3,4

1

2

3

4

Huang&Kim, Phys. Rev. ST Accel. Beams 10, 034801 (2007)


Overview of LCLS

x rayselectrons

electroninjector linac undulator

optics anddiagnostics

nearexperimental

hall

farexperimental

hall

0 111 356 426-132~ -1300z

(m)

2-3 mJFEL

20 mJSpontaneous

3 mJ Highenergy coreEγ > 400 keV

The raw LCLS beam contains FEL and a spontaneous halo


Coherence properties of the LCLS beam• Temporal (longitudinal) coherence - beam’s ability to

interfere with a delayed (but not spatially shifted) version ofitself

LCLS spectral power profile(~10% of the pulse)

• Each SASE spike is temporally coherent, tc ~ 300as at 8keV• Phase relation of SASE spikes is random

Huang&Kim, Phys. Rev. ST Accel. Beams 10, 034801 (2007)

• Spatial (transversal) coherence - beam’s ability to interferewith a spatially shifted (but not delayed) version of itself• LCLS is transversally fully coherent


Outline





X-ray interaction with matter

1. Absorption• Bound-bound, bound-free, free-free• Bound-free (photoionization) tends to dominate for x-rays

2. Scattering• Elastic (“coherent”, Rayleigh scattering)• Inelastic (“incoherent”, Bound-electron Compton scattering)

3. Emission• Inverse process• Fluorescence occurs for hot plasmas on a longer timescale• Auger electron emission tends to dominate for low-Z atoms


Schematic energy diagram of an atom

For our applications, chemical bonding is secondary, so that anatomistic description of matter is often sufficient.

……

shell…K

L

MN

principalquantumnumber

1

2

34

max.number

electrons

2

8

1832

continuum

energy

Hydrogenic energy levels


Total interaction cross sections

102 103 104 105 106 102 103 104 105 106

X-ray energy (eV)

106

104

102

1

10-2

10-4

Crosssection(barn)

Nitrogen (Z=7) Tantalum (Z=73)

photoabsorption

elastic scattering

inelastic scattering

• Low-Z materials absorb less photons than high-Z materials• For large x-ray energies, inelastic scattering dominates over elastic scattering

K KLM

Veigele, Atomic Data 5, 51 (1973)


Photoionization by atomic shellSubshell photoionization cross sections

Nitrogen (Z=7)106

104

102

1

10-2

10-4

Crosssection(barn)

X-ray energy (eV)102 103 104 105 106

1s (K)

2s (L)

2p (L)

Inner-shell photoionization dominates

Verner et al., Atomic Data 55, 233 (1993)


Emission direction of photoelectrons

XFEL beam

!

r B

!

r E

preferred direction of emitted electronsis in the direction of the electric field θ (degrees)

H.K. Tseng et al.,Phys. Rev. A 17,1061 (1978)

θ

Polarization-dependent energy deposition

!

r E

max(dxray,dstraggle)

drange

dstraggle

!

r E

max(dxray,drange)

!

r E

max(dxray,dstraggle)

normal incidence grazing incidence

x

yz


Elastic vs. inelastic scattering

• Photon scattering by a free electron• Classical treatment (Thomson formula)• Relativistic QM treatment (Klein-Nishima formula)

• Photon scattering by an atom• Elastic scattering (without atomic excitation): Rayleigh (“coherent”) scattering

• Inelastic scattering (with atomic excitation): Bound-electron Compton (“incoherent”) scattering

!

d"elastic

d#= F

2 d"T homson

d#

!

d"inelastic

d#= S

d"Klein$Nishima

d#

(F=atomic form factor)

(S=“incoherent” scattering function)


Scattering directionDifferential scattering cross sections at 1, 10, and 100 keV

(in units of Å2/sterad)

Nitrogen (Z=7)

• At larger x-ray energies, elastic scattering occurs primarily in the forward direction• Inelastic scattering is more homogeneous

• Low- and high-Z materials behave similarly

dσelasticdΩ

dσinelasticdΩ

1 keV

10

100 1 keV

10

100

elastic inelastic


Effect of subshell ionization on atomic form factor

photoionization core relaxation

Atomic form factor is the Fourier transform of the electron density

Details of ionization states have strong effect on diffraction pattern

Phys. Rev. A 76, 042511 (2007)

0 1 20

1

2 neutral C C w/ core hole

2s

2p

1s

f

q (a-1

0)

