Post on 31-Aug-2021
transcript
LHC sketches by Sergio Cittolin (CERN) – used with permission
Prof. Andrei A. SeryiJohn Adams Institute
Lecture 6: Plasma acceleration
USPAS16
June 2016
USPAS Course 2016, A. Seryi, JAI 2
Consideration of use
Fu
nd
am
en
tal
kn
ow
led
ge
Niels Bohr Louis Pasteur
Thomas Edison
USPAS Course 2016, A. Seryi, JAI 3
Accelerating structure, metal
(normal-conductive or super-
conductive)“Accelerating structure”
produced on-the-fly in plasma
by laser pulse
Lasers and particle acceleration
• Let’s discuss laser plasma acceleration in detail
USPAS Course 2016, A. Seryi, JAI 4
Maximum field in plasma
x
Inte
gra
l c
on
tou
r
Recall how we derived wp
ElectronIon
Positive Negative
Oscillation
frequency:
to rewrite as:
Use
use:
c
Assume wave is excited by object moving with c
If total charge separation achieved in plasma, max field estimated taking
Thus or
1 GeV/cm for
plasma 1018 cm-3
e
mcnec~E
p
p0
max
w
w cmceE
p2
max
w
p
p
c~~xw
31/2
max cmncm
eV1eE
dV
1d
0
SE0
nexE
0
2
2
2 xneeE
dt
xdmF
m
ne
0
22
p
w
2
e
2
0
ecm
e
4
1r
e
22
p rnc4w
n(n9000~ 2/1
p in cm-3)
USPAS Course 2016, A. Seryi, JAI 5
How to excite plasma
• Thus, short sub-ps pulses needed for plasma excitation
• In absence of short laser pulses other methods suggested:
J.M. Dawson, Phys. Rev. Lett. 43, 267 (1979)
• We see that GeV/cm require plasma with n=1018 cm-3
• Plasma Beat Wave Accelerator (PBWA)
– Two laser pulses of closer frequencies beat at wp
• Self-Modulated Laser Wakefield Accelerator (SMLWFA)
– Instability in a long laser pulse cause modulation at lp
evolves
into
n
cmmm
f
cp
p
p
317101.0
p
p
USPAS Course 2016, A. Seryi, JAI 6
• Availability of short sub-ps pulses of laser or beams
stimulated rapid progress of plasma acceleration
• Plasma Wakefield Accelerator (PWFA)
– A short high energy particle bunch
• Laser Wakefield Accelerator (LWFA)
– A short laser pulse of high intensity
p
p
How to excite plasma
USPAS Course 2016, A. Seryi, JAI 7
Beam and laser bunch/pulse compression
BeamLaser
Both in laser and beam use z-Energy correlation
to compress/stretch the pulse – one more general principle of AS-TRIZ
Compressor
Stretcher
Dipole
Magnet
sBeam
Direction
δE<0
δE>0
δE
t
t
I
δE
t
t
I
Telescope is needed inside stretcher to create “negative distance”
USPAS Course 2016, A. Seryi, JAI 8
CPA – Chirped Pulse Amplification
• CPA: pulse stretching and compressing using time-energy
correlation
– Amplification of chirped pulses was used in radars – the trend from microwave to
optical can be taken as one of generic principles for TRIZ
For visibility
shown same
duration, but
in reality 1000
times longer
USPAS Course 2016, A. Seryi, JAI 9
Laser pulse of high intensityLaser intensity (in vacuum)
(SI) (Gaussian)
Compare with field in a hydrogen atom. Bohr radius and field:
(Gaussian) (SI)
(Recall )
Atomic intensity
A laser with intensity higher than that will ionize gas immediately
cm103.5me
a 9
2
2
B
m
V101.5
a4
e
a
eE 11
2
B0
2
B
a
2
162
a0a
cm
W1051.3
2
cEI
cE2
1I 2
max0 cE8
1I 2
max
3
4212
0mkg
sA108.8
2/1
216
9
maxcm/W10
I1075.2
cm
VE
2/1
216
6
maxcm/W10
I102.9GaussB
Fields in practical units:
(useful to remember that 300 V/cm is ~ same as 1 Gauss)
USPAS Course 2016, A. Seryi, JAI 10
• In fact, Ionization
can occur well below
this threshold due to:
– multi-photon
effects;
– tunneling ionization
Laser intensity
2
162
a0a
cm
W1051.3
2
cEI
Intensity (W/cm2)
Atomic intensity
Relativistic regime : ao ~ 1
Field ionization
of hydrogen
CPA
1010
1015
1020
1023
1960 1970 1980 1990 2000 2010
Year
Progress in peak intensity since laser invention in 1960
