Plasma Accelerators

Bob BinghamCentral Laser Facility

STFC Rutherford Appleton Laboratory, SUPA University of Strathclyde.

HB2016 Malmo 4-8 July 2016

Plasma AcceleratorsLev Landau 1908-1968

Developed theory of wave particle interactions Landau damping 1946. Remained a mystery until John Dawson developed a physical model.

John Dawson 1930-2001Landau Damping first explained by John Dawson 1961originator of plasma wakefield accelerators.

Enrico Fermi 1901-1954

Cosmic ray acceleration Fermi Acceleration 1949

Plasma Accelerators

1) Laser Plasma Wakefield Accelerator LWFA.2) Electron/Positron beam-induced Plasma Wakefield Accelerator PWFA.3) Ion beam-induced Plasma Wakefield Accelerators PWFA.

4) Laser ion acceleration, Sheaths, radiation pressure and shock waves.

Extremely high accelerating gradients:1-100GeV/m

Transient Structures: few ps

Microscopic: 10-100 micron wavelengths

1 EW

1 PW

1 TW

1 GW

1 MW

1 kW

1 W1960 1970 1980 1990 2000 2010

A Brief history of Lasers

Mode-locking (ps)

Q-switching (ns)

Ionisation

1 EW

1 PW

1 TW

1 GW

1 MW

1 kW

1 W1960 1970 1980 1990 2000 2010

A Brief history of Lasers

Mode-locking (ps)

Q-switching (ns)

Ionisation

Limitation due to non-linear processes

Aperture Increase (~ns)

Heating ~ KeV

1 EW

1 PW

1 TW

1 GW

1 MW

1 kW

1 W1960 1970 1980 1990 2000 2010

A Brief history of Lasers

Mode-locking (ps)

Q-switching (ns)

Ionisation

Limitation due to non-linear processes

Aperture Increase (~ns)

Heating ~ KeV

Chirped Pulse Amplification(CPA) (ps, fs)

Relativistic MeV

1 EW

1 PW

1 TW

1 GW

1 MW

1 kW

1 W1960 1970 1980 1990 2000 2010

A Brief history of Lasers

Mode-locking (ps)

Q-switching (ns)

Ionisation

Limitation due to non-linear processes

Aperture Increase (~ns)

Heating ~ KeV

Chirped Pulse Amplification(CPA) (ps, fs)

Relativistic MeV

OPCPA?

Wake Behind a Motor Boat

Light speed surfing on Plasma wakes

Huge gradient (~100GV/m) + Tiny structures (~10-100um)

T.Tajima and J.M. Dawson PRL (1979) LWFAP.Chen, J.M. Dawson et.al. PRL (1983) PWFA

• Laser or beam Pulse

Wake

• Trailing beam

Since 2000 A Plasma Revolution ! ?

evolves to

Laser Wake Field Accelerator(LWFA)A single short-pulse of photons

Self Modulated Laser Wake Field Accelerator(SMLWFA)Raman forward scattering instability

Plasma Beat Wave Accelerator(PBWA)Two-frequencies, i.e., a train of pulses

Laser Wakefield Acceleration

Plasma Wakesphoton beamelectron beamneutrino beamion beams

ne

Plasma Wake

γ , e–+, ν v ≤ c

All very similar

* Drive Plasma Wakes

Tajima and Dawson PRL 1979.

The Bubble Regime

Nature 2004

Courtesy: K. Krushelnick, IC

LBL/Oxford Capillary Guided GeV Laser Plasma Accelerator

• The plasma channel was formed in a hydrogen-filled capillary discharge waveguide (inset). The laser beam was deflected into the capillary using an f/25 off-axis parabola (OAP). Diode 1 and 2 were used to measure the guiding efficiency.

(a) Example of 0.5 GeV bunch. Horizontal axis is beam energy, vertical axis is the beam size in the undeflected plane.

(b) The 0.5 (1.0) GeV beam was obtained in the 225 (310) μm capillary.

(c) and (d) Vertically integrated spectra for the 0.5 and 1.0 GeV beams.