Example: Carbon

F


Atomic processes in low-Z materials after x-ray absorption

K

L

photoionization

K

L

K

L

Auger relaxation

K

L

K

L

electron impact ionziation

K

L

electron equilibration

K

L

three-body recombination

K

L

K

L

recombination

K

L

K

L

electron-ion coupling

K

L

• Most of these processes take place during the pulse• Continuum processes (e.g. melting, spallation, or fracture) take place after the pulse• Non-thermal ion motion can take place during and after the pulse


Outline





LCLS photon beam diagnostics and offset mirrors in the FEE

GasDetector

Gas Attenuator

FixedMask

beam direction

SolidAttenuators

K SpectrometerSoft X-Ray Imager

Thermal Sensor

Slit

electroninjector

GasDetector Direct Imager

(Scintillator) FEL Offset Mirror Systems

linac undulator optics anddiagnostics

nearexperimental

hall

farexperimental

hall

Overview of LCLS

(FEE)


Damage modes and material selections

• Damage = optics degradation or failure

• Possible damage mechanisms:• Melting• Phase change• High-pressure effects (e.g. spallation)• Thermal stress effects and fatigue• Photo-chemical processes

• Both single- and multiple-pulse effects are of concern

• Low-Z materials with high melting points are expected toexhibit a higher damage resistance since they absorb lesslight so that the energy density is smaller

• Since XFEL’s are not available yet, we have performeddamage experiments on existing light sources…


Single-shot damage experiments at FLASH• We have performed single-shot damage experiments at the FEL FLASH

(32 - 6 nm wavelength, 25 fs pulse length, 20 µm beam diameter)

calculated

melt

measured

damage

Si 181 129 ± 65

SiC 82 207 ± 100

B4C 65 289 ± 145

a-C (45nm on Si) 95 ± 50

CVD diamond 107 230 ± 115

Threshold Fluences in mJ/cm2

• The damage threshold is somewhat higher than the expected melt threshold (except Si)• This supports main tenet for designing the x-ray optics• Possible error sources: beam diameter, small number of exposures, and pulse energy measurements

Appl. Phys. Lett. 90, 173128 (2007)


Discovery at FLASH: Damage-resistant single-shot optics

FEDCBA

40µmm

50nm200nm

A FEDCB

During 25 fs pulse (1014 W cm-2)32 nm wavelength

Reflectivity unchanged

Si/C multilayer

Phys. Rev. Lett. 98, 145502 (2007)

After the pulse

After pulse4

50Angle of incidence (degrees)

increasingfluence3

2R

(%)

1

035 40 45

100%

16% Low-fluence


Multiple-shot damage experiments

Experimental results will be postedafter publication


Summary of optics design and damage

• Low-Z, high-melting-point materials are expected to be most resistant to damage

• Experiments at FLASH suggest that1.) The single-pulse damage threshold for bulk materials is comparable to the melting damage threshold.2.) Thin films have a somewhat lower damage threshold

• Multiple-pulse experiments using a UV laser to emulate the XFEL-induced temperature profile suggest that multiple- pulse damage occurs below the melting threshold

1.) Grazing-incidence optics should be ok (but: compare 105 pulses with 107 pulses/day on LCLS)2.) There may be concerns for higher-Z normal-incidence optics exposed to the full FEL beam

• This learning will be directly applicable to optics in theexperimental halls


Outline





Summary of Pulse-Energy Diagnostics in the FEE

• Direct (scintillator) imager using a Ce:YAG– ~100 nJ sensitivity– 10 to 25 % absolute calibration– destructive

• Thermal sensor– <100 µJ pulsed, ~1 µJ average sensitivity– < 7% absolute calibration– destructive

• Gas Detector– ~100 nJ sensitivity– x 2 absolute calibration– “non”-intrusive


Thermal Sensor (“Total Energy Monitor”)

Stephan Friedrich et al., LLNL

• Use a thin low-Z high-κ substrate for FEL absorption• Thermistor deposited on back side to measure temperature rise• Temperature rise is proportional to FEL energy• Cool down through substrate

Nd0.67Sr0.33MnO3 thermistor

FELpulse

Cu heatsink

0.5 mm Sisubstrate

0

10

20

30

40

50

60

-5

0

5

10

15

90 120 150 180 210 240

Nd0.67

Sr0.33

MnO3

sensor on STO-

bufffered Si

Res

ista

nce

[k!

