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, CNR Conference Center, Anacapri, Capri, Italy This work was partially funded by ImPACT Program of Council for Science, Technology and Innovation (Cabinet Office, Government of Japan).
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 Advanced Summer School, 9-16 July 2017, Capri, Italy 2
Contents of Lecture 2 • Some examples of staged laser electron acceleration • Beam matching • transverse & longitudinal • Focusing devices • What are missing in my lecture Advanced Summer School, 9-16 July 2017, Capri, Italy 3
Staging experiments - review -
UCLA2011: 2-stages, 1-laser (probably plasma lens) 1.7 J, 60 fs (30-60 TW) f/8, w0=15 µ m a0=2-2.8 Achievements 1 5 mm 3 mm ✓ QME (460±25 MeV) (He) (He: N2=99.5%:0.5%) ✓ Δ E =340 MeV B. B. Pollock et al., PRL 107, 045001 (2011) Advanced Summer School, 9-16 July 2017, Capri, Italy 5
SIOM2011: 2-stages, 1-laser 40 fs (40-60TW) f/20, w0=16 µ m FWHM J. S. Liu et al., PRL 107 ,035001 (2011) Advanced Summer School, 9-16 July 2017, Capri, Italy 6
SIOM2011: 2-stages, 1-laser Advanced Summer School, 9-16 July 2017, Capri, Italy 7
SIOM2011: 2-stages, 1-laser L 2nd =3mm Advanced Summer School, 9-16 July 2017, Capri, Italy 8
GIST2013: 2-stages, 1-laser (probably plasma lens) Laser 25 J,60 fs, f=4 m (SPM), w 0 =25 µ m FWHM 3x10 19 W/cm 2 (a 0 =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) Advanced Summer School, 9-16 July 2017, Capri, Italy 9
SIOM2013: 2-stages, 1-laser 1st stage 8-9x10 18 cm -3 , L=0.8 mm 2nd stage Density-Down Ramp injection 2-6x10 18 cm -3 , L=1-5 mm W. Wang et al., APL 103 ,243501 (2013) Advanced Summer School, 9-16 July 2017, Capri, Italy 10
SIOM2013: 2-stages, 1-laser 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 Achievements ✓ Delay dependence (wake mapping) ✓ Reduction of divergence ✓ Reduction of energy spread ✓ e-beam diagnosis by Faraday rotation Advanced Summer School, 9-16 July 2017, Capri, Italy 11
2015: 2-stages, 1-laser, (probably plasma lens) • 2-stages, 1-laser, (probably plasma lens) 1.7 J, 34 fs (47 TW) f/14 (f=1 m), w0=20 µ m FWHM 1st jet 2nd jet 0.5 0.5 0.5 or2 mm • 140 MeV (11%FWHM), 300 MeV (17%) • ~20 pC Achievements ✓ QME of 11-17% ✓ ionization injection + acceleration G. Golovin et al., PRSTAB 18, 011301 (2015). Advanced Summer School, 9-16 July 2017, Capri, Italy 12
LBNL2016: 2-stages, 2-laser, discharge plasma lens • 2-stages, 2 -laser, discharge plasma lens 1st laser 1.3 J,45 fs, f=2 m, w 0 =18 µ m 4x10 18 W/cm 2 2nd laser 0.45 J,45 fs, f=2 m, w 0 =18 µ m 1.4x10 18 W/cm 2 Achievements ✓ Delay dependence (wake mapping) ✓ discharge plasma lens ✓ laser injection by folding plasma mirror S. Steinke et al., Nature 530, 190 (2016) Advanced Summer School, 9-16 July 2017, Capri, Italy 13
LBNL2016: 2-stages, 2-laser, discharge plasma lens exp. PIC sim. Capillary : L = 33 mm n0 = 2x10 18 cm -3 Cons ✓ Energy spread is large ✓ Energy gain is small Simulation under optimized parameters 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. Matching is important! Advanced Summer School, 9-16 July 2017, Capri, Italy 14
Osaka U.2014 (Unpublished) Injector-booster scheme of LWFA (2-beam-driven staging LWFA) Long-focus OAP for Booster Gasjet Short-focus OAP with hole Short-focus OAP for Injector Stepped gas-jet target e-bunch with external magnetic field
SIOM2016: 2-stages?, 1-laser Laser 100-120 TW, 33 fs, f=4 m, f/30 (SPM), w 0 =32 µ m FWHM, 3.6-4.3x10 18 W/cm 2 (a 0 =1.3) W. T. Wang, PRL 117 , 124801 (2016) Advanced Summer School, 9-16 July 2017, Capri, Italy 16
SIOM2016: 2-stages?, 1-laser W. T. Wang, PRL 117 , 124801 (2016) Advanced Summer School, 9-16 July 2017, Capri, Italy 17
Transverse beam matching: by tracking Transverse phase space 30 dE/E=10% Example: Laser w r0 =10 µ m � =0.25 � mm-mrad Z=-10Z R laser vacuum waist 10 µ m 20 electron vacuum focus 4.6 µ m (peak) 10 (focus) 14 µ m X' i (mrad) 0 Normalized emittance should be 30 MeV, ε n ~6-10 mm mrad -10 Focus ( � =132 deg) � =0.16 � mm-mrad Electron beam focal parameters are -20 similar to those of the drive laser Peak ( � =87 deg) � =0.10 � mm-mrad In addition, • plasma lens -30 • focusing by capillary discharge current -0.10 -0.05 0.00 0.05 0.10 are also important (LBNL, Nebraska) X i (mm) Advanced Summer School, 9-16 July 2017, Capri, Italy 18
