Laser driven plasma wakefield accelerators and radiation …Laser driven plasma wakefield accelerators and radiation sources: A new paradigm of compact radiation sources Dino Jaroszynski

ASS&S 2010ALPHA-X [email protected]

Laser driven plasma wakefield accelerators and radiation sources:A new paradigm of compact radiation

sources

Dino JaroszynskiUniversity of Strathclyde


Outline of lecture• Large and small accelerators + high power lasers• Laser driven wakes• Ultra-short bunch electron production using wakefield

accelerators • Synchrotron, free-electron laser and betatron sources• Compact X-ray sources based on the wakefield accelerator• Conclusion


CERN – LHC27 km circumference

SLAC

50 GeV in 3.3 km

20 MV/m

7 TeV in 27 km

7 MV/m

Large accelerators depend on superconducting Radio Frequency cavities


Synchrotrons light sources and free-electron lasers: tools for scientists

Synchrotron – huge size and cost is determined by accelerator technology

Diamond

undulatorsynchrotron

DESY undulator


Small accelerator based on plasma

Centimetre long plasma based accelerator

>100 GeV/m


Limitations of present accelerators

GeV

TeV

E e n»



Wakefield accelerators –boat wake analogy

vg

Stationary


Particles accelerated by electrostatic fields of plasma waves

Accelerators:

Surf a 10’s cm long microwave –conventional technology

Surf a 10’s mm long plasma wave –laser-plasma technology

2

max

23

gagg »

[V/cm]E e n»



• Dephasing:

Limits to Energy gain: DW=eEzLacc

• Diffraction:

20

20

max

23

pd g L

g

L a c

a

g t

gg

@

@

• Pump Depletion:For small a0 Ldp >> LdphFor a0 ≥ 1 Ldp ~ Ldph

2 20 /Rz wp l=

~ millimeters!(but be avoided using plasma channels or relativistic self-focusing)

cvg

20

21

43

pdph

gr

gdph

p

Lv c

c aL

l

gw

=-

=

~ 10 cm x 1016/no

0g L

p p

w pg tw w

= »

( ) 2/3 [GeV] ~ 0.038 [TW] crE P P -

2~ 17 [GW]cr gP g


Modelling of Laser Wakefield Acceleration

laser pulse envelopeelectrostatic wakefieldbunch densityenergy density of wakefield

laser pulse envelope dynamics: ponderomotive wakefield excitation -electron bunch acceleration - phase slippage - beam loading

z-vgt (units of λp)

Strathclyde


Efficiency

ideal (almost 100%) conversion of wake energy into bunch energy

all electrons accelerated

wakefield cancels at rear part of bunch

→ bunch slips out of ideal position

→ large spread of accelerating field induces large energy spread

slight loss of energy from bunch to wake

most electrons decelerated

complicated structure of accelerating field along electron bunch

pulse intensity

accelerating wakefield

wakeenergy density

bunch density

at injection just after dephasing

(fs) /cz

• Effect of bunch wakefield = beam loading• important for wake-to-bunch energy transfer • finite charge required for energy absorption from the wakefield


Wakefield efficiencyAt low amplitude, the LWFA scheme suffers not only from a lower energy gain, but also from low efficiency.

Energy transfer from plasma wave to electron limited by dephasing – electron runs into decelerating region due to vg<c - this determines the acceleration length.

Energy transfer from laser pulse to plasma wave is governed by feedback instability, which develops faster at high a0.

Example: 1-D simulation results for Gaussian laser pulse with resonant pulse length, plasma density 1018 cm-3, and 4 different pulse amplitudes.

ct (cm)

Pulse energy (%) Wake amplitude (norm.) Peak value of |a|2

a02=0.25

0.50.75

1

1 1

0.750.75

0.5 0.50.250.25

simulated with laser envelope / quasi-static plasma fluid model

Strathclyde

ct (cm)ct (cm)


Fourier spectrumof laser pulseplasma density modulation

laser pulse envelope

Laser pulse envelope dynamicslaser pulse amplitude: a0

laser pulse energy depletion rate: ωd ~ a02 ωs

Linear regime: a0² « 1, ωd « ωs: pulse energy loss through photon decelerationwithout envelope modulation, static wakefield, low energy efficiency

