Qual Presentation

Plasma Wakefield Accelerators using Multiple Bunches by

Themos Kallos

University of Southern California Wednesday, May 9th 2007ad

SLAC

CERN • SLAC: 50 GeV e- over 3km  17MV/m • LHC : 7 TeV p+ over 27km • ILC : 500 GeV e- over 30km, $6.5B - Too long, too expensive •Limited by wall breakdown

Witness e-

p 

2 c

p



Electric field

e2 n p

 0 me

ATF

SLAC

• 35 MeV/m over 1.7cm Goals: 1. Monoenergetic bunches

• 50 GeV/m over 90cm (higher I, np ) • Energy doubling! (42 GeV84 GeV)

2. Multiply the energy Yakimenko et al., 2003 & Blumenfeld et al., 2007

400

 The transformer ratio is always less than 2: E  2

Wakefield

E+

200

ebeam

0

-400 0 2

1

x 10

4

2

3

Time [ps] Energy Spectrum after 10mm of plasma

 i.e., A small 5 witness at best gains twice the energy of a single symmetric driver

4

Drive Bunch

1.5

Witness Bunch

 How can we do better?

Initial Spectrum

1

Final Spectrum

0.5 0

E

E-

-200

# of particles [100,000 total]

Wakefield Amplitude [MeV/m]

Wakefield and beam density, 1e+016cm-3

54

56

58 60 62 eBeam Energy [MeV]

64

66

68

λp

λp

2m 50 GeV/m

100 GeV

100 GeV

200 GeV

2m 4x50 GeV/m

100 GeV

4 x 100 GeV

500 GeV

ACT II The 2-bunch experiment

 2 Bunches in energy  2 Bunches in time? Figure by W.Kimura

x E Next: In time

Figures by W.Kimura

BEAM SPLITTER

Bolometer signal (arb. unit s)

Detector

TRANSLATING MIRROR

1

.

0.5

0

High Energy Bunch only

0.5

MIRROR CTR LIGHT

3

2

1

0 1 P osition (psec)

2

3

1

1μm Ti foil

 Corresponds to σz1 =150fs, σz2=90fs  Charge Ratio Q1:Q2 = 2:1  500fs apart

Bolometer signal (arb. unit s)

e-BEAM

Fit

.

0.5

0

Both bunches

0.5 3

2

1

0 1 P osition (psec)

2

3

Next: Plasma

n  n0 e

T = 0.6μs

T = 0.3μs



t t0 T

Plasma ON

4x1015 cm-3

[MeV/m] Wakefield (MV/m) EAmplitude

D

[100,000 total] # of particles # Particles

Plasma OFF

W

Wakefield and beam density, 4e+015cm-3 200

0

-200 0

3000 2000

0.5

1

1.5

2

2.5 3 Time [ps] Initial Spectra

3.5

4

4.5

5

Drive beam Witness beam Initial Final

1000 0 56

57

58

59 60 eBeam Energy [MeV]

 -1.3MeV over 6mm  -200MeV/m

61

62

(Witness)

63

1x1016 cm-3

[MeV/m] Wakefield (MV/m) E Amplitude

D

[100,000 total] # of particles # Particles

Plasma OFF Plasma ON

W

Wakefield and beam density, 1e+016cm-3 200 0 -200 0

3000 2000

0.5

1

1.5

2

2.5 3 Time [ps] Initial Spectra

3.5

4

4.5

5

Drive beam Witness beam Initial Final

1000 0 56

57

58

59 60 eBeam Energy [MeV]

61

62

 +0.9MeV over 6mm  +150MeV/m (Witness)

63

E (MV/m)

Wakefield Amplitude [MeV/m]

# Particles

1x1016 cm-3

# of particles [100,000 total]

Plasma OFF Plasma ON

W

Wakefield and beam density, 1e+016cm-3 200

0

-200 0

0.5

1

1.5

2

2.5 3 Time [ps] Initial Spectra

3.5

4

4.5

5

5000 Drive beam Witness beam Initial Final

4000 3000 2000 1000 0 56

57

58

59 60 eBeam Energy [MeV]

61

62

63

 -1.0MeV over 6mm  -165MeV/m (Witness only)  Unloaded gradient: 165+150=315MeV/m (Driver only)

T = 0.3μs

 To be submitted to PRL

ACT III The 100-bunch experiment

13

eBeam Density [cm-3]

x 10

IFEL Microbunched eBeam

3 2 1 0 -1 3.8

4

4.2 4.4 Time [ps]

4.6

Next: Exp. Layout

Electron Beam

Microbunches

Ipeak≈100A σr=75μm

45 MeV

Ipeak≈600A

IFEL Buncher

Capillary Plasma

Energy Diagnostic

1500μm

Wiggler np=1019 cm-3

Laser Beam

λ0=10.6μm, 200ps

Ppeak≈50MW

10.6μm

Resonant for λp=10.6μm

Requirements: Establish Microbunching  Establish 1019 cm-3 Plasma Density Next: IFEL

Energy exchange between electrons and laser E-Field

Position



dW    e ve  Elaser dt

Energy

Position

Energy

Energy

Energy

2%

Position

Position 254cm

Next: In time, CTR

FFT

The spectrum contains all the information of the geometry of the eBeam

Plasma Density [cm-3 ]

