stato simulazioni “self-injection” e “afterburner” · self-injection experiments with flame...

Stato simulazioni “self-injection” e“afterburner”

C. Benedetti1, P. Londrillo1, G. Turchetti1

A. Bacci2, L. Serafini2, P. Tomassini2

1 Dep. of Physics, University of Bologna & INFN/Bologna2 INFN/Milano

LIFE-meeting, Frascati, February 19-20, 2009 – p.1/34

Self-injection experiments with FLAME

Part I: self-injection



• (Half power) FLAME laser

P =150 TW, τfwhm = 24 fs

waist: w0 = 8 ÷ 40 ( 1/e2 radius of the laser intensity profile, wfwhm ≃ 1.2 w0)

norm. vector potential a0 ≡ eAlaser

mc2= 8.5 · 10−10

q

I[W/cm2](λ[µm])2 ≥ 2

LASER PULSE (P=150 TW)

1.2 mm

23 fs PLASMA

• Two regimes:1. w0 < λp ⇒ Nonlinear 3D regime (bubble)2. w0 > λp ⇒ Nonlinear “1D-like” regime (+ properly modulated gas-jet)



• Nonlinear 3D regime (bubble) a

accelerating region

decelerating region

450 460 470 480 490 500-2.0

-1.0

-0.5

0.0

0.5

1.0

2.0

z [µ m]

Ez

[TV

/m]

Longitudinal field

• Rbub ≃ O(λp) E(max)z ≃ 100

p

n0[cm−3] × a0 [V/m]

•

8

<

:

velect ≃ c

vbub ≃ c(1 − 3ω2p/(2ω2

0)) < velect ⇒ acc. length is finite + monochromaticity

aS. Gordienko and A. Pukhov, Phys. Plas. 12 (2005) / W. Luet al.PRSTAB 10 (2007)



• Nonlinear 3D regime (bubble): formulae (in general)

“stability” of the bubble: kp Rbub ≃ kp w0 ≃ 2√

a0

dephasing length: Ld = 23

ω20

ω2p

Rbub

pump depletion: Lpd =ω20

ω2p

cτfwhm, must be Lpd> min(Lgasjet, Ld)

e−energy (dephasing): W [GeV] ≃ 1.7 ×“

P [TW]100

”1/3 “

1018

np[cm−3]

”2/3 “

0.8λ0[µm]

”4/3

charge injected: Q[pC] ≃ 400 ×“

0.8λ0[µm]

” “

P [TW]100

”1/2

• Nonlinear 3D regime (bubble): formulae (for 12

FLAME)

Taking w0 as a free parameter we have

np [cm−3]=7.56 · 1021/(w0[µm])3

Ld[µm] = 0.154 × (w0[µm])4

Lpd[µm] = 1.66 × (w0[µm])3

W [MeV] ≃ 68.3 × Lgasjet[µm]

(w0[µm])2

“

1 − 3.25×(Lgasjet[µm])

(w0[µm])4

”

(for Ld ≥ Lgasjet/2)

Q ≃ 0.5 nCLIFE-meeting, Frascati, February 19-20, 2009 – p.5/34


• Let’s consider some examples:

1. “best” (in terms of monochromaticity) bunch: Ld ≡ Lgasjet ≃ 0.9 ÷ 1 mmw0 ≃ Rbub ≃ 9 µm, I ≃ 1.2 · 1020 W/cm2, a0 = 7.4

Lpd ≃ 1.2 mm > Lgasjet, Ld

np ≃ 1 · 1019 cm−3

W ≃ 400 MeV

2. highest energy for a given Lgasjet (≃ 1 mm): ∂E∂w0

˛

˛

Lgasjet= 0

w0 ≃ Rbub ≃ 10 µm, I ≃ 9.7 · 1019 W/cm2, a0 = 6.7

Ld ≃ 1.5 mm > Lgasjet, Lpd ≃ 1.7 mm > Lgasjet

np ≃ 7.7 · 1018 cm−3

W ≃ 450 MeV (monochromaticity ???)

