beam plasma acceleration

Patric Muggli, HEEAUP05, 06/08/051

Beam PlasmaAcceleration

Patric Muggli

University of Southern CaliforniaLos Angeles, California

USA


• Introduction to PWFA

• Short bunch PWFA results

• Conclusions

• Long bunch PWFA results

• Short bunch production

OUTLINE

• Future

• Motivation

- Propagation of e- and e+ beams in long plasmas

- Acceleration of e- and e+

- Acceleration of e-

- Betatron radiation


THANK YOU!

E-162-E164-E164X Collaborations:

UCLA

C. Barnes, F.-J. Decker, P. Emma, M. J. Hogan, R. Iverson, P. Krejcik, C. O’Connell,H. Schlarb, R.H. Siemann, D. Walz

Stanford Linear Accelerator Center

B.E. Blue, C. E. Clayton, C. Huang, C. Joshi, D. Johnson, W. Lu, K. A. Marsh, W. B. Mori, S. Wang, M. Zhou

University of California, Los Angeles

S. Deng, T. Katsouleas, S. Lee, P. Muggli , E. Oz

University of Southern California


• Could a beam-driven plasma accelerator (PWFA) with ≈10 GeV/m accelerating gradient be used to double the energy of a linear collider?

MOTIVATION

• Plasmas can sustain very large accelerating gradients: 10-100 GeV/m (laser or particle beam driven plasma accelerators)

• Limited by rf surface breakdown ≤200 MV/m(?)

• SLAC: ≈200, 70 MW Klystrons ≈50 GeV e-/e+ in ≈3 km Average gradient ≈17 MV/m 3 km

• Next linear collider (ILC): ≈35 MV/m(?), 15 km for 500 GeV?


PLASMA WAKEFIELD (e-)

• Plasma wave/wake excited by a relativistic particle bunch

• Plasma e- expelled by space charge forces => energy loss (ion channel formation rc≈(nb/ne)1/2r + focusing

• Plasma e- rush back on axis => energy gain

• Plasma Wakefield Accelerator (PWFA) = TransformerBooster for high energy accelerator

++++++++++++++ ++++++++++++++++

----- --- ----------------

---- -----------

-------- ------- -------------------- - -

-

---- - -- ---

------ -- -- ---- - - - - - --

---- - -- - - - --- --

- -- - - - - -

---- - ----

------

electron beam

+ + + + + + + + + + ++ + + + + + + + + + + + + + +

+ + + + + + + + + + + + + + ++ + + + + + + + + + + + + + +-

- --

--- --

Accelerating Decelerating (Ez)

+ + + + + + + + + + + + + + +

+ + + + + + + + + + + + + + +

Focusing (Er)Defocusing

• Linear scaling: Eacc ≅110(MeV/m)N 2×1010

σz /0.6mm( )2 ≈ 1/z

2

@ kpez≈√2 or ne≈1014 cm-3 (with kpez <<1)

U C L A


PLASMA WAKEFIELD ACCELERATOR

Driver bunch: high-charge (3N), modest emittance, shaped? Witness bunch: low charge (N), good emittance

ion column focusing preserves emittance beam loading for ∆E/E<<1

Typical PWFA parameters: ne≈1016 cm-3, fpe≈900 GHz, fpe≈300 µm G ≈10-20 GeV/m N ≈1.51010 e-

D≈60 µm, W≈30 µm, ∆t≈150 µm

++++++++++++++ ++++++++++++++++

----- --- ----------------

---- -----------

-------- ------- -------------------- - -

-

---- - -- ---

------ -- -- ---- - - - - - --

---- - -- - - - --- --

- -- - - - - -

---- - ----

------

+ + + + + + + + + + ++ + + + + + + + + + + + + + +

+ + + + + + + + + + + + + + ++ + + + + + + + + + + + + + +-

- --

--- --

Accelerating Decelerating (Ez)

+ + + + + + + + + + + + + + +

+ + + + + + + + + + + + + + +

Focusing (Er)Defocusing

+ +

+ +

+ +

+ +

Driver Bunch:E0 => ≈0

Witness Bunch:E0 => ≥2E0

Plasma provides focusing and acceleration


PLASMA WAKEFIELD EXISTENCE


PLASMA WAKEFIELD EXPERIMENT@ SLAC

3 km e-/e+

LINACFinal Focus Test Beam

3 km for 50 GeV e- and e+ add 1 GeV over <1 m?


EXPERIMENTAL SET UP

• Optical Transition Radiation(OTR)

5 10 15 20 25 30 35 40 45 50

5

10

15

20

25

30

35

40

y

x10 20 30 40 50 60

10

20

30

40

50

60

y

x

- 1:1 imaging, spatial resolution <9 µm

e-, e+

N=21010

z=0.7 mmE=28.5 GeV

IonizingLaser Pulse

(193 nm) Li Plasma

ne≈21014 cm-3

L≈1.4 m

CherenkovRadiator

Streak Camera(1ps resolution)

Bending MagnetsX-Ray

Diagnostic

Optical TransitionRadiators Dump

∫Cdt

Quadrupoles

Imaging Spectrometer25 m

IP0: IP2:xz

y

• Plasma: Laser-ionized lithium vapor


Long e-- beam:E 28.5 GeVN <21010 e-

z 0.63 mm (2.1 ps)x=y ≤70 µm nb ≥41014 cm-3

xN 510-5 m-radyN 0.510-5 m-rad

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

-300

-200

-100

0

-15 -10 -5 0 5 10 15

ElectronFieldsChenKun.kg

τ ( )ps

PLASMA WAKEFIELD FIELDS (E-162, e-)