Nonlinear regime: a0² ~ 1, ωd ~ ωs: pulse energy loss through photon decelerationand strong envelope modulation, dynamic wakefield, better energy efficiency

z-vgt (units of λp) k / k0


Trapping and acceleration

X [mm]

z-vt (z-vt) example:

• 4 MeV beam in 3.5 x 1017 cm-3 plasma• Laser pulse acts as filter, rejecting electrons outside spot size• Initial bunch spot size can be larger than laser spot size (i.e. if we accept losses)• Contrast with conventional injection requires small bunch spot to avoid energy spread• Accelerated bunch has low transverse emittance

Ln g

Strathclyde


ALPHA-X started in 2002 Advanced Laser Plasma High-energy Accelerators towards X-raysCompact femtosecond duration particle, synchrotron, free-electron laser and gamma ray source l = 2.8 nm – 1 mm (<1GeV beam)

70 75 80 85 90 95 1000

250500750

1000

No. e

lect

rons

/ MeV

[a.u

.]Electron energy [MeV]

(b)

(a)

electron beam spectrumPhase contrast

imagingwith 50 keV

photons

beam emittance: <1 p mm mrad

electron bunch duration: 1-3 fs

0.7%gsg

<

Brilliant particle source: 10 MeV → GeV, kA peak current, fs duration

FEL

1J 30 fs

1019 cm-3


ALPHA-X all-optical injection experiments on ASTRA

800 nm

350 – 540 mJ

40 fs

F/16 mirror

gg ≈ 10

1018 Wcm-2 in 25 mm spot

a0 ~ 0.7 – 1

ne~ 1.5 x 1019cm-3

S. Mangles et al. Nature 2004

3%dgg

»

ALPHA-X: Imperial/RAL/Strathclyde

t ~ 5 – 10 fsI ~ 5 kA

Few fs duration electron bunch

20

max

2150

3gag

g = »


LBNL - Oxford campaign (ALPHA-X) team: GeV beams from capillary

Pre-formed plasma channels –Spence & Hooker (PRE 2001)

W. Leemans, … S. Hooker, (Nature Physics 2006)

ALPHA-X: Oxford & Berkeley

Channels manufactured using laser machining techniques – Jaroszynski et al., (Royal Society Transactions, 2006)


1 GeV beams

50 pC 30 pC

Acceleration to 1 GeV in 33 mm long pre-formed plasma channels

5% shot-to-shot fluctuations in mean energy

W. Leemans, … S.Hooker, (Nature Physics 2006)

E = 0.48 GeV±6% and an r.m.s. spread <5%.

12TW (73fs) - 18TW (40fs)

E = (0.50 +/-0.02) GeVΔE = 5.6% r.m.sΔθ = 2.0 mrad r.m.s.Q = 50 pCLaser ~ 1 Jgg ≈ 30

ALPHA-X: Oxford & Berkeley

20

max

22000

3gag

g = »


210

BENDINGMAGNET

UNDULATOR

ELECTRON ENERGYSPECTROMETER

LASER IN

PLASMA ACCELERATOR

RADIATIONSPECTROMETER

Strathclyde: ALPHA-X beam line

8 m

TOPS laser:1.1 J @ 10 Hzl = 800 nm30 fs

Jaroszynski et al., (Royal Society Transactions, 2006)


Experimental Results – energy stability

Electron Spectrometer: 200 consecutive shots (spectrum on 196 shots)

69 90 124 185Energy (MeV)

100 consecutive shotsMean E0 = (137 ± 4) MeV

2.8% stability


Strathclyde: Measured energy spread

0.7%gsg

=

Further accelerate to 1 GeV would give

beam loading simulations →

Shot to shot variation in mean energy: . . . 6%r m sgg

D»

60 MeV 100 MeV

Wiggins et al., SPIE Proc. SPIE 735914 (2009)

0.05%gg

D<

70 75 80 85 90 95 1000

250500750

1000

No. e

lect

rons

/ MeV

[a.u

.]

Electron energy [MeV]

(b)


Emittance of Strathclyde beam

0 50000 100000

-1.0 -0.5 0.0 0.5 1.0

-3

-2

-1

0

1

2

3

counts

(b) x'

[mra

d]

x [mm]

θxσx

xσx

x

x¢

-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5

-6

-4

-2

0

2

4

6

0 5000 10000x'

[mra

d]

x [mm]

counts

• divergence 4 mrad• eN,x < (5.5±1) p mm mrad

• divergence 6 mrad• hole size correction• limited by detection system• eN,x < (7.8±1) p mm mrad

A measure of the upper limit of emittance

Shanks et al.,Proc. SPIE 735907 (2009).