A Phenomenological framework of LWFA in the blowout regime and the optimal scaling

W. Lu et al., PR-STAB (2007)

•Laser and plasma matching

•Wake excitation

•Laser guiding (self-guiding or by a plasma channel)

•Local pump depletion

•Wake phase velocity and dephasing

•Self and external injection

•Beam loading

10fs .3nC 1.5GeV electron beam produced by a 200TW 30fs laser pulse

The Blowout/Bubble Regime:

Beam driver:Rosenzweig et al.,P.R.A 1991

Laser driver:W. B. Mori et al., IEEE 1991

Continuous Bubble injection:A. Pukhov et al., A.P. B 2002

Key physics issues for a plasma accelerator

The structure issue:Wake excitation for given drivers ……

The energy spread and efficiency issue:Beam loading, pulse shaping, transformer ratio ……

The stability issue:Driver evolution, matching, guiding, instabilities ……

The injector issue:Self-injection, wave breaking, controlled injection ….

The overall design issue:Parameter optimization for a plasma based accelerator

to match the requirements of beam parameters

Beam-Induced Plasma Wakefield Accelerator (PWA)

• P. Chen, J.M. Dawson et al.

Experiments: E157 Stanford Linear Accelerator SLAC/UCLA 30 GeV driver, 1014 cm-3 plasma

Argonne National Lab (ANL/UCLA) aiming for 1 GeV/m, 1012 particles per

pulse, 100 Hz repetition rate, emittance of 1mm.mrad

plasma

drive beam

driven beam (accelerating

beam)density fluctuations of a plasma

(plasma wave)

Courtesy Chan Joshi

Positron driven wakefields

Courtesy Chan Joshi

Courtesy Chan Joshi

Proton Driven Plasma Wakefield AcceleratorThe CERN AWAKE Experiment

Schematic of experimental area using an available tunnel as the transfer line from the SPS beam. Goal accelerate electron beam to 1GeV. PI A Caldwell

Short Proton DriverGoal to accelerate electrons to TeV in 600m

Caldwell et al Nature Physics 2009

Ion acceleration

• Laser – electrons - ionsDrivelaserbeam

TargetL

Ion acceleration

L < τc/2 ~ 5μmRecirculation, refluxing

• Laser – electrons - ionsDrivelaserbeam

TargetL

t=2L/c

Drivelaserbeam

TargetL

Target NormalSheath acceleration

Fields TV/m

Front surfaceacceleration

21

20

10 ))((5.27)( −− = WcmIVcmE

)()/( 35.0 −≈= cmne

cmcmVE e

peω

At surface of a solid

ne = 1020 cm-3

E ~ 10 GV/cm

Proton efficiency scaling

Laser pulse energy (J)0 100 200 300 400

Con

vers

ion

effic

ienc

y (%

) to

prot

ons

with

ene

rgy

grea

ter t

han

4 M

eV

0

1

2

3

4

5

6

7

810 micron25 micron

• Conversion efficiency scales linearly with laser energy

• Maximum measured conversion efficiency ~6%

• Theoretical limit ~20%

Robson et al, Nature Physics 3, 58 (2007)

∝ EL

Courtesy D Neely

Need 250 MeV protons (ion oncology)

• Hit it harder – generally works.• New laser……

• Try something new• Light pressure

"Please, sir, I want some more." From O Twist, Illustration by George Cruikshank

foto (c) 1997 Fred Espenak

Light Pressure

• At very high intensities a new mechanism can dominate

• The light pressure pushes the whole target forward I/c

• Requires -“perfect” pulse -minimum mass target-very high intensities (> PW)

• Predicted to have -high efficiency-narrow band energy spectrum

250 500 750 1000

102

103

104

105

Energy (MeV)

Pro

ton

Ene

rgy

Spe

ctru

m (a

rb. u

nits

)

250 500 750 1000

102

103

104

105

Energy (MeV)

Circular Polarization Linear Polarization

PIC simulations by Alex Robinson. See New Journal of Physics, 10, 013021 (2008)

Light PressureThe light pressure pushes the whole target forward

Requires -“perfect” pulse -minimum mass target-very high intensities

- Significant advantages

250MeV protons require Intensities of 1022 W/cm2

Laser driven ions (current capability)

Vulcan gives 400J in 600fs ~1 PW = 1013 ions in 2 ps of ion energy 1-60 MeV

Gemini gives 30J in 40fs ~1 PW = few x 1011 ions in 1 ps of ion energy 1-30 MeV

1 shot every 30 mins = 0.2W average laser power

1010 ion/sec = nA

1 shot every 20 secs = 1.5W average laser power

mid 1010 ion/sec = few nA

Laser driven ions (future capability 3-4 years)

High repetition rate Ti:S gives 40-80J in 40fs ~1PW

= 1012 ions in 1 ps of energy 1-30 MeV= 1011 ions in 1 ps of energy 100-200 MeV ?