]

1/R

dR

/dT

[%/K

]

Temperature [K]


Overview of the LCLS Gas Detector

x rays x rays

PMT

bandpass filtervacuum window

differentialpumping

differentialpumping

N2 gas

• The gas detectors provide a non-intrusive measure of the FEL pulse energy• in real-time,• pulse-by-pulse• window-less (differentially pumped)

• Infer FEL pulse energy from the near-UV fluorescence radiation of a volume where the LCLS beam intersects a N2 gas• The amount of near-UV radiation correlates to the intensity of the LCLS beam

Br


• Alternative design: Ionization chambers, use electrodes to measure electron and/or ion current

• At low pressures, ionization ~ pulse energy• “Successfully” used at FLASH• Design too large for hard x-rays

• At high pressures• Secondary ionization and space charges• Voltage required to quickly remove ions would be large => possible gas breakdown

• Reasons to use N2:• Low cost and safe• N2 luminescence is very well understood since it is used in air fluorescence techniques:

• To determine yield of nuclear explosions through charged particles• To detect cosmic ray air showers

Why did we choose this design?


• N2 molecules absorb a fraction of the x-rays by K-shell photoionization, emitting photoelectrons of energy (Ex-ray−0.4 keV)• Ionized nitrogen relaxes by Auger decay, emitting Auger electrons of energy ~ 0.4 keV• High-energy electrons deposit their energy into the N2 gas until they are thermalized or reach the detector walls• Excited gas relaxes under the emission of near-UV photons

x-rays

photo e-Auger e-

N2 gas

Br

Overview of the physical processes

“TheSimpleModel”


Other physical effects (neglected in “The Simple Model”)

• X-rays are scattered into the walls

• Slow secondary electrons may reach the detector walls

• Ions may reach the detector walls

• Space charge effects

• Spontaneous radiation

• Long afterglow

To test applicability of “The Simple Model”, we build a prototype and performedexperiment at SSRL in “quasi-steady-state”


Gas detector SSRL prototype

Photo Multiplier Tube

Magnet Coils

Gas Feedand

Pressure Control AvalanchePhotodiode

Port for pumping

Be window

Port for florescence samples

Chamber liners: SS, colloidal-graphite, Au


10 100105

106

107

108

B off B=276 Gauss

Pressure (Torr)

Gas Detector Signal (measured at SSRL)

J. Appl. Phys. 103, 053306 (2008)

PMT Signal(# UV photons/

1012 8keV photons)


10 100

B=0

B=0 B=276 Gauss

Pressure (Torr)

measured calculated

Measured signal (colloidal-graphite coating) agrees with calculationswithin a factor of < 2 !!

Comparison of calculated and measured Gas Detector Signal

10 100105

106

107

108

B off B=276 Gauss

Pressure (Torr)


1012 8keV photons)


10 100105

106

107

108

colloidalgraphite

SS

B off B=276 Gauss

Pressure (Torr)

Gas Detector Signal (measured at SSRL)

Stainless-steel coating results in a 2X larger signal than colloidal-graphite coating


1012 8keV photons)


Luminescence Signal of Solid Materials

105

106

107

108Al2O3

SSAu

BeSi

O2

Cu

SiAl

grap

hite

PMT

Sign

al(a

rb. u

nits

)

PMM

A

Luminescence of SS >> Luminescence of graphite


How does LCLS differ from SSRL?

• Spontaneous radiation• Has larger divergence than fundamental and can be shuttered off

• ~ 360X larger average intensity

• Pulse energy:• SSRL: 8.3 keV• LCLS: 0.83 – 8.3 keV=> Low-energy effects, including space charge confinement

• Pulse length• SSRL is “quasi-steady-state” with ~ 1012 x-ray photons/ sec• LCLS is pulsed with ~ 3x1012 xray photons / 100 fs pulse=> Measurement of time-dependent signal will provide new insight


0 5 10 15 200

2x107

4x107

6x107

e

nerg

y de

posi

tion

rate

(keV

/ns)

time (ns)

energy deposited into N2 walls end caps

0 – 15 nsPhotoelectrons hitting end caps

~ 1 nsX rays scattered into walls

0 – 200 ns (?)Secondaries hitting walls and end caps0 – 45 nsEnergy of photoelectrons deposited into N2