Experimental Results – charge

LANEX 2Imaging Plate

y = 2.488xR² = 0.953

0

2

4

6

8

0 1 2 3

Imag

ing

Plat

e Ch

arge

(pC)

Lanex 2 counts (x 108)

Cross-calibration in progress


Radiation sources: Synchrotron and Free-electron laser (FEL):

a potential 5th generation light source• Use output of wakefield accelerator to drive compact synchrotron light source or FEL

• Take advantage of electron beam properties

• Coherent spontaneous emission: prebunched FEL I~I0(N+N(N-1)f(k))

• Ultra-short duration electron bunches: I >10 kA

• Operate in superradiant regime: FEL X-ray amplifier (self-similar evolution)

Potential compact future synchrotron source and x-ray FEL

• Need a low emittance GeV beam with < 10 fs electron beam with I > 10 kA

• Operate in superradiant regime: SASE alone is not adequate: noise amplifier

• Need to consider injection (from HHG source) or pre-bunching


Compact synchrotron source

Undulator radiation emitted into cone

Wavelength: and

Normalised undulator potential

22 2

21(1 );

2 2 2u u

u

aN

l ll g qg l

D= + + »

1qg

»

ˆ

2u

ueBa

mcl

p=

1

uN g

Strathclyde

lu – undulator wavelength


Undulator radiation demonstration• Strathclyde, Jena, Stellenbosch collaboration• 55 – 70 MeV electrons•VIS/IR synchrotron radiation

Schlenvoigt .., Jaroszynski et al., Nature Phys. 4, 130 (2008)Gallacher, ….Jaroszynski et al. Physics of Plasmas, Sept. (2009)

• Measured sg /g ~ 2.2 – 6.2%• Analysis of undulator spectrum andmodelling of spectrometer

sg /g closer to 1%


Electron and optical spectra:undulator as an electron spectrometer

Strathclyde, Jena & Stellenbosch

H-P Schlenvoigt, .. D.A. Jaroszynski: Nature Physics, 2008


Scaling with energy

22 2

2 12 2

u uahll g Jg

æ ö= + +ç ÷

è ø

h – harmonic number

Extrapolate to 1 GeV:

400 eV photons

B = 2 x1023

ph/sec/mrad²/mm²/0.1%BW

Strathclyde, Jena & Stellenbosch


Free-electron laserlaboratory frame

undulator: periodic magnetic field

electron bunch

coherent radiation

electron bunch undulator field: seen as propagating field

electron rest frame

2

2 12 2

u uallg

æ ö= +ç ÷

è ø

coherent backscattered field

ullg

=

lu

probe

probe

Bunching due to ponderomotive force

Strathclyde

lu – undulator wavelength


Free-electron laser driven by wakefield accelerator

• Combination of undulator and radiation fields produces ponderomotive force which bunches electron on a wavelength scale

• Laser field grows exponentially at a rate governed by• Matched electron beam gain coefficient: r = 1.1 g -1Bu lu

4/3Ipk1/3 en

-1/3

• Gain length

• Need slice energy spread dg/g<r and slice emittance en<4lbgr/lu or en<gl (matched)

• Slice length: cooperation length: 30 – 100 periods i.e. <1 fs for x-rays –several pC

2 3u

gL lp r

=

2

2 12 2

u uallg

æ ö= +ç ÷

è ø

See Bonifacio et al. (Nuova Cimento 1990, 1992)


Free-electron laser

Ultimate goal of technology: l ~ 1.5 nm x-ray FEL requiring ~1 GeV

• Growth of an injected or spontaneous field in a FEL amplifier is given by I = I0 exp(gz),

• g = 4pr31/2/lu – small signal gain,

• r - FEL gain parameter - a function of the beam energy, current and emittance.

• en = g s W is the normalised slice emittance of the beam.

