LWFA electrons: staged acceleration 2/2 Masaki Kando - - PowerPoint PPT Presentation

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LWFA electrons: staged acceleration 2/2 Masaki Kando - - PowerPoint PPT Presentation

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Lecture: LWFA electrons: staged acceleration 2/2 Masaki Kando kando.masaki@qst.go.jp Kansai Photon Science Institute QST, Japan Advanced Summer School on Laser-Driven Sources of High Energy Particles and Radiation 9-16 July 2017,

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LWFA electrons: 
 staged acceleration 2/2

Masaki Kando

kando.masaki@qst.go.jp

Kansai Photon Science Institute QST, Japan

Advanced Summer School on “Laser-Driven Sources of High Energy Particles and Radiation” 9-16 July 2017, CNR Conference Center, Anacapri, Capri, Italy

Lecture:

This work was partially funded by ImPACT Program of Council for Science, Technology and Innovation (Cabinet Office,
 Government of Japan).

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Advanced Summer School, 9-16 July 2017, Capri, Italy

Review of the Part 1 lecture

  • Introduction of staged acceleration
  • Accelerator physics basics
  • Beam dynamics
  • Transverse motion
  • Longitudinal motion
  • Transfer matrix
  • Comparison of RF accelerators and LWFA

2

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Advanced Summer School, 9-16 July 2017, Capri, Italy

Contents of Lecture 2

  • Some examples of staged laser electron

acceleration

  • Beam matching
  • transverse & longitudinal
  • Focusing devices
  • What are missing in my lecture

3

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Staging experiments

  • review -
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Advanced Summer School, 9-16 July 2017, Capri, Italy

UCLA2011: 2-stages, 1-laser (probably plasma lens)

5

  • B. B. Pollock et al., PRL 107, 045001 (2011)

3 mm (He: N2=99.5%:0.5%) 1 5 mm (He) ✓ QME (460±25 MeV) ✓ ΔE=340 MeV

Achievements

1.7 J, 60 fs (30-60 TW) f/8, w0=15 µm a0=2-2.8

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Advanced Summer School, 9-16 July 2017, Capri, Italy

SIOM2011: 2-stages, 1-laser

6

  • J. S. Liu et al., PRL 107,035001 (2011)

40 fs (40-60TW) f/20, w0=16 µm FWHM

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Advanced Summer School, 9-16 July 2017, Capri, Italy

SIOM2011: 2-stages, 1-laser

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Advanced Summer School, 9-16 July 2017, Capri, Italy

SIOM2011: 2-stages, 1-laser

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L2nd=3mm

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Advanced Summer School, 9-16 July 2017, Capri, Italy

GIST2013: 2-stages, 1-laser (probably plasma lens)

9 Laser 25 J,60 fs, f=4 m (SPM), w0=25 µm FWHM 3x1019 W/cm2 (a0=3.7) gap between stages ~ 2 mm laser is focused to the middle of the gap H.-T. Kim et al., PRL 111, 165002 (2013)

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Advanced Summer School, 9-16 July 2017, Capri, Italy

SIOM2013: 2-stages, 1-laser

10

  • W. Wang et al., APL 103,243501 (2013)

2nd stage 2-6x1018 cm-3, L=1-5 mm 1st stage 8-9x1018 cm-3, L=0.8 mm Density-Down Ramp injection

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Advanced Summer School, 9-16 July 2017, Capri, Italy

SIOM2013: 2-stages, 1-laser

11 ✓ Delay dependence (wake mapping) ✓ Reduction of divergence ✓ Reduction of energy spread ✓ e-beam diagnosis by Faraday rotation

Achievements Parameters 1st stage only 2-stages Energy ~30 MeV 310-530 MeV spread 10-15% ~3%-50% Divergence ~3 mrad ~1 mrad Charge ~100 pC 1pC~100pC

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Advanced Summer School, 9-16 July 2017, Capri, Italy

2015: 2-stages, 1-laser, (probably plasma lens)

12

  • G. Golovin et al., PRSTAB 18, 011301 (2015).
  • 2-stages, 1-laser, (probably plasma lens)

1.7 J, 34 fs (47 TW) f/14 (f=1 m), w0=20 µm FWHM 0.5 0.5 or2 mm ✓ QME of 11-17% ✓ ionization injection + acceleration

Achievements

1st jet 2nd jet 0.5

  • 140 MeV (11%FWHM), 300 MeV (17%)
  • ~20 pC
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Advanced Summer School, 9-16 July 2017, Capri, Italy

LBNL2016: 2-stages, 2-laser, discharge plasma lens

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  • 2-stages, 2-laser, discharge plasma lens
  • S. Steinke et al., Nature 530, 190 (2016)

1st laser 1.3 J,45 fs, f=2 m, w0=18 µm 4x1018 W/cm2 2nd laser 0.45 J,45 fs, f=2 m, w0=18 µm 1.4x1018 W/cm2 ✓ Delay dependence (wake mapping) ✓ discharge plasma lens ✓ laser injection by folding plasma mirror

Achievements

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Advanced Summer School, 9-16 July 2017, Capri, Italy

LBNL2016: 2-stages, 2-laser, discharge plasma lens

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exp. PIC sim.