Plasma:ne 0-21014 cm-3

L 1.4 m, laser ionized

2-D PIC Simulation OSIRISne=1.51014 cm-3

Experiment: nb>ne => non linear, blow-out regime

Front

Blow-Out. Focusing @ r

EnergyGain

EnergyLoss

• Uniform focusing field (r,z)

Typical parameters:


PLASMA FOCUSING OF e-

Beam Envelope Model for Plasma Focusing

Multiple foci (betatron oscillation) within the plasma

x,y(z) at fixed ne => x,y(ne) at fixed z

Plasma Focusing Force > Beam “Emittance Force” (beam=1/K> plasma)

0

50

100

150

200

0 1 2 3 4 5BeamFocusing(z).graph

No Plasman

e=0.03×1014 cm-3 Plasma Lens

ne=1.5×1014 cm-3 3rd Betatron Pinch

( ) z m

OTR

∂2σ∂z2 +K 2σ =

ε2

σ 3

K =ωpe

2γc∝ ne( )

1/2

In an ion channel:

Envelope equation:

€

W =Er

rc=

Bθ

r=

12

neeε 0c

with a focusing strength:

=6 kT/m@ ne=21014 cm-3

Plasma


FOCUSING OF e-

OTR Images ≈1m downstream from plasma

0

50

100

150

200

250

300

0 0.5 1 1.5 2

BetaronFitLongBeta.graph

Plasma OFFPlasma ONEnvelope

(Plasma Density×1014 cm-3)

L=1.4 m0=50 µm

N=12×10-5 m-rad

0=1.16 m

a0=-0.5

Focusing of the beam well described by a simple model (nb>ne): Plasma=

Ideal Thick LensNo emittance growth observed as ne is increased

Stable propagation over L=1.4 m up to as ne =1.81014cm-3

K≥1/0

0

100

200

300

400

500

600

0 0.5 1 1.5 2

07250cwMatchedBetatron.graph

Plasma OFFPlasma ONEnvelope Equation Fit

(Plasma Density×1014 cm-3)

=30 µm

N=44×10 -5 -m rad

=0.11 ma=0

K≤1/0

Channeling of the beam over 1.4 m or >120

= Matched Propagation over long distance!

ne, matched =1.6-2.51014 cm-3

0 ≈K

PRL 88(13), 154801 (2002) PRL 93, 014802 (2004)


WAKEFIELD FIELDS for e- & e+

e- e+

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

-15 -10 -5 0 5 10 15


τ (p)

0

100

200

300

-15 -10 -5 0 5 10 15

PositonFieldsChenKun.kg

τ (p)

• Blow-Out• Accelerating “Spike”

• Fields vary along r, stronger

• Less Acceleration, “linear-like”

ne=1.51014 cm-3

homogeneous, QUICKPIC

r=35 µmr=700 µm=1.81010

d=2 mm


e- & e+ FOCUSING FIELDS*

Ex (GV/m)

0

1500

-1500

0-3750 3750

x (µ

m)

z (µm)

e-

Ex (GV/m)

0

700

-700

0-3750 3750

x (µ

m)

z (µm)

e+

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

-200 -150 -100 -50 0 50 100 150 200

Exz=0Electrons1.5e14

x (µm)

x

2x

3x

e--0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

-200 -150 -100 -50 0 50 100 150 200

Exz=0Positrons1.5e14

x (µm)

e+

x0=y0=25 µmz=730 µmN=1.91010 e+/e-

ne=1.51014 cm-3 *QuickPIC

Linear, no abberations

Non-linear,abberations


FOCUSING OF e-/e+

0 50 100 150 200 250 300 350 400 450 500

50

100

150

200

250

300

0 50 100 150 200 250 300 350 400 450 500

50

100

150

200

250

300

0 50 100 150 200 250 300 350

50

100

150

200

250

30050 100 150 200 250 300 350

50

100

150

200

250

300

e-

e+

ne=0 ne≈1014 cm-3

2mm

2mm

• Ideal Plasma Lens in Blow-Out Regime

• Plasma Lens with Aberrations

• OTR images ≈1m from plasma exit (x≠y)

Qualitative differences


EXPERIMENT / SIMULATIONS

x0=y0=25µm, Nx=39010-6, Ny=8010-6 m-rad, N=1.91010 e+, L=1.4 m

Downstream OTR

0

500

1000

1500

2000

-0.5 0 0.5 1 1.5 2 2.5

PE390by80resultsOTR

FWHMx@otr (µm)FWHMy@otr (µm)

ne (×1014 cm-3)

Excellent experimental/simulation results agreement!

SimulationsExperiment

0

500

1000

1500

2000

-2 0 2 4 6 8

12230cl-n-md4TriangOTR.kg

x-laser OFFy-laser OFFx-laser ONy-laser ON

UV (mJ) OFFUV Energy (mJ)

No -tron oscillations


EMITTANCE / SIMULATIONS

x0=y0=25µm, Nx=39010-6, Ny=8010-6 m-rad, N=1.91010 e+, L=1.4 m

Possible solution: hollow plasma channel for e+

Slice emittance growth for e+

e- core emittance preserved, phase mixing

0 2 4 6 8 10 12 14 16-1.5

-1

-0.5

0

0.5

1

1.5x 10-12

Front Back

10-9

10-8

10-7

0 0.5 1 1.5

Electrons1.5e142

( ) z m

Total

#4Slice

e-

10-9

10-8

10-7

0 0.5 1 1.5

Positrons1.5e142

( ) z m

Total

#4Slicee+

ne=1.5x1014cm-3

Patric Muggli, HEEAUP05, 06/08/0518U C L A



• Conclusions



OUTLINE

• Future

• Motivation






-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

-300

-200

-100

0

-15 -10 -5 0 5 10 15


τ ( )ps

PLASMA WAKEFIELD FIELDS (E-162, e-)