USPAS Course 2016, A. Seryi, JAI 11
Types of ionization
Direct ionization
Multi-photon
ionization
Tunneling ionization
With even more laser intensity – barrier
suppression ionization (BSI)
USPAS Course 2016, A. Seryi, JAI 12
Laser intensity for barrier suppression ionization
Coulomb potential of hydrogen atom distorted
by homogeneous field :
Find position of the maximum:
Equate potential value at max to hydrogen ionization potential
The critical field for hydrogen is therefore
Which corresponds to intensity
xex
e)x(V
2
2/1
max /ex
eV6.13a2
eEe2xV
B
2
ion
2/13
max
16
E
a16
e a
2
B
c
214ac cm/W104.1
256
II
V(x)
0 x
xmax
-Eion
-eEx
USPAS Course 2016, A. Seryi, JAI 13
Intensity (W/cm2)
Atomic intensity
Relativistic regime : ao ~ 1
Field ionization
of hydrogen
CPA
1010
1015
1020
1023
1960 1970 1980 1990 2000 2010
Year
2
162
a0a
cm
W1051.3
2
cEI
214ac cm/W104.1
256
II
Progress in peak intensity since laser invention in 1960
Laser intensity
USPAS Course 2016, A. Seryi, JAI 14
Normalized vector potentialThe laser field can be written in terms of
the vector potential of the laser field A as
For linearly polarized field
We see that it is useful to define the
normalized vector potential as
We see that
Compare momentum gained
by e- in one cycle of laser field with
The amplitude a0 will indicate if the electron motion in laser field relativistic
a0 >> 1 – relativistic, a0 << 1 – non relativistic
with amplitude
In practical
unitswhere
ABA
E
,
tc
w eA tkzcosA0
c
AE 0
0
w
w
eEtEe cme
2
ecm
eAa
cm
eEa
e
00
w
m
1037.1
cm/WIa
2
1
18
2
0
w
c2
USPAS Course 2016, A. Seryi, JAI 15
Intensity (W/cm2)
Atomic intensity
Relativistic regime : ao ~ 1
Field ionization
of hydrogen
CPA
1010
1015
1020
1023
1960 1970 1980 1990 2000 2010
Year
2
162
a0a
cm
W1051.3
2
cEI
214ac cm/W104.1
256
II
Progress in peak intensity since laser invention in 1960
a0 ~1 for red laser
Laser intensity
USPAS Course 2016, A. Seryi, JAI 16
CPA-compressed pulse
• Qualitative temporal profile of CPA-compressed laser pulse
– Pre- and post-pulses typically cased by nonlinear properties of the
elements of CPA system and non-ideal properties of the initial laser pulse
10-10
1
-200 -100 1000
Co
ntr
as
t r
ati
o
t(ps)
Pre-pulses Post-pulses
Main pulse
10-5
USPAS Course 2016, A. Seryi, JAI 17
• Note in particular
– Ionization front starting at the front tail of laser
– Laser pulse length similar of shorter than plasma wavelength
– Electrons trapped in the first bubble
Laser acceleration - conceptually
Intense laser
τL - pulse duration
Trapped
electrons
Instantaneous
electron density λp - plasma wavelength
+ ++
+++
---
---+++
--- +
++
---
---+
++
Ez
Ionization front
+++
+
+
+++
+++
++
+ ----
--
USPAS Course 2016, A. Seryi, JAI 18
Formation of bubble – ponderomotive forceFirst, assume laser field homogeneous:
Motion of electron:
Now, assume E has
gradient in y:
Find time average of
force acting on e-:
tcosEE 0 w
tcosm
eEy
m
eE
m
Fy
2
0 ww
tcosy
EytcosEtcosyEE 0
00 w
ww
t
0
2
0
ttcos
y
Etcos
m
eEF w
w
w
Ponderomotive force pushes
electrons out from the high intensity region
y
E
m4
e
y
EE
m2
eF
2
0
2
2
002
2
t
w
w
eˉ
Lasery
x
Fp
Fp
I(y)--
USPAS Course 2016, A. Seryi, JAI 19
• Ponderomotive force of short (50fs), intense (1018 W cm-2) laser pulse
expels plasma electrons while heavier ions stay at rest
• Electrons attracted back to ions, forming a bubble (blow-out regime) and
setting up plasma wave which trails laser pulse
• Electric fields within plasma wave of order 100 GV/m formed
Laser-Driven Plasma Acceleration
USPAS Course 2016, A. Seryi, JAI 20