3. W = 1 GeV monochromatic electron beam (with gas jet):w0 ≃ Rbub ≃ 14 µm, I ≃ 5 · 1019 W/cm2, a0 = 4.8

Ld ≡ Lgasjet ≃5.6 mm, Lpd ≃ 4.4 mm < Lgasjet (!!!)np ≃ 3 · 1018 cm−3

4. Out of “bubble” regime: a0 . 3.5

w0 & 19 µm, I < 2.6 · 1019 W/cm2

PIC simulation (with ALaDyn) of the case #1LIFE-meeting, Frascati, February 19-20, 2009 – p.6/34


• 3D ALaDyn PIC simulation @ CINECA (∼ 14000 CPUh = 7 days on 80 CPUs)

domain: (80×80×80) µm3

grid: 1439×131×131 ⇒ res. in the center: 18 points/µm long., 3 points/µm trasv.

25 ×106 numerical particles

∼ 20000 time steps



• 3D simulation of the case #1: c t = 200 µm (injection)

0 100 200 300 400 500 0

0.01

0.02

0.03

E [MeV]

dN

/dE

[arb

. uni

ts]



• 3D simulation of the case #1: c t = 500 µm

0 100 200 300 400 500 0

0.01

0.02

0.03

E [MeV]

dN

/dE

[arb

. uni

ts]




0 100 200 300 400 500 0

0.01

0.02

0.03

E [MeV]

dN

/dE

[arb

. uni

ts]




0 100 200 300 400 500 0

0.01

0.02

0.03

E [MeV]

dN

/dE

[arb

. uni

ts]

⇒Monochromatic peak!! W = (160 ± 5) MeV, Q = 0.45 nC (FWHM)




0 100 200 300 400 500 0

0.01

0.02

0.03

E [MeV]

dN

/dE

[arb

. uni

ts]




0 100 200 300 400 500 0

0.01

0.02

0.03

E [MeV]

dN

/dE

[arb

. uni

ts]

⇒ Several peaks (post-dephasing pattern) !!W1 = (236 ± 9) MeV, Q = 0.8 nC (FWHM)W2 = (170 ± 5) MeV, Q = 0.35 nC (FWHM)

W3 = · · ·LIFE-meeting, Frascati, February 19-20, 2009 – p.13/34


• The simulated energy (∼ 200 MeV) is LOWER than the theoretical value (∼ 400 MeV):

1. beam loading effect (perturbation of Ez in the bunch region) [small effect]2. Anticipate dephasing ⇓

⇒ Why do we have an almost complete dephasing already at c t ∼ 700 µm instead ofc t ∼ 1000 − 1100 µm as expected?



• The anticipate dephasingis due to a coherent “up-shift” of the accelerating field Ez (or to alower velocity for the bubble compared to the theo. val.) which occurs for high densities andhigh laser intensities

-ct=400um

-ct=700um

-50 -40 -30 -20 -10 0-2.0

-1.0

0.0

1.0

2.0

ξ=z-vbubble

t [µm]

Ez [T

V/m

]

np=1019cm-3-- a

0=7.5

-ct=400um

-ct=700um

-50 -40 -30 -20 -10 0-1.0

-0.5

0.0

0.5

1.0

ξ=z-vbubble

t [µm]

Ez [T

V/m

]

np=6*1018cm-3-- a

0=5.4

⇒ This phenomenon (largely) reducesthe energy gain: even a fictitious particle which movesat the bubble velocity would see a decreasing accelerating field



• A (very) simple phenomenological model:

we model the longitudinal (accelerating) field in the following way

Ez(ξ, t) = E0(t) +1

2

mω2p

eξ

where ξ = z − vbubble t and E0(t) = αt is the uniform longitudinal field.

for the energy gain we obtain the following expression

Wcorrected =W0

1 + 43

ω20

αe

mω4p

we measure the “up-shifting rate” α directly form the simulation and we get

Wcorrected ≃ W0

2.27≃ 175 MeV

⇒ in agreement with simulations forc t=700µm



• The field up-shift (or the lower bubble velocity) is probably related to the gathering of chargein front of the laser. The laser pulse undergoes a significant front erosion: the intensity profilebecomes more and more steep yielding an increase in the (longitudinal) ponderomotive force

significantfront erosion

770 780 790 800-60

-30

0

30

60

z [µ m]

Ex [T

V/m

]

np=1019cm-3-- a

0=7.5

770 780 790 800-30

-15

0

15

30

z [µ m]

Ex [T

V/m

]

np=6*1018cm-3-- a

0=5.4

⇒ The effect is important only at high densities and intensities (see left plot for comparison).