• r ~ 0.001 to 0.02 for our expected electron beam parameters but need slice energy spread dg / g < 2r i.e. 0.2 – 4%

• gain length < 10 lu

EXAMPLE: ALPHA-X: 4 nm source assuming a 1 GeV beam with 100 pC charge and a duration of 10 fs we get a peak current of 10 kA. With a 1.5 cm period undulator with a field of B field of 1 T we get a r ≈ 0.005, which gives a gain length of 10lu and a constraint on the energy spread of ≈ 1%, which may be achievable. To achieve saturation we need about 100 – 200 undulator periods.


Predicted Synchrotron radiation and SASE FEL for Strathclyde undulator

350 400 450

0

1x1012

2x1012

3x1012

Phot

on F

lux

[Pho

tons

/0.1

% B

W]

Photon energy [eV]

SASE FEL

350 400 450

0.0

5.0x105

1.0x106

1.5x106

Phot

on F

lux

[Pho

tons

/0.1

% B

W]

Photon energy [eV]

Peak Brilliance: 2.97 x 1025 photons/sec/mrad²/mm²/0.1%b.w.

Photon flux into 200 mrad

matched beam SASE FEL

synchrotron radiation

Synchrotron:

Peak Brilliance B = 3 x 1025

ph./sec/mrad2/mm2/0.1% b.w. for 10 Hz

Average brilliance B = 2.5 x 1011

With laser improvements: 1 kHz: rep rate: average brilliance B >1013

FEL: B >106 times higher

sg /g = 0.1%

Ipk = 12 kA

en = 1 pmm mrad

Nu = 200

te < 10 fs


Electronenergy (MeV)

Radiationl

(nm)

Emittance criterion

(p mm mrad)

Gain parameter

r

Relative energy spread

90 261 3 0.011 0.007150 94 2 0.006 0.004500 8 0.6 0.002 0.001(?)

LWFA-driven FEL• High FEL gain criteria: en < lg/4p & sg/g < r• Experimental en £ 0.8p mm mrad & sg/g £ 0.007• For fixed sg = 0.6 MeV, sg/g reduces at short l

3/12

221

úúû

ù

êêë

é÷÷ø

öççè

æ=

x

uu

A

p aII

psl

gr

lu = 15 mm, N = 200, au = 0.38

ALPHA-X Undulator

STEADY STATE SIMULATION RESULTS (100 MeVelectrons)Saturation power(1st harmonic): 20 GW@ saturation distance: 1.8 m

UNDULATOR RADIATION EXPERIMENTSIn progress for improving beam transport andobserving gain


Predicted SASE FEL Power growthE = 1 GeV

Q = 100 pC

Ipk = 30 kA

en = 1 p mm mrad

dg/g = 0.1%

b = 0.5 m

r = 0.0065

Eph = 422 eV

Bpk = 6 x 1031

phot/sec/mm2/mrad2

/0.1% BW

6.3 x 1012

coherent photons per pulse


UndulatorSpectra

( ) 2

2222

12

uN++÷÷

ø

öççè

æ= gq

gs

ldl g

2 2

3.5 mrad 200

0.40

120 nm

q gdl q gl

dl

» »

» »

»

85% of electron beam through undulator

2

2 12 2

u uallg

æ ö= +ç ÷

è ø

near field

far field

Speckle: evidence of coherent emission?


Synchrotron radiation from an ion channel wiggler: betatron radiation

• Wiggler motion – electron deflection angle q ~(px/pz) is much larger than the angular spread of the radiation j=(1/γ)

• Only when k & p point in the same direction do we get a radiation contribution.

• Spectrum rich in harmonics – peaking at• Radiation rate therefore only emission at dephasing length

1uag >> >>

deflection angle – au /g

j=1/g

338

ucrit

ah »2W gµ dL


Betatron radiation


Increase in wiggler parameter

10-9 10-8

0

1

2

Wavelength [m]

au = 0.6

Powe

r [x1

0-6 p

er u

nit f

requ

ency

and

sol

id a

ngle

]

10-9 10-8

0

1

2

au = 1

10-9 10-8

0

1

2

au = 2

10-9 10-8

0

1

2au = 3


X-ray generation in a plasma wakeStrong radial forces cause synchrotron or betatron oscillations of electron beam

Ion channel radius: electrostatic field

Dense pencil electron beam – radius re<<ri and re<<1/kp

Restoring force given by Gauss law:

Oscillation at the betatron frequency (in bubble):

Emitted synchrotron radiation viewed in the lab frame

h – harmonic number

hcrit - maximum intensity at harmonic

Undulator/wiggler deflection parameter

ei e

p

nr rn

»