Simulation courtesy Prof Simon Hooker
USPAS Course 2016, A. Seryi, JAI 21
• Wave breaking
– Self-injection of
background
plasma electrons
to the wake when
some particles
outrun the wake
How e- gets into the bubble – wave breaking
• Other methods
– External injection (difficult for so short bunches)
– Methods which involve two laser pulses and mix of
two gases with different ionization potential
USPAS Course 2016, A. Seryi, JAI 22
• As laser propagates through the gas/plasma, several competing
effects are important
– Dephasing
– Depletion
– Longitudinal compression by plasma waves
– Self focusing
• Including relativistic effect – electrons of plasma at centre become
relativistic and have higher mass
– Diffraction
• Small laser beam (~30m) will diffract very fast
• Includes ionization caused diffraction (centre where intensity is higher
ionized first)
• A possible solution – create a channel with plasma density profile
n(r) to guide laser
– A particular solution – capillary discharge channel developed in
Oxford
Importance of laser guidance
USPAS Course 2016, A. Seryi, JAI 23
• Capillary channel allowed exceeding 1GeV
laser plasma acceleration for the first time
Capillary with lower
plasma density in the
centre
Capillary channel designed by Prof Simon Hooker
Importance of laser guidance
USPAS Course 2016, A. Seryi, JAI 24
• 1 GeV acceleration & monoenergetic beam
– Use of guiding capillary was essential
First ever 1 GeV from laser plasma accelerator
1GeV acceleration in just 3cm of plasmaW. Leemans, B. Nagler, A. Gonsalves, C. Toth, K. Nakamura, C. Geddes, E.
Esarey, C. B.Schroeder, & S. Hooker, Nature Physics 2006
Plasma density 2.7x1018 cm-3, 40 TW laser with 1018 W/cm2
USPAS Course 2016, A. Seryi, JAI 25
Recent energy record
4.2 GeV, 2014W. Leemans et al., PRL 113, 245002 (2014)
USPAS Course 2016, A. Seryi, JAI 26
Transverse fields in the bubble
+++
+ ++
+
+++
++++
++
+
++ ++ +
+ ++
++++++ +
++
+
The ions are heavy and are inside of
the bubble. They produce focusing
force.
(Gaussian)
Assume cylindrical symmetry
Focusing force
Assume electron is relativistic with g
r s
It will oscillate in this field as
The period of oscillation is therefore
dV4d SE
rne2eE 2
rc2mc
rne2
ds
rd2
2
p
2
2
2
2
g
w
g
p2 g
USPAS Course 2016, A. Seryi, JAI 27
Betatron radiation
• Strong radial electric field within plasma wave cause
transverse oscillation of electron bunch
• Generates bright betatron radiation in 1- 100 keV
range
• Let’s estimate parameters of this radiation
USPAS Course 2016, A. Seryi, JAI 28
• Strong radial electric field within plasma wave cause
transverse oscillation of electron bunch
• Generates bright betatron radiation in 1- 100 keV
range
• Let’s estimate parameters of this radiation
c) d) e)a) b)
Betatron radiation
USPAS Course 2016, A. Seryi, JAI 29
Synchrotron radiation
on-the-back-of-the envelope – power loss (recall)
dVEW 2
Energy in the field left behind (radiated !):
The field the volume2r
eΕ dSrV 2
2
2
2
22 rr
erE
dS
dW
Energy loss per unit length:
Compare with
exact formula: 2
42
R
γe
3
2
dS
dW
Substitute and get an estimate:22γ
Rr
2
42
R
γe
dS
dW22γ
R1
v
cRr
R + rR
Field left behind
Field lines
Gaussian units on this page!
USPAS Course 2016, A. Seryi, JAI 30
Synchrotron radiation
on-the-back-of-the envelope – photon energy (recall)
During what time ∆t the observer
will see the photons?
Observer
1/γ
g
2
vg = c
RPhotons emitted during travel
along the 2R/γ arc will be observed.
For γ>>1 the emitted
photons goes into 1/ γ
cone.
c
v1
γ
2RdS
Photons travel with speed c, while particles with v.