Capillary : L = 33 mm n0 = 2x1018 cm-3 ✓ Energy spread is large ✓ Energy gain is small

Cons

e-injection: 350 MeV, 10 pC, dE/E=6% rms 2nd laser is matched to the capillary waveguide. (w0=40µm) laser energy is increased to 1J. Simulation under optimized parameters

Matching is important!

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Stepped gas-jet target with external magnetic field Short-focus OAP for Long-focus OAP for Short-focus OAP with hole

Gasjet Injector Booster e-bunch

Osaka U.2014 (Unpublished) Injector-booster scheme of LWFA (2-beam-driven staging LWFA)

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Advanced Summer School, 9-16 July 2017, Capri, Italy

SIOM2016: 2-stages?, 1-laser

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  • W. T. Wang, PRL 117, 124801 (2016)

Laser 100-120 TW, 33 fs, f=4 m, f/30 (SPM), w0=32 µm FWHM, 3.6-4.3x1018 W/cm2 (a0=1.3)

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Advanced Summer School, 9-16 July 2017, Capri, Italy

SIOM2016: 2-stages?, 1-laser

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  • W. T. Wang, PRL 117, 124801 (2016)
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Advanced Summer School, 9-16 July 2017, Capri, Italy

Transverse beam matching: by tracking

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  • 30
  • 20
  • 10

10 20 30

X'i (mrad)

  • 0.10
  • 0.05

0.00 0.05 0.10

Xi (mm) wr0=10 µm Z=-10ZR Laser =0.25 mm-mrad Peak (=87 deg) =0.10 mm-mrad Focus (=132 deg) =0.16 mm-mrad

Transverse phase space Example: laser vacuum waist 10 µm electron vacuum focus (peak) 4.6 µm (focus) 14 µm dE/E=10% Normalized emittance should be 30 MeV, εn~6-10 mm mrad

Electron beam focal parameters are similar to those of the drive laser In addition,

  • plasma lens
  • focusing by capillary discharge current

are also important (LBNL, Nebraska)

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Advanced Summer School, 9-16 July 2017, Capri, Italy

Longitudinal beam matching: by tracking

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  • 20
  • 15
  • 10
  • 5.0

0.0 5.0 10 15 20 50 100 150 200 250 300 350 17 MeV 10 MeV 150 MeV 1.0 MeV

Energy Gain (MeV) Injection Phase (deg.)

2TW, 790 nm n=1.3x1017 cm-3 100 fs

Before dephasing, bunching effect is not so effective. Input shape is somehow conserved.

0.85 fs/deg

In simplified estimation, ΔE/E=1% ±2.2% of λp ΔE/E=0.1% ±0.71% of λp

1.9 fs 5.9 fs

λp=80 µm (Laser :100 fs)

We have to inject very short electrons into next stage wakefield.

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Advanced Summer School, 9-16 July 2017, Capri, Italy

Beam matching: PIC+Tracking

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  • 1. Choose parameters



 


  • 2. Run simulation with test particles

  • 3. Select required final beam quality
  • 4. Calculate the required input beam quality


to achieve the final beam quality. Energy spread 0.3% around 928 MeV ne/nc = 10−3 WL = 5 J

simulation by T. Esirkepov

τ = 30 fs

w0 = 16 µm FWHM

multiparametric 2D

Energy 20, 40, …, 160 MeV X, px, Y, py: wide enough

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Advanced Summer School, 9-16 July 2017, Capri, Italy

Beam matching: not yet optimized

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εn=5.92 mm-mrad dE/Ef=0.32%, Ef=928 MeV

Output

εn=14.6 mm-mrad dE/E =0.11%, Ei=160.5 MeV Transverse phase space (y-y’)

Input(should be)

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Advanced Summer School, 9-16 July 2017, Capri, Italy

Emittance growth

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  • T. Mehrling et al., PRST-AB 15,111303 (2012).

If the input beam is not matched, the emittance increases.