Longitudinal beam matching: by tracking 2TW, 790 nm n=1.3x10 17 cm -3 100 fs 20 Before dephasing, bunching effect is not so effective. 17 MeV 15 10 MeV Input shape is somehow conserved. 150 MeV 1.0 MeV 10 Energy Gain (MeV) In simplified estimation, 5.0 Δ E/E= 1% 5.9 fs 0.0 ±2.2% of λ p -5.0 Δ E/E= 0.1% 1.9 fs ±0.71% of λ p -10 λ p=80 µm (Laser :100 fs) -15 0.85 fs/deg -20 We have to inject very short electrons 0 50 100 150 200 250 300 350 into next stage wakefield. Injection Phase (deg.) Advanced Summer School, 9-16 July 2017, Capri, Italy 19
Beam matching: PIC+Tracking simulation by T. Esirkepov 1. Choose parameters n e /n c = 10 − 3 τ = 30 fs W L = 5 J w 0 = 16 µ m FWHM 2. Run simulation with test particles Energy 20, 40, …, 160 MeV X, px, Y, py: wide enough 3. Select required final beam quality multiparametric Energy spread 0.3% around 928 MeV 2D 4. Calculate the required input beam quality to achieve the final beam quality. Advanced Summer School, 9-16 July 2017, Capri, Italy 20
Beam matching: not yet optimized Output ε n =5.92 mm-mrad dE/Ef=0.32%, Ef=928 MeV Input(should be) ε n =14.6 mm-mrad dE/E =0.11%, Ei=160.5 MeV Transverse phase space (y-y’) Advanced Summer School, 9-16 July 2017, Capri, Italy 21
Emittance growth T. Mehrling et al., PRST-AB 15,111303 (2012). If the input beam is not matched, the emittance increases. Advanced Summer School, 9-16 July 2017, Capri, Italy 22
Extraction I. Dornmair et al., PRST-AB 18, 041302 (2015) Advanced Summer School, 9-16 July 2017, Capri, Italy 23
Focusing device ~ transverse ~
Conventional magnetic devices: Quadrupole Quadrupole magnet Horiz focus and Vert defocus F x = − kx , F z = + kz or vice versa p p 0 1 1 x 2 ! x 1 ! cos( KL ) K sin( KL ) p B C B C B p p p C = B C x 0 x 0 B C K sin( KL ) cos( KL ) @ A � 2 1 p p 0 1 1 z 2 ! z 1 ! cosh( � KL ) � K sinh( � KL ) p B C B C B p p p C = B C z 0 z 0 B C � K sinh( � KL ) cosh( � KL ) @ A � 2 1 Thin lens approximation: Focal length f = B ρ x 2 ! ! x 1 ! z 2 ! 1 ! z 1 ! 1 0 0 , B 0 L = = x 0 � 1 / f 1 x 0 z 0 1 / f 1 z 0 2 1 2 1 Magnetic Rigidity J. Holmes, US Part. Acc. School 2009 B ρ = p / ( qe ) Triplet Doublet Doublet Q can focus in both direction. Stigmatic focus can be achieved But astigmatic . (check this using transfer matrix) with Triplet . Advanced Summer School, 9-16 July 2017, Capri, Italy 25
Conventional magnetic devices: Solenoids Solenoidal magnet B Don’t you feel strange that an axial magnetic field focuses a beam? Focal length = (2 B ρ ) 2 4 f = R B 2 L ( qeB s / γ mv ) 2 ds • Not effective for relativistic particles 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 Advanced Summer School, 9-16 July 2017, Capri, Italy 26
Plasma focusing devices 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 = e ( E + v × B ) F = e 2 λ e Overdense regime beam line density ( n e > n b ) λ e = Underdense regime 2 πε 0 r plasma line density ( n e < n b ) Overdense: the force is stronger in the center of the beam; nonlinear focusing Underdense : force is uniform in the beam; uniform focusing γ e mc 2 r = − 2 π r e n F K = − n = min( n b , n e ) γ In LEA, plasma is created automatically near the focus; this lens exists automatically! P. Chen, Particle Accelerators 1985 Advanced Summer School, 9-16 July 2017, Capri, Italy 27
Passive plasma lens :Jena Group 650 mJ, 28 fs Experiment f/12, w0=120 µ m 2 FWHM a0=2.2 Lg=8-24 mm Simulation Acc. section Focusing (Gas-jet ) 95%He+5%N 2 , H 2 , n e =(0.4-1.6)x10 19 cm -3 n e =1.0x10 19 cm -3 L=2.5 mm L=2.5 mm Bunch density Overdense regime nb~2x10 15 cm -3 Lg=8.75 mm n e,lens =1.6x10 19 cm -3 S. Kuschel et al., PRST-AB 19 , 071301 (2016) Advanced Summer School, 9-16 July 2017, Capri, Italy 28
Passive plasma lens :Jena Group Advanced Summer School, 9-16 July 2017, Capri, Italy 29
Recommend
More recommend