At point B, separation between photons and particles is
A B
Therefore, observer will see photons during 3γc
Rβ1
γc
2R
c
dSΔt
R
γc
2
3ω
3
c
Compare with exact formula:Estimation of characteristic frequency
R
γc
Δt
1ω
3
c
USPAS Course 2016, A. Seryi, JAI 31
Synchrotron radiation
on-the-back-of-the envelope – number of photons (recall)
We estimated the rate of energy loss: And the characteristic frequency:R
γcω
3
c 2
42
R
γe
dS
dW
The photon energy2
e
33
cc mcλR
γ
R
cγωε
2
2
emc
er
c
eα
2
α
rλ e
e where
Number of photons emitted per unit length R
γ
dS
dW1
dS
dN
c
(per angle q: )θγαN
Gaussian units on this page!
=>
&
USPAS Course 2016, A. Seryi, JAI 32
Estimations of betatron radiationWe found that relativistic electron with gwill oscillate in the field of ions as
Period of oscillation is p2 g
rb
If amplitude of oscillation is rb
then the radius of curvature
of the trajectory is
rc2mc
rne2
ds
rd2
2
p
2
2
2
2
g
w
g
b
2
2
rπ4
λR
Substitute and get the radius of curvature as
b
2
2
p
rπ2
λγR
R
γc
2
3ω
3
c Substitute into and get estimation of
radiation wavelength brγ3π
λλ
2
2
p
c
Assume 1GeV (g=2E3), p=0.03mm, rb=0.001mm => c=0.25 A or ~50 keV
and Ng per is ~0.3
Useto estimate Ng photons
emitted per R
γ
dS
dN
p
b2
γλ
rα2πγ2N
Many hard photons!
USPAS Course 2016, A. Seryi, JAI 33
• Strong radial electric field
within plasma wave cause
transverse oscillation of
electron bunch
• Generates very bright
betatron radiation in 1- 100
keV range
Betatron radiation sources
S. Kneip et al., Appl. Phys. Lett. 99, 093701 (2011)
USPAS Course 2016, A. Seryi, JAI 34
Towards light sources
S. Kneip et al., Nature Physics 2010
Vulcan
Petawatt25 keV
Hercules10 KeV
LBNL
2.
Genera
tio
n3.
Genera
tio
n
DAISY
ESRF
DAISY
LBNL
slicing bending
magnet
slicing undulator
Doris 3 wiggler
8
3 VuV undulator
SOLEIL
DAISY
Petra 3 X-ray undulatorID9
U20
DAISY
bending magnet
other light sources from A. Rousse et al, EPJD, 2008
Betatron x-ray source shown
to have comparable brightness
to 3rd generation light source
S. Kneip et al., Applied Physics Letters 2011
Small source size ideal for
phase contrast imaging
Z.Najmudin, et al
LP acceleration for medicine
USPAS Course 2016, A. Seryi, JAI 35
Phase contrast imaging
• Absorption (left) and phase contrast (right) X-ray imaging
– and comparison of reconstructed image (middle)
Absorption Phase contrast
X-rays
X-rays
Wave fronts
Reconstructed
images
Inte
ns
ity
Inte
ns
ity
Object Object
USPAS Course 2016, A. Seryi, JAI 36
LP acceleration for medicine
Imaging with Gemini laser-plasma
acceleration and betatron radiation
Small size of emitting area => use of phase contrast
technique => many applications in medical imaging
Lopes N. et al. “X-ray phase contrast imaging of
biological specimens with femtosecond pulses of
betatron radiation from a compact laser plasma
wakefield accelerator.” In Preparation (2016).
Bone tomography
Cole J. et al., Sci. Reports (2015) “X-ray
phase contrast imaging of biological
specimens with femtosecond pulses of
betatron radiation from a compact laser
plasma wakefield accelerator.”.
Laser-
Plasma X-ray Src
& FEL
Z.Najmudin, et al
USPAS Course 2016, A. Seryi, JAI 37
Challenge of stability pulse-to-pulse
USPAS Course 2016, A. Seryi, JAI 38
– Use a train of pulses separated by
plasma period to resonantly excite
wakefield – MP-LWFA
– Energy stored efficiently in plasma wave
– Can tune pulse separation to avoid
saturation (unlike beat-wave scheme)
– Fibre lasers: ~kW average power
at wall-plug efficiencies > 20%
– Fibre lasers can generate trains
of short pulsesS.Hooker, R.Bartolini, S.Mangles, A.Tünnermann, L.Corner, J.Limpert,
A.Seryi, R.Walczak. Jan 30, 2014, J.Phys. B47 (2014) 234003
Challenge of efficiency & repetition rate
USPAS Course 2016, A. Seryi, JAI 39
MP-LWFA: outline concept– 1D and 3D fluid simulations
show:
• Single pulse Eacc = 0.160 GV/m
• Gradient increases linearly up
to ~ 60 pulses
• Max Eacc = 9.6 GV/m (~70
pulses)
• ΔW = 2.5 GeV in Ld = 265 mm
• Eacc rolls over due to loss of
resonance (relativistic mass
increase)...