1 shot every 0.1 secs = 400W average laser power

1013 ion/sec = μA

A Real Challenge for Plasma Based Acceleration

From “Acceleration” to “Accelerator”

A systematic and deep understanding of all therelevant physics is needed to achieve this goal!

This requires accelerator, plasma and laserphysicists to join forces.

The future looks bright.

Thank you

•Laser driven ions • >10% ion conversion efficiency now possible •Heavy ions, Electrons (>GeV), Gamma rays (0.1-10MeV), neutrons,•Light pressure (250 MeV, 30%?)•Multi pulse offers beam manipulation

Conclusions

Laser and Plasma wakefield accelerators

Laser Plasma Accelerators

• The electric field of a laser in vacuum is given by

• For short pulse intense lasers,

• Unfortunately, this field is perpendicular to the direction of propagation and no significant acceleration takes place.

• The longitudinal electric field associated with electron plasma waves can be extremely large and can accelerate charged particles.

Introduction

• General Principles– Laser-plasma accelerators– Electron-beam-plasma accelerators– Theory – Simulations– Experiments– Future

Spectrum with weak shock. M=1.35 : Te =1 MeV : Ti =2keVPropagating in plasma expanding at 0.1c.

Slice off part of ion distribution -better agreement with experiment

Conclusion• Laser driven ions

• >10% ion conversion efficiency now possible •Heavy ions, Electrons (>GeV), Gamma rays (0.1-10MeV), neutrons,•Light pressure (250 MeV, 30%?)•Multi pulse offers beam manipulation

• Future directions• 10PW, European Laser Infrastructure • New diode drivers increase average power x1000 (3-5 years)• New UK consortium laser ion applications grant 2013-2018• Effect of high dose rates on biological systems• Target technology Cryo Deuterium, liquid targets• Medical ion energies on 4-5 year timescale

Located in the FFTB

FFTB

e-

N=1-2 · 10 10

σz=0.1 mmE=30 GeV

IonizingLaser Pulse(193 nm)

Li Plasmane- 6 · 10 15 cm-3

L- 30 cm

CerenkovRadiator

Streak Camera(1ps resolution)

X-RayDiagnostic

Optical TransitionRadiators Dump

25 m

Cdt

Not to scale!

Spectrometer

PWFA Experiments @SLAC Share Common Apparatus

SLAC Plasma Wakefield Expt.

a,b) Density of electron pulse (brown) and plasma electrons (blue) at two different points in the plasma (12.3 and 81.9 cm). Scalloping features are the result of increasing focusing force.

c) Maximum energy reached after 85 cm. Saturation occurs due to the beam head spreading to the point that it can no longer ionize the lithium vapour.

a) Energy spectrum of electrons in the 30-100 GeV range. Electrons reach 85 GeV (3x106 e/GeV).

b) Experimental (blue) and simulation (red)Reference: Blumenfeld et al. Nature (2007)

Betatron x-ray emission from a LWFA.Electrons trapped at the back of the wakefield are subject totransverse and longitudinal electrical forces; they are subsequentlyaccelerated and wiggled to produce broadband, synchrotron-likeradiation in the keV energy range.

Najmudin et al 2015 Phil. Tran. Royal Soc.

Raw data of electron spectra and corresponding X-ray beams (Astra Gemini laser.)

Betatron Radiation

X-ray energies > 20 keV

Single-shot x-ray phase contrast image of a cricket taken using the Astra Gemini Laser. This 200 TW laser produces 1 GeVelectron beams and very hard x-rays (with critical energy >30 keV).The image shows minimal absorption, indicative of high flux of photons at energies >20 keV, for which the phase-shift cross-section greatly exceeds (>100×) that for absorption.