212 pF m rw ^= -

02p

r

n erE

e=

2 22 2

2 3/231 ( ) 1 ( )

2 2 2h e ee p e

a ach h

b b bl pl g j g jg w g

æ ö æ ö= + + = + +ç ÷ ç ÷

è ø è ø

338crit

ah b»

29phot fN abp a=

2 / 3 pa rb bgb p g l^= =

gw

wb 2p=



Manufacture of plasma capillaries for laser wakefield accelerators

300 mmDeveloped at Strathclyde in 2000

After one year…..(Jaroszynski et al., Royal Society Transactions, 2006)

This method of manufacture is now used by all groups using plasma capillaries


Typical high energy spectra: Gemini experiment using plasma channel 85% of shots


Extending to higher energies:

calculation


Synchrotron, betatron and FEL radiation peak brilliance

ALPHA-X ideal 1GeV bunch

FEL: Brilliance 5 – 7 orders of magnitude larger

lu = 1.5 cm

en = 1 p mm mrad

te = 10 fs

Q = 100 – 200 pC

I = 25 kA

dg/g < 1%

I(k) ~ I0(k)(N+N(N-1)f(k)) FEL = spontaneous emission x 107

betatron source


Conclusions• Laser driven plasma waves are a useful way of accelerating charged

particles and producing a compact radiation source: 100 – 1000 times smaller than conventional sources

• Some very good properties: sub 10 fs electron bunches potentially shorter (< 1 fs?) and high peak current (up to 35 kA?), en < 1 p mm mrad, dg/g < 1%?.

• Slice values important for FEL - potentially 10 times better. Wide energy range, wide wavelength range: THz – x-ray

• Good candidate for FEL – coherence & tuneability• Betatron radiation – towards fs duration gamma rays• Still in R&D stage – need a few years to show potential• Challenges: rep rate, stability, energy spread and emittance, higher

charge and shorter bunch length, beam transport• Synchronised with laser – can combine radiation, particles (electrons,

protons, ions), intrinsic synchronisation• A compact light source for every university or 5th Generation light

source? A paradigm shift?• Setting up a new centre of excellence: SCAPA: the Scottish Centre

for the Application of Plasma based Accelerators: based in Glasgow and part of a pooling effort: SUPA – The Scottish Universities Physics Alliance


Strathclyde:Team: Dino Jaroszynski (director), Maria-Pia Anania, Constantin Aniculaesei, Rodolfo Bonifacio, Enrico Brunetti, Ronan Burgess, Sijia Chen, Silvia Cipiccia, David Clark, Bernhard Ersfeld, John Farmer, Ranaul Islam, Riju Issac, Tom McCanny, Grace Manahan, Adam Noble, Guarav Raj, Richard Shanks, Xue Yang, Gregory Vieux, Gregor Welsh and Mark WigginsCollaborators: Gordon Rob, Brian McNeil, Klaas Wynne, Ken Ledingham and Paul McKenna

ALPHA-X: Current and past collaborators:Lancaster U., Cockcroft Institute / STFC - ASTeC, STFC – RAL CLF, U. St. Andrews, U. Dundee, U. Abertay-Dundee, U. Glasgow, Imperial College, IST Lisbon, U. Paris-Sud - LPGP, Pulsar Physics, UTA, CAS Beijing, LBNL, FSU Jena, U. Stellenbosch, U. Oxford, LAL, U. Twente, TUE, …

ALPHA-X project

Support:

University of Strathclyde, Scottish Funding Council, RCUK, EPSRC, E.U. Laserlab, EuroLEAP, ELI

consortium


Quiz1. To reach very high electron energies should you go to higher or

lower densities?2. How does the plasma bubble radius depend on plasma

density?3. To increase the dephasing length, should the plasma density

be increased or decreased?4. In betatron radiation, keeping the plasma density and electron

energy constant, will the peak X-ray photon energy increase or decrease if you increase the betatron amplitude rb?

5. In a free-electron laser, what parameters can you change to reach higher photon energies? Indicate whether each parameter increases or decreases.


FIN

Thank you

Documents

Laser driven plasma wakefield accelerators and radiation …Laser driven plasma wakefield accelerators and radiation sources: A new paradigm of compact radiation sources Dino Jaroszynski