• ... but this can be overcome by
re-tuning pulse train
Simulations by Naren Ratan
Laser-plasma parameters
E = 10 mJ / pulseτ = 100fs
w0 = 20 μm
a0 = 0.1
ne = 1.7 × 1017 cm-3
Controlled
injection
JAI team, in collaboration with Jena (Germany)
USPAS Course 2016, A. Seryi, JAI 40
Laser Plasma acceleratorModern synchrotrons-based light sources
are big machines (several 100s meters)
Similar electron energies (3-6 GeV) as in synchrotrons, can be reached in a much more compact plasma accelerator using the “wake” created by a laser in a gas jet.
Provided that we solve the challenges of stability, efficiency and repetition rate, we can create, based on plasma acceleration, compact (~10m) light sources – betatron X-ray and eventually an FEL
Dipole
magnet
Gas jet
Electron
dump
X-ray
beam
Specimen
X-ray
detector
Focusing
high power
laser
USPAS Course 2016, A. Seryi, JAI 41
Evolution of computers
and light sources
USPAS Course 2016, A. Seryi, JAI 42
Evolution of computers
and light sources
USPAS Course 2016, A. Seryi, JAI 43
Motivation
• “Livingston plot” shows
great history of accelerators
and great inventions
• … and shows signs of the
need for the next revolution
in accelerator technology
1930 1940 1950 1990198019701960 2000 2010 2020
1015 eV
1016 eV
1017 eV
10 TeV
1 TeV
100 TeV
100 GeV
10 GeV
1 GeV
100 MeV
10 MeV
1 MeV
100 KeV
Betatron
Generators
Cyclotrons
Linacs
Colliders
TevatronLHC
USPAS Course 2016, A. Seryi, JAI 44
Can the next collider be
based on plasma
acceleration?
USPAS Course 2016, A. Seryi, JAI 45
Aiming to TeV
Concept of 1 TeV linear collider
based on laser acceleration
(Leemans & Esarey Phys. Today 2009)
Many stages of acceleration
are necessary
USPAS Course 2016, A. Seryi, JAI 46
• In beam driven acceleration, the driver has v=c and de-phasing of
witness from driver is not an issue
• For laser acceleration, laser propagating in media (plasma) has v<c
and accelerating electrons will soon de-phase from plasma wave
The need for multi-stage acceleration
2
p
2
pdω
ωλL
For laser drive the group velocity2
2
p
gω
ω1v
Dephasing happen when electron outrun wave by half a period
For relativistic electron the dephasing time td thus given by2
λt)v-(c
p
dg
Substitute the above and get dephasing length
USPAS Course 2016, A. Seryi, JAI 47
Accelerators
LasersPlasma
HEP discovery
machines
HEP applications in ~20 yrs or more
USPAS Course 2016, A. Seryi, JAI 48
Compact light
sources
Accelerators
LasersPlasma
HEP discovery
machines
HEP applications in ~20 yrs or more
USPAS Course 2016, A. Seryi, JAI 49
Accelerators
LasersPlasma
Compact light
sources
HEP discovery
machines
Impact on society within ~5 years
HEP applications in ~20 yrs or more
a) Compton light sourcesb) SRF based Compt. src.c) Laser-Plasma light src.
USPAS Course 2016, A. Seryi, JAI 50
Ion acceleration
Strongest motivation –
proton therapy
Heidelberg Ion-Beam Therapy Center
-
-
-
--
-
--
-
-
---
-
--
-
--
-
--
++
++
++
++
+
+
++
+
+-
Blow-off
plasma
Hot electrons
Electron sheath
Accelerated protons
Titanium foil
TNSA (RPA, light sail, etc.)
USPAS Course 2016, A. Seryi, JAI 51
• Beam-driven plasma acceleration
• Max energy achieved 80 GeV (doubling
SLAC linac energy)
• Next gen experiments at FACET (SLAC)
Ez Electron
beam
Accelerating
++
+
+
++
++
+
--
---
--
--- Decelerating
--
-- -- ---
-
- ---
-
- ---
-
PWFA