Betatron Radiation

Najmudin Z et al 2014 Phil. Trans. R. Soc.

Plasma betatronX-rays : source size of few microns.

Divergence < 100mradPulse duration < 100fs.Broadband spectrum keV range

Energy doubling of PWFA: 42 GeV in less than one meter!

GeV LWFA in cm scale plasma

Snapshot of wakefield Controlled injection by colliding laser pulse

”Dream Beam“ Multi-GeV energy gain of PWFA

Ionization induced injection Boosted frame simulation:Full scale modeling of 10-100GeV stages

2GeV LWFA in a gas cell

Simulations (from above paper)

Shock Mach number 2 – broader spectrum than experiment

Another experiment – Najmudin et al PoP 18, 056705 (2011)

Broader spectrum – more like simulations

Proton scaling with laser parameters

Robson et al, Nature Physics 3, 58 (2007)

Laser intensity (W/cm2)1019 1020 1021

Max

imum

pro

ton

ener

gy (M

eV)

0

10

20

30

40

50

60

70Fuchs et al Nat Phys 2006isothermal model

•Mora PRL 90, 185002 (2003): isothermal expansion model provides good fit:• Fuchs et al Nat. Phys. 2, 48 (2006):• Scaling study up to ~5×1019 W/cm2;

Proton scaling with laser parameters

Robson et al, Nature Physics 3, 58 (2007)

Laser intensity (W/cm2)1019 1020 1021

Max

imum

pro

ton

ener

gy (M

eV)

0

10

20

30

40

50

60

70Fuchs et al Nat Phys 2006isothermal model

Laser intensity (W/cm2)1019 1020 1021

Max

imum

pro

ton

ener

gy (M

eV)

0

10

20

30

40

50

60

70Fuchs et al Nat Phys 2006isothermal model10 micron (1 ps)25 microns (1ps)25 micron (various)

• Scaling study up to ~6×1020 W/cm2

• Isothermal model overestimates energies

•Mora PRL 90, 185002 (2003): isothermal expansion model provides good fit:• Fuchs et al Nat. Phys. 2, 48 (2006):• Scaling study up to ~5×1019 W/cm2;

Proton scaling with laser parameters

Robson et al, Nature Physics 3, 58 (2007)

Laser intensity (W/cm2)1019 1020 1021

Max

imum

pro

ton

ener

gy (M

eV)

0

10

20

30

40

50

60

70Fuchs et al Nat Phys 2006isothermal model

Laser intensity (W/cm2)1019 1020 1021

Max

imum

pro

ton

ener

gy (M

eV)

0

10

20

30

40

50

60

70Fuchs et al Nat Phys 2006isothermal model10 micron (1 ps)25 microns (1ps)25 micron (various)

Laser intensity (W/cm2)1019 1020 1021

Max

imum

pro

ton

ener

gy (M

eV)

0

10

20

30

40

50

60

70Fuchs et al Nat Phys 2006isothermal model10 micron (1 ps)25 microns (1ps)25 micron (various) isothermal model • Scaling study up to ~6×1020 W/cm2

• Isothermal model overestimates energies

•Mora PRL 90, 185002 (2003): isothermal expansion model provides good fit:• Fuchs et al Nat. Phys. 2, 48 (2006):• Scaling study up to ~5×1019 W/cm2;

Proton scaling with laser parameters

Robson et al, Nature Physics 3, 58 (2007)

Laser intensity (W/cm2)1019 1020 1021

Max

imum

pro

ton

ener

gy (M

eV)

0

10

20

30

40

50

60

70Fuchs et al Nat Phys 2006isothermal model

Laser intensity (W/cm2)1019 1020 1021

Max

imum

pro

ton

ener

gy (M

eV)

0

10

20

30

40

50

60

70Fuchs et al Nat Phys 2006isothermal model10 micron (1 ps)25 microns (1ps)25 micron (various)

Laser intensity (W/cm2)1019 1020 1021

Max

imum

pro

ton

ener

gy (M

eV)