• Simulation at lower density (n = 6 · 1018 cm−3) and intensity (a0 = 5.4) ⇒NO field up-shift observed ⇒ we expect an energy of Wtheo ≃ 440 MeV according to W. Lutheory

0 200 400 600 0

0.005

0.010

0.015

0.020

E [MeV]

dN

/dE

[arb

. uni

ts]

⇒ Wsim ≃ (420 ± 40) MeV, Q = 0.4 nC (FWHM)



• Parameters for the best bunchin sim. #1 (@ c t = 700 µm)

Wpeak = 160 ± 5 MeV (FWHM)

Considering the particles with|W − 160| < 10:

σx ≃ 0.8 µmǫxn ≃ 5.5 mm mrad

σy ≃ 0.7 µmǫyn ≃ 4.2 mm mrad

Q = 0.75 nCσz ≃ 2.2 µmI ≃ 40 kA



• Nonlinear “1D-like” regime : generation of a high current e− bunch containing slices withlow emittanceand low momentum spread(see AOFEL a)⇒ a properly modulated gas-jet is required (injection after density downramp b)

aV. Petrillo et al., PRSTAB 11, 070703 (2008)bS. Bulanovet al., PRE58/5, R5257 (1998) / P. Tomassiniet al., PRSTAB6, 121301 (2003)LIFE-meeting, Frascati, February 19-20, 2009 – p.20/34


• Laser parameters:

λ0 [µm] I [W/cm2] τFWHM [fs] waist [µm]

0.8 8.5 × 1018 20 23

• Plasma profile:

n0 [× 1019cm−3] ℓtrans [µ m] n1 [× 1019 cm−3] Lacc [µ m] n2 [× 1019 cm−3]

1.0 10 0.75 330 0.4



• Slice analysis of the accelerated bunch (3D simulation)

γ σz [µm] Q [pC] (δγ/γ)s [%] ǫsn [mm mrad] σs

x,y [µm] Is [kA]

45 1.7 160 0.55 0.2 0.3 4-5

⇒ The current can be raised increasingw0: I ∝ w20 [for instance I(w0 = 40) > 30 kA]


Afterburner experiments with "SPARC"

Part II: afterburner



• PWFA :

1. a driver (electron) bunch creates a wakefieldin the plasma2. a trailing/witness (electron) bunch accelerates in the wakefield

DECELERATING

ACCELERATING

9000 9500 10000 10500-3

0

3

z [µm]

Ez [G

V/m

]

Longitudinal field

⇒ Is it possible to accelerate the witness keeping a good beam quality?



• Features:

wake length ≃ λp = 10.5 µmq

n[1019 e/cm3]

⇒ this limits the length of the witness bunch if we want to keep under control itsmonochromaticity during acceleration (σwitness

z ≪ λp)

wake transverse “radius” Rb ∝ driver density⇒ limits the transverse sizeof the witness bunch (σwitness

r < (≪)Rb)

longitudinal wakefield amplitude ∝ √np & driver density

transverse confining force (in the blowout regime) is linear and depends onbackground ion density

transformer ratio: R = E+

E−

(E+ → max. accel. field behind the bunch, E− → maxdecel. field inside the bunch) ⇒ given a driver with energy W0, the maximum energygain of a trailing bunch is ∆W = RW0 (for any finite length driver with a symmetriclongitudinal charge distribution in the linear regime we have R ≤ 2)



• Driver bunch from ”SPARC” (same beamline): [from ASTRA simulations by A. Bacci]

E 145.9 MeV

δE/E (rms) 8.8 · 10−3

Q 1.75 nC

σx 34.74 µm

σy 34.80 µm

σz 63.08 µm

ǫx 3.06 mm mrad

ǫu 3.06 mm mrad

• Witness bunch: we have tried with several Gaussian buncheschanging the length, the charge(keeping fixed to 1 kA the current) and the transverse size (in order to study the mismatcheffects), injected∼ 1 ps after the driver

• Plasma: we have taken np ≃ 7 · 1015 e/cm−3 (pre-ionized, 5 cm long). The driver bunchcreates an “ellipsoidal” wake (blow-out regime) whose semiaxes are approximately (200 ×90) µm.



