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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
ASS&S 2010ALPHA-X [email protected]
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
ASS&S 2010ALPHA-X [email protected]
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
ASS&S 2010ALPHA-X [email protected]
Synchrotrons light sources and free-electron lasers: tools for scientists
Synchrotron – huge size and cost is determined by accelerator technology
Diamond
undulatorsynchrotron
DESY undulator
ASS&S 2010ALPHA-X [email protected]
Small accelerator based on plasma
Centimetre long plasma based accelerator
>100 GeV/m
ASS&S 2010ALPHA-X [email protected]
ASS&S 2010ALPHA-X [email protected]
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»
ASS&S 2010ALPHA-X [email protected]
ASS&S 2010ALPHA-X [email protected]
• 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
ASS&S 2010ALPHA-X [email protected]
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
ASS&S 2010ALPHA-X [email protected]
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
ASS&S 2010ALPHA-X [email protected]
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)
ASS&S 2010ALPHA-X [email protected]
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
ASS&S 2010ALPHA-X [email protected]
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
ASS&S 2010ALPHA-X [email protected]
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
ASS&S 2010ALPHA-X [email protected]
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 = »
ASS&S 2010ALPHA-X [email protected]
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)
ASS&S 2010ALPHA-X [email protected]
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 = »
ASS&S 2010ALPHA-X [email protected]
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)
ASS&S 2010ALPHA-X [email protected]
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
ASS&S 2010ALPHA-X [email protected]
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)
ASS&S 2010ALPHA-X [email protected]
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).
ASS&S 2010ALPHA-X [email protected]
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
ASS&S 2010ALPHA-X [email protected]
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
ASS&S 2010ALPHA-X [email protected]
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
ASS&S 2010ALPHA-X [email protected]
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%
ASS&S 2010ALPHA-X [email protected]
Electron and optical spectra:undulator as an electron spectrometer
Strathclyde, Jena & Stellenbosch
H-P Schlenvoigt, .. D.A. Jaroszynski: Nature Physics, 2008
ASS&S 2010ALPHA-X [email protected]
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
ASS&S 2010ALPHA-X [email protected]
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
ASS&S 2010ALPHA-X [email protected]
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)
ASS&S 2010ALPHA-X [email protected]
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.
ASS&S 2010ALPHA-X [email protected]
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
ASS&S 2010ALPHA-X [email protected]
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
ASS&S 2010ALPHA-X [email protected]
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
ASS&S 2010ALPHA-X [email protected]
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?
ASS&S 2010ALPHA-X [email protected]
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
ASS&S 2010ALPHA-X [email protected]
Betatron radiation
ASS&S 2010ALPHA-X [email protected]
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
ASS&S 2010ALPHA-X [email protected]
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=
ASS&S 2010ALPHA-X [email protected]
ASS&S 2010ALPHA-X [email protected]
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
ASS&S 2010ALPHA-X [email protected]
Typical high energy spectra: Gemini experiment using plasma channel 85% of shots
ASS&S 2010ALPHA-X [email protected]
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
ASS&S 2010ALPHA-X [email protected]
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
ASS&S 2010ALPHA-X [email protected]
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
ASS&S 2010ALPHA-X [email protected]
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.