0

10

20

30

40

50

60

70Fuchs et al Nat Phys 2006isothermal model10 micron (1 ps)25 microns (1ps)25 micron (various) isothermal model

Laser intensity (W/cm2)1019 1020 1021

Max

imum

pro

ton

ener

gy (M

eV)

0

10

20

30

40

50

60

70Fuchs et al Nat Phys 2006isothermal model10 micron (1 ps)25 microns (1ps)25 micron (various) isothermal model2-phases model2-phases with 3-D effects

• Scaling study up to ~6×1020 W/cm2

• Isothermal model overestimates energies

• Model revised to include dual temperature phase; Mora, PRE 72, 056401 (2005)

250 MeV Protons require ~ mid 1022 Wcm-2

•Mora PRL 90, 185002 (2003): isothermal expansion model provides good fit:• Fuchs et al Nat. Phys. 2, 48 (2006):• Scaling study up to ~5×1019 W/cm2;

Shock wave Ion accelerationHaberberger et al (Nature Phys. 8, 95 (2012))used multiple pulses to produce accelerated ions with narrow energy spread.

Note sawtooth shape.

The Blowout/Bubble Regime

The challenges:

Ion channel formed by crossing (fluid model breaks down) Multi-dimensional (2D/3D) Electromagnetic in nature Highly relativistic plasma motion Trapping and crossing are different

Trajectory crossing

Driven by an electron beam: nb>np Driven by a laser pulse: a0>~2

Full scale 3D PIC simulations of LWFA:From GeV to 100GeV

Channel-guided LWFA with external injection (.5-100GeV)

M. Tzoufras et al., JPP 2012

Boosted Frame simulation for 10-100GeV:

S. Martins et al., Nature Physics (2010)

Proton scaling with intensity

• Defocus results in •Reduced intensity•Lower maximum proton energy

•Vulcan PW 1 ps 1054 nm illumination• 2 micron think Al targets

• Lower energy protons suited for•Fast Ignition•Secondary heating

Conversion EfficiencyComparison with previous studies

• Defocus reduces intensity - proton energy

•Defocus enables thin targets – higher efficiency

Robson et al, Nature Physics 3, 58 (2007)

P(PW) τ(fs) np (cm-3) w0 (μm) L(m) a0 ∆nc/np Q(nC) E(GeV)

0.020 30 1×1018 14 0.016 1.76 60% 0.18 0.99

0.040 30 1.5×1018 14 0.011 2.53 40% 0.25 0.95

0.100 30 2.0×1018 15 0.009 3.78 0% 0.40 1.06

0.200 100 1.0×1017 45 0.52 1.76 60% 0.57 9.9

2.0 100 3.0×1017 47 0.18 5.45 0% 1.8 10.2

2.0 310 1.0×1016 140 16.3 1.76 60% 1.8 99

40 330 4.0×1016 146 4.2 7.6 0% 8 106

20 1000 1.0×1015 450 500 1.76 60% 5.7 999

1000 1000 6.5×1015 460 82 12.1 0% 40 1040

Note: Channel guiding: 60% and 40%; Self-guiding: 0%; external injection: 60%; self-injection: 40% and 0% P/Pc=0.7 for 60% case, and 2 for 40% case

A road map of single stage LWFA

The Self-Modulation Instability

Long proton beam Neutral plasma

Affects long drive beams.

J Hollaway 2012

The Self-Modulation Instability

Long proton beam Neutral plasma

Affects long drive beams.

J Hollaway 2012

The Self-Modulation Instability

Long proton beam Neutral plasma

Affects long drive beams.

J Hollaway 2012

The Self-Modulation Instability

Long proton beam Neutral plasma

Affects long drive beams.

J Hollaway 2012

The Self-Modulation Instability

Long proton beam Neutral plasma

Affects long drive beams.

J Hollaway 2012

The Self-Modulation Instability

Long proton beam Neutral plasma

Affects long drive beams.

J Hollaway 2012

The Self-Modulation Instability

Long proton beam Neutral plasma

Affects long drive beams.

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++

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J Hollaway 2012

The Self-Modulation Instability

Long proton beam Neutral plasma

Affects long drive beams.

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++

+

+

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+

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Neutral plasma

Self-modulated driver beamJ Hollaway 2012