Plasma Density for Various Capillary Lengths 60kV Discharge, 0.6mm Diameter 1.06E+19 9.6E+18 8.6E+18 7.6E+18 6.6E+18 5.6E+18 4.6E+18 3.6E+18 2.6E+18 1.6E+18 6E+17

 We do not have above 1019 yet… 20mm

Typical error bar

16mm 12mm new pulser 8mm new pulser 6mm 4mm new pulser

0.0

0.5

1.0

1.5

Neutral Gas Pressure [atm]

2.0

 Small ionization fractions (<10%)  Large energy density required…  …in very short time  Plasma current (kA) deflects beam  Dynamic pressure yields lower density (2-7 times)

Photos by J.H.Chen

Encore The 7-bunch experiment

 If Mohamed can’t go to the mountain, the

mountain must go to Mohamed

 1019cm-3 at 10.6μm 1018cm-3 at 33.5μm

 Create ~30μm microbunches by using a metal grid to block portions of the initial eBeam

Time Energy

Energy

Energy z

Time

Time

x

Distance  350μm separation  200μm wide (fwhm) Add small witness bunch!

Muggli et al., 2007

 6x50pC drivers  λp = 50μm  np = 4.4x1017 cm-3

Wakefield Amplitude [MeV/m]

Wakefield and beam density, 4e+017cm -3 400 eBeam Wakefield

200 0 -200 -400

0

0.2

0.4

0.6

0.8

1 Time [ps]

1.2

1.4

1.6

1.8

2

# of particles [100,000 total]

Energy Spectrum after 10mm of plasma 10000 8000 6000 4000 2000 0

54

56

58

60 62 eBeam Energy [MeV]

64

66

68

Wakefield Amplitude [MeV/m]

Wakefield and beam density, 4e+017cm -3 400 eBeam Wakefield

200 0 -200 -400

0

0.2

0.4

0.6

0.8

1 Time [ps]

1.2

1.4

1.6

1.8

2

# of particles [100,000 total]

Energy Spectrum after 10mm of plasma 10000 8000 6000 4000 2000 0

54

56

58

60 62 eBeam Energy [MeV]

64

66

68

Wakefield Amplitude [MeV/m]

Wakefield and beam density, 4e+017cm -3 400 eBeam Wakefield

200 0 -200 -400

0

0.2

0.4

0.6

0.8

1 Time [ps]

1.2

1.4

1.6

1.8

2

# of particles [100,000 total]

Energy Spectrum after 10mm of plasma 10000 8000 6000 4000 2000 0

54

56

58

60 62 eBeam Energy [MeV]

64

66

68

Wakefield Amplitude [MeV/m]

Wakefield and beam density, 4e+017cm -3 400 eBeam Wakefield

200 0 -200 -400

0

0.2

0.4

0.6

0.8

1 Time [ps]

1.2

1.4

1.6

1.8

2

# of particles [100,000 total]

Energy Spectrum after 10mm of plasma 10000 8000 6000 4000 2000 0

54

56

58

60 62 eBeam Energy [MeV]

64

66

68

Wakefield Amplitude [MeV/m]

Wakefield and beam density, 4e+017cm -3 400 eBeam Wakefield

200 0 -200 -400

0

0.2

0.4

0.6

0.8

1 Time [ps]

1.2

1.4

1.6

1.8

2

# of particles [100,000 total]

Energy Spectrum after 10mm of plasma 10000 8000 6000 4000 2000 0

54

56

58

60 62 eBeam Energy [MeV]

64

66

68

Wakefield Amplitude [MeV/m]

Wakefield and beam density, 4e+017cm -3 400 eBeam Wakefield

200 0 -200 -400

0

0.2

0.4

0.6

0.8

1 Time [ps]

1.2

1.4

1.6

1.8

2

# of particles [100,000 total]

Energy Spectrum after 10mm of plasma 10000 8000 6000 4000 2000 0

54

56

58

60 62 eBeam Energy [MeV]

64

66

68

Average Temperature [F]

85 75 65 55 45 35 25

Los Angeles VS ATF

LA ATF

Time Source: Weather.com

Thank you!

Bane et al., 1985

• The transformer ratio is 2π-times proportional to the number of plasma wavelengths under the beam • Not trivial to create these beams! Next: Multiple beams

OSIRIS (Fortran)

Themosiris (matlab)

Particle zpositions ,v

• Quasi 2D

i

i

• No field updates  Lorentz dp  Force   dt

EvB c

t

  En, m , Bn, m

  n, m , j n, m

• x1000 faster • Plasma density scans

2n n  n  n , E  bunch t 2 t

Hγ(434nm)

Hβ(486nm)

Hα(656nm)

Kaganovich et al., 1997

Ratio of CTR harmonics

10

8

10

6

10

4

10

2

10

0

Experiment Data Range

0

Ratio of CTR harmonics vs microbunching Ratio of 1st/2nd Ratio of 1st/3rd Ratio of 2nd/3rd

0.5 1 1.5 z of each microbunch [ m]

 All 3 data sets agree around σz=0.7μm

2

Theory & Simulation

Wakefield Evolution @65MeV – Resonant Case 7GeV/m 1

2

3

The electron beam density x100 (1), the theoretical wakefield (2) and the Osiris simulated wakefield (3) after 1mm of propagation in the plasma. Units: 1=300GeV/m