• ALaDyn - 3D simulation # 1: parameters & particle density plot

E [MeV] ∆E/E [rms] σx,y [µm] ǫx,y [mm mrad] Q [pC] σz [µm]

145.9 5 · 10−3 10 (3.3 matched) 2 63 8

ct = 5 mm ct = 4 cm



• Accelerating field (at different times), energy gain (+170 MeV [final]) & momentum spread(∼ 3.5% [final]) of the witness

-simulation-theory

0 1.5e+04 3e+04 4.5e+04 0

100

200

300

400

z [µm]

E [M

eV]

-simulation

-theory

0 1.5e+04 3e+04 4.5e+04 0

0.01

0.02

0.03

0.04

z [µm]

∆ E

/E [r

ms]



• Semiaxes and norm. emittances for the witness bunch (not matched)

-sigma_x-sigma_y-sigma_z-theory

0 1.5e+04 3e+04 4.5e+04 0

3

6

9

12

z [µm]

σ x,σy,σ

z [µm

]

-epsi_x-epsi_y-theory

0 1.5e+04 3e+04 4.5e+04 1

2

3

4

5

z [µm] ε nx

,εny

[m

m m

rad]

⇒ the slow damping and the increase of the period of the mismatch oscillations are both dueto the bunch acceleration

⇒ the emittance increase is due to the mismatch and to the asymmetry in the acceleration ratebetween the head and the tail of the bunch



• Transverse and longitudinal phase-space for the bunches at ct = 4.5 cm

-20 -10 0 10 20-10

-5

0

5

10

x [µ m]

p x/mc

⇒ after ∼ 5 cm inside the plasma the driver is not completely depleted



• The emittance increase can be reduced in two ways:

i. matching the beam envelope:

σ2x,match =

ǫx,norm

γκ, κ2 =

2πnpe2

mc2γ

unfortunately for ǫx,norm = 2 mm mrad the matched size is very small: σx,match=3.3µm (difficult to achieve)⇒ ALaDyn - 3D simulation # 2:


145.9 5 · 10−3 3.3 (matched) 2 63 8

ii. decreaseσz of the witnessin order to reduce the head-tail asymmetry in theacceleration (this will decrease also the final mom. spread)⇒ ALaDyn - 3D simulation # 3:


145.9 5 · 10−3 7 2 20 2.5



• Comparison of the emittance growth (left) and momentum spread evolution (right) in thethree simulations

-theory

-sim_#1

-sim_#2

-sim_#3

0 1.5e+04 3e+04 4.5e+04 1

2

3

4

5

z [µ m]

ε nx [m

m m

rad]

norm. emittances

-sim_#1

-sim_#2

-sim_#3

-theory

0 1.5e+04 3e+04 4.5e+04 0

0.01

0.02

0.03

0.04

z [µ m]

∆ E

/E (

rms)

mom. spread

⇒ simulation #3 (the one with σz = 2.5 µm, not matched) combines a moderate change in theemittance (from 2 mm mrad to 2.3 mm mrad) together with a smaller momentum spread(approximately a factor ∼ 3.2) compared to simulation #2


Conclusions

Conclusions


Conclusions

The FLAME laser (@ half power) can accelerate self-injected electrons in the “bubble”regime up to energies of 200 ÷ 400 MeV in ∼ 1 mm gas-jet. Monochromatic bunches(∼ 2% mom. spread) are possible. The normalized emittances are not particularlygood (∼ 5 mm mrad) but this seems to be an intrinsic limit of the “bubble” regime

Bunches with low (slice) emittance (but lower energy compared to the “bubble”regime) can be obtained using the nonlinear LWFA with longitudinal injection afterdensity downramp

PWFA experiments with a driver from "SPARC" are possible: the energy gain for thewitness is ∼ 150-200 MeV after a plasma of 5 cm. Preservation of the emittance andthe monochromaticity is possible provided that the witness is sufficiently shortcompared to the plasma wavelength

Using the electron bunch obtained in the “bubble” regime as a driver for an afterburnerand generating the witness with "SPARC" would be an attractive option


stato simulazioni “self-injection” e “afterburner” · self-injection experiments with flame...

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