Plasma:ne 0-21014 cm-3

L 1.4 m, laser ionized

2-D PIC Simulation OSIRISne=1.51014 cm-3

Experiment: nb>ne => non linear, blow-out regime

e-- beam:E 28.5 GeVN 21010 e-

z 0.63 mm (2.1 ps)x=y 70 µm nb 41014 cm-3


Front

Blow-Out. Focusing

EnergyGain

EnergyLoss

• Uniform focusing field (r,z) • Large decelerating/accelerating fields

Typical parameters:


• CHERENKOV (aerogel)

- Spatial resolution ≈100 µm - Energy resolution ≈30 MeV- Time resolution: ≈1 ps

EXPERIMENTAL SET UP

10 20 30 40 50 60 70 80 90 100

20

40

60

80

100

120

140

y,E

x

E-162:

e-, e+

N=21010

z=0.7 mmE=28.5 GeV

IonizingLaser Pulse

(193 nm) Li Plasma

ne≈21014 cm-3

L≈1.4 m

CherenkovRadiator

Streak Camera(1ps resolution)

Bending MagnetsX-Ray

Diagnostic

Optical TransitionRadiators Dump

∫Cdt

Quadrupoles

Imaging Spectrometer25 m

IP0: IP2:xz

y

• Plasma: Laser-ionized lithium vapor


e- ACCELERATIONPRE-IONIZED, LONG BUNCH

Time resolution needed, but shows the physics

Energy gain smaller than, hidden by, incoming energy spread

-200

-150

-100

-50

0

50

100

150

200

-6 -4 -2 0 2 4 6 8

ne=1.5×1014 (cm-3)

ne=1.8±0.1×1014 (cm-3)

( ) Time ps

+z

+2z

+3z

-2z

-z

Peak energy gain: 279 MeV, L=1.4 m, ≈200 MeV/m

PRL 93, 014802 (2004)

z≈730 µmN=1.21010 e+

kpz≈√2


ENERGY LOSS/GAIN e+

Excellent agreement!

Plasma Off

Front Back

ne=1.81014cm-3

Loss Gain

Front Back

ne=1.81014cm-3

Experiment 2-D Simulationz≈730 µmN=1.21010 e+

• Loss ≈ 70 MeV

• Gain ≈ 75 MeV

• Loss ≈ 45 MeV/m 1.4 m=63 MeV

• Gain ≈ 60 MeV/m 1.4 m=84 MeV

PRL 90, 214801, (2003)

(over 1.4 m)

B.E Blue, UCLA


NUMERICAL SIMULATIONS: E-164/X, e-

E-164X: z=20-10 µm: >10 GV/m gradient! (r dependent! kpr≈1)

0.01

0.1

1

10

100

1000

10 100 1000

AccDeccFields(sigmaz)

Accel. (Useful) r=20 ( )µm

. ( ) Accel Usefulr=10 ( )µm

. Deccel r=20 ( )µm

. Deccel r=10 ( )µm

z ( )µm

0.2 GeV/m4.343106

fp=2 .8 THz, W=3MT/m @ ne=1017 cm-3

Gradient Increases with 1/z (N=cst)

N=1010 e-, kpz≈√2

ne≈1.4x1017 cm-3 for kpz≈√2 and z=20 µm

Patric Muggli, HEEAUP05, 06/08/0524U C L A



• Conclusions



OUTLINE

• Future

• Motivation






28 GeV28 GeV

Existing bends compress to Existing bends compress to <100 fsec<100 fsec

~1 Å~1 Å

Add 12-meter chicane compressor Add 12-meter chicane compressor in linac at 1/3-point (9 GeV)in linac at 1/3-point (9 GeV)

Add 12-meter chicane compressor Add 12-meter chicane compressor in linac at 1/3-point (9 GeV)in linac at 1/3-point (9 GeV)

Damping RingDamping Ring

9 ps9 ps 0.4 ps0.4 ps<100 fs<100 fs

50 ps50 ps

SLAC LinacSLAC Linac

1 GeV1 GeV 20-50 GeV20-50 GeV

FFTBFFTBRTLRTL

30 kA30 kA

80 fsec FWHM80 fsec FWHM

1.5%1.5%

Short Bunch Generation In The SLAC Linac

Courtesy of SPPS

• Bunch length/current profile is the convolution of an incoming energy spectrum and the magnetic compression

Chirping Compression


e- BUNCH MANIPULATION

Energy spectrum <-> phase space <-> current profile

PWFA: accelerate e- in the back of the bunch

Front

BackAccelerated

electrons

Front

Back

Acceleratedelectrons

LiTrack:K. Bane,P. EmmaSLAC


Accelerated e- originate from ≥0.9 GeV below the bunch max. energy!


ACCELERATED e-

≈0.9 GeV


Front

Back


Short bunches can field-ionize their own plasma and create their own accelerating structure (E-164X, after-burner?)