0 – 18 nsPhotoelectrons hitting walls?X rays scattered into detector window

UV signal within

Time dependence of gas detector signal from the 8keV fundamental

0 20 40 60 80 1000

2x107

4x107

6x107

UV

photo

ns (

arb

. units)

time (ns)

signal from N

2 (!~25ns)

walls (!~1ns) end caps (!~1ns)

relative amplitude of curvesis not known

signalto bemeasured

UV

pho

tons

(arb

. uni

ts)

2

4

6


LCLS Gas DetectorSummary and Conclusions

• We have developed a non-intrusive window-less detector to measure the FEL pulse energy in real-time and pulse-by-pulse

• Calibration will be provided by a calorimeter

• We have tested the detector in a quasi-steady-state mode of operation at SSRL:

• Our models capture the relevant physics• Most discrepancies can be attributed to different luminescence behaviors of the chamber walls

• Using the Gas Detector at LCLS is more challenging:• Higher intensity• Larger wavelength range• Shorter pulses

• Time-dependent measurements hold the promise to provide further insights into the workings of the detector


Outline





Diffraction image single biological molecules with ultrashortpulses before the absorbed energy has time to alter the structure

CCD collectingdiffraction pattern

Particle injection

XFEL output:8 keV,< 70 fs,

2x1012 photonsin 100 nm spot

Our goal is to understand the XFEL pulse and sample requirements.

Neutze et al,Nature 406, 752 (2000)


Effect of the limited temporal coherence of the LCLS beam

Scattering factor for a single SASE spike(Gaussian-shaped):

Diffraction pattern is the incoherent sumof multiple SASE spikes.

At LCLS at 8 keV, the particles have to be smaller than 500 nmto achieve atomic resolution

Coherence time ~ maximum time delay of two beams scatteredinto the highest resolution part of the diffraction pattern

Optics Express, Vol. 16 Issue 4, pp.2840-2844 (2008)


Damage dynamics in biological molecules•• Requires an understanding of the x-ray–molecule interactions:

• Trade-off between the pulse length and pulse intensity versus image resolution• Can we, by design, reduce the effect of x-ray damage and thereby enable longer pulses?

• We have developed several theoretical models to address the x-ray damage question:

• Hydrodynamics two-fluid model• computationally fast: can treat large as well as small molecules

• Molecular dynamics• calculate classical motion of each atom in molecule• limited by computer resources to small molecules


Charging and trapping of ‘Free’ Electrons• Photo-, Auger-, and secondary electrons are free initially• Positive molecule charge increases with time• Eventually, free electrons are trapped

e-

e-

Electron escapes if

)surface(r2

eQE

)center(r

eQE

electron

electron

>

>

Electron trapped if

)surface(r2

eQE

)center(r

eQE

electron

electron

<

<

Molecule with positive net charge Q


One-Dimensional Continuum Model for Radiation Damage• Assumptions:

• Sample is initially a homogeneous continuum• Sample has spherical symmetry• Treat free electrons and ions as separate fluids that interact by the Coulomb force• Rate equations are used to model ionization of each atomic species (H,C,N,O,…)

“real” molecule Continuum model

PRE 69, 051906 (2004)PRE 77 (2008)


Damage Dynamics for H48.6C32.9N8.9O8.9S0.7

• Collisional ionization is dominant initially• Heavier atoms get ionized faster• Captured photoelectrons accelerate ionization

0

1x104

2x104

(1,1)(2,0)

(0,0)

(1,0)

(1,2)

(2,1)

(2,2)

(2,3)

(2,4)

(K,L)Carbon

Numberof Atoms

0 40Time (fs) 0 10 20 30 400.0

0.5

1.0

1.5

2.0

R/R0

• Higher-charged outer layers explode faster than inner layers• Inner part of molecule is more strongly ionized

R=50A, τ=40fs, fluence=6x1012 photons/100nm diameter

Time (fs)


Preliminary estimate of pulse parameters

0 100 200

2

4

6

8

10

1013

1012

3x1012

1011

3x1011

Molecule Radius (A)

0 100 200

9fs6fs5fs

4fs

3fs

2fs

Molecule Radius (A)

1fs

FluenceDetermined by signal required to classifyeach image by angular orientation. (*)

Pulse lengthDetermined by image degradationdue to damage at required fluence.

resolution(Å)

molecule radius (Å)

The maximum pulse length is determined by a competition between signal and damage using the hydro model

(*) Ignores effect of damage on classification.

(Huldt, Szoke and Hajdu, 2004).