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Advanced Summer School, 9-16 July 2017, Capri, Italy

Extraction

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  • I. Dornmair et al., PRST-AB 18, 041302 (2015)
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Focusing device ~ transverse ~

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Advanced Summer School, 9-16 July 2017, Capri, Italy

Conventional magnetic devices: Quadrupole

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Quadrupole magnet

  • J. Holmes, US Part. Acc. School 2009

Fx = −kx, Fz = +kz Focal length Horiz focus and Vert defocus

  • r vice versa

Doublet Doublet Q can focus in both direction. But astigmatic. (check this using transfer matrix)

x2 x0

2

! = B B B B B @ cos( p KL)

1 p K sin(

p KL)

  • p

K sin( p KL) cos( p KL) 1 C C C C C A x1 x0

1

!

z2 z0

2

! = B B B B B @ cosh( p KL)

1 p K sinh(

p KL)

  • p

K sinh( p KL) cosh( p KL) 1 C C C C C A z1 z0

1

!

x2 x0

2

! = 1 1/f 1 ! x1 x0

1

! , z2 z0

2

! = 1 1/f 1 ! z1 z0

1

! Thin lens approximation: f = Bρ B0L Bρ = p/(qe) Magnetic Rigidity Stigmatic focus can be achieved with Triplet. Triplet

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Advanced Summer School, 9-16 July 2017, Capri, Italy

Conventional magnetic devices: Solenoids

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Don’t you feel strange that an axial magnetic field focuses a beam? B Solenoidal magnet f = 4 R (qeBs/γmv)2ds = (2Bρ)2 B2L

  • Not effective for relativistic particles

Focal length The fringe field of a solenoidal magnet causes rotation in azimuthal direction. vphi appears! then longitudinal Bs focuses!

Humphries, Jr. ,Principles of Charged Particle Acceleration

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Advanced Summer School, 9-16 July 2017, Capri, Italy

Plasma focusing devices

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Plasma lens (passive plasma lens)

  • Plasma neutralizes space charge of an electron beam.
  • The self-magnetic field focuses the electron beam.

Note: Return current weakens focusing. If a plasma wake is excited by the e-beam it affects focusing(defocusing).

F = e2λe 2πε0r F = e(E + v × B) λe =      beam line density (ne > nb) plasma line density (ne < nb)

Overdense regime Underdense regime Overdense: the force is stronger in the center of the beam; nonlinear focusing Underdense : force is uniform in the beam; uniform focusing

n = min(nb, ne) K = − F γemc2r = −2πren γ

In LEA, plasma is created automatically near the focus; this lens exists automatically!

  • P. Chen, Particle Accelerators 1985
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Advanced Summer School, 9-16 July 2017, Capri, Italy

Passive plasma lens :Jena Group

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  • S. Kuschel et al., PRST-AB 19, 071301 (2016)
  • Acc. section

95%He+5%N2, ne=1.0x1019 cm-3 L=2.5 mm 650 mJ, 28 fs f/12, w0=120 µm2 FWHM a0=2.2 Focusing (Gas-jet ) H2, ne=(0.4-1.6)x1019 cm-3 L=2.5 mm

Overdense regime

Bunch density nb~2x1015 cm-3

Lg=8-24 mm Simulation Experiment Lg=8.75 mm ne,lens=1.6x1019cm-3

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Advanced Summer School, 9-16 July 2017, Capri, Italy

Passive plasma lens :Jena Group

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Advanced Summer School, 9-16 July 2017, Capri, Italy

Plasma focusing devices

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Active plasma lens (discharge plasma)

  • J. van Tilborg et al., PRL 115, 184802 (2015)

∂Bφ ∂r = µ0I0 2πR2

From Ampere’s law

k = e∂Bφ ∂r 1 mγec

Focusing strength parameter

ne ≈ 7 × 1018cm−3 I0 = 300 A R = 125 µm

The focusing effect by a (passive) plasma lens was not considered in this paper.

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Advanced Summer School, 9-16 July 2017, Capri, Italy

Comparison of various focusing devices

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L B or B’ Symme tric focal length (thin lens) focal length for 1GeV e- Quadrupole ~20 cm 10-100 T/m No >0.167 m Triplet of Q ~10+2 0+10 10-100 T/m Yes >0.834 m Solenoidal lens ~10 cm 2 T Yes 55 m Passive plasma lens 1 mm

  • Yes

335 µm (nb*1~3.3x1017 cm-3) Active plasma lens ~10 cm 3000 T/m Yes 11 mm f = Bρ B0L f = (2Bρ)2 B2L f = 2ε0(Bρ)2 Lmn = γ 2πrenL f = Bρ B0L f = 6(Bρ)2 B02L3

L/2+L+L/2 Magnetic Rigidity

pc[GeV] ∼ 0.3qB[T]ρ[m] Bρ = p/(qe)

*1) 10pC, r=10µm, 2fs

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Advanced Summer School, 9-16 July 2017, Capri, Italy

What is not discussed in the Lecture

  • Space charge effects
  • Beam-loading effects
  • See Hidding’s lecture, Benedetti’s lecture
  • Coherent Synchrotron Radiation
  • See Ferrario’s lecture 3

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