0

2 1014

4 1014

6 1014

8 1014

1 1015

1.2 1015

109 1010 1011 1012

GasVaporIonization

Ionization Rate (s

-1)

E-Field (V/m)

Cs I

Cs II

Li I

Li IIHe I He IINO IXe IXe IIXe III

0 10 20 30-30 -20 -10

-4

-2

0

2

4

r/r

z/ z

LiVapor

Plasma

∫Wdt≈0

∫ Wdt=1

W s−1[ ]≅1.52×1015 4n*

ξi

n*Γ 2n*( )20.5

ξi3/2

E

⎛

⎝ ⎜

⎞

⎠ ⎟

2n*−1

e−6.83

ξi3/ 2

E

⎛

⎝ ⎜

⎞

⎠ ⎟

N=1.81010, r=10 µm, z=20 µm in LiEr.max≈47 GV/m

I= ionization potential = 5.45 eV for LiIE(t)= electric field in GV/mn*=effective quantum number =3.68Z/I

1/2

see for example D. Bruhweiler et al., Phys. of Plasmas to be published,and P.Muggli et al, AAC-2002 Proceedings

e--BEAM FIELD-IONIZATIONTunneling ionization rate (ADK model):

Threshold process

€

Er ,peak (r ≈ 1.6σ r ,z = 0) ≈ 5.2 ×10−10 Nσ rσ z


“PLASMA SOURCE”• Lithium vapor in a heat-pipe oven

Tunnel-ionization: ne=no, Li

P. Muggli et al., IEEE TPS (1999)

Li HeHe

Pre

ssu

re

L

Boundary Layersn0=0.5-3.51017 cm-3

T=700-1050°CL=10-20 cmPHe≈1-40 T0 0 z

e-

Heater Wick

Cooling Jackets

BeWindow

Plasma LightDiagnostic

: removes laser-related variations


• Coherent Transition Radiation (CTR)- CTR Energy≈Ipeak≈1/z

• Cherenkov (aerogel)

- Spatial resolution ≈100 µm - Energy resolution ≈30 MeV

EXPERIMENTAL SET UP

y,E

x

e-

N=1.81010

z=20-12µmE=28.5 GeV

Optical TransitionRadiators

IP0: Li Plasma ne≈0-3x1017 cm-3

L≈10-20 cm

Plasma light

X-RayDiagnostic,

e-/e+

Production

CherenkovRadiator Dump

∫Cdt

ImagingSpectrometer

IP2:

xz

y

EnergySpectrum“X-ray”

25m

CoherentTransition

Radiation andInterferometer

• X-ray Chicane

-Energy resolution ≈60 MeV

E

Energy Spectrum before …Energy Spectrum after…

… the plasmaPeak CurrentBunch length


N≈1.81010 e-/bunch

Accelerated charge >7% or >220 pCEnergy loss is peak current or bunch length dependent

ne≈2.551017 cm-3, L≈10 cm

0

+2

+4

-4

-2

0 +5-5X (mm)

Rel

ativ

e E

nerg

y (G

eV)

0 +5-5X (mm)

0 +5-5X (mm)

7.9

GeV

CTR=247 CTR=299 CTR=283 CTR=318ne=0

Gain

Loss

0 +5-5X (mm)

≈3 GeV!

Energy gain reaches ≈3+1 GeV


0

1 104

2 104

3 104

4 104

5 104

-2.5 -2 -1.5 -1 -0.5 0 0.5 1

4XProfiles2.55e17Plasma ONPlasma ONPlasma ONPlasma OFF

Relative Energy (GeV)

Details of the incoming energy spectra are visible

Matching of incoming energy spectra with LITrack will allow for the unfolding of the effects

ne≈2.551017 cm-3 INCOMING SPECTRA

Energy Spectra before the Plasma (@ x-ray chicane)L≈10 cm, N≈ 1.81010

Front

Back


0

1 104

2 104

3 104

4 104

5 104

-2.5 -2 -1.5 -1 -0.5 0 0.5 1

3IdenticalXsprctra

Plasma ONPlasma ONPlasma ON


Identical incoming energy spectra/events

“Identical” outgoing energy spectra/events 0

2 104

4 104

6 104

8 104

1 105

1.2 105

-6 -4 -2 0 2

3IdenticalCsprctraPlasma ONPlasma ONPlasma ON


E

x

≈10 GeV

SIMILAR IN,SIMILAR OUT

IN

OUT


Very consistent acceleration, varies with incoming bunch parameters

Gain

ne≈2.81017 cm-3, L≈10 cmN≈ 1.81010 e-/bunch, arranged by CTR

QuickTime™ and a decompressor

are needed to see this picture.

E

x

Ene

rgy

(GeV

)31.5

30.5

29.5

28.5

27.5

26.5

25.5

24.5

E

x

EnergyGain

EnergyGain


Betatron X-rays

• X-ray synchrotron radiation from electrons betarton oscillations.

+ + + + +

e- beam- -

- - X-rays-

-

-

-

( ) MeVrnfrc opoc 6.49,,

2

3 232

=== γγω

ω β

( ) mGeVrnfKkcmrdz

dEopee /3.4,,

3

1 2222222 === γγ β

• Plasma ion column acts as a “Plasma Wiggler” lead to X-ray synchrotron radiation.

ne=3e17 cm-3,=56000, r0=10 µm, B/r= 9 MT/m , = 2cm

Wiggler strength:

Critical frequency on-axis (K>>1):

Particle energy loss:


Positron Production Experimental Setup

Collimators

e- Extraction

e-

z

x

Plasma

40 m10 cm

Bending Magnet

hν Target

8mm

Devon Johnson, UCLA

Plasma length: Lp=10 cm, Nelectrons=9.6x109

Plasma-conversion target distance: 40 m!