Initial LCLS pulse duration: ~70 fs

LCLS number of photon/8 keV pulse: 1012

PRE 71, 061919 (2005)


Effect of a tamper on explosion dynamics

without tamper with tamper

neutralizedhot core

chargedlayer

tamper (sacrificialcharged layer)

0 5 10 15 200

20

40

60

R (A)

time (fs)0 5 10 15 20

0

20

40

60

R (A)

time (fs)

molecule

Tamper (H2O)

Encapsulating the molecule with a sacrificial layer (e.g. H2O) reduces damage

PRL 98, 198302 (2007)


Repair of diffraction patterns• The effect of ionization damage can be significantly reduced if we know the type of atoms in the molecule and (roughly) their ionization physics:

1.) We developed a simplified strategy to “repair” diffraction pattern for the case ofstationary atoms randomly-ionized atoms (on average spatially homogeneous)

• Given average statistical information about the ionization process, one canshow that

(i) For the case of mono-atomic ionization-damaged particles, a perfect correction (“repair”) of pulse- and shot-averaged diffraction

pattern is possible!

(ii) For the case of a more generic particle, partial “repair” of the diffraction pattern is possible

2.) Apply this limited “repair” strategy to the actual case in which atoms move and ionization is not spatially homogeneous


1 100

5

10

15

20

25

R factor

(%)

number of diffraction patterns

Crystallographic R Factor• Except close to the molecule (ordered solvent), the atoms in the tamper are positioned randomly (unordered solvent) and cannot be seen in the averaged diffraction pattern

• A tamper reduces the radial atomic motion - H2O is a likely choice (natural solvent)- He is less effective since it does not ionize strongly

• A tamper leads to a radially more homogeneous ionization of the molecule (advantageous for “repair” of patterns)

• A tamper does not necessarily reduce the amount of ionization damage

- It possibly reduces ionization since it fosters recombination- It possibly accelerates ionization by capturing photoelectrons earlier in the pulse

• A tamper will make image classification more difficult- As a disordered solvent a tamper will not affect the shot-averaged diffraction pattern

Effect of tamper on x-ray diffraction imaging

repair

tamper+repair


Atomistic Model: Massively-Parallel Molecular Dynamic(in progress)

Study damage dynamics of large molecules (>> 10,000 atoms):• Check validity of continuum models• Check effectiveness of tampers and repair strategies

We have developed an MD code for small molecules beyond state-of-the-art:• Particle-particle interaction based on Hansen-McDonald potential• Relevant atomic physics is included, including three-body recombination


0 5 10 15 20 25 3010

(1,2)

(1,4)

(2,2)

Time (fs)

(2,4)

We have verified the ionization dynamicsin the MD code by comparison to continuum model

(w/out secondary ionization)

C540 Bucky Ball

(K,L) electrons for C in C540

100

500

Numberof

Ions

thick = MDthin = continuum model


Movie:Molecular Dynamics Simulations of Lysozyme

Irradiated by an LCLS PulsePulse energy = 2.3 mJ (1012 8 keV photons)

● H ● C ● N ● O● S

• 1960 atoms, number of particles in the simulation is <N2>time= 7243.6

• Simulation includes photoionization, Auger decay, and electron impact ionization

• Light H atoms escape first

• Outer part of molecule expands first due to shielding of center by trapped electrons; this effect will be more pronounced for large molecules

• Pulse length in simulation is 30 fs; LCLS pulse will be ~70 fs initally, and various schemes to reduce pulse length are planned


Results of x-ray imaging of biological molecules

• Pulse length of 10 - 50 fs are necessary to avoid damage

• Using a molecular tamper helps extending the allowable pulse length

• Incorporation of an ionization repair technique in the data analysis also helps


Conclusions• XFEL’s will open an exciting new field of ultra-short high-intensity x-raymaterial interaction

• A large range of energy densities and physical phenomena can beaccessed

• X-ray optics must be designed to withstand damage• Low-Z materials• Grazing incidence• Placement at a large distance from the undulator

• Novel photon diagnostics are being developed to characterize the beamproperties

• Studies of x-ray interaction with biomolecules have help defining thenecessary pulse requirements for future imaging experiments

Ultrafast x-ray-matter interaction at LCLS...4/2/08 sphr_slac_ais 14 Elastic vs. inelastic scattering • Photon scattering by a free electron • Classical treatment (Thomson formula)

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