Photon beam radius @ target ≈ 35 cm, collimated to r≈8 mm

e+ detection using magnetic spectrometer and 100 µm surface barrier detectors (SBDs), phospor screen and intensified camera

Detector

e+

SectorMagnet


Simulation Results

Simulated Positron DetectedSimulated Radiated Photon Spectrum

Lp=10 cm, Nelectrons=9.6x109, 8 mm dia

ne= 1017 cm-3 => 2.4x106 e+

ne=2x1017 cm-3 => 6.9x106 e+

ne=3x1017 cm-3 => 1.2x107 e+

0.4 X0 titanium target≈4% photons collected

# e+ between 0-40 MeV3x108 e+ with L≈10 cm plasma(100% collection)

Plasma wiggler as e+ source?


CONCLUSIONS

Plasmas can transport and accelerate multi-GeV particle bunches

Particle energy gain measured: ≈4 GeV over 10 cm!

Accelerating gradient ≈40 GeV/m over ≈10 cm!

Acceleration very consistent and repeatable.

Field-ionized PWFA => Long, dense plasmas

Numerical tools are availabe to support experimentals results and project PWFA into the future

No physics limitations observed so far

SingleBunchOnly!


e- and e+:Driver bunches: z=63 µm, r=5 µm, N=31010

e-/e+, 50 -> 0 GeV

Witness bunches: z=32 µm, r=5 µm, N=11010 e-/e+, 50 -> 100+ GeV

Delay: d=200 µmPlasma: ne=1.8 1016 cm-3, L=7, 21 m

Accelerating gradient: 8, 3 GV/m, ∆E/E <10%

PLASMA AFTERBURNER (EXAMPLE)

S. Lee et al., PRST-AB (2001)

3 km

IP

50 GeV50 GeV ee--

50 GeV50 GeV e e++

e-PWFA e+PWFA

LENSES

7m 21m

100+ GeV, e-/e+ Collider


QuickTime™ and aMPEG-4 Video decompressor


Simulations by C. Huang, UCLA

SIMULATION CHALLENGE

Driver Witness

Doubling the energy of a 500 GeV bunch possible! …… in only ≈30 m (≈17 GeV/m)! (simulation)

Driver

Witness

>0.5 TeV

ND=3x1010, Nw=1010,

Nx=Ny=2230x10-6 m-rad, x=y=15 µm , (beam matched to the plasma) zD=145 µm , zW=10 µm, ∆z=100 µmNe=5.66x1016 cm-3, Lp=30 m

L≈30 m


Driver Witness

>0.5 TeV

L=0 m L≈10 m

L≈20 m L≈30 m

Simulationsby

C. Huang UCLA


Doubling the energy of 500 GeV bunch possible! …… in only ≈30 m! (simulation)

ND=3x1010, Nw=1010,

Nx=Ny=2230x10-6 m-rad, x=y=15 µm , (beam matched to the plasma) zD=145 µm , zW=10 µm, ∆z=100 µmNe=5.66x1016 cm-3, Lp=30 m, pre-ionized, Gradient>17 GeV/m



… CPU time 1 week on 16 proc. to 2 weeks on 32 proc.!

∆E/E≈5%FWHM

Head erosion Wake loading evolution

Stability with real beam parameters (x,y, x,y)

Narrow energy spread, could be improved with optimization …


FUTURE

Longer plasma (≈30 cm)for 10 GeV energy gainTwo-bunch experimentsfor beam acceleration

Doubling the energy of the 28.5 GeV SLAC beam in ≈70 cm

Explore application of PWFA to a real HEC …

Adjust afterburner concept parameters to a NLC, and optimize them

Develop numerical tools

6

4

2

0Cur

rent

(kA

)

0 0.1 0.2 0.3-0.1Z (mm)

∆z≈145 µmQ≈11%

(not optimized!)

Identify key experiments to be performed towards an afterburner


OTHER PWFAS

Argone National Laboratory:-propagation, energy gain, two-bunch experiments, simulations

Brookhaven National Laboratory:-linear wakefields, and PWFA driven by a train of bunches

Yerevan Physics Institute, Armenia:-Acceleration of a single bunch in a multi-bunch driven wake

Budker Institute, Novosibirsk, Russia:-e- and e+ PWFAs, simulations


HALO FORMATIONx0≈y0≈25 µm, Nx≈39010-6, Ny≈8010-6

m-rad, N=1.91010 e+, L≈1.4 m

Very nice agreement

0

0.2

0.4

0.6

0.8

1

0 0.5 1 1.5 2 2.5

P390by80peakHalo5

x-Peak, OFFx-Halo, OFFy-Peak, OFFy-Halo, OFF

x-Peak, ONx-Halo, ONy-Peak, ONy-Halo, ON

mean(UN OFF) (mJ)

Experiment Simulation

0

0.2

0.4

0.6

0.8

1

0 0.5 1 1.5 2 2.5

P390by80PeakHaloFraction

x-Peak Fractionx-Halo Fractiony-Peak Fractiony-Halo Fraction

ne (×1014 cm-3)


24

26

28

30

32

0.0001 0.01 1

Plasma OFF

Plasma ON

Bunch Charge Fraction

b)

24

26

28

30

32

0 0.5 1 1.5 2 2.5 3

Plasma OFF

Plasma ON

Intensity [a.u.]

Energy Gain

Energy Loss

a)

Ene

rgy

[GeV

]

31.5

30.5

29.5

28.5

27.5

26.5

25.5

24.5No Plasma 2.8x1017 cm-3

a) b)

1%95%

DETAILED ANALYSIS

Energy gain = energy of 1% charge point

Energy loss = energy of 95% charge point

>2.

7 G

eV

PRL (2005)


DETAILED ANALYSIS

ne= 1.01017 cm-3

Energy loss, but no gain (p>z)

ne= 2.51017 cm-3

Energy loss and gain

ne= 3.51017 cm-3

More, earlier loss and gain

Empty symbols: plasma OUTFilled symbols: plasma IN

Outcome depends on bunch “length”, peak current, profileRecover current profiles

≈1.7 GeV

≈4 GeV

-6

-5

-4

-3

-2

-1

0

1

2

-100 0 100 200 300 400 500 600

07132cxr_1cga_so

OFF 1% , 1×10 17

95% , 1OFF ×10 17

1% , 1ON ×10 17

95% , 1ON ×10 17

1% , 2.5OFF ×10 17

95% , 2.5OFF ×10 17

1% , 2.5ON ×10 17

95% , 2.5ON ×10 17

1% , 3.5OFF ×10 17

95% , 3.5OFF ×10 17

1% , 3.5ON ×10 17

95% , 3.5ON ×10 17

( )Relative Energy GeV

≈ CTR Energy Ipeak

≈ 1/z

≈1-1.2 GV

Cippin

CTR Energy (a.u.) ≈Ipeak≈ 1/z


0

1 104

2 104

3 104

4 104

5 104

-2.5 -2 -1.5 -1 -0.5 0 0.5 1

3XspectrawithTail

Plasma ONPlasma OFFPlasma ON


ne≈2.511017 cm-3, L≈10 cm, N≈1.81010

Confirm: e+ gain energy from below the head energy

Find similar incoming bunches with 2 on incoming spectra.

ORIGIN OF ACCELERATED e-

Retrieve energy of accelerated e+ from incoming spectra and LITrack simulations

ON ONOFF

≈10 GeV

E

x


N≈1.81010 e-/bunch

Accelerated charge >7% or 220 pCEnergy gain depends on the details of the incoming beam (x,y,z)

ne≈2.551017 cm-3, L≈10 cm RESULTS

0

+2

+4

-4

-2

0 +5-5X (mm)

Rel

ativ

e E

nerg

y (G

eV)

0 +5-5X (mm)

0 +5-5X (mm)

7.9

GeV

Pyro=247 Pyro=299 Pyro=283 Pyro=318ne=0

Gain

Loss

0 +5-5X (mm)

≈3 GeV!

Energy gain reaches ≈4 GeV


0

2 104

4 104

6 104

8 104

1 105

1.2 105

-6 -4 -2 0 2

%CSpectra2.55e17

Plasma ONPlasma ONPlasma ONPlasma ONPlasma OFF


Charge Fraction at E>0: 6.8-7.9% of total charge or ≈220 pC!

ne≈3.51017 cm-3 ENERGY SPECTRAL≈10 cm, N≈ 1.81010

EnergyGain

EnergyLoss

Energy Spectra after the Plasma (@ Cherenkov)

Peak energy gain above the beam head: ≈1.5 GeVtotal gain: ≈2.5 GeV

Variations from incoming energy spectrum variations


40 50 60 70 80 90 100 1100

50

100

150

200

250

300

350

Particle distribution

Energy (Gev)

30%

70%E/E=6%

L=0 L≈1m

L≈2m L≈3m136800 c/p

Driver Witness

50 GeV energy gain in 3 meters !

Simulations by C. Huang, UCLA


• 2-bunch experiments, for beam acceleration!

• ≈10 GeV acceleration in long plasma

Next experiments:


Laser Wake Field Accelerator(LWFA)

A single short-pulse of photons

Trapped particles

evolves to

Self Modulated Laser Wake Field Accelerator(SMLWFA)

Raman forward scattering instability

Trapped particles

Plasma Beat Wave Accelerator(PBWA)

Two-frequencies, i.e., a train of pulses

Injected particles

Plasma Wake Field Accelerator(PWFA)

A high energy particle bunch

Injected particles

4 PLASMA ACCELERATORS*

*Pioneered by J.M. Dawson at UCLA


e- BUNCH MANIPULATION

Energy spectrum <-> phase space <-> current profile


Front

Back


Front

Back


LiTrack:K. Bane,P. EmmaSLAC


Accelerated e- originate from 0.9-1.4 GeV below the bunch max. energy!


ACCELERATED e-

≈1.4 GeV

≈0.9 GeVAccelerated

electrons

Quote energy above the bunch head/front energy, analysis will reveal real energy gain

Front

Back


Witness@ L≈3 m

QuickTime™ and aMPEG-4 Video decompressor


50 GeV energy gain in 3 meters !

40 50 60 70 80 90 100 1100

50

100

150

200

250

300

350

Particle distribution

Energy (Gev)

30%

70%E/E=6%

Simulations by C. Huang, UCLA JP1.126 Wednesday afternoon!


Driver Witness

• 2-bunch experiments, for beam acceleration!• ≈10 GeV acceleration in long plasma

Next experiments:


-40

-20

0

20

40

0

1

2

3

4

5

-100 -50 0 50 100PWFAfieldsSuhzi

z (µm)

PLASMA WAKEFIELD FIELDS (e-)

Plasma:ne=n0 0-3.51017 cm-3

L ≈10 cm

3-D PIC Simulation OSIRIS

N=1010 e-, ne=2.11017 cm-3, L=3 cm

• Much larger accelerating field

e-- beam:E 28.5 GeVN 1.81010 e-

z 20 µm (70 fs)x=y 15 µm nb 2.51017 cm-3


Front

Focusing(r=r)

EnergyGain

EnergyLoss

Typical parameters:

c

• Reach kpr≈1, (≈”linear” theory)


NEAR FUTURE

Long plasma => Large energy gain (2Eo in 70 cm?)Short positron bunches?

Notch in the LI10 chicane => 2-bunch experiment!?!Beam acceleration with finite energy spectrum

(XFEL beams? SLAC, DESY?)


12 12 mmmm1.5 %1.5 %

6 mm6 mm0.08 %0.08 %

6 mm6 mm1.2 %1.2 %

1.2 mm1.2 mm1.1 %1.1 %

1.2 mm1.2 mm1.6 %1.6 %

50 50 mmmm1.6 %1.6 %

50 50 mmmm1.5 %1.5 %

energy energy profileprofile

phasephasespacespace

temporal temporal profileprofile

1.19 GeV1.19 GeV

1.19 GeV1.19 GeV

1.19 GeV1.19 GeV

9 GeV9 GeV

9 GeV9 GeV

28 GeV28 GeV

28 GeV28 GeV

Particle tracking in 2D…Particle tracking in 2D…C

ourt

esy

of S

PP

S


Energy loss ≈ peak current ≈ CTR energy ≈ 1/z

ne≈2.551017 cm-3, ENERGY LOSS

Peak energy loss gradient ≥3.4 GeV/10 cm!

L≈10 cm, N≈ 1.81010 e-/bunch

-5

-4

-3

-2

-1

0

0 100 200 300 400 500 600 700

95%Eloss(Pyro)2.55e17

Plasma OFFPlasma ON

CTR Pyro Amplitude (a.u.)

Max. Loss:≈3.4 GeV

≈Ipeak≈1/z

Peak Energy Loss

≈Ipeak ≈1/z

-2

-1.5

-1

-0.5

0

0 100 200 300 400 500 600 700

MeanEloss(Pyro)2.55e17

Plasma OFFPlasma ON


Max. Loss:≈1.5 GeV

Mean Energy Loss

Re

lativ

e M

ea

n E

ner

gy

(GeV

)

Re

lativ

e M

in. E

ner

gy

(GeV

)


ENERGY SPECTROMETER(NON-INVASIVE, UPSTREAM OF PLASMA)

Plasma

QuickTime™ and aTIFF (LZW) decompressor


QuickTime™ and aTIFF (LZW) decompressor


e-

• Measure incoming bunch spectrum

C.D. BarnesPhD. ThesisStanford 2004


e-: ne0=21014 cm-3, c/p=375 µm e+: ne0=21012 cm-3, c/p=3750 µm

r=35 µmr=700 µm

• Uniformfocusing force (r,z)

=1.81010

• Non-uniformfocusing force (r,z)

d=2 mm

QuickTime™ and aTIFF (Uncompressed) decompressor


BlowOut

30 beamFront

Back

QuickTime™ and aTIFF (Uncompressed) decompressor


30 beamFront

Back

3-D QuickPIC simulations, plasma e- density:e- & e+ BEAM NEUTRALIZATION

e- e+


• Optical Transition Radiation (OTR)

• Cherenkov (aerogel)

- Spatial resolution ≈100 µm - Energy resolution ≈30 MeV

EXPERIMENTAL SET UP

-1:1 imaging, spatial resolution ≈9 µm

y,E

x

Since E-162:

U C L A

e-

N=1.81010

z=20-12µmE=28.5 GeV


IP0: Li Plasma Gas Cell: H2, Xe, NO

ne≈0-1018 cm-3

L≈2.5-20 cm

Plasma light

X-RayDiagnostic,

e-/e+

Production


∫Cdt

ImagingSpectrometer

IP2:

xz

y


25m

CoherentTransition


y

x

Upstream

y

x

Downstream

• X-ray Chicane


• Plasma Light

E


L≈10 cm, N≈ 1.81010

ne≈3.51017 cm-3 RESULTS

Pyro=358 Pyro=383

0

+2

+4

-4

-2

0 +5-5X (mm)

Rel

ativ

e E

nerg

y (G

eV)

Pyro=427

0 +5-5X (mm)

0 +5-5X (mm)

0 +5-5X (mm)

Pyro=484

0 +5-5X (mm)

Pyro=466ne=0

Min.Gain

Min.Loss

+1.5 GeV

Many similar events in a data setAcceleration with significant charge: ≈1.5+1 GeV

Lower gain than @ 3.51017 cm-3


ANALYSIS EXAMPLE

Retrieve bunch energy distribution/current profile for energy gain events

Event with Gain Incoming Spectrum

PLASMA ON PLASMA OFF

Incoming Spectrum

IncomingEnergyDistribution

IncomingEnergyDistribution

M.J. Hogan

E

x

E


TRAPPING OF PLASMA e-

No Trapping

Trapping

610 640580Wavelength (nm)

LiI @ 610 nm

Plasma Light Spectrum

Continuum

Evidence for plasma e- trapping:• Excess charge after the plasma

1.5 1010

2 1010

2.5 1010

3 1010

0 100 200 300 400 500 600

TrappedParticlesE164XXI

Plasma OFFPlasma ON


TrappingThreshold?

• Excess light from OTR screen• Continuum light emission on plasma light spectrum

Trapping mechanism?Dark current limit for the PWFA?


AAC’04 AB INTEGRATION

P. Muggli and J.S.T. Ng, AAC’04 AIP Proceedings


NLC AfterBurn US SC AfterBurnCMS Energy (GeV) 1000 2000 1000 2000Linac Length (km) 14.1 0.13 30 0.21Repetition Rate (Hz) 120 120 5 5

Bunch Charge (1010) 1.5 1.1 / 0.4 2 1.5 / 0.5Bunches/RF Pulse 96 2820 Bunch Separation 2.8 ns 0.6 ps 337 ns 1 psEff. Gradient (MV/m) 52 4000 35 2400

Plasma Density (1/m3) 2.00E+22 9.00E+21

x (10at IP -8 - )m rad 360 360 960 960

y (10at IP -8 - )m rad 4 4 4 4

Pl Lens Reduction 10 11 x / y ( )at IP nm 219 / 2.1 37 / 3.9 489 / 4.0 67 / 4.3

z ( )at IP um 110 32 300 35Υave 0.27 5 0.11 3.5

Pinch Enhancement 1.4 1.1 1.7 1 Beamstrahlungd (%)B 8.4 40 5.9 32

+/ -Photons per e e 1.2 2 1.6 1.7 (1033)Luminosity 31 10 38 10

NLC and TESLA Parameters2 TeV 2 TeV Based on upgrade of

proposed next linear collider“Warm”=11.4 GHz“Cold”=1.3 GHz

http://www.slac.stanford.edu/xorg/accelops/

AAC’04 AB INTEGRATION

Courtesy of T. Raubenheimer, SLAC


DETAILED ANALYSIS: PRELIMINARY

CTR Pyro signal

Litr

ack

peak

Cur

rent

(kA

)

“Confirm” expected dependency

(M.J. Hogan)


NEAR FUTURE (II)

Notch in the LI10 chicane => 2 bunches

Acceleration with finite energy spectrum

Long plasma => Large energy gain (2Eo in 70 cm?)

Acceleration with finite energy spectrum


MODUS OPERANDI

• Choose ne and LINAC beam parameters (N, …)

• At a given density vary/optimize acceleration signal- Incoming energy spectrum (phase ramp)- FFTB R56

- beam waist location

• Match incoming spectra with LITrack-> Incoming bunch current profile-> Input into PWFA theory/simulations

• Acquire data with inherent variations- Energy spectra IN and OUT- Beam images b/a plasma- Standard beam parameters (N, position, …)

Kpz≈√2 -> ne≈1.41017 cm-3 for z=20 µm

• Compare events with same incoming energy spectra


SLICE ANALYSIS RESULTSSINGLE EVENT

ne=0.71014 cm-3

Front

E

τ

ne=1.81014 cm-3

Front

E

τ

• Use low ne events as “plasma off”

• Select events by ne, and by position on the streak camera slit

≈3z

≈500 MeV

∆E

≈-17

0 M

eV


e- ENERGY GAIN/LOSS

• Average energy gain (slice average): 156 ±40 MeV (≈3107 e-)• Average energy loss (slice average): 159±40 MeV (@ ne=1.81014 cm-

3)

ps slice analysis results

-200

-150

-100

-50

0

50

100

150

200

-6 -4 -2 0 2 4 6 8

ne=1.5×1014 (cm-3)

ne=1.8±0.1×1014 (cm-3)

( ) Time ps

+z

+2z

+3z

-2z

-z 0

100

200

300

400

500

600

700

800

-400 0 400 800 1200 Energy (MeV)

ne=1.8×1014 (cm-3)

ne=7×1013 (cm-3)

• Energy gain by particles ≈279 MeV in the last (-6 ps) 1 ps slice• Peak accelerating gradient ≈200 MeV/m (L=1.4 m)

(with incoming energy chirp subtracted) slices @ τ=-6 ps


EXPERIMENTAL SET UP

e-

N=1.81010

z=20-12µmE=28.5 GeV


IP0: Li Plasma Gas Cell: H2, Xe, NO

ne≈0-1018 cm-3

L≈2.5-20 cm

Plasma light

X-RayDiagnostic,

e-/e+

Production


∫Cdt

ImagingSpectrometer

IP2:

xz

y


25m

CoherentTransition


• X-ray Chicane


E

• Coherent Transition Radiation (CTR)- CTR Energy≈Ipeak≈1/z


e- & e+ FOCUSING FIELDS

-400

-300

-200

-100

0

100

200

-250

-200

-150

-100

-50

0

-4 -2 0 2 4Er(z)ele1.e15

( )z mm

r=r

r=3r

-700

-600

-500

-400

-300

-200

-100

0

100

0

50

100

150

200

250

-4 -2 0 2 4Er(z)posi1.5e14

( )z mm

r=3r

r=r

QuickPIC x0≈y0≈25 µm, Nx≈39010-6, Ny≈8010-6 m-rad, N=1.91010 e+,

z≈730 µm, ne=1.5 10-6, L≈1.1 cm

• Uniform focusing force (r,z) • Non-uniform focusing force (r,z)

• Weaker focusing force • Stronger focusing force

Front Back Front Back

e+: focusing fields vary along r and z!


• 1-D Relativistic Plasma Wave:

r ∇ ⋅

r E =

ρε0

kpE =ωpe

cE =

neeε0

• Fields in rf cavities

• Limited by rf surface breakdown ≤200 MV/m(?)

• SLAC: ≈200, 70 MW Klystrons ≈50 GeV e-/e+ in ≈3 km Average gradient ≈17 MV/m

•

LARGECollective response!

• High gradient, high-energy plasma accelerator?

ACCELERATING FIELDS

@ ne=1014 cm-3 (fpe≈100 GHz)

E =mec

2

ε0

⎛

⎝ ⎜

⎞

⎠ ⎟

1/ 2

ne1/2 ≅100 ne cm−3( ) =1GV/m

3 km

• Next linear collider (ILC): ≈35 MV/m(?), 15 km for 500 GeV?

Ez

p c

beam plasma acceleration

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